AN EMPIRICAL STUDY ON THE EXPECTATIONS HYPOTHESIS OF
THE PHILIPPINE TERM STRUCTURE OF INTEREST RATES,
THE BOND RISK PREMIUM,
AND ITS MACROECONOMIC DETERMINANTS
A Thesis
Presented to the
Faculty of the School of Economics
University of Asia and the Pacific
In Partial Fulfillment
of the Requirements for the Degree of
Master of Science in Industrial Economics
By
Ivy T. Zuñiga
April 2015
© Ivy T. Zuñiga. 2015. All Rights Reserved.
ACKNOWLEDGMENTS
These words will never be enough to express my gratitude to the people
who made this accomplishment worth remembering. This page is not a simple list
of persons who are very dear to me, but a note for others to know how kindhearted
and selfless these people are. They are my true inspirations.
Above all, I humbly offer this work to our Lord. This is His more than mine.
If not for His continuous graces and guidance, I would not have survived every trial
and handled every success that came my way. He is the real source of my strength.
To my adviser who (discreetly) treats me as his favorite student, Dr. Victor
Abola, thank you for greatly believing in me. I’ve never felt so appreciated by a
professor until you came along. You did not only share your academic expertise,
but you taught me that hard work really does pay off.
To the ever diligent and genuine Mr. Edwin Pineda, thank you for taking
time to read and study my thesis. I know that you’ve had a hard time understanding
my seemingly “abstract” topic, but your eagerness and enthusiasm towards my
work encouraged me to keep the discussion simple and sweet. I have learned from
you that equations will be senseless if their worth are not explicitly explained.
To my patient and cheerful external reader, Mr. Reynaldo Montalbo, Jr.,
thank you for imparting your expertise as a practitioner in the field. I am grateful
for the persistent effort to improve my work by allowing me to present the thesis to
the FMIC traders. That opportunity was a memorable one, and I will forever be
thankful for introducing me to the “real world”.
To Ms. Jovi Dacanay, my professional mentor, even though we rarely had
our mentoring sessions in my last year in the University, I have always kept your
pieces of advice close to my heart. Your motherly instincts toward us are wellvalued because we have understood that you only want what’s best for us and for
the Industrial Economics Program.
To the most loved fathers of the School of Economics: Dr. U, Dr. Terosa,
Dr. Manzano, and Sir Perry, thank you for taking good care of the Industrial
Economics Program. You are living proofs that the School of Economics is, indeed,
the best choice we’ve ever made. Your simple “How are you?” and support to our
education mean so much to us.
To the other Industrial Economics Program Staff and School of Economics
Faculty, thank you for sharing your warm greetings and sweet smiles whenever we
enter the SEC Faculty room. Even though we, thesis writers, take up your working
space and add unnecessary noise in the office, especially during break times, we
are still thankful for the service you provide us and for facilitating things well for
the students of IEP. You are the reasons why the SEC continues to prosper all these
years.
To my best friends, the IEP fifths, namely: Chela, Jose, Rey, Mon, Keren,
Sarmie, Apple, Jo, Rige, Keng, Francis, Mar, German, Rose, Althea, Raf, Rap, and
Lyndon, you are the best reasons why I cherished my college life. I look forward to
each day, not to solely work on my thesis, but to see you, listen to your unique
stories, and just laugh to even the pettiest things. You bring out the cheerfulness
and optimism in me (even though I was sometimes rude to you, guys… Sorrryyy).
As we part ways, let’s not forget each other and always try our best to catch up. I
will surely miss you and our bonding moments, but I shall look forward to the day
we meet each other again – with our dreams with us.
To my Chocoholics family back in Naga: Meg, Charm, Micah, Jenoi, Beno,
Camcam, Lala, Nille, Cathoi, and Rizza, you did not cease to be my constant
confidants even though I am 8 hours away from you. I always get touched when
you tell me you’re excited to see me in our reunions and anniversaries, and I always
get crushed inside when I tell you I can’t be there because of school requirements.
But now, I shall make it a point to spend my vacation with you, guys. We shall have
our legendary hang outs – like in our high school days.
To my family and relatives, thank you for being there no matter what. I
would not be the person that I am if not for the upbringing you provided me.
Remember that all of the fruits of my labor are because of you and for you.
To my second family, my Balanghai and Capinpin friends, you are the best
favors I received from God. You have been my closest sisters – my home away
from home – and I will always be grateful for the love and concern. Thank you for
watching over me and making sure that I always have that smile on my face. Your
overflowing prayers lifted me up but your sincerity kept my feet on the ground.
And lastly, to my UA&P friends: Sabio, Peer Facilitators, University
Student Government (USG) 2013-2014, and the Business Economics Association
(BEA), thank you for making my stay in the University the best so far. I have always
told others that my best decision yet was to go to UA&P, but I think that you made
my decision even more fulfilling. Your friendships kept me sane amidst the tons of
academic work. I have learned so much from you and our experiences together will
forever stay in my heart. All I can say is, I am blessed to have met all of you.
For all of these, I could not ask for more. Indeed, this thesis is an answered
prayer. The experience was heaven sent – just like the people in these pages.
TABLE OF CONTENTS
Page
Acknowledgments
List of Tables
List of Figures
Executive Summary
x
xi
xii
CHAPTER
I
INTRODUCTION
A. Background of the Study
B. Statement of the Problem
C. Objectives of the Study
D. Significance of the Study
E. Scope and Limitations
F. Definition of Terms
1
1
7
8
8
10
11
II
REVIEW OF RELATED LITERATURE
A. The Expectations Hypothesis
1. Term Spread Regression Models
a) Derivation of Term Spread Regression Model for
Projection of Long Rates
b) Derivation of Term Spread Regression Model for
Projection of Short Rates
2. Forward Spread Regression Models
B. Empirical Tests of the Expectations Hypothesis
1. Term Spread Regression Results
2. Forward Spread Regression Results
3. Why the Expectations Hypothesis Tests Failed
C. Bond Risk Premium
1. Estimating the Bond Risk Premium
a) Observable Proxy for the BRP
b) Term Premium Specification Based on a Term
Structure Model
D. Macroeconomic Variables and the Bond Risk Premium
21
21
24
III
THEORETICAL FRAMEWORK AND
METHODOLOGY
A. Theoretical Framework
1. Term Spread Model for Predicting Changes in the
Short Rate
2. Term Spread Model for Predicting Changes in the
Long Rate
24
25
26
27
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34
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38
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40
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49
IV
V
3. Model for Predicting Excess Holding Period Returns
4. Bond Risk Premium
5. Macroeconomic Factors and the Bond Risk Premium
B. Conceptual Framework
C. Empirical Methodology
D. Data Requirements
50
52
53
63
63
72
RESULTS AND DISCUSSION
A. Preliminary Analysis of Data
B. Current Developments of the Philippine Bond Market
1. Size and Composition
2. Liquidity
C. Expectations Hypothesis Testing using Term Spread
Models
D. Expectations Hypothesis Testing using Forward Spread
Models
E. Estimation of the Bond Risk Premium
F. Macroeconomic Variables and the Bond Risk Premium
1. Whole Sample Test
2. Periodical Sample Test (Crisis and Post-Crisis
Periods)
3. Short Rate Bond Risk Premium and Macroeconomic
Variables
4. Long Rate Bond Risk Premium and Macroeconomic
Variables
G. Economic Implications of Macro-BRP Relationship
74
74
80
80
85
SUMMARY, CONCLUSIONS, AND
RECOMMENDATIONS
A. Summary of Results and Conclusions
B. Limits of the Study and Recommendations
89
94
97
105
107
108
110
112
116
124
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131
APPENDIX
A. Zero Coupon Bond Yields Obtained from the
Bloomberg Terminal
B. Data for Two-Period Case
C. Data for N-Period Case
D. Two-Period Case Term Spread Regression Model
Results using HAC Newey-West Test
E. N-Period Case Term Spread Regression Model Results
using HAC Newey-West Test
F. Computed Excess Holding Returns of Bond Yields
under the Two-Period Case
G. Computed Excess Holding Returns of Bond Yields
under the N-Period Case
133
142
146
150
152
154
158
H. Term Spread Regression Model Results of Predicting
Excess Bond Returns using HAC Newey-West Test
(Two-Period and N-Period Case)
I. Two-Period Case Forward Spread Regression Model
Results using HAC Newey-West Test
J. N-Period Case Forward Spread Regression Model
Results using HAC Newey-West Test
K. Forward Spread Regression Model Results of
Predicting Excess Bond Returns using HAC Newey-West
Test (Two-Period and N-Period Case)
L. Term Spread Regression Model with Moving Average
Bond Risk Premium Results using HAC Newey-West
Test (Two-Period and N-Period Case)
M. Term Spread Regression Model with Squared Excess
Returns Bond Risk Premium Results using HAC NeweyWest Test (Two-Period and N-Period Case)
N. Term Spread Regression Model with GARCHGenerated Standard Deviation Bond Risk Premium
Results using HAC Newey-West Test (Two-Period and
N-Period Case)
O. Term Spread Regression Model with GARCHGenerated Variance Bond Risk Premium Results using
HAC Newey-West Test (Two-Period and N-Period Case)
P. Macroeconomic Variables for the Panel Regression
Q. Results of the Fixed Effects Panel Regression for the
Whole Sample Case (All Variables & Selected Variables)
R. Results of the Fixed Effects Panel Regression for the
Periodical Case (2006 to 2010 & 2011 to 2014) (All
Variables & Selected Variables)
S. Results of the Fixed Effects Panel Regression for the
Short Rate BRP and Long Rate BRP (2006 to 2014) (All
Variables & Selected Variables)
T. Results of the Fixed Effects Panel Regression for the
Short Rate BRP with Periodical Tests (All Variables &
Selected Variables)
U. Results of the Fixed Effects Panel Regression for the
Long Rate BRP with Periodical Tests (All Variables &
Selected Variables)
BIBLIOGRAPHY
162
165
167
169
172
175
178
181
184
188
189
191
193
195
197
LIST OF TABLES
Table
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Page
McCallum’s Collection of Empirical Results, Change in Long
Rates
McCallum’s Collection of Empirical Results, Change in Short
Rates
Regressions of Change in the Spot Rate on the Forward Rate
Spread
Regressions of Change in the Spot Rate on Adjacent Forward
Rates
Explanatory Variables, Definitions, and Expected
Relationship with BRP
Correlations of Bond Yields
Statistical Details of Bond Yields (Whole Sample &
Subsamples)
Term Spread Prediction of Future Changes in the Short Rate
Term Spread Prediction of Future Changes in the Long Rate
Term Spread Prediction of Excess Returns
Forward Spread Prediction of Changes in Short Rate and
Long Rate
Forward Spread Prediction of Excess Returns
Term Spread Prediction of Future Changes in the Short Rate
with Bond Risk Premium
Term Spread Prediction of Future Changes in the Long Rate
with Bond Risk Premium
Regression Results of Whole Sample
Regression Results of Periodical Sample
Regression Results of Short Rates (2006 to 2014)
Regression Results of Short Rates (2006 to 2010 and 2011 to
2014)
Regression Results of Long Rates (2006 to 2014)
Regression Results of Long Rates (2006 to 2010 and 2011 to
2014)
Summary of Macro-BRP Regressions
x
29
31
32
33
61
75
77
91
92
93
95
96
101
103
108
110
111
112
114
116
123
LIST OF FIGURES
Figure
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
Page
Federal Funds Rates vs. 10-year Bond Yield During the
Interest Rate Conundrum
Decomposition of the 10-Year US Treasury Yield
Philippine 91-Day T-Bills and 10-Year T-Bonds
Risk & Return Tradeoff Principle
Supply and Demand in the Money Market
Framework for Real and Financial Markets
Relationship of Macroeconomic Determinants of the Bond
Risk Premium
Conceptual Framework of the Study
Summary of Methodologies of the Study
3-month to 10-year Monthly Bond Yields (2006 to 2014)
Philippine Yield Curve (2006 to 2014)
3-month vs. 10-year Yield Spread (Yearly Average)
Size of Philippine Bond Market in LCY Billions
Size of Philippine Bond Market (% of GDP)
Outstanding Bonds in Foreign Currency (Local Sources)
Size of Bond Market of ASEAN +1 (% of GDP) (as of
December 2014)
Bills-to-Bond Ratio of the Philippines
Bills-to-Bonds Ratio of ASEAN +3 (as of December 2014)
Trading Volume of Philippine Government Bonds (2013
Average)
Trading Volume of Government Bonds in the ASEAN
Market +3 (2013 Average)
Turnover Ratio of Philippine Government Bonds (Yearly
Average)
Bonds Turnover Ratio in ASEAN Market +4 (as of June
2013)
Estimated Bond Risk Premium Using Moving Average
Method
Estimated Bond Risk Premium Using Squared Excess
Returns
Conditional Standard Deviation of Excess Returns from
GARCH (1,1)
Conditional Variance of Excess Returns from GARCH (1,1)
xi
2
4
5
55
56
59
60
65
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100
EXECUTIVE SUMMARY
The Expectations Hypothesis (EH) is one of the main theories that explain
the term structure of interest rates. It postulates that the yield curve is formed
through investors’ expectations – such that the long rate is the simple average of
the current short rate, the expected future short rates over the life of the long bond,
and a risk premium. The traditional form of the EH assumes that the bond risk
premium is constant or zero, making long-term rates purely based on the outlook
of rational investors. Hence, the Expectations Hypothesis is also known as the Pure
Expectations Hypothesis (PEH), Traditional Expectations Hypothesis (TEH), or the
Rational Expectations Hypothesis (REH).
More than a theoretical concept, the EH is a helpful framework used by
academics, researchers, and financial analysts in further investigating the condition
of a country’s interest rates. Common empirical tests are called term spread
regression models, where the term spread (the difference between the long rate and
the short rate) are used to predict changes in the short rates and long rates. A 𝛽
coefficient of 1 is required to confirm that a 1% change in the term spread would
induce short rates and long rates to change by an equal magnitude.
However, empirical tests performed by various authors (using data abroad),
found out that the strict or pure form of the Expectations Hypothesis did not hold
true. The resulting 𝛽 coefficients did not achieve the required values. For the short
rates, 𝛽 values were significantly lower than 1, which implies that a 1% change in
the term spread translates to a “less-than-1” change in the short rates. For the long
rates, 𝛽 coefficients were significantly greater than 1 while some even reached
xii
negative values. This implies that a 1% change in the term spread induces long rates
to increase by more than 1 or to decline.
These results gained mixed explanations from authors. Some say that the
errors came from inaccurate econometric treatments, while others comment that it
is due to the overreaction of long rates to the current short rates. Among these
explanations, the reason that gained the most attention from researchers is the
exclusion of the bond risk premium (BRP) in the estimation of the EH. For them,
the bond risk premium should not be zero or constant, but present and time-varying.
Since the BRP is unobservable and cannot be directly measured, several studies
have focused on various ways of estimating it, and then inputting these estimates
into the EH regression tests to see if the results would improve.
Due to the limited number of researches done on the Philippine term
structure of interest rates, this thesis aimed to provide a benchmark study about the
condition of the country’s interest rates in conformity with the requirements of the
Expectations Hypothesis. This study is also motivated by the developing
government debt market in the country, the growing importance of interest rates in
investment and trading decisions, and the flourishing potential of the EH as a
framework for monitoring interest rates.
For the empirical tests, calculated Philippine zero coupon yields were used.
The tests were divided into two based on McCallum’s study: the two-period case
(which involves one-period bonds and two-period bonds) and the n-period case
(which includes one-period bonds and bonds with maturities more than twoperiods). Term spread regression models were employed to test if Philippine bond
xiii
yields will satisfy the following conditions: 1) The term spread must perfectly
predict changes in short rates; 2) The term spread must perfectly predict changes in
long rates; and 3) The term spread must not forecast excess bond returns (as we are
assuming a zero/constant bond risk premium). All of these will be achieved if the
value of the 𝛽 coefficients appeared to be 1 for the first and second condition, and
0 for the third.
Results of the tests show that Philippine bond yields do not conform to the
implications of the Expectations Hypothesis. This is because the term spread did
not “perfectly” forecast changes in the short rates and in the long rates. For the short
rates, the term spread only predicted up to 52% of the changes in the short rate –
such that for every 1% change in the term spread, short rates may only change by
0.52%. The tests on the long rates, on the other hand, produced negative 𝛽 values,
signaling a fall on the long rates when the term spread increases. Moreover, the
term spread was able to predict excess bond returns (as the 𝛽 values were not zero).
This suggests that the bond risk premium may not really be zero (as required by the
EH). All of these findings point to the rejection of the Expectations Hypothesis.
Due to the failure of the EH tests, this study readily assumed (as suggested
also by various literature) that the distortion came from the exclusion of a timevarying bond risk premium in the term spread regression models. Hence, the bond
risk premium for the Philippine bond yields was estimated. The BRP can be
modeled using proxies for risk, and to represent risk, interest rate volatility was
measured. Three different measures of volatility were obtained as adopted from the
study of Boero and Torricelli (2000). These are the: 1) moving average of absolute
xiv
changes in the short rate over the previous six periods; 2) square of expected excess
holding period return; and estimates of conditional standard deviations and
variances from the univariate GARCH (Generalized Autoregressive Conditional
Heteroskedasticity) (1,1) model.
The BRP values obtained from each estimation technique were inputted into
the term spread regression models and their effects were evaluated using goodnessof-fit tests by Gujarati (2011). These are the Adjusted R2, F-statistic, Akaike
Information Criterion (AIC), and Schwarz Information Criterion (SIC). The
Adjusted R2 and F-statistic must have large values for they are measuring the
significance of the variables in explaining the dependent variable, whereas the AIC
and SIC represent estimates of information loss so lower values are needed. The
improvement of the 𝛽 coefficients were also considered.
From the three proxies of the BRP, the GARCH-generated conditional
variances were deemed to be the best BRP estimates for the short rates, while the
GARCH-generated conditional standard deviations best fitted the BRP of the long
rates. This is because of the large Adjusted R2 and F-statistic values and the least
AIC and SIC values they generated from the regression tests.
For the short rates, the GARCH-generated conditional variances increased
the 𝛽 values of the term spread by a couple of points while improving the predictive
power of the model. For the long rates, the GARCH-generated standard deviations
made the 𝛽 coefficients positive (from their previously negative values) and the
model’s predictive power also increased. Even though the 𝛽 values were not exactly
1, the resulting 𝛽 coefficients from the regression tests still signify that the term
xv
spread can be a powerful tool in forecasting changes in interest rates. The resulting
positive 𝛽 values from the regression tests signal increases of interest rates for an
increase in the term spread. Hence, it would be safe to assume that when long rates
rise, short rates may also increase; and short rates may fall when long rates decline.
The next objective of the study is to identify the various macroeconomic
variables that significantly influence the estimated BRP. Several economic data and
some yield indicators were used as explanatory variables of the BRP. These were
the: Meralco sales (as a proxy for economic growth), Philippine inflation, pesodollar rate, money supply (M2), OFW remittances, BSP policy rate, US inflation,
gross international reserves, federal funds rate, budget deficit as a percent of GDP,
government debt as a percent of GDP, Philippine Stock Exchange Index, lagged
values of the bond risk premium, and the spread of the bond pairs.
The analyses was divided into crisis (2006 to 2010) and post-crisis (2011 to
2014) periods for both the short rate BRP and long rate BRP. Results show that
world macroeconomic factors had more dominant effects on the BRP during the
crisis periods. This finding highlights the vulnerability of the country’s financial
system to global shocks during the global financial crisis. Some of these foreign
variables are the gross international reserves, US inflation, and peso-dollar
exchange rate.
On one hand, for the post-crisis periods (2011 to 2014), the effect of foreign
economic variables have died down and only domestic factors were observed to
significantly influence the estimated BRPs. This only confirms the country’s
increased resiliency against global shocks after the 2008 financial crisis. This may
xvi
be due to the intensified macroprudential measures implemented by the Bangko
Sentral ng Pilipinas (BSP), so that players in the financial system may be cautious
when undergoing risky deals. Large domestic savings from overseas Filipino
workers (OFW) and business process outsourcing (BPO) remittances also fortified
the country from external shocks.
Additionally, it was also observed that among the explanatory variables, the
most persistent predictors of the BRP are its lagged values (𝐵𝑅𝑃(−1)) and the bond
spread. This denotes that investors or traders are highly sensitive to the past
condition of bond rates and the relationship of long-term yields with short-term
yields, more than economic factors. Investors closely watch the situation of the
financial market in requiring respective BRPs, thus exhibiting the so called adaptive
expectations (AE). This behavior hypothesizes that people form their current
decisions from the direction of past data.
Overall, the findings of the macro-BRP relationship tests imply that the
country’s bond market have gained sufficient resistance from external shocks after
the global financial crisis. The country has learned a lesson from its past, and in
order to prevent any mistakes, it is doing its best to build up its defenses. A factor
that may have contributed to this is the fact that the Philippine bond market is still
relatively small and young compared to other developing nations. The government
debt market is also less integrated into the international scene making it less
affected by global macroeconomic variables.
xvii
Furthermore, it is noticed that unlike the interest rates of some developed
countries such as the US, Philippine interest rates are very hard to predict. This
observation strengthens the idea that that Philippine bond yields (especially, the
short rates) are not yet strongly anchored on macroeconomic variables. This is the
reason why the country must intensify researches about Philippine interest rates to
develop an appropriate framework that investors and policymakers can rely on.
Such effort would make interest-rate monitoring easier and estimation of interest
rates and of the bond risk premium possible.
Even though Philippine bond yields rejected the implications of the
Expectations Hypothesis, the term spread regression tests still suggest that the slope
of the yield curve may be an effective predictor of changes in short-term and longterm bond yields. Moreover, despite the fact that the relationship of the BRP and
macroeconomic variables were not consistent through time, the tests still show that
the estimated bond risk premium of the Philippines is, one way or another, related
to some macroeconomic data. This is a good indication that the debt market is
gradually being characterized by rational investor decisions. Thus, as the country’s
bond market moves towards advancements and increased participation in the
international arena, we can only hope for a more competitive and efficient debt
system.
xviii
CHAPTER I
INTRODUCTION
A. Background of the Study
The Expectations Hypothesis (EH) is one of the most explored theories
when studying the term structure of interest rates. Basically, the EH asserts that
long-term rates are determined by the movement of short-term rates, and vice-versa
via expectations. This theory, therefore, suggests that investors cannot profitably
exploit arbitrage opportunities between short rates and long rates because long rates
and short rates are perfect substitutes.
Academics and researchers have been very interested in the dynamics of the
EH as evidenced by the numerous studies done on data abroad. Most of these
studies came from developed countries such as US, Canada, UK, Germany, etc.
This is because the study of the EH tells a lot about the real conditions of the
financial market. One concrete phenomenon where the study of the EH proved most
useful was during the advent of the so-called “interest rate conundrum” or
“Greenspan’s conundrum” in the US from 2004 to 2006, which appears to be
bothering the US economy at present.
The interest rate conundrum pertains to the strange and unexpected plunge
of long-term interest rates despite the increase of the Federal Funds Rate and
improving economic conditions in the US. This occurrence baffled the economy
because it went against one implication of the EH, which is the no-arbitrage
principle. According to theory, an upward-sloping yield curve (i.e., long-term rates
1
are greater than short-term rates) must induce expected future short-term rates to
rise in order to produce equal returns. Unfortunately, when the Fed (under the
supervision of Alan Greenspan) increased its federal funds rate in 2004 from 1.0%
to 5.25%, long maturity rates eventually fell.1 It was on August 2006 that 10-year
bond yields at 4.88% were outperformed by the federal funds rate (which stayed at
5.25% for quite some time). With this, Greenspan failed to tighten credit and
restrain excesses that contributed to the global financial crisis.
7
6
Percent
5
4
3
2
1
2000-01
2000-07
2001-01
2001-07
2002-01
2002-07
2003-01
2003-07
2004-01
2004-07
2005-01
2005-07
2006-01
2006-07
2007-01
2007-07
2008-01
2008-07
2009-01
2009-07
2010-01
2010-07
2011-01
2011-07
2012-01
2012-07
2013-01
2013-07
2014-01
2014-07
2015-01
0
Federal Funds Rate
10-Year Bond Yield
Figure 1. Federal Funds Rates vs. 10-year Bond Yield During the Interest Rate
Conundrum
Source of Basic Data: Federal Reserve Bank of New York
This might have arrived as a surprise to policymakers, but to some financial
researchers and academics who have been studying the EH, the conundrum might
have been predicted to happen soon. Earlier studies observed that real data did not
conform to the empirical tests of the EH theory. Historical bond rates proved that
Roger Craine and Vance Martin, “Interest Rate Conundrum” Coleman Fung Risk Management
Research Center Working Papers 2 (2009): 1.
1
2
long rates are not purely the average of expected short rates. Hence, a rise in the
long rates may not prompt an equal increase in future short rates, and vice-versa.
Some studies even found out that the relationship can be negative at times – which
implies a fall in the expected short rates even though the long rates are rising, and
vice-versa.
Findings of these papers showed that there is some distortion present in the
data that needs to be incorporated into financial models to accurately satisfy the
hypothesis. Several experimental methods have emerged to solve this puzzle, but
most of them point to the distortion caused by the so-called bond risk premium
(BRP). Ben Bernanke, in his speech in the Annual Monetary/Macroeconomics
Conference in March 2013, pointed out that “the largest portion of the downward
move in long-term interest rates since 2010 is due to a fall in the term premium”.2
Figure 2 shows that the BRP/term premium fell dramatically during the conundrum
and even reaching negative after 2011. This may indicate that investors are
confident enough that bonds would not be too vulnerable to interest rate risks.
Bernanke enumerated two factors that may have contributed to the general
downward trend of the term premium. These are the: 1) decline in the volatility of
Treasury yields because of the zero-interest rate policy (and still expected to remain
there for some time); and the 2) increasing negative correlation of bonds and stocks
Ben Bernanke, “Long-Term Interest Rates” (online copy of speech, Annual Monetary/
Macroeconomics Conference: The Past and Future Monetary Policy, Federal Reserve Bank of San
Francisco, San Francisco, California, March 1, 2013)
http://www.federalreserve.gov/newsevents/speech/bernanke20130301a.htm (accessed April 4,
2015).
2
3
implying that bonds have become more valuable as a safe-haven instrument against
risks than other assets.
Figure 2. Decomposition of the 10-Year US Treasury Yield
Source: Board of Governors of the Federal Reserve System
Why is a conundrum dangerous in the first place? Since short rates are
difficult to manage there can be a possibility that an inverted yield curve may
appear, such that the returns of short-term bonds exceed those of long-term bonds
– which is a conventional indicator of a recession. An inverted yield curve suggests
that market players are more willing to buy long-term instruments even if they
receive a lower yield. Investors find the short-term state of the economy too risky
to make investments, prompting a rise in the short-term rate due to increased
inflation or increased term premium.3 According to an article, inverse Treasury
yield curves had forecasted the recessions of 1981, 1991, 2000, and even the 2008
Gary North, “The Yield Curve: The Best Recession Forecasting Tool” Gary North’s Specific
Answers, http://www.garynorth.com/public/department81.cfm (accessed April 4, 2015)
3
4
financial crisis.4 Because of such forecasting power, the yield curve and its
underlying assumptions must be studied and closely monitored so that anomalies
(or even recessions at worst) in the financial market may be prevented.
In the case of the Philippine interest rates, an interest rate conundrum has
not happened yet. Figure 3 shows that since 1991, long-term bonds are still greater
than short-term bonds. Moreover, yield curves are still concave upwards. All of
these still point to a relatively healthy and normal financial system.
20
18
16
Percent
14
12
10
8
6
4
2
1999M01
1999M08
2000M03
2000M10
2001M05
2001M12
2002M07
2003M02
2003M09
2004M04
2004M11
2005M06
2006M01
2006M08
2007M03
2007M10
2008M05
2008M12
2009M07
2010M02
2010M09
2011M04
2011M11
2012M06
2013M01
2013M08
2014M03
2014M10
0
91-Day T-Bills
10-Year T-Bonds
Figure 3. Philippine 91-Day T-Bills and 10-Year T-Bonds
Source of Basic Data: Bloomberg, Philippine Dealing Systems (PDS)
Nonetheless, the “normality” of the movement of interest rates should not
be a reason for researchers and policymakers to become complacent about the
market. Besides, the Bangko Sentral ng Pilipinas (BSP) has not been very detailed
about its framework when it comes to monitoring the rates of the debt market since
it is highly focused on inflation targeting. Hence, the BSP may not have the
Kimberly Amadeo, “How an Inverted Yield Curve Predicts a Recession,” about news,
http://useconomy.about.com/od/glossary/g/Inverted_yield.htm (accessed April 4, 2015).
4
5
appropriate paradigm to tackle interest rate gyrations since the country has not
experienced an interest rate conundrum. But, what if an interest rate conundrum in
the Philippines happens? How would the BSP, the market participants, and the
overall financial market reach to it? In the first place, are Philippine interest rates
even vulnerable to such a conundrum?
For us to find out, empirical tests on the term structure of interest rates must
primarily be done, specifically anchored on a theory that explains the relationship
of short rates and long rates or perhaps a framework that incorporates the estimation
of the bond risk premium. The theory that has the implications closest to these
topics is the Expectations Hypothesis (EH).
However, the abundance of literature on the empirical tests of the EH on
data abroad comes in stark contrast with the Philippine case. As far as the EH is
concerned, no basic and focused studies have been done yet on the Philippine term
structure of interest rates. Perhaps, the value of doing a study on the EH has not
been emphasized yet for developing countries like ours. Nevertheless, it is worth
noting that a study on the EH is not only useful to policymakers as a framework for
monitoring the condition of the domestic interest rates, but also to investors as a
guide for making the right decisions when trading in the free market. On this
ground, it is essential to provide a benchmark study using Philippine data that other
researchers can develop on.
This thesis, therefore, aims to perform the basic econometric tests of the
Expectations Hypothesis on Philippine domestic interest rates using bond rates.
Knowing that the financial market is not frictionless, and that the Philippine bond
6
market is not as efficient as in developed countries, it is hypothesized in this study
that distortions would be present. This would allow empirics to dissatisfy the theory
and thus, an estimation of the bond risk premium is necessary. The same tests are
replicated to assess if the BRP indeed plays a major role in the relationship of the
EH and the term structure of interest rates. Lastly, macroeconomic factors affecting
the BRP are identified to highlight the interconnectedness of elements within the
financial system. But beyond all these, this study ultimately hopes to explore the
implications of the results and findings on the bond market and interest rates of the
country.
B. Statement of the Problem
Due to the abundance of literature on the Expectations Hypothesis (EH) of
bond yields gained from developed countries, this study replicates the basic
empirical studies of the EH using Philippine data. In order to learn more about the
condition of the Philippine domestic interest rates with respect to the EH, the
existence of the bond risk premium and its macroeconomic determinants, and their
implications on the financial market, this research aims to answer the main
question:
1. Do Philippine bond yields conform to the Expectations Hypothesis (EH)
with the inclusion of an estimated bond risk premium (BRP)?
7
C. Objectives of the Study
In order to answer the principal question of this study, the following
objectives must be satisfied:
1. To empirically test the validity of the Expectations Hypothesis using
Philippine bond yields;
2. To estimate the bond risk premium in the term structure of Philippine
bond yields;
3. To assess if an estimated bond risk premium improves or does not
improve the empirical tests done on the Expectations Hypothesis;
4. To identify the macroeconomic variables that influence the estimated
bond risk premium; and
5. To determine the implications of the study’s findings on the Philippine
bond market.
D. Significance of the Study
There are several reasons why this study should done. First and foremost,
the Expectations Hypothesis (EH) can be cited as one of the core theories that
explain the structure of interest rates. If there has been a limited study done on the
Philippine term structure of interest rates and the EH, it is possible that the market’s
knowledge about interest rates can still be inadequate. The findings of this study
can, thus, shed light to new information on how Philippine interest rates perform
under the assumptions of a theory. If the empirics were to reject the hypothesis,
then sources of distortions can be identified from where recommendations or
possible solutions can be aimed at.
8
Secondly, a deeper analysis of the Philippine bond rates can be useful from
the perspective of policy-making or regulations when it comes to interest ratetargeting. In the case of the US, during the interest rate conundrum, the Federal
Reserve did not expect that the strong link between the Federal Funds rate has
apparently weakened, therefore failing to manipulate long-term rates via short-term
nominal rates. If only researchers were able to communicate their findings that
long-term rates were not as reactive to short-term rates or that the relationship of
the two are negative, the Fed could have mitigated the effects of the conundrum
and helped save the financial system during the global crisis. In the same way, the
EH can be a promising framework that the Bangko Sentral ng Pilipinas (BSP) or
the Philippine Dealing Systems (PDS) Group can use when monitoring the
movement of short rates and long rates or when utilizing monetary policy facilities.
The outcomes of this study can signal any irregularity in the system that the BSP
or PDS Group can consider to implement the optimal response needed.
Lastly, the findings concerning the bond risk premium shall have substantial
informational value to bond investors and traders. Results of the study can show if
interest rates are only driven by market sentiment or if they move along other
macroeconomic variables as stated by theory. Hence, investors and traders can be
better informed whether they can use the EH as a model in taking their respective
positions in the market whenever new macroeconomic data have surfaced.
9
E. Scope and Limitations
This study aims to test the Expectations Hypothesis (EH) based on one of
the widely used empirical methods. These are the term spread regression models.
Forward spread regression models were also done to validate the results. Advanced
studies have featured several versions of these models but due to the limited tenors
of interest rates data we have in the Philippines, only McCallum’s (1994) EH
models are considered.5
In the estimation of the bond risk premium (BRP), only interest rate
volatility shall be considered as a proxy measure, as this thesis only aims to
establish a baseline study of the theory. Volatility was estimated in three ways,
which are the: 1) moving average of the short rate, 2) square of excess returns, and
3) simple univariate GARCH (1,1) model6 as replicated from the study of Boero
and Torricelli (2000). The value estimates gained from the three methods shall
represent the BRP for the respective long-term rates. Each of the estimated BRP
were plugged into the term spread regression models and goodness-of-fit criteria
were used to select the best BRP proxy.
Several macroeconomic variables that are hypothesized to affect the BRP
were also be included in the analysis to pinpoint which macroeconomic data have
significant (positive or negative) relationships with the BRP. These are electricity
sales (as a proxy for economic growth), inflation, peso-dollar exchange rate, excess
liquidity, OFW remittances, monetary stance, federal funds rate, budget deficit (as
5
See Chapter 2 and Chapter 3 for further elaboration about the models used in the study.
See Definition of Terms and Chapter 3 for an elaboration of the univariate GARCH (1,1)
method.
6
10
% of GDP), government debt (as % of GDP), stock market activity, and gross
international reserves. The lagged values of the estimated bond risk premium were
also included, along with the bond spread.
To simplify the testing of the EH, monthly yields of zero coupon bonds
from 2006 to 2014 would be used for the tests and analyses of the study. Since the
Philippines does not issue zero coupon bonds anymore, bond yields stripped off
their coupon effects were obtained using Bloomberg’s time series of calculated zero
coupon bond yields.7 The following bond tenors that will be included are: 3-month,
6-month, 1-year, 2-year, 3-year, 5-year, and 10-year.
F. Definition of Terms
ARIMA-GARCH
ARIMA-GARCH stands for Autoregressive Integrated Moving Average –
Generalized Autoregressive Conditional Heteroskedasticity, which is a
combination of ARIMA process of data and GARCH model. A time series
data is considered ARIMA (𝑝,𝑑,𝑞) when it has to be differenced 𝑑 times
and then the ARMA (Autoregressive and Moving Average) model is
applied to it – where 𝑝 denotes the number of autoregressive (AR) terms, 𝑑
denotes the number of times the series has to be differenced before it
becomes stationary, and 𝑝 is the number of moving average (MA) terms.
Thus, an ARIMA (2,1,2) time series has to be differenced once (𝑑 = 1)
before it becomes stationary and the first-differenced stationary time series
7
Coupon bond yields can be manually stripped off their coupon effects using a method called
bootstrapping.
11
can be modeled as an ARMA (2,2) process, that is, it has two AR terms and
two MA terms.8
GARCH enters the picture when the error variance of the time series data is
related to the squared error terms several periods in the past. This model can
have the GARCH (𝑝,𝑞) model in which there are 𝑝 lagged terms in the
squared error term and 𝑞 terms of the lagged conditional variances.9
Augmented Dickey-Fuller (ADF) Test
ADF is a test for unit root in a time series data. This is also a statistical test
for the stationarity or non-stationarity of the data. The usual rule is, if the
probability value obtained from the test is less than 0.05, the null hypothesis
(i.e., the data has unit root) must be rejected. Otherwise, the null hypothesis
must be accepted.
Bills-to-Bonds Ratio
This measure was used by the Asian Development Bank (ADB) as an
indicator of bond market size. This is calculated as:
𝑇𝑜𝑡𝑎𝑙 𝐵𝑖𝑙𝑙𝑠 𝑡𝑜 𝐵𝑜𝑛𝑑𝑠 𝑅𝑎𝑡𝑖𝑜 =
𝑇𝑜𝑡𝑎𝑙 𝑂𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝐺𝑜𝑣𝑒𝑟𝑛𝑚𝑒𝑛𝑡 𝐵𝑖𝑙𝑙𝑠
𝑇𝑜𝑡𝑎𝑙 𝑂𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝐺𝑜𝑣𝑒𝑟𝑛𝑚𝑒𝑛𝑡 𝐵𝑜𝑛𝑑𝑠
where bills pertain to government securities of 1 year or less in maturity
while bonds pertain to government securities of more than 1 year in
8
Damodar Gujarati, Basic Econometrics: International Edition (New York: McGraw-Hill, 2003),
840.
9
Damodar Gujarati, Basic Econometrics: International Edition (New York: McGraw-Hill, 2003),
862.
12
maturity. This also gives a hint if a country’s bond market is characterized
by short maturity bonds or long maturity bonds.10
Bond Pairs
This pertains to the pairing of a short rate and a long rate for the regression
models of the Expectations Hypothesis. The following bond pairs are as
follows: 3-month and 6-month bonds, 6-month and 1-year bonds, 1-year
and 2-year bonds, 1-year and 3-year bonds, 1-year and 5-year bonds, and 1year and 10-year bonds.
Bond Risk Premium (BRP)
According to Ilmanen (2012), the bond risk premium refers to the return
advantage of long-term bonds over short-term bonds. It is also known as the
compensation for risk that investors require in investing in long-term bonds
than short-term bonds. In this study, the bond risk premium was measured
by using the volatility of interest rates as a proxy. This implies that the more
volatile a certain bond is, the riskier it is, hence, a higher risk premium is
needed. Alternatively, the less volatile a certain bond is, the less risky it is,
hence, a lower risk premium is required.
Three measures of bond risk premium were done in this paper. These are
the: 1) moving average of the 1) moving average of the short rate, 2) square
of excess returns, and 3) univariate GARCH (1,1) generated measures of
“Bills-to-Bonds Ratio,” Asian Bonds Online,
http://asianbondsonline.adb.org/philippines/data/bondmarket.php?code=Bills_Bonds_Ratio_Total
(accessed April 5, 2015).
10
13
conditional standard deviations and conditional variances from the study of
Boero and Torricelli (2000).
Bond Turnover Ratio
This measure was used as an indicator of liquidity in the bond market by
the ADB. This is computed using the formula:
𝐵𝑜𝑛𝑑𝑠 𝑇𝑢𝑟𝑛𝑜𝑣𝑒𝑟 𝑅𝑎𝑡𝑖𝑜 =
𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑏𝑜𝑛𝑑𝑠 𝑡𝑟𝑎𝑑𝑒𝑑
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑠𝑖𝑛𝑔 𝑏𝑜𝑛𝑑𝑠
The average amount of outstanding bonds is equal to the average amount
at the end of the previous and current quarters. The higher the turnover ratio,
the higher is the liquidity of the secondary bonds market.11
Bond Yields/Bond Returns
This figure refers to the return that an investor gets on a bond which usually
refers to yield-to-maturity, or the total return that one will receive if the
bond is held to maturity. In this study, however, zero-coupon bond yields
were used. The term “bond yield” was used interchangeably with “bond
return” in this study.
Correlogram Specification
This is a graphical and numerical display of autocorrelation statistics of time
series data. It is also a diagnostic test to determine if a certain time series
data has unit root or are non-stationary. It is also known as Autocorrelation
Function (ACF). If the ACF value is within the 95% confidence interval,
then there is sufficient statistical evidence for the null hypothesis to be
“Bonds Turnover Ratio,” Asian Bonds Online,
http://asianbondsonline.adb.org/philippines/data/bondmarket.php?code=Bond_turn_ratio
(accessed April 5, 2015).
11
14
rejected. This means that the data do not have unit root or are stationary.
Otherwise, the data are non-stationary.
Covariance
This is a measure of co-movement between two variables. A positive
covariance means that two variables move together while a negative
covariance means that the variables move in opposite directions. The
formula for covariance is:12
∑𝑛𝑖=1(𝑥𝑖 − 𝑥̅ )(𝑦𝑖 − 𝑦̅)
𝐶𝑂𝑉(𝑥, 𝑦) =
𝑛−1
where:
𝑦 = dependent variable
𝑥 = independent variable
𝑛 = number of data points in the sample
𝑦̅ = mean of dependent variable 𝑦
𝑥̅ = mean of independent variable 𝑥
Excess Bond Returns/Excess Holding Period Returns
Excess bond returns pertains to the return on a long-term bond relative to
the return on a short-term bond (risk-free investment). This paper adopted
the definition of excess bond returns or excess holding return by Mankiw,
Goldfeld, and Shiller (1986). The excess bond returns is expressed as:
𝐸𝐻𝑅 = 𝐻𝑡 − 𝑟𝑡
“Statistical Sampling and Regression: Covariance and Correlation,” PreMBA Analytical
Methods, https://www0.gsb.columbia.edu/premba/analytical/s7/s7_5.cfm (accessed April 17,
2015).
12
15
where:
𝑟𝑡 ≡ short-term bond yield
𝐻𝑡 ≡ holding period return
𝐻𝑡 was calculated as:
𝐻𝑡 ≈ 𝑅𝑡 −
𝑅𝑡+1 − 𝑅𝑡
𝜕
where:
𝑅𝑡 ≡ long-term bond yield at the current period
𝑅𝑡+1 ≡ long-term bond yield at the next period
𝜕 ≡ constant equal to the average long-term yield
Fixed Effects Panel Regression
Fixed effects is one of the specifications used when doing a panel
regression. A panel dataset contains observations on multiple entities
(individuals), wherein each entity is observed at two or more pints in time.13
This was used in the regression tests for the macroeconomic determinants
of the BRP. The fixed effects method was used, as opposed to the random
effects model, because we would want to take into account the time-variant
nature of the explanatory variables. The random effects specification is used
only when the effects of time-invariant variables should be included.
Forward Rates
Forward rates are the rates applicable to a financial transaction that will
happen in the future. In the context of bonds, they are calculated to
“Regression with Panel Data”
http://www.econ.brown.edu/fac/Frank_Kleibergen/ec163/ch10_slides_1.pdf (accessed April 25,
2015).
13
16
determine future yields. For example, an investor can either purchase a oneyear Treasury bill and hold it to maturity, or purchase a six-month T-bill
and buy another six-month bill once the former matures. Under the principle
of no-arbitrage, the investor will be indifferent between the two choices.
The spot rate of the one-year and six-month bonds will be known, but the
value of the six-month bill purchased six months from now shall be
unknown. Given the six-month and 1-year spot rates though, the forward
rate on a six-month bill can be computed. It is the rate that equalizes the
return between two types of investment tenors.14
Forward Spread
This refers to the difference between the forward rate of a long rate and the
forward rate of a short rate used for the forward spread regression models –
an alternative test of the Expectations Hypothesis done to validate and
compare with the results of the term spread regression models.
Kurtosis
This is a statistical measure that describes the variability of data around the
mean. A high kurtosis depicts a graph with fat tails signifying an even-out
data distribution, whereas a low kurtosis portrays a graph with skinny tails
indicating that the distribution is concentrated around the mean. It is also
called as the “volatility of volatility”.15 Kurtosis, in this study, was used to
describe the condition of the bond yields before, during, and after the global
“Forward Rate” Investopedia, http://www.investopedia.com/terms/f/forwardrate.asp (accessed
April 4, 2015).
15
“Kurtosis,” Investopedia, http://www.investopedia.com/terms/k/kurtosis.asp (accessed April 5,
2015).
14
17
financial crisis. Conventionally, higher kurtosis values appeared during the
crisis years signifying the high level of volatility and risk present.
N-Period Case
This pertains to the term spread regression model done by McCallum (1994)
on bonds with maturities more than two periods. The following bond pairs
were used for the n-period case regression tests: 1-year and 3-year, 1-year
and 5-year, and 1-year and 10-year.
One-Period Bond
This refers to the yield of a bond held for one period. In this study, the
following bond tenors were considered under the classification of a oneperiod bond: 3-month bond, 6-month bond, and 1-year bond.
Skewness
Skewness is also a statistical measure that describes the location of data,
which can be symmetrical or non-symmetrical. In the case of investment
returns, non-symmetrical or skewed distributions are more common –
which can be positively skewed or negatively skewed. Positively skewed
distributions (or long right tails) meant frequent small losses and a few
extreme gains or that extremely bad scenarios are unlikely to happen.
Negatively skewed distributions (or long left tails), on the other hand, meant
frequent small gains and a few extreme losses or greater chance for
extremely negative outcomes.16
“Quantitative Methods – Skew and Kurtosis,” Investopedia,
http://www.investopedia.com/exam-guide/cfa-level-1/quantitative-methods/statistical-skewkurtosis.asp (accessed April 5, 2015).
16
18
Term Spread
This refers to the difference between the bond pairs or the difference
between a long rate and a short rate used for the term spread regression
models in testing the Expectations Hypothesis.
Trading Volume
This was also used as an indicator of bond market liquidity by the ADB.
This pertains to the total traded value of local government bonds in the
secondary market in US dollars.17
Two-Period Bond
This refers to the yield of a bond held for two periods, which is usually twice
that of the period of one-period bonds. Hence, two-period bonds in this
study are the 6-month bond, 1-year bond, and 2-year bond.
Two-Period Case
This pertains to the term spread regression models done by McCallum
(1994) on one-period bonds and two-period bonds. The following bond
pairs were used for the two-period case regression tests: 3-month and 6month, 6-month and 1-year, and 1-year and 2-year.
Univariate GARCH (1,1) Model
GARCH
stands
for
Generalized
AutoRegressive
Conditional
Heteroskedasticity. This econometric technique is commonly used to model
the volatility of some financial time series data. GARCH assumes that the
“Trading Volume,” Asian Bonds Online,
http://asianbondsonline.adb.org/philippines/data/bondmarket.php?code=Trading_Volume
(accessed April 5, 2015).
17
19
variance of the error term (residual) is affected by its past values.
Furthermore, the GARCH specification asserts that the best predictor of the
variance in the next period is a weighted average of the long-run average
variance, the variance predicted for this period, and the new information in
this period that is captured by the most recent squared residual. Such an
updating rule is a simple description of adaptive or learning behavior.18
For this study, the volatility of excess returns was estimated using the
GARCH (1,1) model. This signifies that the excess returns might possess
an ARCH (1) effect (current volatility of the residuals is affected by the
previous residual) and a GARCH (1) effect (current volatility of the
residuals is affected by its previous volatility).
Zero Coupon Bonds
These are also called pure discount bonds which are bonds that have been
stripped off their coupons. They do not pay an interest during the life the
bond but the payment of the interest and principal happens at the end of the
bond’s maturity. According to some studies about the Expectations
Hypothesis (EH), zero coupon bonds are used to simplify the testing of the
term spread regression models. If zero coupon bonds are not available in
one’s financial market, coupon bonds can be converted to zero coupon
bonds via a process called bootstrapping. In this study, zero coupon
Philippine bonds with different tenors were directly obtained using the
Bloomberg terminal.
Robert Engle, “GARCH 101: The Use of ARCH/GARCH Models in Econometrics”, Journal of
Economic Perspectives 15 (2001), 159.
18
20
CHAPTER II
REVIEW OF RELATED LITERATURE
A. The Expectations Hypothesis
The Expectations Hypothesis (EH) is one among the three major theories
that try to explain the term structure of interest rates.19 The key assumption of this
theory is that bonds, despite having different maturities, are “perfect substitutes”;
hence, bonds’ expected returns are equal. In practice, “the expectations theory
postulates that an investor can earn the same amount of interest by investing in a
one-year bond today and rolling that investment into a new one-year bond after a
year compared to buying a two-year bond today”.20
Munasib provided the following example to illustrate the no-arbitrage
assumption of the EH:21
1. Buy $1 one-year bond (short bond) and buy another one-year bond upon
maturity (also known as the Rolling Strategy)
2. Buy $1 of two-year bond and hold it (also known as the Maturity
Strategy)
19
The term structure of interest rates shows the relationship of yields across various maturities.
The graphical representation of it is called the yield curve. The two other theories that attempt to
describe the yield curve are the Liquidity Preference Theory and Market Segmentation Theory
which shall not be discussed in this paper.
20
“Expectations Theory,” Investopedia.
http://www.investopedia.com/terms/e/expectationstheory.asp (accessed September 26, 2014)
21
Abdul Munasib, “Term Structure of Interest Rates: The Theories”, Econ 3313 – Handout 03,
Middle Tennessee State University, http://raptor1.bizlab.mtsu.edu/sdrive/FMICHELLO/Fin%204910%20Options,%20Futures%20and
%20other%20Derivatives/Extra%20Readings/Term%20structure%20of%20interest%20rates.pdf
(accessed December 26, 2014).
21
For the EH, to hold true, Investment Strategy 1 must have an equal return
with Investment Strategy 2. Consider the following notations:
𝐸𝑅1 ≡ expected return for Investment Strategy 1 or the Rolling Strategy
𝐸𝑅2 ≡ expected return for Investment Strategy 2 or the Maturity Strategy
𝑖𝑡 ≡ interest rate of a one-period bond at time t
𝑒
𝑖𝑖+1
≡ expected interest rate of a one-period bond at time t+1
𝑖2𝑡 ≡ interest rate of a two-period bond at time t
For Investment Strategy 1 (Rolling Strategy), the expected return is:
𝑒
𝐸𝑅1 = [(1 + 𝑖𝑡 ) + (1 + 𝑖𝑡 )𝑖𝑖+1
]−1
𝑒
𝑒
𝐸𝑅1 = 𝑖𝑡 + 𝑖𝑖+1
+ 𝑖𝑡 (𝑖𝑡+1
)
𝑒
𝐸𝑅1 ≈ 𝑖𝑡 + 𝑖𝑖+1
𝑒 )
since 𝑖𝑡 (𝑖𝑡+1
≅0
For Investment Strategy 2 (Maturity Strategy), the expected return is:
𝐸𝑅2 = [(1 + 𝑖2𝑡 ) + (1 + 𝑖2𝑡 )𝑖2𝑡 ] − 1
𝐸𝑅2 = 𝑖𝑡 + (𝑖2𝑡 )2
𝐸𝑅2 ≈ 2𝑖2𝑡
since (𝑖2𝑡 )2 ≅ 0
By EH,
𝑒
𝑖𝑡 + 𝑖𝑖+1
= 2𝑖2𝑡
𝑖2𝑡 =
𝑒
𝑖𝑡 + 𝑖𝑡+1
2
(Eq. 1)
Equation 1 shows that the two-period interest rate must equal the average
of the current short-term rate and the future short-term rate expected to hold over
the two-period horizon. The same follows for a bond that is more than two-years in
maturity, as shown in Equation 2.
22
𝑖𝑛𝑡 =
𝑒
𝑒
𝑒
𝑖𝑡 + 𝑖𝑡+1
+ 𝑖𝑡+2
+⋯+ 𝑖𝑡+(𝑛−1)
𝑛
.
(Eq. 2)
Therefore, if the current short-term rate changes, so will the long-term rates.
Thus, the EH also posits that “interest rates for different maturities tend to move
together over time”.22 In summary, the EH asserts that
1
𝑚
𝑛,𝑚
𝑟𝑡𝑛 = ( ) ∑𝑘−1
𝑖=0 𝐸𝑡 𝑟𝑡+𝑚𝑖 + 𝜃
𝑘
(Eq. 3)
where:
𝑟𝑡𝑛 ≡ long-term (n-period) rate
𝑟 𝑚 ≡ short-term (m-period) rate
𝑛
𝑘 = 𝑚 ≡ is an integer
𝜃 𝑛,𝑚 ≡ term-specific but constant risk premium
Similar to Equation 1, Equation 3 states that the long rate is the simple
average of the current short rate and expected future short rates up to n-m periods
in the future. 𝜃 𝑛,𝑚 is the predictable excess return on the n-period bond over the mperiod bond. The term-specific premium may vary with m and n but is assumed to
be constant through time.23 The relationship between the n and m period rates in
Equation 3 implies that an upward-sloping yield curve predicts an increase in short
rates and consequently in long rates, and vice-versa. In order to investigate this,
Abdul Munasib, “Term Structure of Interest Rates: The Theories”, Econ 3313 – Handout 03,
Middle Tennessee State University. An empirical study on the Philippine term structure of interest
rates by Diaz (2012) confirmed this claim via cointegration tests between the benchmark 91-day
and 10-year rates.
23
Campbell & Shiller (1991) put the risk premium to be constant through time, but the stricter
version of the EH (known as the Pure Expectations Hypothesis) assumes that the term premium is
null or zero. This is because the PEH posits that interest rates are established strictly on the basis
of expectations about future rates. Secondly, the theory assumes that market players are riskneutral (i.e. indifferent to maturity because they do not view long-term bonds as being riskier than
short-term bonds). In this study, however, we shall test if the term premium of Philippine bond
rates is indeed zero or not.
22
23
various approaches have been developed. Two common methods are the term
spread regression models and the forward spread regression models.
1. Term Spread Regression Models
The term spread regression models aim to use the difference
between the long rate and the short rate (term spread) as a predictor of two
outcomes: a) future changes in the long rate and b) future changes in the
short rate. The studies of Mankiw, Goldfeld, and Shiller (1986), Campbell
and Shiller (1991), Campbell (1995), Tzavalis and Wickens (1997), Dai and
Singleton (2002), and many others, have used the term spread regression
models to test the EH. Equation 3 can be transformed into a regression
model to investigate these two assumptions.
a. Derivation of Term Spread Regression Model for Projection of Long
Rates
The first approach starts from the assumption that the one-period
return on an n-period bond must be equal to the one-period short rate and a
disturbance term known as the risk premium (Equation 4). Following
Geiger’s (2011) notations, the derivation is as follows:
𝐸𝑡 (𝑟𝑛,𝑡+1 ) = 𝑖1,𝑡 + 𝑥𝑟𝑛
(Eq. 4)
[𝑖𝑛,𝑡 − (𝑛 − 1)][𝐸𝑡 (𝑖𝑛−1,𝑡+1 )] − 𝑖𝑛,𝑡 = 𝑖1,𝑡 + 𝑥𝑟𝑛 (Eq. 5)
[𝐸𝑡 (𝑖𝑛−1,𝑡+1 )] − 𝑖𝑛,𝑡 =
(𝑖𝑛,𝑡 − 𝑖1,𝑡 )
(𝑛−1)
𝑖𝑛−1,𝑡+1 − 𝑖𝑛,𝑡 = 𝛼1,𝑛 + 𝛽1,𝑛
−
𝑥𝑟𝑛
(𝑛−1)
(𝑖𝑛,𝑡 − 𝑖1,𝑡 )
(𝑛−1)
+ 𝜃𝑛,𝑡
(Eq. 6)
(Eq. 7)
24
where Equation 6 tells us that the expected one-period change in the long
rate, [𝐸𝑡 (𝑖𝑛−1,𝑡+1 )] − 𝑖𝑛,𝑡 , is equal to the average term spread over the
remaining periods (n-1),
(𝑖𝑛,𝑡 − 𝑖1,𝑡 )
(𝑛−1)
, minus the average term premium over
𝑥𝑟
𝑛
the remaining periods, (𝑛−1)
.
Equation 7 transforms Equation 6 into a directly testable regression
model that can be consistently tested via ordinary least squares. This is
because the term premium, 𝜃𝑛,𝑡 , or the forecast error, under rational
expectations, is assumed to be orthogonal or uncorrelated to the current
information at time t. In this way, the term spread shall be uncorrelated also
with the errors. To satisfy the EH, the projection of the changes in the long
rate (left-hand side) onto the slope of the yield curve (right-hand side)
should give an 𝛼1,𝑛 coefficient of zero, and a 𝛽1,𝑛 coefficient of one.24
b. Derivation of Term Spread Regression Model for Projection of Short
Rates
Alternatively, Equation 3 can also be used to derive the formula for
testing if the term spread is able to predict expected changes in the short
rate. From the basic assumption that the long rate is a simple average of the
current short rate and the expected short rates in the future, plus an assumed
constant risk premium, as shown in Equation 8:
Felix Geiger, “The Theory of the Term Structure of Interest Rates,” in the The Yield Curve and
Financial Risk Premia, (Berlin: Springer-Verlag, 2011), 69-70.
24
25
𝑖𝑛,𝑡 =
1
𝑦
∑𝑛−1
𝐸
(𝑖
)
+
∅
𝑡
1,𝑡+𝑗
𝑗=0
𝑛,
𝑛
(Eq. 8)
the short rate can be subtracted from both sides of the equation to achieve
the term spread regression model.
1
𝑛
1
𝑛
𝑦
∑𝑛−1
𝑗=0 [𝐸𝑡 (𝑖1,𝑡+𝑗 ) − 𝑖1,𝑡 ] = 𝑖𝑛,𝑡 − 𝑖1,𝑡 − ∅𝑛
(Eq. 9)
∑𝑛−1
𝑗=0 (𝑖1,𝑡+𝑗 − 𝑖1,𝑡 ) = 𝛼2,𝑛 + 𝛽2,𝑛 (𝑖𝑛,𝑡 − 𝑖1,𝑡 ) + 𝜀𝑛,𝑡 (Eq. 10)
Equation 10 implies that the yield spread, (𝑖𝑛,𝑡 − 𝑖1,𝑡 ), predicts the
expected changes in the short rate, specifically the weighted cumulative
expected change in the short rate over the life of the long rate,
1
𝑛
∑𝑛−1
𝑗=0 (𝑖1,𝑡+𝑗 − 𝑖1,𝑡 ). Based on the EH, the expression above also suggests
that whenever the long-term yield exceeds the current short-term yield (or
a rise in the term spread), future short rates are expected to rise so that the
returns between the two are equal. Similar to Equation 7, if the EH holds,
𝛼2,𝑛 must approach zero and 𝛽2,𝑛 should converge to unity so that an
observed positive term spread is associated with increasing future shortterm rates.25
2. Forward Spread Regression Models
Other studies have also explored the usefulness of forward rates26 in
investigating the EH. Some of these are Fama and Bliss (1987) and
Felix Geiger, “The Theory of the Term Structure of Interest Rates,” in the The Yield Curve and
Financial Risk Premia, (Berlin: Springer-Verlag, 2011), 69-70.
26
Walsh introduced forward rates as an equal measure of the expected one-period ahead rates
under the EH. He defined it in the case of a two-period bond and a one-period bond as: 𝑓𝑡1 =
25
(1+𝐼𝑡 )2
(1+𝑖𝑡 )
− 1.
26
Cochrane and Piazessi (2002). Geiger called this the “unbiased test of the
EH” since under the assumptions of the EH, forward rates proxy as unbiased
and optimal predictors of future interest rates”.27 Hence, current forward
rates should appropriately predict future short rates.28 The forward spread
regression model came from Equation 7 as a predictor of future short rate
changes:
𝑖1,𝑡+𝑛 − 𝑖1,𝑡 = 𝛼3,𝑛 + 𝛽3,𝑛 (𝑓𝑛,𝑛+1 − 𝑖1,𝑡 ) + 𝜀𝑛,𝑡
(Eq. 11)
where:
𝑖1,𝑡 ≡ interest rate of a one-period bond at time t
𝑖1,𝑡+𝑛 ≡ interest rate of a one-period bond during the life of the nperiod bond
𝑓𝑛,𝑛+1 ≡ forward rate that equalizes the returns of the one-period
bond and n-period bond
𝜀𝑛,𝑡 ≡ disturbance term/risk premium
If the EH holds, Equation 11 implies that 𝛼3,𝑛 must have a
coefficient of zero and a 𝛽3,𝑛 coefficient of one.
B. Empirical Tests of the Expectations Hypothesis
A multitude of studies have tested the EH’s empirical validity. Majority of
them used US bonds data while covered the term structure of other OECD29 and
Carl Walsh, “The Term Structure of Interest Rates,” in the Monetary Theory and Policy,
(Massachusetts: The MIT Press, 2010), 467.
28
Felix Geiger, “The Theory of the Term Structure of Interest Rates,” in the The Yield Curve and
Financial Risk Premia, 70.
29
Frederic Mishkin, “A Multi-Country Study of the Information in the Term Structure about
Future Inflation,” National Bureau of Economic Research (1989).
27
27
G730 countries. However, almost all of the basic empirical tests failed to satisfy the
EH with 𝛽 coefficients significantly different from one. For some, the 𝛽
coefficients were even significantly less than zero. The collection of literature on
the EH tests assembled by McCallum (1994) are shown in Tables 1 and 2.
1. Term Spread Regression Results
McCallum segregated the results for the change in short rates and
change in long rates.31 Table 1 shows the slope coefficients for the model
that predicts changes in long rates. Results of the regression tests show that
almost all of the 𝛽 coefficients were significantly below zero. The absolute
value of the slopes also increase with the maturity of the bond.32 The same
results were also arrived at by Hardouvelis (1994) for the study on G7
countries which analyzed the behavior of the 10-year and 3-month
government bond yields between the periods of 1968-1992. He found out
that the long rates move contrary to that implied by theory.33
The negative coefficients from the term spread models of the long
rates imply that as the yield spread increases, the long yield has the tendency
to fall. Campbell (1995) argued that when the long yields fall the short rates
have the tendency to decline even more (if the EH is followed), thereby
Gikas Hardouvelis, “The term structure spread and future changes in long and short rates in the
G7 countries: Is there a puzzle?,” Journal of Monetary Economics (1993).
31
Empirical tests for the term spread as a predictor of change in short rates was called the twoperiod case by McCallum, while testing the changes in long rates was called the n-period case.
The two-period case pertains to the relationship between yields on one-period and two-period
bonds, whereas the n-period case covers bonds with maturities of more than two periods.
32
Bennett McCallum, “Monetary Policy and the Term Structure of Interest Rates” NBER Working
Paper 4938 (1994), 4, 10.
33
The same results were also achieved by Mankiw, Goldfeld, and Shiller (1986).
30
28
resulting to a greater yield difference between the short rate and the long
rate. The EH, however, requires the future change in long yields to increase
to offset the corresponding rising of the yield curve.34
On the other hand, some EH tests produced results consistent with
theory. An example of which is the study on the German term structure of
interest rates by Boero and Torricelli (2000). Nearly all pairs of maturities
had coefficient estimates that were consistently positive, although not
always significantly so. For the authors, their results suggest that “it is easier
to predict changes in interest rates over longer horizons”. Boero and
Torricelli, nevertheless, overruled the previous statement after having very
low R2 values, indicating that the term spread has poor predictive content
for changes in the long rate.35
Table 1. McCallum’s Collection of Empirical Results, Change in Long Rates
Slope
Coefficient
Evans & Lewis (1994)
1964-1988
1 mo.
2
-0.17
Evans & Lewis (1994)
1964-1988
1 mo.
4
-0.70
Evans & Lewis (1994)
1964-1988
1 mo.
6
-1.27
Evans & Lewis (1994)
1964-1988
1 mo.
8
-1.52
Evans & Lewis (1994)
1964-1988
1 mo.
10
-1.89
Campbell & Shiller (1991)
1952-1987
1 mo.
2
0.00
Campbell & Shiller (1991)
1952-1987
1 mo.
4
-0.44
Campbell & Shiller (1991)
1952-1987
1 mo.
6
-1.03
Campbell & Shiller (1991)
1952-1987
1 mo.
12
-1.38
Campbell & Shiller (1991)
1952-1987
1 mo.
24
-1.81
Campbell & Shiller (1991)
1952-1987
1 mo.
48
-2.66
Campbell & Shiller (1991)
1952-1987
1 mo.
60
-3.10
Campbell & Shiller (1991)
1952-1987
1 mo.
120
-5.02
Hardouvelis (1994)
1954-1992
3 mo.
120
-2.90
Source: Bennett McCallum, “Monetary Policy and the Term Structure of Interest Rates” NBER
Working Paper 4938 (1994).
Study
Sample Period
Short Rate
N+1
John Campbell, “Some Lessons from the Yield Curve,” The Journal of Economic Perspectives
5, no. 3 (1995), http://www.jstor.org/stable/2138430.
35
Gianna Boero and Costanza Torricelli, “The Information in the Term Structure of German
Interest Rates” (2000).
34
29
Table 2 also shows McCallum’s collection of literature that tested
the term spread on future changes in the short rate. Similar to the results
from the long rates, majority of the 𝛽s were significantly different from the
desired coefficient of one. Some were greatly below than 1, negative at
times, and for some highly exceeding one. These results suggest various
implications for the relationship of the term spread and the future changes
of short rates. If 𝛽s are significantly below 1, increases in the term spread
may not be well-translated in the changes of short rates. If 𝛽s are
significantly negative, just like the case of the long rate regression results,
increases in the term spread will cause short rates to fall; and if 𝛽s
significantly exceed one, any increase in the term spread will result to an
overreaction of future short rates.36
Nevertheless, compared to the widely contradicting results for
changes in long rates, findings of the regression tests for predicting short
rate changes have been more unified and consistent. Most of the results
gathered by Mankiw, Goldfeld, and Shiller (1986), Boero and Torricelli
(2000), and Campbell and Shiller (1991), produced 𝛽 coefficients which are
positive (consistent with the relationship dictated by the EH theory), with
some closely approaching one. Additionally, some of the regressions, such
as in Germany’s case, showed higher information content (higher R2 values)
than for longer bond tenors. These findings support the claim that the term
36
The overreaction of long rates to short rates have been studied by Mankiw and Summers (1984)
in their paper entitled “Do Long-Term Interest Rates Overreact to Short-Term Interest Rates?”.
30
spread has greater ability in predicting future changes of short rates than
long rates.
Table 2. McCallum’s Collection of Empirical Results, Change in Short Rates
Study
Sample Period
Short Rate
Slope
Coefficient
1959-1979
0.23
Mankiw & Miron (1986)
3 mo.
1951-1958
-0.33
Mankiw & Miron (1986)
3 mo.
1934-1951
-0.25
Mankiw & Miron (1986)
3 mo.
1915-1933
0.42
Mankiw & Miron (1986)
3 mo.
1890-1914
0.76
Mankiw & Miron (1986)
3 mo.
1964-1988
0.42
Evans & Lewis (1994)
1 mo.
1952-1987
0.50
Campbell & Shiller (1991)
1 mo.
1952-1987
0.19
Campbell & Shiller (1991)
2 mo.
1952-1987
-0.15
Campbell & Shiller (1991)
3 mo.
1952-1987
0.04
Campbell & Shiller (1991)
6 mo.
1952-1987
-0.02
Campbell & Shiller (1991)
12 mo.
1952-1987
0.14
Campbell & Shiller (1991)
36 mo.
1952-1987
2.79
Campbell & Shiller (1991)
60 mo.
1959-1982
0.46
Fama (1984)
1 mo.
1984-1991
-0.01
Roberds, Runkle, & Whiteman (1993)
3 mo.
1979-1982
0.19
Roberds, Runkle, & Whiteman (1993)
3 mo.
1975-1979
0.43
Roberds, Runkle, & Whiteman (1993)
3 mo.
Source: Bennett McCallum, “Monetary Policy and the Term Structure of Interest Rates” NBER
Working Paper 4938 (1994).
2. Forward Spread Regression Results
Apart from the tests done on the term spread models, several authors
have also investigated the EH using the forward spread method. Some of
these authors are Fama and Bliss (1987), Mishkin (1988)37, Cochrane and
Piazessi (2005), Fama (2006), and Bulkley, Harris, and Nawosah (2008).
Mishkin (1988), for example, had two kinds of tests using forward rates.
First, he investigated the relationship between the expected changes in the
spot rate (current short rate) and the forward rate-spot rate spread.38
Mishkin’s paper is a refinement of Fama’s (1984) study.
𝜏
Mishkin’s first regression model is: 𝑅𝑡+𝜏 − 𝑅𝑡+1 = 𝛼1 + 𝛽1 (𝐹𝜏𝑡 − 𝑅𝑡+1 ) + 𝜂𝑡+𝜏−1
; and the
𝜏
second one is: 𝑅𝑡+𝜏 − 𝑅𝑡+𝜏−1 = 𝛼2 + 𝛽2 (𝐹𝜏𝑡 − 𝐹(𝑡 − 1)𝑡 ) + 𝜂𝑡+𝜏−1 , where 𝑅𝑡+𝜏 is the one37
38
31
Secondly, he examined the relationship between the change in the spot rate
and the difference between two adjacent forward rates. Mishkin used
Treasury bills with tenors from one month up to six months for his data.
The results are shown in Tables 3 and 4, respectively.
For Mishkin’s results in Table 3, he concluded that “the forward
rate-spot rate differential for the 1-month ahead, 𝐹2𝑡 − 𝑅𝑡+1 , has significant
predictive power and significant explanatory power for the change in the
spot rate one month ahead, 𝑅𝑡+2 − 𝑅𝑡+1 ”.39 It can be observed, however,
that the forward spread’s predictive power decreases as the predictive
horizon lengthens. Additionally, he noted that examining the results per
subperiod is important because this affects the stochastic process of interest
rates. Overall, Mishkin concluded for this first set of tests on US bonds that
“the term structure has more predictive power for spot rates from October
1979 onwards”.40
Table 3. Regressions of Change in the Spot Rate on the Forward Rate Spread
Sample
Period
2/59 –
7/82
2/59 –
1/64
2/64 –
1/69
2/69 –
1/74
2/74 –
1/79
𝑹𝒕+𝟐 −
𝜷
0.41**
(0.11)
0.44**
(0.12)
0.52**
(0.13)
0.32**
(0.07)
0.69**
(0.17)
𝑹𝒕+𝟏
R2
0.11
0.22
0.39
0.12
0.10
𝑹𝒕+𝟑 −
𝜷
0.27
(0.18)
0.34**
(0.10)
0.40**
(0.14)
0.17
(0.16)
0.10
(0.25)
𝑹𝒕+𝟏
R2
0.03
0.16
0.19
0.01
0.00
Dependent Variable
𝑹𝒕+𝟒 − 𝑹𝒕+𝟏
𝑹𝒕+𝟓 −
𝜷
R2
𝜷
0.25
0.01
0.21
(0.24)
(0.15)
0.28
0.06
0.05
(0.16)
(0.11)
0.22
0.04
0.32**
(0.12)
(0.09)
0.61**
0.13
0.07
(0.18)
(0.17)
0.31
0.02
0.20
(0.29)
(0.22)
𝑹𝒕+𝟏
R2
0.01
0.00
0.18
0.00
0.02
𝑹𝒕+𝟔 −
𝜷
0.16
(0.11)
0.06
(0.14)
0.26**
(0.08)
0.15
(0.11)
-0.12
(0.18)
𝑹𝒕+𝟏
R2
0.01
0.01
0.14
0.02
0.01
month rate observed at time 𝑡 + 𝜏 − 1 and 𝐹𝜏𝑡 is the forwad rate for month 𝑡 + 𝜏 observed at time
𝑡.
39
Frederic Mishkin, “The Information in the Term Structure,” National Bureau of Economic
Research 2575 (1988): 8.
40
Frederic Mishkin, “The Information in the Term Structure,” National Bureau of Economic
Research 2575 (1988): 9.
32
Table 3 continued
2/79 –
0.61** 0.15
0.43
0.04
0.29
0.01
0.43
0.03
0.50
0.03
7/82
(0.21)
(0.32)
(0.37)
(0.33)
(0.37)
1/59 –
0.40** 0.11
0.30*
0.04
0.34**
0.02
0.20
0.02
0.16
0.01
6/86
(0.09)
(0.15)
(0.10)
(0.11)
(0.10)
1/59 –
0.44** 0.14
0.25**
0.04
0.34**
0.05
0.12
0.01
0.05
0.00
9/79
(0.06)
(0.08)
(0.10)
(0.09)
(0.09)
10/79 –
0.71** 0.20
0.59
0.08
0.47
0.03
0.58
0.06
0.64*
0.07
9/82
(0.23)
(0.33)
(0.35)
(0.31)
(0.30)
10/82 –
0.51** 0.26
0.64**
0.23
0.61**
0.17
0.13
0.02
-0.03
0.00
6/86
(0.12)
(0.15)
(0.21)
(0.17)
(0.17)
Source: Frederic Mishkin, “The Information in the Term Structure,” National Bureau of Economic
Research 2575 (1988): 7.
Notes: Standard errors are in parentheses.
* = significant at 5% level
** = significant at 1% level
The results for the marginal predictive power of forward rates (i.e.,
forward rates with one period interval) on the monthly changes in future
spot rates were slightly less favorable than the previous one. The last row
of Table 4 shows that adjacent forward rates provide significant predictive
power for the change in the spot rate up but only up to 3 months in the
future. Moreover, when Mishkin further tested the robustness of the results
of the two regressions, he concluded that there is more coefficient instability
(thus, less robust) for the marginal prediction equations than there were for
the forward rate-spot rate model.41
Table 4. Regressions of Change in the Spot Rate on Adjacent Forward Rates
Sample
Period
2/59 –
7/82
2/59 –
1/64
2/64 –
1/69
2/69 –
1/74
2/74 –
1/79
𝑹𝒕+𝟐 −
𝜷
0.41**
(0.11)
0.44**
(0.12)
0.52**
(0.13)
0.32**
(0.07)
0.69**
(0.17)
𝑹𝒕+𝟏
R2
0.11
0.22
0.39
0.12
0.10
𝑹𝒕+𝟑 −
𝜷
-0.03
(0.12)
0.45**
(0.10)
0.34**
(0.12)
0.21
(0.12)
-0.00
(0.23)
𝑹𝒕+𝟐
R2
0.00
0.21
0.21
0.06
0.00
Dependent Variable
𝑹𝒕+𝟒 − 𝑹𝒕+𝟑
𝑹𝒕+𝟓 −
𝜷
R2
𝜷
-0.02
0.00
0.04
(0.11)
(0.08)
0.25*
0.07
0.11
(0.11)
(0.09)
0.18
0.04
0.21
(0.14)
(0.11)
0.16
0.04
-0.08
(0.09)
(0.06)
-0.55
0.10
-0.02
(0.49)
(0.16)
𝑹𝒕+𝟒
R2
0.00
0.03
0.14
0.01
0.00
𝑹𝒕+𝟔 −
𝜷
0.00
(0.06)
0.19**
(0.06)
0.12
(0.07)
-0.08
(0.06)
-0.09
(0.08)
𝑹𝒕+𝟓
R2
0.00
0.09
0.07
0.04
0.02
Frederic Mishkin, “The Information in the Term Structure,” National Bureau of Economic
Research 2575 (1988): 10.
41
33
Table 4 continued
2/79 –
0.61** 0.15
-0.59*
0.07
-0.36
0.02
0.03
0.00
0.26
0.01
7/82
(0.21)
(0.28)
(0.29)
(0.23)
(0.37)
1/59 –
0.40** 0.11
0.03
0.00
0.07
0.00
0.05
0.00
0.02
0.00
6/86
(0.09)
(0.11)
(0.10)
(0.07)
(0.06)
1/59 –
0.44** 0.14
0.25**
0.06
0.06
0.00
0.02
0.00
-0.03
0.00
9/79
(0.06)
(0.08)
(0.11)
(0.06)
(0.05)
10/79 –
0.71** 0.20
-0.56*
0.07
-0.24
0.09
0.00
0.25
0.01
0.01
9/82
(0.23)
(0.27)
(0.27)
(0.22)
(0.34)
10/82 –
0.51** 0.26
0.42*
0.13
0.60**
0.28
0.14
0.03
0.06
0.00
6/86
(0.12)
(0.17)
(0.16)
(0.12)
(0.13)
Source: Frederic Mishkin, “The Information in the Term Structure,” National Bureau of Economic
Research 2575 (1988): 10.
Notes: Standard errors are in parentheses.
* = significant at 5% level
** = significant at 1% level
3. Why the Expectations Hypothesis Tests Failed
If we would look at the vast literature which attempted to study the
Expectations Hypothesis (EH), majority of them arrived at the conclusion
that empirical tests reject the EH in its constant term premium form. This
observation remains true for both US data and data from European
countries.42 Geiger (2011), nonetheless, argued that “this does imply that
interest rate expectations are impossible to be inferred from the term
structure, but rather reflects the insight that the EH and its single-equation
representation only predicts future yield levels to a limited extent”. Still, it
can be said that there is some element of truth in the EH.
Several reasons have been put forth regarding the failure of the EH.
The study of Campbell and Shiller (1991), that focused on measurement
errors in modelling the EH, argued that the main failure of the EH was
primarily caused by the overreaction of long rates to current short rates. This
42
Empirical support is only found at the short end of the yield curve (<1 year) for both US and
European data.
34
excessive sensitivity of long rates to short rates have also been investigated
by the study of Mankiw and Summers (1984). However, Mankiw and
Summers, likewise, decisively rejected this claim. Campbell and Shiller,
thus, suggested several econometric resolutions to compute for the EH more
accurately.43
Campbell (1995) argued that the failure of the EH can be explained
by biases in estimating the EH due to the variability of excess returns in
long bonds. Since expected excess returns appear on both sides of the
equation (Equation 7), they bias 𝛽1 down due to its negative effect on the
dependent variable and positive effect on the regressor. On the other hand,
excess returns also have the tendency to bias 𝛽2 up since changing
expectations of excess returns only positively affect the right-hand side of
the equation (Equation 10).
Moreover, Mankiw and Miron (1986) considered the effect of
monetary policy on the predictive power of the yield spread for future
interest rate movements. They found out that there are only specific periods
in which the EH fit the data, specifically before the founding of the Federal
Reserve (Fed) since rates were more predictable that time. According to
Geiger (2011), Mankiw and Miron’s finding suggest that “firstly, the
predictive power of the EH changes across different monetary policy
regimes, and secondly, a central bank that heavily manipulates interest rates
John Campbell and Robert Shiller, “Yields Spreads and Interest Rate Movements: A Bird’s Eye
View,” The Review of Economic Studies 58, no.3 (1991), http://www.jstor.org/stable/2298008
43
35
makes it harder for market participants to forecast future movement of
interest rates if the short rate follows a random walk”.44
Finally, from the literature surveyed in this study, majority of the
authors insisted that the error of the regression models primarily came from
the omission of a time-varying term premium in the regressions that is
correlated with the term spread.45 This was argued by Tzavalis and Wickens
(1997), Balfoussia and Wickens (2007), and McCallum (1994) that
recognized the need to incorporate the risk premium in the estimation of the
EH via econometric adjustments. Geiger (2011) also posited that the
underlying sources of risk and how they are translated into the variability of
the term premia are important to explain the validity of the EH. The earlier
studies of Fama (1984), Mankiw (1986), and Hardouvelis (1988), and
McCallum (1994), on the other hand, argued in favor of the possibility of
time variation in the term premium due to policy regime changes.
C. Bond Risk Premium
The bond risk premium (BRP) has been equally studied as the EH since
academic researchers have identified it as the main candidate for why the yield
spread is unable to forecast future interest rates correctly. As defined by Ilmanen
(2012), the bond risk premium or the term premium46 is the “expected return
Felix Geiger, “The Theory of the Term Structure of Interest Rates,” in the The Yield Curve and
Financial Risk Premia, (Berlin: Springer-Verlag, 2011), 73.
45
Elias Tzavalis and Michael Wickens, “Explaining the Failures of the Term Spread Models of the
Rational Expectations Hypothesis of the Term Structure,” Journal of Money, Credit, and Banking
29, no. 3 (1997), http://www.jstor.org/stable/2953700
46
Bond risk premium and term premium is used interchangeably in this study. The terms bond
risk premia and term premia may, at times, be mentioned.
44
36
advantage of long-duration bonds over short-term (one-period) bonds”.47 It is also
known as the compensation for risk that investors demand for investing in longterm bonds than shorter ones, since it is presumed that time is associated with risks.
Mathematically, the BRP was illustrated as 𝜃 𝑛,𝑚 in Equation 3. Nevertheless,
unlike the previous assumption of the EH, it is anticipated that the BRP is no longer
zero or constant but present and/or time-varying.
In the case of the US, the identification of the bond term premia has been
very significant especially during the interest rate conundrum in 2004 to 2005. Ben
Bernanke, former Fed Chairman from 2006 to 2014, discussed in his speech last
March 2013, that the biggest contributor to low rates during the conundrum, despite
the Fed raising the federal funds, was the decline in the term premium. Some of the
known causes of a very low or negative premium were central bank purchases of
government debt, safe-asset demand, and lastly, the global savings glut (that
resulted to some countries’ massive accumulation of foreign exchange reserves).48
From the US’ experience, estimating the bond risk premia can be used as a signaling
tool for any anomaly in the market such as the interest rate conundrum. This is
because the US conundrum suggested that the global monetary system is in bad
shape. If the term premium could be estimated accurately monitored, economic and
financial crises may effectively be prevented.
47
Antti Ilmanen, Expected Returns on Major Asset Classes (Research Foundation of CFA
Institute: John Wiley & Sons, Inc., 2012), 57.
48
“Conundrum: a glut-wrenching experience”, The Economist, November 20, 2014.
http://www.economist.com/blogs/freeexchange/2014/11/conundrums.
37
1. Estimating the Bond Risk Premium
Mankiw, Goldfeld, and Shiller (1986), Tzavalis and Wickens
(1997), Balfoussia and Wickens (2007), Boero and Torricelli (2000), and
many other studies hypothesized that the failure of the EH was caused by
the omission of the BRP in the regression tests. However, these studies also
recognized that the BRP is not directly observable and not that easy to find
a proxy for.49 Estimation procedures should, therefore, be done to
incorporate the BRP into the regression equation.
Nevertheless, Geiger (2011) noted that there is still no consensus on
how to measure the term premia. Hence, researchers have experimented on
a wide set of model specifications and estimation techniques to estimate the
BRP. These methods are clustered into two general approaches by
Balfoussia and Wickens (2007) into:50
a. Observable Proxy for the BRP
The observable proxy method pertains to selecting a directly
recognizable variable that may imitate the magnitude or behavior of the
bond risk premium. It can also be a variable that is highly correlated to the
excess returns or disturbance term of the term spread regression models.
Putting an observable proxy for the term/risk premium was carried
out differently by various studies. Shiller, Campbell, and Schoenholtz
49
Ilmanen (2012) also acknowledged that the BRP is unobservable hence, estimating techniques
must be done.
50
Hiona Balfoussia and Mike Wickens, “Macroeconomic Sources of Risk in the Term Structure”,
Journal of Money, Credit, and Banking 39, no. 1 (2007), http://www.jstor.org/stable/4123075
38
(1983), for example, used a measure of credit volume that measures the
relative amount of activity in the short end of the market (than the long end)
to predict risk premiums.51 They regressed excess returns on six-month bills
on the previous quarter’s ratio of short borrowing (<1 year) to long (>1 year)
financing by US corporations. They found out that the volume ratio is
indeed a significant predictor of excess returns from 1959 to 1982.
However, it is not significant over the shorter bonds in the earlier sample
period from 1959 to 1979, while the volume ratio is only 10% significant in
predicting excess returns on long-term bonds.
Campbell (1987) used latent variables such as the expected returns
on hedge portfolios on bills, bonds, and common stocks assumed to drive
risk premia; however, data strongly rejected the latent variable models.52
Simon (1989), on the other hand, suggested that the term premium is
proportional to the square of the excess holding period return.53
Furthermore, Tzavalis and Wickens (1997) argued that the ex-post holdingperiod return of one maturity can be used as a good BRP proxy of other
maturities.54 Similarly, Cochrane and Piazzesi’s (2002) study supported
Tzavalis and Wickens’ findings upon using a tent-shaped function of
Robert Shiller, John Campbell, and Kermit Schoenholtz, “Forward Rates and Future Policy:
Interpreting the Term Structure of Interest Rates”, Brookings Papers on Economic Activity 1983,
no.1 (1983), http://www.jstor.org/stable/2534355.
52
John Campbell, “Stock Returns and the Term Structure,” National Bureau of Economic
Research Working Paper 1626 (1985), 7.
53
David Simon, “Expectations and Risk in the Treasury Bill Market,” The Journal of Financial
and Quantitative Analysis 24, no. 3 (1989), http://www.jstor.org/stable/2330816.
54
Elias Tzavalis and Michael Wickens, “Explaining the Failures of the Term Spread Models of the
Rational Expectations Hypothesis of the Term Structure,” Journal of Money, Credit, and Banking
29, no. 3 (1997), http://www.jstor.org/stable/2953700.
51
39
forward rates as a single-factor representation of the BRP to predict oneyear excess holding-period returns.55
Mankiw, Goldfeld, and Shiller (1986) and Boero and Torricelli
(2000), used measures of volatility as a way to proxy for the BRP. Mankiw,
Goldfeld, and Shiller, assumed that the term premium is positively related
to risk; thus, the riskier a certain investment instrument is, a higher term
premium would be assigned by investors to it. They assumed that
“substantial fluctuation in perceived risk could explain the rejection of the
EH”. They used the following variables to inspect which highly affects
excess returns: 1) interest rate volatility, 2) consumption, 3) stock market
activity, and 4) change in asset supplies.56 In the same way, Boero and
Torricelli directly used the following as proxies for excess returns/risk
premium: 1) moving average of absolute changes in the short rate over the
previous six periods; 2) expected square of excess holding period returns;
and 3) estimates of conditional variances from GARCH models.
b. Term Premium Specification Based on a Term Structure Model
Other studies have also specified the term premium through latent
affine stochastic discount factors (SDF). SDF models refer to “pricing an
John Cochrane and Monika Piazzesi, “Decomposing the Yield Curve,” National Bureau of
Economic Research (2008),
http://faculty.chicagobooth.edu/john.cochrane/research/papers/interest_rate_revised.pdf.
56
Gregory Mankiw, Stephen Goldfeld, and Robert Shiller, “The Term Structure of Interest Rates
Revisited,” Brookings Papers on Economic Activity 1986, no.1 (1986), http://www.
jstor.org/stable/2534414.
55
40
asset as the expected discounted value of its pay-off next period”57 (see
Cochrane (2000), Bolder (2001), Chib (2009), and Smith and Wickens
(2003) for a more detailed discussion of SDF models).
Balfoussia and Wickens (2007) posited that the risk premia obtained
from an SDF model were derived from the conditional covariances of the
excess return over the risk-free rate. Cochrane (2000) stated that there are
two major approaches to asset pricing: 1) absolute asset pricing which
involves pricing an asset with respect to its exposure to fundamental sources
of macroeconomic risk; and 2) relative asset pricing which prices an asset
with respect to the prices of other assets.58 Alternatively, Balfoussia and
Wickens (2007) also discussed that SDF models can be single factor affine
models (wherein all bond yields are a function of the short rate and with a
fixed shape of the yield curve through time) or multifactor affine models
(that is argued to be more flexible but over-constrained). With all of these
information, Balfoussia and Wickens (2007), therefore, developed their
methodology based on the SDF model to estimate the contribution of
macroeconomic variables to the term premia.59
Ilmanen (2012) also suggested that another approach to estimate the
BRP is through a survey. The survey is the most direct way of assessing the
market’s expectations. Values can be obtained right away and by
Hiona Balfoussia and Mike Wickens, “Macroeconomic Sources of Risk in the Term Structure,”
Journal of Money, Credit, and Banking 39, no. 1 (2007), http://www.jstor.org/stable/4123075.
58
Peter Smith and Michael Wickens, “Asset Pricing and Observable Stochastic Discount Factors,”
Journal of Economic Surveys 16 (2002), 397-446.
59
Hiona Balfoussia and Mike Wickens, “Macroeconomic Sources of Risk in the Term Structure,”
Journal of Money, Credit, and Banking 39, no. 1 (2007), http://www.jstor.org/stable/4123075.
57
41
subtracting the measure from current long-term yield gives the estimate of
the BRP. However, it is noted that academics have recently veered away
from gathering data through surveys because of the tedious efforts
associated to it. Likewise, the survey approach in this research shall not be
given focus. This is because no such surveys have been done in the
Philippines.60
D. Macroeconomic Variables and the Bond Risk Premium
Due to the unobservable nature of the BRP, several studies have used
macroeconomic variables or country data that may aid in estimating the term
premium. Mankiw, Goldfeld, and Shiller (1986), for example, associated excess
returns with some common sources of risk such as interest rate volatility,
consumption, and activity of the stock market, and changes in asset supplies (or the
relative supply of long-term and short-term bonds). Unfortunately, none of these
factors satisfactorily explained the large variation in the term premium, and thus
lead to the failure of the EH.61
Balfoussia and Wickens (2007) also considered three observable
macroeconomic factors to estimate the variability of the bond risk premia. These
were consumption, output, and inflation. They used a multivariate GARCH
(Generalized Autoregressive Conditional
Heteroskedasticity)
model
with
60
Antti Ilmanen, Expected Returns on Major Asset Classes (Research Foundation of CFA
Institute: John Wiley & Sons, Inc., 2012), 56.
61
Gregory Mankiw, Stephen Goldfeld, and Robert Shiller, “The Term Structure of Interest Rates
Revisited,” Brookings Papers on Economic Activity 1986, no.1 (1986), http://www.
jstor.org/stable/2534414.
42
conditional covariances in the mean of the excess holding-period returns.
Balfoussia and Wickens found out that inflation was the main source of risk at all
maturities, while consumption was a less important source of risk.62 Similarly, Lee
(1995) used output and money supply as the sources of the time-varying risk premia
in the term structure. Lee’s empirical tests were summarized by the ARIMAGARCH
(Autoregressive
Integrated
Moving
Average
–
Generalized
Autoregressive Conditional Heteroskedasticity) model, and he found out that the
uncertainties related to output (industrial production) and money supply (M1) were
significant in all the risk premium equations and they showed explanatory power
for the monthly excess returns.63
Ilmanen (2012), on the other hand, enumerated the four key drivers of the
BRP. The first BRP driver was level-dependent inflation uncertainty, which was
considered as the most important secular driver of required expected real bond
yields and BRPs. The intuition is that, higher inflation levels are associated with
greater inflation uncertainty, which warrants higher required premia for holding
nominal bonds. The second BRP driver was the equity and/or recession-hedging
ability or also known as the stock-bond correlation. Ilmanen argued that the stockbond correlation in the US reached negative levels around 1998, which reflected
the government bond’s role as the ultimate safe-haven asset. Additionally, Ilmanen
Hiona Balfoussia and Mike Wickens, “Macroeconomic Sources of Risk in the Term Structure,”
Journal of Money, Credit, and Banking 39, no. 1 (2007), http://www.jstor.org/stable/4123075.
63
Sang-Sub Lee, “Macroeconomic Sources of Time-Varying Risk Premia in the Term Structure of
Interest Rates,” Journal of Money, Credit, and Banking 27, no. 2 (1995),
http://www.jstor.org/stable/2077883.
62
43
posited that the stock-bond correlation is likely to be negative even with low and
stable inflation expectations.
The next BRP driver is the supply and demand factors which contribute to
the time-varying nature of the risk premia. Some examples of these are the: 1) fiscal
supply (maturity structure of government debt and public-debt-to-GDP ratio) since
the impact on bond yields of high debts/deficits is greater when expected inflation
is also high and initial fiscal conditions are poor; 2) regulatory effects and pension
fund demand which allows the yield curve to be flat or inverted at long maturities;
and 3) foreign flows which characterized the “savings glut” in 2004 to 2005. Lastly,
Ilmanen stated that the shape of the yield curve is closely interrelated with various
cycles in the economy which includes business cycles, credit cycles, and monetary
policy cycles. Ilmanen found out that the yield curve of the BRP is distinctly
countercyclical, which means that at periods near business cycle troughs, required
term premium is high, while at periods near business cycle peaks, required term
premium is low.64
Finally, Chantapacdepong (2007) examined the relationship of the risk
premia on holding 6-month Treasury bills in 43 countries65 (as the dependent
variable) with other macroeconomic variables (as the explanatory variables). These
variables were classified as domestic economic variables (economic growth,
inflation rate, and real effective exchange rate), government/fiscal variables
(government debt as a percent of GDP and fiscal deficit as a percent of GDP), and
64
Antti Ilmanen, Expected Returns on Major Asset Classes (Research Foundation of CFA
Institute: John Wiley & Sons, Inc., 2012), 61-75.
65
Chantapacdepong has representative countries from developed, developing, and less developed
countries around the world.
44
institutional
variables
(political
constraints
and
political
risk
index).
Chantapacdepong’s results showed that the risk premia were highly correlated with
the political risk index (𝜌 = 0.63), political constraint index (𝜌 = 0.58), and inflation
(𝜌 = 0.57). Other variables followed: real effective exchange rate (REER) (𝜌 =
0.50), economic growth (𝜌 = 0.43), and budget deficit as a percent of GDP (𝜌 =
0.17).66
Apart from the correlations, regression was also used to identify if these
factors are significant predictors of the BRP. Chantapacdepong’s results showed
that inflation (𝛽 = 1.41) and economic growth (𝛽 = -1.73) were significant
predictors at the 5% level. Budget deficit as a percentage of GDP has a predictive
power (𝛽 = 1.62) at the 10% level. Debt-to-GDP and the volatility of the REER
were not significant at all, but also contains some degree of prediction at 𝛽 = 0.17
and 𝛽 = 0.22, respectively. When the political and institutional variables were
added, the results did not change; inflation, deficit-to-GDP, and economic growth
still showed strong predictive powers for the BRP. Chantapacdepong concluded
that “the short run macroeconomic circumstances are the ones that highly explain
the risk premia”; that is, higher inflation, lower growth, and higher government
deficit all lead to a higher risk premia.67
Pornpinun Chantapacdepong “Determinants of the time varying risk premia,” (Discussion Paper
No. 07/597, Department of Economics, University of Bristol, 2007), 18-34.
67
Pornpinun Chantapacdepong “Determinants of the time varying risk premia,” (Discussion Paper
No. 07/597, Department of Economics, University of Bristol, 2007), 35-36.
66
45
CHAPTER III
THEORETICAL FRAMEWORK AND METHODOLOGY
This study aims to empirically test the applicability of the Expectations
Hypothesis (EH) on Philippine bond yields. As a benchmark study, this paper shall
be a basic development from the various research papers that investigated the EH.
For the first objective, which is to empirically test the EH, the two-period case and
n-period case models of McCallum (1994) would be employed. For the
measurement of the bond risk premium (BRP), this study would use interest rate
volatility as a proxy for risk. Finally, to identify relationships with macroeconomic
variables, a mix of the experimental regressions done by Mankiw, Goldfeld, and
Shiller (1986), Chantapacdepong (2007), and Ilmanen (2012) would be used.
A. Theoretical Framework
This thesis study shall revolve around its main theoretical basis which is the
Expectations Hypothesis (EH). The hypothesis is illustrated by Equation 3 which
shows that the long rate is just the simple average of the current short rate and the
expected future short rates over the life of the long rate. This implies that the
movement of the long-term rate can be determined by the movement of the current
and expected short-term rates, and vice-versa. Hence, this supports the claim that
under the EH, long-term bonds and short-term bonds are perfect substitutes or
applies the notion of the “no-arbitrage principle”.
1
𝑚
𝑛,𝑚
𝑟𝑡𝑛 = ( ) ∑𝑘−1
𝑖=0 𝐸𝑡 𝑟𝑡+𝑚𝑖 + 𝜃
𝑘
(from Eq. 3)
46
For investment instruments to be considered perfect substitutes, they must
have inherent characteristics that goes in consonance with the implications of the
theory. The EH, for instance, have the following implications:68
1. The term spread must predict expected changes in future short-term rates;
2. The term spread must predict expected changes in future long-term rates; and
3. The term premium must be constant or zero (which implies that the term
spread must not forecast the excess holding returns on long-term rates).
These assumptions are a set of criteria to say that a specific set of investment
instruments or assets follow the EH rule. If one of these conditions is rejected, we
can say that the EH does not hold anymore.
Equation 3 can be used to derive the corresponding empirical equations to
test the validity of the assumptions of the EH. These empirical equations are called
term spread models. A wide set of literature developed on various term spread
equations, however, this thesis searched for an appropriate model that would fit the
availability of bond maturities in the Philippines. Thus, this study shall adopt
McCallum’s (1994) EH models.69
McCallum classified the term spread models into two. These are the twoperiod case and the n-period case. This was done to allow for the unique properties
of the bond maturities featured in his study. The two-period case is used to tackle
the relationship between yields on one-period bonds and two-period bonds, while
the n-period case is employed to test the relationship of one-period bonds and longterm rates with maturities of more than two periods.
68
69
This summary of EH assumptions came from Mankiw, Goldfeld, and Shiller (1986).
This part shall take up McCallum’s notations.
47
1. Term Spread Model for Predicting Changes in the Short Rate
The EH posits that the long rate (𝑅𝑡 ) is related to the current short
rate (𝑟𝑡 ) and the expected future short rates (𝐸𝑡 𝑟𝑡+1 ) as follows:
𝑅𝑡 = 0.5 (𝑟𝑡 + 𝐸𝑡 𝑟𝑡+1 ) + 𝜉𝑡
(Eq. 12)
where 𝜉𝑡 is the term premium that is assumed constant.70 Defining the
expectational error (or the error in forecasting future short rates) 𝜖𝑡+1 =
𝑟𝑡+1 − 𝐸𝑡 𝑟𝑡+1, Equation 12 implies
0.5 (𝑟𝑡+1 − 𝑟𝑡 ) = (𝑅𝑡 − 𝑟𝑡 ) − 𝜉𝑡 + 0.5𝜖𝑡+1
(Eq. 13)
If a constant term premium is assumed, 𝜉𝑡 = 𝜉, and assuming rational
expectations which makes the expectation error, 𝜖𝑡+1, orthogonal or
uncorrelated with 𝑅𝑡 and 𝑟𝑡 , the constant coefficient 𝛼 and the slope
coefficient 𝛽 in the regression model
0.5 (𝑟𝑡 − 𝑟𝑡−1 ) = 𝛼 + 𝛽 (𝑅𝑡−1 − 𝑟𝑡−1 ) + 𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑎𝑛𝑐𝑒 𝑡𝑒𝑟𝑚
(Eq. 14)
should have probability limits of zero and one, respectively. Equation 13
tells us that the average change in the short rate, 0.5 (𝑟𝑡+1 − 𝑟𝑡 ), must be
equal term spread, (𝑅𝑡 − 𝑟𝑡 ), less the term premium, 𝜉𝑡 , plus the average
expectation error, 0.5𝜖𝑡+1 .
In Equation 14, the 𝛼 coefficient indicates that with everything in
the model held constant, the term spread will not be able to predict future
changes in the short rate; whereas, the expected 𝛽 coefficient of one implies
that the term spread can “perfectly” predict the changes in the short rate,
such that every percentage change in the term spread translates to an equal
70
For now, this basic model of the EH shall assume a constant term premium.
48
percentage change in the short rate. A standard way of estimating Equation
14 is by using the ordinary-least squares (OLS) method.
2. Term Spread Model for Predicting Changes in the Long Rate
For testing the relationship between the long rate and the term
spread, McCallum used a different model called the n-period case. This
model is made fit for bonds with a maturity of more than two periods.
Following the same notations as in the two-period case, the EH relationship
between the long rate and short rate can be expressed as
𝑅𝑡 − 𝑁𝐸𝑡 (𝑅𝑡+1 − 𝑅𝑡 ) = 𝑟𝑡 + 𝜉𝑡 ,
(Eq. 15)
where 𝑁 + 1 is the measure of duration of the long rate (where for discount
bonds or zero-coupon bonds, the duration is equal to its maturity). The lefthand side of the equation represents the one-period holding return on the
long rate.71 Equation 15 means that the one-period holding return in any
long period bond must be equal to the return of the current short rate plus
the term premium. The empirical model becomes
𝑁(𝑅𝑡+1 − 𝑅𝑡 ) = (𝑅𝑡 − 𝑟𝑡 ) − 𝜉𝑡 + 𝑁𝜀𝑡+1
(Eq. 16)
where 𝜀𝑡+1 = 𝑅𝑡+1 − 𝐸𝑡 𝑅𝑡+1 , or the expectational error that is made in
forecasting future long rates. 𝜀𝑡+1 is also assumed to be orthogonal or
uncorrelated with 𝑅𝑡 and 𝑟𝑡 . If the term premium, 𝜉𝑡 , is assumed to be
constant, a regression in the form of:
McCallum noted that 𝑁𝐸𝑡 (𝑅𝑡+1 − 𝑅𝑡 ) is only an approximation of the expected capital loss on
the long bond. This has been adopted so that only two maturities will be involved in the model.
Due to the limited type (maturities) of zero coupon bonds that the Philippines has, this was also
chosen to be the empirical model for this thesis.
71
49
𝑁(𝑅𝑡 − 𝑅𝑡−1 ) = 𝛼 + 𝛽(𝑅𝑡−1 − 𝑟𝑡−1 ) + 𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑎𝑛𝑐𝑒 𝑡𝑒𝑟𝑚
(Eq. 17)
should have probability limits of zero for 𝛼 and one for 𝛽 after OLS
estimation. The 𝛼 and 𝛽 coefficients of Equation 17 have the same
implications as in Equation 16, but now changes in the long rate are the ones
estimated by the term spread.
3. Model for Predicting Excess Holding Period Returns
The EH also posits that the term premium, 𝜉𝑡 , is constant through
time. Mankiw, Goldfeld, and Shiller (1986) tested this assumption by
combining it with another assumption that the expectation error, 𝜐𝑡+1,72
cannot be forecasted with information available at time t. This also implies
that the excess holding return, 𝐻𝑡 − 𝑟𝑡 , cannot be forecasted using variables
known at time t:
𝐻𝑡 73 − 𝑟𝑡 = 𝜉𝑡 + 𝜐𝑡+1
(Eq. 18)
Equation 18 can be transformed into its regression form
𝐻𝑡 − 𝑟𝑡 = 𝛼 + 𝛽𝑋𝑡 + 𝜐𝑡+1
(Eq. 19)
and can be estimated via OLS by regressing the excess return on any
variable determined at time t. For the EH to hold, the 𝛽 coefficient must be
zero.
72
This notation can be considered as a representation of the expectation errors for the term spread
model for the short rate and the term spread model for the long rate.
73
The holding return, as defined by Mankiw, Goldfeld, and Shiller (1986), can be expressed in
1+𝑃𝑡+1 − 𝑃𝑡
𝑅
−𝑅
terms of prices, 𝐻𝑡 ≡
, or yields, 𝐻𝑡 ≡ 𝑅𝑡 − 𝑡+1 𝑡. A linearized version of the holding
𝑃𝑡
return was also presented: 𝐻𝑡 ≈ 𝑅𝑡 −
𝑅𝑡+1 − 𝑅𝑡
𝜌
𝑅𝑡+1
, where 𝜌 is a constant equal to the average of the
long rate.
50
Indeed, there can be a limitless number of variables available at time
t that can be plugged in Equation 19, but Mankiw, Goldfeld, and Shiller
already suggested two specific variables to be tested. The first variable is
the lagged values of the excess return. The excess return must not be
forecasted by the lagged values of 𝜐𝑡+1. If by chance, the 𝛽 coefficient is
not zero, it can be hypothesized that the excess returns and its lagged values
are serially correlated thus, indicating the presence of a time-varying risk
premium.74
The second variable is the spread between the long rate and the short
rate (𝑅𝑡 − 𝑟𝑡 ). In order to satisfy the EH, the term spread must not forecast
the excess holding period returns, which further supports the assumption
that the term premium is zero. If it does, this can be another indication that
a time-varying risk premium may be present.75
Previous studies done on the EH highlighted the importance of correcting
the term spread models via econometric techniques to achieve unbiased estimates.
Thus, diagnostic tests of the residuals and elements of the equation would be done
to check for any errors such as serial correlation or heteroskedasticity.76
Gregory Mankiw, Stephen Goldfeld, and Robert Shiller, “The Term Structure of Interest Rates
Revisited,” Brookings Papers on Economic Activity 1986, no.1 (1986), http://www.
jstor.org/stable/2534414.
75
Gregory Mankiw, Stephen Goldfeld, and Robert Shiller, “The Term Structure of Interest Rates
Revisited,” Brookings Papers on Economic Activity 1986, no.1 (1986), http://www.
jstor.org/stable/2534414.
76
Elias Tzavalis and Michael Wickens, “Explaining the Failures of the Term Spread Models of the
Rational Expectations Hypothesis of the Term Structure,” Journal of Money, Credit, and Banking
29, no. 3 (1997), http://www.jstor.org/stable/2953700
74
51
4. Bond Risk Premium
In this thesis, it is considered that the rejection of any or all
assumptions of the EH signals for the presence of a bond risk premium
(BRP), specifically, a time-varying risk premium. Thus, to deeply examine
the effect of the BRP on the EH tests, the BRP must be measured. For this
study to be established as a startup study about the EH of the term structure,
simple measurement methods such as observable proxies for the BRP would
be employed.
Among the different observable proxies suggested by relevant
literature, this thesis considered the estimations of Mankiw, Goldfeld, and
Shiller (1986), and Boero and Torricelli (2000). They measured the BRP
using proxies of risk. Mankiw, Goldfeld, and Shiller associated the term
premium as the measure for risk associated with holding a long-term bond,
𝜉𝑡
𝑅𝐼𝑆𝐾𝑡
(Eq. 20)
which is positively related with each other.
Risk, on the other hand, is also unobservable, but imperfect proxies
for it can be obtained. For this study, various measures of interest rate
volatility are employed, with the assumption that volatility is directly
proportional to risk,
𝑅𝐼𝑆𝐾𝑡
𝑉𝑂𝐿𝑡 .
(Eq. 21)
From the definition of term premium as an investor’s compensation
for risk, assuming risk-averse investors, the required expected return for
holding long-term bonds must rise when they are riskier. Consequently, if
52
long-term bonds are less risky, the required compensation of investors must
also fall. It can, thus, be said that greater interest rate volatility is also
associated with a greater term premium, and reduced interest rate volatility
with a smaller term premium.77
Mankiw, Goldfeld, and Shiller (1986) also considered a plausible
model of volatility as a proxy for risk, which is expected volatility,
𝑅𝐼𝑆𝐾𝑡
𝐸𝑡 (𝑉𝑂𝐿𝑡 )
(Eq. 22)
which is also positively related to risk. However, expected volatility is also
unobservable hence, actual volatility was adopted as an imperfect proxy for
expected volatility. It also follows from the EH that the measurement error
between actual and expected volatility is uncorrelated with the term spread
at time t.78
5. Macroeconomic Factors and the Bond Risk Premium
Several studies on the EH have cited the relevance of
macroeconomic factors that affect or are related to the BRP. One of which
was Chantapacdepong (2007) who examined the determinants of the timevarying risk premia. Chantapacdepong used three classifications of
macroeconomic variables which are the domestic and foreign economic
variables, government/fiscal variables, and institutional variables, and used
Gregory Mankiw, Stephen Goldfeld, and Robert Shiller, “The Term Structure of Interest Rates
Revisited,” Brookings Papers on Economic Activity 1986, no.1 (1986), http://www.
jstor.org/stable/2534414.
78
Gregory Mankiw, Stephen Goldfeld, and Robert Shiller, “The Term Structure of Interest Rates
Revisited,” Brookings Papers on Economic Activity 1986, no.1 (1986), http://www.
jstor.org/stable/2534414.
77
53
cross sectional regressions to identify the relationship of these data to the
estimated BRP.
Since studies on the BRP of the Philippines have been very limited
and they have not identified the corresponding correlations and/or expected
relationship of the BRP with various macroeconomic variables, this thesis
would rely on a new framework. This new basis is a combination of three
well-known frameworks which are the Risk-Return Tradeoff Principle, the
Supply and Demand Framework in the Money Market, and the Framework
for Real and Financial Markets. In this study, it shall be considered that
factors contributing to higher bond returns (either coming from the supply
or demand side of Treasury funds) shall be associated with higher risk and
hence, higher BRP. Consequently, factors that contribute to lower bond
returns shall be associated with lower risk and thus, lower BRP.
Figure 4 shows the simple and straightforward relationship between
risk and return. The Risk-Return Tradeoff Principle primarily asserts that
risk and investment returns have a direct positive relationship. Potential
return rises with increased risk, while low potential returns are associated
with lower risk.
On the other hand, Figure 5 illustrates the interaction of the supply
of money and demand for money that determines the level of interest rates.
Money supply (MS) is considered fixed in the long-run that explains the
vertical line graph, while money demand (MD) is comparable to the
appearance of aggregate demand (i.e. downward sloping). The initial
54
equilibrium point (point A) is where MS1 and MD1 intersects. An increase
in money supply (MS1 to MS2), with money demand held constant (at MD1),
shall induce interest rates to fall (from r1 to r2) at equilibrium point B. The
opposite shall happen if a decrease in money supply happens, ceteris
paribus. On the other hand, when there is an increase in money demand
(MD1 to MD2), with money supply held constant (at MS1), will cause
interest rates to increase (r1 to r3) and equilibrium point will be at point C.
If a decrease in money demand happens, interest rates shall decrease, ceteris
Return
paribus.
Risk
Figure 4. Risk & Return Tradeoff Principle
Source: “Risk-Return Tradeoff”, Investopedia,
http://www.investopedia.com/terms/r/riskreturntradeoff.asp
55
Figure 5. Supply and Demand in the Money Market
Source: Mankiw, Gregory. Macroeconomics. 5th edition. New York: Worth Publishers,
2003.
The next step is to find out the factors affecting money supply and
money demand in the Philippines that contribute to the rise and fall of
domestic interest rates. For this, we shall rely on the framework of Abola
(2014) below which highlights the underlying relationships between
domestic interest rates and macroeconomic variables (both domestic and
foreign).
Figure 6 shows that domestic interest rates are directly influenced
by foreign interest rates. As explained by Abola (2014), foreign interest
rates (especially US) have a positive relationship with domestic interest
rates. Higher interest rates in the US would allow capital flight from
Philippine assets. This lessens the supply of funds available locally. Ceteris
paribus, a decrease in supply will result to an increase in domestic interest
56
rates. Hence, an increase in US interest rates also prompts an increase in
Philippine interest rates. However, Abola argued that the transmission of a
change in foreign interest rates is not 1-for-1 but only 1/3 o3 33%.79
Furthermore, interest rates are also determined by the domestic
supply of funds and demand for funds. The funds supply and demand, in
turn, are affected by domestic macroeconomic variables. Demand for funds
is influenced by: 1) the demand of private firms, 2) demand of the public
sector or the National Government (NG); 3) additional demand resulting
from inflation; and 4) sometimes, output or gross domestic product (GDP).
The supply of funds, on the other hand, is determined by income measured
by GDP and OFW remittances (which becomes Gross National Product
(GNP)) in the form of savings. The impact of GNP growth, in turn, is
affected by the foreign exchange rate. BSP’s monetary stance is also a
determinant of the supply of funds.80
Combining the three frameworks, a diagram of macroeconomic
determinants of the bond risk premium is demonstrated in Figure 7. Figure
7 shows that the bond risk premium (BRP) is directly associated to risk, that
is, higher risk means a higher BRP and lower risk needs a lower BRP. Risk,
on the other hand, is directly associated to bond returns such that increased
bond returns entails higher risk, while lower bond returns involves lower
Victor Abola, “Domestic Interest Rates: After disasters, a downward trend”, Recent Economic
Indicators, November 2014.
80
Victor Abola, “Domestic Interest Rates: After disasters, a downward trend”, Recent Economic
Indicators, November 2014.
79
57
risk. This encapsulates the risk-return tradeoff principle exemplified by
Figure 4.
The third level of the diagram pertains to the relationship of bond
returns with the supply and demand of funds. Basically, higher bond returns
are produced when money demand is high while money supply is held
constant. The outcome is the same when money supply is low while money
demand is held constant. Thus, factors that positively affect money demand
(or negatively affect money supply) are considered to be the variables which
contribute to a higher BRP. On the other hand, lower bond returns are
produced when money supply is high while money demand is held constant
(or when money demand is high while money supply is held constant).
Hence, factors that positively affect money supply (or negatively affect
money demand) are considered to contribute to a lower BRP.
The main macroeconomic variables that affect the supply of and
demand for Treasury funds are also enumerated in Figure 7, as compiled
from the framework of real and financial markets by Abola (2014).81 These
macroeconomic variables are to be supplemented by some factors used by
Bico (2010). Some of these factors are the bond spread and the lagged
values of the dependent variable.82 Additionally, although Abola classified
monetary policy under the factors that inversely affect the BRP, this study
shall adopt the finding of Bico that bond yields are positively related to
81
M2 (broad money) or M3 was also included by Abola in one of the interest rate frameworks that
he developed. M2 or M3
82
C. Bico, “Estimating and Forecasting the Philippines Zero-Coupon Yield Curve: A Multimethod
Approach” (Thesis, University of Asia and the Pacific, 2010), 64-71.
58
BSP’s monetary stance and thus, contributes to higher risk and a higher
BRP. This assertion is also confirmed by the finding of Ireland (2015) that
a “monetary policy tightening increases the [bond risk] premia while
monetary policy easing works to decrease them”.83 Stock market activity
was also included as suggested by the study of Ilmanen (2012) which has a
positive effect on BRP.
US and Global Environment
World Economic Growth
World Financial Markets
Foreign Interest Rates/FX Rates
Stocks
Bonds
Commodities
OFW
P/$ Rate
BSP
Supply of Funds
PSEi
Domestic
Interest Rates
T-Bonds
Inflation
Demand for Funds
Fiscal Balance
Savings
For Production
GNP Growth
Figure 6. Framework for Real and Financial Markets
Source: Abola, Victor. “Domestic Interest Rates: After disasters, a downward trend.”
Recent Economic Indicators, November 2014.
Peter Ireland, “Monetary Policy, Bond Risk Premia, and the Economy,” National Bureau of
Economic Research (2015): 28.
83
59
High Bond Risk Premium
Low Bond Risk Premium
High Risk = High Bond Returns
Low Risk = Low Bond Returns
Increase in Money Demand
Increase in Money Supply
(with Money Supply held constant)
(with Money Demand held constant)
 Private sector demand
 Public sector demand (i.e.,
National Government)
 Domestic Inflation
 Peso-Dollar Rate
 Foreign variables (US
Inflation and US Treasury
Rates)
 Gross Domestic Product
(GDP)
 Gross National Product
(GNP) or OFW Remittances
 Gross International Reserves
(GIR)
 Foreign Investments
 M2 or M3
 BSP’s Monetary Policy
Figure 7. Relationship of Macroeconomic Determinants of the Bond Risk
Premium
Source of Macroeconomic Concepts: Abola, Victor. “Domestic Interest Rates: After
disasters, a downward trend.” Recent Economic Indicators, November 2014.
To uncover the underlying effects of these explanatory variables to
the BRP, the estimated risk premium shall be regressed against the
mentioned
macroeconomic
variables.
In
this
way,
researchers,
policymakers, and investors shall know what factors to focus on when
monitoring the country’s interest rates.
The macroeconomic variables, their definitions, and corresponding
expected signs are summarized in the table below:
60
Table 5. Explanatory Variables, Definitions, and Expected Relationship
with BRP
Variable
Notation
Definition
Domestic and Foreign Economic Variables
In order to fit the frequency
of the data, monthly sales
GDP
growth of Meralco
(Economic
𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠
(electricity sales) can be
Growth)
used as a proxy for
economic growth.
This pertains to the year-onyear growth of the
Price
𝑔𝑖𝑛𝑓
Consumer Price Index (CPI)
with a monthly frequency.
This refers to the average
monthly peso-dollar
Peso-Dollar
exchange rate. To remove
𝑔𝑓𝑜𝑟𝑒𝑥
Rate
the general trend of the
peso, the growth rate was
used.
M2 is the measure of broad
money available in the
financial system. This
includes the currency in
Excess Liquidity
𝑔𝑚2
circulation, peso demand
deposits, peso savings, and
time deposits. Monthly
growth rate was used.
This pertains to the monthly
OFW
OFW remittances in dollars.
𝑔𝑜𝑓𝑤𝑟𝑒𝑚
Remittances
Growth rate was also used
to remove the trend.
This is the overnight policy
rate or the reverse
repurchase rate used by the
Monetary
Bangko Sentral ng Pilipinas
𝑔𝑟𝑟𝑝
Stance
(BSP). The monthly growth
rates were used to achieve
robust results.
This pertains to the monthly
US Prices
growth of inflation in the
𝑔𝑢𝑠𝑐𝑝𝑖
US.
This refers to the average
monthly overnight policy
Federal Funds
rate in the US. Growth rate
𝑔𝑓𝑒𝑑𝑟𝑎𝑡𝑒
Rate
was used to remove the
trend.
Expected
Relationship
with BRP
–
+
+
–
–
+
+
+
61
Gross
International
Reserves
𝑔𝑔𝑖𝑟
These are the foreign assets
readily controlled by the
BSP for financing and
managing imbalances. They
are used as indicators of the
country’s liquidity and
ability to pay imports and
foreign obligations. Growth
rates were used to remove
the trend in the data.
–
Government/Fiscal Variables
Budget Deficit
𝑔𝑑𝑒𝑓𝑖𝑐𝑖𝑡
Government
Debt
𝑔𝑑𝑒𝑏𝑡
This refers to the monthly
budget deficit of the
government as a percentage
of GDP, measured using net
domestic financing. Growth
rate was used to remove the
underlying trend.
This refers to the monthly
growth rate of the debt of
the government as a
percentage of GDP.
+
+
Institutional Variables
Stock Market
Index
𝑔𝑝𝑠𝑒𝑖
This represents the monthly
performance of the stock
market. The growth rate of
the index was used to
remove the trend.
+
Additional Variables
Lag of Bond
Risk Premium
𝑏𝑟𝑝𝑙𝑎𝑔
Bond Spread
𝑠𝑝𝑟𝑒𝑎𝑑
This pertains to the lagged
value of the estimated bond
risk premium per bond pair.
With this, we can check if
the present value of the BRP
is highly affected by its past
value.
This pertains to the slope of
the yield curve, or simply
the difference between two
certain maturities which are
the bond pairs.
+
+
Source: Abola (2014), Chantapacdepong (2007), Bico (2010), and Ilmanen (2012)
62
B. Conceptual Framework
The framework below illustrates the relationships of the major concepts
discussed in this research. Figure 8 shows that the Expectations Hypothesis (EH)
assuming a constant term premium holds true if standard tests satisfy three specific
implications which are: 1) The term spread must predict future changes in the short
rates; 2) The term spread must predict future changes in the long rate; and 3) The
term spread must not predict the excess returns. If any of these assumptions is
rejected, it can be said there is some disturbance affecting the EH model. In this
study, this disturbance is readily assumed to be the bond risk premium (BRP).
Since the BRP is unobservable, estimation techniques must be done to
measure it. An estimated BRP can be plugged in into the EH model but now
assuming a time-varying risk premium. The conditions of the former EH model
must still hold hence, diagnostic tests would be required to inspect if the standard
regression method improved the previous results or not. Finally, to deepen the
discussion about the estimated BRP, macroeconomic variables affecting it or highly
correlated to it would be examined.
C. Empirical Methodology
The methodologies used in this study were made to correspond to each
research objective. The first objective, which is to empirically test the validity of
the assumptions of the Expectations Hypothesis (EH) on Philippine bond yields,
shall be achieved by applying the bond yields into the term spread models and
excess returns model.
63
The first term spread model shall forecast future changes in the short rate
denoted by
0.5 (𝑟𝑡 − 𝑟𝑡−1 ) = 𝛼1 + 𝛽1 (𝑅𝑡−1 − 𝑟𝑡−1 ) + 𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑎𝑛𝑐𝑒 𝑡𝑒𝑟𝑚,
(from Eq. 14)
while the second version of the EH model shall relate the term spread model to
future changes in the long rate, that is
𝑁(𝑅𝑡 − 𝑅𝑡−1 ) = 𝛼2 + 𝛽2 (𝑅𝑡−1 − 𝑟𝑡−1 ) + 𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑎𝑛𝑐𝑒 𝑡𝑒𝑟𝑚.
(from Eq. 15)
For the EH to be satisfied, the coefficients of 𝛼1 and 𝛼2 must approach zero while
the coefficients of 𝛽1 and 𝛽2 must equal unity or one by estimating the two models
via ordinary least squares (OLS).
To test the third assumption of the EH, which is that excess returns must not
predict excess returns, Equation 19 would be tested via OLS.
𝐻𝑡 − 𝑟𝑡 = 𝛼 + 𝛽𝑋𝑡 + 𝜐𝑡+1
(from Eq. 19)
using the variables recommended by Mankiw, Goldfeld, and Shiller (1986) which
should produce 𝛽 coefficients of zero. These variables are the lagged values of the
excess returns
𝐻𝑡 − 𝑟𝑡 = 𝛼 + 𝛽 (𝐸𝑅𝑙𝑎𝑔𝑔𝑒𝑑 ) + 𝜐𝑡+1
(Eq. 23)
and the term spread
𝐻𝑡 − 𝑟𝑡 = 𝛼 + 𝛽 (𝑅𝑡 − 𝑟𝑡 ) + 𝜐𝑡+1 .
(Eq. 24)
Diagnostic tests of the residuals for Equations 15, 18, and 20 would be
performed to consistently estimate the equation and achieve unbiased results.
Corresponding corrective econometric techniques would be applied if signs of
serial correlation or conditional heteroskedasticity are present.
64
Expectations
Hypothesis
with constant
bond risk
premium
changes in
short rate
otherwise
must
changes in
predict
long rate
re-testing
excess
returns
must
not
Expectations
Hypothesis
with timevarying bond
risk premium
Bond
Risk
Premium
Macroeconomic
Factors
Figure 8. Conceptual Framework of the Study
The next research objective aims to estimate the bond risk premium for the
respective bond maturities of the Philippines. To fulfill this, several measures of
the BRP would be done, specifically following the proxies of Boero and Torricelli
(2000). Boero and Torricelli took off from the assumption of Mankiw, Goldfeld,
and Shiller’s (1986) that the term premium can be modeled using proxies for risk;
and to represent risk, interest rate volatility can be measured. Boero and Torriceli
used three alternative measures for volatility. These are the:
65
1. moving average of absolute changes in the short rate computed over the
previous 6 periods84
𝐵𝑅𝑃𝑀𝐴,𝑡 =
𝑚
𝑚
∑5𝑖=0 |𝑅𝑡−𝑖
− 𝑅𝑡−𝑖−1
|
6
;
(Eq. 25)
2. square of expected excess holding period return
𝐵𝑅𝑃(𝐸𝑅)2 ,𝑡 = 𝐸𝑡 (𝐻𝑡 − 𝑟𝑡 )2 ; and
(Eq. 26)
3. estimates of conditional standard deviations and variances from the
univariate GARCH model
𝐵𝑅𝑃𝐺𝐴𝑅𝐶𝐻 = ℎ𝑡 ,
(Eq. 27)
specifically, the lag structure GARCH (1,1), where:
2
ℎ𝑡 = 𝛼 + 𝛽1 𝜀𝑡−1
+ 𝛽2 ℎ𝑡−1 .
(Eq. 28)
Boero and Torricelli (2000) adopted these three measures from various researches
as well. The first measure was used by Fama (1976), Jones and Roley (1983), and
Simon (1989). The second one was used by Simon (1989) and Harris (1998).
Lastly, the third measure was adopted from the initial works of Engle, Lilien, and
Robins (1987) which also used ARCH-in-mean (Autoregressive Conditional
Heteroskedasticity-in-mean) models, and subsequently developed into GARCH
models.
Once the BRP has been estimated, they will be individually plugged into
the extended versions of the regression Equations 14 (for the short rate) and 15 (for
the long rate), as follows:
84
Since the same short rates are used for the long rate case (or the n-period case), the moving
average of the change in the long rates would be considered.
66
Moving Average:
0.5 (𝑟𝑡 − 𝑟𝑡−1 ) = 𝛼1 + 𝛽1 (𝑅𝑡−1 − 𝑟𝑡−1 ) + 𝛾𝐵𝑅𝑃𝑀𝐴,𝑡 + 𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑎𝑛𝑐𝑒 𝑡𝑒𝑟𝑚
(Eq. 29)
𝑁(𝑅𝑡 − 𝑅𝑡−1 ) = 𝛼2 + 𝛽2 (𝑅𝑡−1 − 𝑟𝑡−1 ) + 𝛾𝐵𝑅𝑃𝑀𝐴,𝑡 + 𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑎𝑛𝑐𝑒 𝑡𝑒𝑟𝑚
(Eq. 30)
Square of Excess Returns:
0.5 (𝑟𝑡 − 𝑟𝑡−1 ) = 𝛼1 + 𝛽1 (𝑅𝑡−1 − 𝑟𝑡−1 ) + 𝛾𝐵𝑅𝑃(𝐸𝑅)2,𝑡 + 𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑎𝑛𝑐𝑒 𝑡𝑒𝑟𝑚
(Eq. 31)
𝑁(𝑅𝑡 − 𝑅𝑡−1 ) = 𝛼2 + 𝛽2 (𝑅𝑡−1 − 𝑟𝑡−1 ) + 𝛾𝐵𝑅𝑃(𝐸𝑅)2,𝑡 + 𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑎𝑛𝑐𝑒 𝑡𝑒𝑟𝑚
(Eq. 32)
GARCH (1,1)
0.5 (𝑟𝑡 − 𝑟𝑡−1 ) = 𝛼1 + 𝛽1 (𝑅𝑡−1 − 𝑟𝑡−1 ) + 𝛾𝐵𝑅𝑃𝐺𝐴𝑅𝐶𝐻 + 𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑎𝑛𝑐𝑒 𝑡𝑒𝑟𝑚
(Eq. 31)
𝑁(𝑅𝑡 − 𝑅𝑡−1 ) = 𝛼2 + 𝛽2 (𝑅𝑡−1 − 𝑟𝑡−1 ) + 𝛾𝐵𝑅𝑃𝐺𝐴𝑅𝐶𝐻 + 𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑎𝑛𝑐𝑒 𝑡𝑒𝑟𝑚
(Eq. 32)
These models shall accomplish the third objective. To evaluate the said BRP
proxies, goodness of fit evaluations were done. This study used the four criteria of
Gujarati (2011), which are the Adjusted R2, F-statistic, Akaike Information
Criterion (AIC), and Schwarz Information Criterion (SIC).85
Adjusted R2
The Adjusted R2, similar to the R2, captures the proportion of
variation in the dependent variable accounted by the independent variables.
The adjusted R2, nonetheless, adjusts for the number of terms in a model,
thus, the adjusted R2 only improves if the added explanatory value is
considered significant (or has a significant t-stat value).86
C. Bico, “Estimating and Forecasting the Philippine Zero-Coupon Yield Curve: A Multimethod
Approach” (Thesis, University of Asia and the Pacific, 2010), 45-46.
86
J. Bico, “Estimating and Forecasting the Philippine Zero-Coupon Yield Curve: A Multimethod
Approach” (Thesis, University of Asia and the Pacific, 2010), 46.
85
67
F-Statistic
This tests the overall significance of a set of variables in explaining
the dependent variable (Wooldridge, 2009). The F-test assesses the validity
of the null hypothesis that is, the coefficients of the explanatory variables
are zero (thus, does not have an effect on the dependent variable). The
desired result for this study is for the null to be rejected. To achieve this, a
higher the value of the F-statistic is needed or a probability value of less
than 0.05.87
Akaike Information Criterion (AIC)
The AIC is commonly used in selecting the best regression model.
The AIC puts a harsher penalty (equivalent to
2𝑘
𝑛
, where k is the number of
regressors and n is the number of observations) for adding more variables
into the model just like the adjusted R2. It rewards goodness of fit but
includes a penalty for overfitting (or increasing the number of parameters
to improve a model). The AIC represents an estimate of information loss to
minimize the uncertainty that a model is close to the true model. Hence, the
model with the lowest AIC is the most efficient.88
Schwarz Information Criterion (SIC)
The SIC (also known as Schwarz’ Bayesian Information Criterion)
is an alternative to the AIC which imposes a harsher penalty factor (equal
“The F-test,” The F-Test for Linear Regression,
http://facweb.cs.depaul.edu/sjost/csc423/documents/f-test-reg.htm (accessed April 15, 2015).
88
“Akaike Information Criterion,” Wikipedia,
http://en.wikipedia.org/wiki/Akaike_information_criterion (accessed April 15, 2015).
87
68
𝑘
to [𝑛 ln 𝑛]) . Similarly, the model with the lowest SIC is the most efficient.
The SIC also mitigates the risk of overfitting to filter the unnecessary
complicated models. Because of its harsher penalty, SIC prefers simpler
models than the AIC.89
Apart from the four criteria, the improvement of the 𝛼 and 𝛽 coefficients
were also considered.
The fourth objective, which is to identify the macroeconomic variables that
highly affect the estimated BRP, would be achieved via a panel regression model
where the dependent variables are the estimated BRP. The fixed effects
specification was used as we are interested in analyzing the impact of the
explanatory variables which are time-varying.90 Different variations of tests would
be done – whole sample test, short rate tests, long rate tests, and analysis according
to two periods (2006 to 2010 and 2011 to 2014) for both the short rate and long
rate. The division of the periods was done to compare the condition of interest rates
during the crisis and after the crisis. They are denoted as follows:
Model 1: Whole Sample
𝐵𝑅𝑃𝑖𝑡 = 𝛼 + 𝛽𝑏𝑟𝑝(−1)𝑖𝑡 + 𝛽𝑠𝑝𝑟𝑒𝑎𝑑𝑖𝑡 + 𝛽𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠𝑖𝑡 + 𝛽𝑔𝑖𝑛𝑓𝑖𝑡 + 𝛽𝑔𝑓𝑜𝑟𝑒𝑥𝑖𝑡 +
𝛽𝑔𝑚2𝑖𝑡 + 𝛽𝑔𝑜𝑓𝑤𝑟𝑒𝑚𝑖𝑡 + 𝛽𝑔𝑟𝑟𝑝𝑖𝑡 + 𝛽𝑔𝑢𝑠𝑐𝑝𝑖𝑖𝑡 + 𝛽𝑔𝑓𝑒𝑑𝑟𝑎𝑡𝑒𝑖𝑡 + 𝛽𝑔𝑔𝑖𝑟𝑖𝑡 +
𝛽𝑔𝑑𝑒𝑓𝑖𝑐𝑖𝑡𝑖𝑡 + 𝛽𝑔𝑑𝑒𝑏𝑡𝑖𝑡 + 𝛽𝑔𝑝𝑠𝑒𝑖𝑖𝑡
(Eq. 33)
where: 𝑖 = whole sample (for both short rates and long rates)
𝑡 = 2006 to 2014
“Bayesian Information Criterion,” Statistical & Financial Consulting by Stanford PhD,
http://stanfordphd.com/BIC.html (accessed April 15, 2015).
90
On the contrary, the random effects specification is used when the effect of time-invariant
variables (such as gender, culture, religion, etc.) wants to be investigated.
89
69
Model 2: Short Rate
𝐵𝑅𝑃𝑖𝑡 = 𝛼 + 𝛽𝑏𝑟𝑝(−1)𝑖𝑡 + 𝛽𝑠𝑝𝑟𝑒𝑎𝑑𝑖𝑡 + 𝛽𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠𝑖𝑡 + 𝛽𝑔𝑖𝑛𝑓𝑖𝑡 + 𝛽𝑔𝑓𝑜𝑟𝑒𝑥𝑖𝑡 +
𝛽𝑔𝑚2𝑖𝑡 + 𝛽𝑔𝑜𝑓𝑤𝑟𝑒𝑚𝑖𝑡 + 𝛽𝑔𝑟𝑟𝑝𝑖𝑡 + 𝛽𝑔𝑢𝑠𝑐𝑝𝑖𝑖𝑡 + 𝛽𝑔𝑓𝑒𝑑𝑟𝑎𝑡𝑒𝑖𝑡 + 𝛽𝑔𝑔𝑖𝑟𝑖𝑡 +
𝛽𝑔𝑑𝑒𝑓𝑖𝑐𝑖𝑡𝑖𝑡 + 𝛽𝑔𝑑𝑒𝑏𝑡𝑖𝑡 + 𝛽𝑔𝑝𝑠𝑒𝑖𝑖𝑡
(Eq. 34)
where: 𝑖 = short rate sample (BRP for 3-month and 6-month, 6-month and 1year, and 1-year and 2-year)
𝑡 = 2006 to 2014
Model 3: Long Rate
𝐵𝑅𝑃𝑖𝑡 = 𝛼 + 𝛽𝑏𝑟𝑝(−1)𝑖𝑡 + 𝛽𝑠𝑝𝑟𝑒𝑎𝑑𝑖𝑡 + 𝛽𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠𝑖𝑡 + 𝛽𝑔𝑖𝑛𝑓𝑖𝑡 + 𝛽𝑔𝑓𝑜𝑟𝑒𝑥𝑖𝑡 +
𝛽𝑔𝑚2𝑖𝑡 + 𝛽𝑔𝑜𝑓𝑤𝑟𝑒𝑚𝑖𝑡 + 𝛽𝑔𝑟𝑟𝑝𝑖𝑡 + 𝛽𝑔𝑢𝑠𝑐𝑝𝑖𝑖𝑡 + 𝛽𝑔𝑓𝑒𝑑𝑟𝑎𝑡𝑒𝑖𝑡 + 𝛽𝑔𝑔𝑖𝑟𝑖𝑡 +
𝛽𝑔𝑑𝑒𝑓𝑖𝑐𝑖𝑡𝑖𝑡 + 𝛽𝑔𝑑𝑒𝑏𝑡𝑖𝑡 + 𝛽𝑔𝑝𝑠𝑒𝑖𝑖𝑡
(Eq. 35)
where: 𝑖 = long rate sample (BRP for 1-year and 3-year, 1-year and 5-year, and
1-year and 10-year)
𝑡 = 2006 to 2014
Model 4: 2006 to 2010
𝐵𝑅𝑃𝑖𝑡 = 𝛼 + 𝛽𝑏𝑟𝑝(−1)𝑖𝑡 + 𝛽𝑠𝑝𝑟𝑒𝑎𝑑𝑖𝑡 + 𝛽𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠𝑖𝑡 + 𝛽𝑔𝑖𝑛𝑓𝑖𝑡 + 𝛽𝑔𝑓𝑜𝑟𝑒𝑥𝑖𝑡 +
𝛽𝑔𝑚2𝑖𝑡 + 𝛽𝑔𝑜𝑓𝑤𝑟𝑒𝑚𝑖𝑡 + 𝛽𝑔𝑟𝑟𝑝𝑖𝑡 + 𝛽𝑔𝑢𝑠𝑐𝑝𝑖𝑖𝑡 + 𝛽𝑔𝑓𝑒𝑑𝑟𝑎𝑡𝑒𝑖𝑡 + 𝛽𝑔𝑔𝑖𝑟𝑖𝑡 +
𝛽𝑔𝑑𝑒𝑓𝑖𝑐𝑖𝑡𝑖𝑡 + 𝛽𝑔𝑑𝑒𝑏𝑡𝑖𝑡 + 𝛽𝑔𝑝𝑠𝑒𝑖𝑖𝑡
(Eq. 36)
where: 𝑖 = whole sample (for both short rates and long rates)
𝑡 = 2006 to 2010
Model 5: 2011 to 2014
𝐵𝑅𝑃𝑖𝑡 = 𝛼 + 𝛽𝑏𝑟𝑝(−1)𝑖𝑡 + 𝛽𝑠𝑝𝑟𝑒𝑎𝑑𝑖𝑡 + 𝛽𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠𝑖𝑡 + 𝛽𝑔𝑖𝑛𝑓𝑖𝑡 + 𝛽𝑔𝑓𝑜𝑟𝑒𝑥𝑖𝑡 +
𝛽𝑔𝑚2𝑖𝑡 + 𝛽𝑔𝑜𝑓𝑤𝑟𝑒𝑚𝑖𝑡 + 𝛽𝑔𝑟𝑟𝑝𝑖𝑡 + 𝛽𝑔𝑢𝑠𝑐𝑝𝑖𝑖𝑡 + 𝛽𝑔𝑓𝑒𝑑𝑟𝑎𝑡𝑒𝑖𝑡 + 𝛽𝑔𝑔𝑖𝑟𝑖𝑡 +
𝛽𝑔𝑑𝑒𝑓𝑖𝑐𝑖𝑡𝑖𝑡 + 𝛽𝑔𝑑𝑒𝑏𝑡𝑖𝑡 + 𝛽𝑔𝑝𝑠𝑒𝑖𝑖𝑡
(Eq. 37)
where: 𝑖 = whole sample (for both short rates and long rates)
𝑡 = 2011 to 2014
Model 6: Short Rate (2006 to 2010)
𝐵𝑅𝑃𝑖𝑡 = 𝛼 + 𝛽𝑏𝑟𝑝(−1)𝑖𝑡 + 𝛽𝑠𝑝𝑟𝑒𝑎𝑑𝑖𝑡 + 𝛽𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠𝑖𝑡 + 𝛽𝑔𝑖𝑛𝑓𝑖𝑡 + 𝛽𝑔𝑓𝑜𝑟𝑒𝑥𝑖𝑡 +
𝛽𝑔𝑚2𝑖𝑡 + 𝛽𝑔𝑜𝑓𝑤𝑟𝑒𝑚𝑖𝑡 + 𝛽𝑔𝑟𝑟𝑝𝑖𝑡 + 𝛽𝑔𝑢𝑠𝑐𝑝𝑖𝑖𝑡 + 𝛽𝑔𝑓𝑒𝑑𝑟𝑎𝑡𝑒𝑖𝑡 + 𝛽𝑔𝑔𝑖𝑟𝑖𝑡 +
𝛽𝑔𝑑𝑒𝑓𝑖𝑐𝑖𝑡𝑖𝑡 + 𝛽𝑔𝑑𝑒𝑏𝑡𝑖𝑡 + 𝛽𝑔𝑝𝑠𝑒𝑖𝑖𝑡
(Eq. 38)
where: 𝑖 = short rate sample (BRP for 3-month and 6-month, 6-month and 1-year,
and 1-year and 2-year)
𝑡 = 2006 to 2010
70
Model 7: Long Rate (2006 to 2010)
𝐵𝑅𝑃𝑖𝑡 = 𝛼 + 𝛽𝑏𝑟𝑝(−1)𝑖𝑡 + 𝛽𝑠𝑝𝑟𝑒𝑎𝑑𝑖𝑡 + 𝛽𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠𝑖𝑡 + 𝛽𝑔𝑖𝑛𝑓𝑖𝑡 + 𝛽𝑔𝑓𝑜𝑟𝑒𝑥𝑖𝑡 +
𝛽𝑔𝑚2𝑖𝑡 + 𝛽𝑔𝑜𝑓𝑤𝑟𝑒𝑚𝑖𝑡 + 𝛽𝑔𝑟𝑟𝑝𝑖𝑡 + 𝛽𝑔𝑢𝑠𝑐𝑝𝑖𝑖𝑡 + 𝛽𝑔𝑓𝑒𝑑𝑟𝑎𝑡𝑒𝑖𝑡 + 𝛽𝑔𝑔𝑖𝑟𝑖𝑡 +
𝛽𝑔𝑑𝑒𝑓𝑖𝑐𝑖𝑡𝑖𝑡 + 𝛽𝑔𝑑𝑒𝑏𝑡𝑖𝑡 + 𝛽𝑔𝑝𝑠𝑒𝑖𝑖𝑡
(Eq. 39)
where: 𝑖 = long rate sample (BRP for 1-year and 3-year, 1-year and 5-year, and
1-year and 10-year)
𝑡 = 2006 to 2010
Model 8: Short Rate (2011 to 2014)
𝐵𝑅𝑃𝑖𝑡 = 𝛼 + 𝛽𝑏𝑟𝑝(−1)𝑖𝑡 + 𝛽𝑠𝑝𝑟𝑒𝑎𝑑𝑖𝑡 + 𝛽𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠𝑖𝑡 + 𝛽𝑔𝑖𝑛𝑓𝑖𝑡 + 𝛽𝑔𝑓𝑜𝑟𝑒𝑥𝑖𝑡 +
𝛽𝑔𝑚2𝑖𝑡 + 𝛽𝑔𝑜𝑓𝑤𝑟𝑒𝑚𝑖𝑡 + 𝛽𝑔𝑟𝑟𝑝𝑖𝑡 + 𝛽𝑔𝑢𝑠𝑐𝑝𝑖𝑖𝑡 + 𝛽𝑔𝑓𝑒𝑑𝑟𝑎𝑡𝑒𝑖𝑡 + 𝛽𝑔𝑔𝑖𝑟𝑖𝑡 +
𝛽𝑔𝑑𝑒𝑓𝑖𝑐𝑖𝑡𝑖𝑡 + 𝛽𝑔𝑑𝑒𝑏𝑡𝑖𝑡 + 𝛽𝑔𝑝𝑠𝑒𝑖𝑖𝑡
(Eq. 40)
where: 𝑖 = short rate sample (BRP for 3-month and 6-month, 6-month and 1-year,
and 1-year and 2-year)
𝑡 = 2011 to 2014
Model 9: Long Rate (2011 to 2014)
𝐵𝑅𝑃𝑖𝑡 = 𝛼 + 𝛽𝑏𝑟𝑝(−1)𝑖𝑡 + 𝛽𝑠𝑝𝑟𝑒𝑎𝑑𝑖𝑡 + 𝛽𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠𝑖𝑡 + 𝛽𝑔𝑖𝑛𝑓𝑖𝑡 + 𝛽𝑔𝑓𝑜𝑟𝑒𝑥𝑖𝑡 +
𝛽𝑔𝑚2𝑖𝑡 + 𝛽𝑔𝑜𝑓𝑤𝑟𝑒𝑚𝑖𝑡 + 𝛽𝑔𝑟𝑟𝑝𝑖𝑡 + 𝛽𝑔𝑢𝑠𝑐𝑝𝑖𝑖𝑡 + 𝛽𝑔𝑓𝑒𝑑𝑟𝑎𝑡𝑒𝑖𝑡 + 𝛽𝑔𝑔𝑖𝑟𝑖𝑡 +
𝛽𝑔𝑑𝑒𝑓𝑖𝑐𝑖𝑡𝑖𝑡 + 𝛽𝑔𝑑𝑒𝑏𝑡𝑖𝑡 + 𝛽𝑔𝑝𝑠𝑒𝑖𝑖𝑡
(Eq. 41)
where: 𝑖 = long rate sample (BRP for 1-year and 3-year, 1-year and 5-year, and
1-year and 10-year)
𝑡 = 2011 to 2014
Corresponding relationships (whether positively related or negatively related)
would be verified while the impact of each variable shall be indicated by the 𝛽
coefficients.
Lastly, implications of the study on the bond market shall be formulated by
compiling and summarizing the findings of the various tests. Recommendations
regarding the implications of the study will also be enumerated to benefit the sectors
to which this thesis is aimed at.
71
To summarize, all of the empirical methodologies discussed above are
shown in Figure 9.
D. Data Requirements
For the tests of the Expectations Hypothesis (EH), monthly zero-coupon
government bond yields from 2006 to 2014 are used. Since the country no longer
issues zero coupon bonds, theoretical bond yields computed via bootstrapping
obtained through the Bloomberg terminal are employed in the models.
The bond yields that are going to be examined have the following tenors: 3month, 6-month, 1-year, 2-year, 3-year, 5-year, and 10-year. For the two-period
case of the EH tests, the tenors included are the: 1) 3-month and 6-month bonds, 2)
6-month and 1-year bonds, and the 3) 1-year and 2-year bonds. For the n-period
case, the short rate, 𝑟𝑡 , shall be the 1-year bonds and the following long rates are
the 3-year, 5-year, and 10-year bonds. The estimation of the bond risk premium
(BRP) would also make use of the same bond yield pairs.
The macroeconomic variables needed for the tests of correlation and
predictive power are the monthly growth rates of the following: Meralco sales
(proxy for GDP/economic growth), Philippine inflation, peso-dollar rate, money
supply (M2), OFW remittances, BSP policy rate, US inflation, gross international
reserves, federal funds rate, budget deficit as a percent of GDP, government debt
as a percent of GDP, Philippine Stock Exchange Index, lagged values of the bond
risk premium, and the spread of the bond pairs.
72
Empirical Test of the EH on Philippine Bond Yields
Methodologies:
* Estimation of the term spread models of the EH
using OLS
* Applicaion of corrective econometric techniques for
serial correlation and/or conditional
heteroskedasticity
Estimation of the Bond Risk Premium
Methodologies:
* Estimation of the risk premium using various
observable proxies of volatility
* Selection of one best BRP proxy
Empirical Test of the EH with Bond Risk Premium
Methodologies:
* Replication of the Term Spread Models of the EH
using OLS including a time-varying risk premium
* Applicaion of corrective econometric techniques
for serial correlation and/or conditional
heteroskedasticity
Macroeconomic Variables and the BRP
Methodologies:
* Evaluate the impact of various macroecoomic
variables to the estimated BRP via regression.
Figure 9. Summary of Methodologies of the Study
73
CHAPTER IV
RESULTS AND DISCUSSION
A. Preliminary Analysis of Data
Figure 10 illustrates the movement of bond yields through time. It is
observed that bond yields had been gradually falling from 2006 to 2014. By
inference also, it shows that interest rates of short-term bonds are greater than longterm bonds. This is an indication of the possibility that long-term rates differ from
short-term rates via a factor (cited as the term premium), thereby diverging from
the assumption of the Pure Expectations Hypothesis (PEH) that the bond risk
premium is zero.91
12.0000
10.0000
PERCENT
8.0000
6.0000
4.0000
2.0000
2006M01
2006M05
2006M09
2007M01
2007M05
2007M09
2008M01
2008M05
2008M09
2009M01
2009M05
2009M09
2010M01
2010M05
2010M09
2011M01
2011M05
2011M09
2012M01
2012M05
2012M09
2013M01
2013M05
2013M09
2014M01
2014M05
2014M09
0.0000
3mo
6mo
1y
2y
3y
5y
10y
Figure 10. 3-month to 10-year Monthly Bond Yields (2006 to 2014)
Source of Basic Data: Bloomberg, First Metro Investment Corporation (FMIC)
91
The traditional version of the Pure Expectations Hypothesis asserts that the bond risk premium
is zero, while the modified form known as the Expectations Hypothesis (EH) asserts that the bond
risk premium is constant.
74
Simple correlations among the bond yields were also explored. Table 6
shows that correlation is high among neighboring tenors. Consequently, as one
tenor moves farther away from another, its correlation coefficient weakens. This
observation can be compared to the thesis results of Diaz (2012) that confirmed the
possible long run equilibrium relationship among adjacent bond yields (such as
between the 91-day and 182-day, 364-day, and 10-year rates, and between 10-year
rates and 91-day, 182-day, 364-day, 2-year, and 5-year rates) using the Johansen
Cointegration test from 2005 to 2011.92
Table 6. Correlations of Bond Yields
m3
m6
y1
y2
y3
y5
y10
m3
1.00
0.97
0.97
0.93
0.91
0.90
0.88
m6
0.97
1.00
0.98
0.94
0.92
0.89
0.85
y1
0.97
0.98
1.00
0.97
0.95
0.92
0.88
y2
0.93
0.94
0.97
1.00
0.97
0.93
0.88
y3
0.91
0.92
0.95
0.97
1.00
0.95
0.90
y5
0.90
0.89
0.92
0.93
0.95
1.00
0.94
0.88
0.85
0.88
0.88
0.90
0.94
1.00
y10
Source of Basic Data: Bloomberg, First Metro Investment Corporation (FMIC)
The statistical details of the bond yields are shown in Table 7, for both the
whole sample and the two subsamples classified into the global financial crisis
period (2006 to 2011)93 and the post-crisis period (2012 to 2014).
Undoubtedly, the bond returns at the advent and during the turmoil of the
global financial crisis were much higher than the whole sample and the post-crisis
period with a mean of 4.63% for the 3-month bonds to 8.14% for the 10-year bonds.
J. Diaz, “The Philippine Term Structure of Interest Rates: An Empirical Analysis” (Thesis,
University of Asia and the Pacific, 2012), 87.
93
This division was based on several written articles (such as in The Economist and The
Guardian) that traced the timeline of the Global Financial Crisis.
92
75
Standard deviation of the bond yields were also higher when compared to the postcrisis results, signaling the elevated volatility of rates before and during the crisis.
The kurtosis of the bond yields during the crisis also indicate that yields were very
volatile as they were too scattered from the mean. Moreover, the measure of
skewness signified that there were more chances for negative outcomes at the shortend of the yield curve than the long-end. This might have signaled that a crisis was
about to happen soon as short-term instruments were viewed to be riskier than longterm bonds.
Even though the financial sector was cited to be “fairly stable” when the
crisis hit, adverse macroeconomic consequences (weak economic growth, high
unemployment rates, tight credit availability abroad, weak consumer spending, risk
averse market, etc.) and uncertainties present during the financial collapse caused
the market to demand higher returns. 94
After the crisis, the Federal Reserve and other large countries and
institutions joined forces to inject enough liquidity for the global economy to
recover.95 The global market has been doubly cautious about the financial system
that financial institutions have tried to protect themselves from external shocks by
stocking up big reserves. The Bangko Sentral ng Pilipinas (BSP) also bulked itself
with great dollar reserves and implemented precautionary measures for banks.
Josef Yap, Celia Reyes, and Janet Cuenca, “Impact of the Global Financial and Economic Crisis
on the Philippines,” Philippine Institute for Development Studies (2009): 1-9.
95
Larry Elliot, Global financial crisis: five key stages (2007-2011), in The Guardian,
http://www.theguardian.com/business/2011/aug/07/global-financial-crisis-key-stages (accessed
March 19, 2015).
94
76
Bond markets, thus, rallied, bringing yields to their record lows until the
present amidst the increased liquidity built over the years. This is confirmed by the
post-crisis bond returns which were well below the whole sample mean with an
average difference of 184 basis points (bps) across all maturities. Volatility of bond
returns also tempered after the crisis periods, with standard deviations below 1%
(except for the 2-year bond) and kurtosis levels lower than during the crisis period.
Table 7. Statistical Details of Bond Yields (Whole Sample & Subsamples)
Mean
Whole Sample
Risk Free
Bond Yields
Median
Max.
Min.
Std.
Dev.
Skewness
m3
3.17
3.69
8.91
0.10
1.95
m6
3.45
4.03
8.69
0.18
2.04
y1
3.87
4.40
7.79
0.41
2.06
y2
4.60
4.74
10.24
1.93
1.97
y3
4.99
5.22
10.72
1.98
1.91
y5
5.65
5.89
11.42
2.16
1.81
y10
6.70
6.99
10.69
2.91
2.01
2006-2010 (Financial Crisis Period)
Risk Free
m3
4.63
4.31
8.91
1.20
1.21
Bond Returns
m6
5.00
4.78
8.69
1.47
1.22
y1
5.45
5.22
7.79
2.55
1.17
y2
6.05
5.66
10.24
3.56
1.32
y3
6.34
5.90
10.72
4.24
1.31
y5
6.90
6.55
11.42
4.78
1.22
y10
8.14
8.37
10.69
5.91
1.14
2011-2014 (Post-Financial Crisis Period)
Risk Free
m3
1.32
1.30
3.20
0.10
0.79
Bond Returns
m6
1.48
1.54
3.22
0.18
0.76
y1
1.85
1.90
3.81
0.41
0.77
y2
2.74
2.55
4.74
1.93
0.69
y3
3.26
3.22
5.43
1.98
0.86
y5
4.05
3.90
6.49
2.16
0.98
y10
4.85
4.45
7.55
2.91
1.20
Source of Basic Data: Bloomberg, First Metro Investment Corporation (FMIC)
Kurtosis
0.19
0.14
0.09
0.41
0.41
0.29
-0.11
2.24
1.98
1.77
2.25
2.62
2.94
2.00
0.39
0.12
0.05
0.72
1.01
1.18
0.19
5.34
4.28
2.65
3.26
3.76
5.04
2.66
0.27
0.01
0.26
1.60
0.76
0.18
0.44
2.39
2.32
2.79
4.97
3.10
2.42
2.17
The movement of the bond yields can also be analyzed using yield curves.
The yield curves of the sample are plotted in Figure 11 by taking the yearly average
of the 3-month to 10-year bonds. It can be observed that Philippine yield curves are
most of the time increasing and concave. Again, from visual inspection, we notice
77
a substantial flattening of the yield curve from 2006 to 2014. Highest yields were
obtained in 2006 while the lowest ones were in 2013.
However, further slicing into the periods would reveal how the yield curves
behaved amidst the financial crisis affecting countries abroad. Before the bursting
of the housing bubble, around 2006 to 2007, yield curves shifted downwards,
indicative of lower bond yields across maturities. The bond market was at a rally
point, unaware of what could happen next.
When the crisis started in 2008, the yield curve began to shift up. This
economic shock quaked the bond market and made the investors more cautious.
Due to heightened uncertainties in the long run, market demand diverted its focus
on the short rates that plunged by 160 bps, while long rates did not budge at all. As
the crisis normalized in 2010, regained market sentiment pushed the yield curve
downwards. From 2011, continuous flattening of the yield curve was experienced
up until yields reached record lows in 2013. 2014, was then again, characterized by
an increase in yields after the termination of the Fed’s stimulus package in October
2014 that raised expectations for an increase in US interest rates.
Bond yield spreads also highlight the condition of bonds during the crisis
years and post-crisis years. Yield spreads are defined as the difference between the
quoted rates of two investment maturities. Usually, yield spreads are used as
measures of “risk” because a higher absolute value of the spread indicates a steeper
yield curve. A steeper yield curve signals the market’s risk aversion for long
maturities and great demand for short maturities. It is measured in basis points
where 1% is equal to 100 basis points (bps).
78
Figure 12 clearly shows that average yield spreads were more elevated
during the crisis years (2009 to 2011), indicative of the heightened risk aversion for
long term investments of the market players. This finding also indicates that East
Asian countries were still vulnerable to external shocks due to the increased
financial market integration. Since non-residents still have a great hold of the
country’s dollar-denominated bonds (ROPs) at a share of 58% as of end-2008,
effects of the crisis have been more pronounced.96 Nonetheless, after the crisis
years, we can see that spreads have returned to their pre-crisis levels, now below
the nine-year spread average of 351 bps.
10.00
9.00
PERCENT
8.00
2006
7.00
2007
6.00
2008
5.00
2009
2010
4.00
2011
3.00
2012
2.00
2013
1.00
2014
0.00
m3
m6
y1
y2
y3
y5
y10
BOND TENORS
Figure 11. Philippine Yield Curve (2006 to 2014)
Source of Basic Data: Bloomberg, First Metro Investment Corporation (FMIC)
Diwa Guinigundo, The impact of the global financial crisis on the Philippines financial system –
an assessment, BIS no. 54, http://www.bis.org/publ/bppdf/bispap54s.pdf (accessed March 19,
2015).
96
79
500
450
400
Basis Points (bps)
350
300
250
200
150
100
50
0
2006
2007
2008
2009
2010
2011
2012
2013
2014
Figure 12. 3-month vs. 10-year Yield Spread (Yearly Average)
Source of Basic Data: Bloomberg, First Metro Investment Corporation (FMIC)
B. Current Developments of the Philippine Bond Market
1. Size and Composition
Since 2006, the size of the Philippine bond market in terms of local
currency value has been growing at a steady pace. Figure 13 shows that as
of December 2014, the total peso value of the bond market already reached
P4.6 T, a 107% improvement from the bond market size in 2006.
Nevertheless, the share-to-GDP of government bonds is seen to be
gradually declining as the size of the corporate bond market has been
accelerating (in Figure 14). From government securities’ (GS) GDP share
at 37.9 % in 2006, it has fallen to 30.8% in December 2014. On the contrary,
from corporate bonds’ meager share-to-GDP at 0.81% in 2006, it has grown
to 6.0% at present. This demonstrates the increasing ability of corporations
to finance their activities with debt – that may indicate increased liquidity
or cash position of private industries.
80
The outstanding amount of foreign-denominated bonds of the
Philippines (also known as ROPs) is also expanding. It has reached US
$34.9 as of December 2014, from its 2006 volume at US $25.4. Currently,
76.9% of total ROPs are government securities, while the rest are corporate
bonds (19.4%) and bonds from banks and financial institutions (3.6%).
5000
4500
Government
Corporate
4000
in LCY Billions
3500
3000
2500
2000
1500
1000
500
0
2006
2007
2008
2009
2010
2011
2012
2013
2014
Figure 13. Size of Philippine Bond Market in LCY Billions
Source of Basic Data: Asian Development Bank, Asian Bonds Online
45
Government
Corporate
40
35
% of GDP
30
25
20
15
10
5
0
2006
2007
2008
2009
2010
2011
2012
2013
2014
Figure 14. Size of Philippine Bond Market (% of GDP)
Source of Basic Data: Asian Development Bank, Asian Bonds Online
81
However, the country’s bond market still lags behind its ASEAN
neighbors. The government securities debt market of China, Malaysia,
Singapore, and Thailand outperforms the volume of the Philippines at
30.8% of GDP – but the Philippines’ is way better than the bond markets of
Vietnam and Indonesia. In terms of corporate bonds, the country’s volume
is slowly catching up with the rest. Corporate bonds are still bigger than
Indonesia’s and Vietnam’s.
50
45
40
in USD Billions
35
30
25
20
15
10
5
0
2006
2007
Government
2008
2009
2010
2011
Banks and Financial Institutions
2012
2013
2014
Other Corporates
Figure 15. Outstanding Bonds in Foreign Currency (Local Sources)
Source of Basic Data: Asian Development Bank, Asian Bonds Online
In terms of composition, the bills-to-bonds ratio is a good indicator
to look at. This tells us if the country’s bond market is greatly composed of
either short-term debts (bills less than or equal to one year in maturity) or
long-term debts (bonds more than one year in maturity). The ratio is
calculated by diving the total outstanding government bills to the total
outstanding government bonds.
82
80.0
Government
70.0
Corporate
60.5
57.3
60.0
49.8
% of GDP
50.0
42.7
40.0
32.5
32.1
30.8
30.0
20.0
19.0
18.1
21.7
13.0
10.0
6.0
2.2
0.3
0.0
CN
ID
MY
PH
SG
TH
VN
Figure 16. Size of Bond Market of ASEAN +1 (% of GDP)
(as of December 2014)
Source of Basic Data: Asian Development Bank, Asian Bonds Online
Figure 17 shows that from 2006, the composition of the Philippine
debt market has transitioned from being prominently composed of bills to
having an increasing share of long-term bonds. The decline specifically
happened amidst the global financial crisis in 2009. This may imply that
through time (or after the crisis), the Bureau of the Treasury (BTr) has opted
to supply long-term bonds than short-term ones as a way of managing its
liabilities. Recently, the BTr and the Department of Finance (DOF)
expressively launched its domestic liability management program in August
2014, by re-issuing more than P140 B worth of 10-year benchmark bonds97,
“The Republic of the Philippines Announced the Results of its Domestic Liability Management
Program”, Bureau of the Treasury, http://www.treasury.gov.ph/wpcontent/uploads/2014/08/Results-Announcement.pdf (accessed April 6, 2015).
97
83
as a way of “rebalancing its debt portfolio, fostering efficient pricing of GS,
and enhancing trading of GS”.98
0.6
Bills-to-Bonds Ratio
0.5
0.4
0.3
0.2
0.1
Dec-14
Jul-14
Feb-14
Sep-13
Apr-13
Jun-12
Nov-12
Jan-12
Aug-11
Oct-10
Mar-11
May-10
Jul-09
Dec-09
Feb-09
Sep-08
Apr-08
Nov-07
Jun-07
Jan-07
Aug-06
Mar-06
0
Figure 17. Bills-to-Bond Ratio of the Philippines
Source of Basic Data: Asian Development Bank, Asian Bonds Online
Relative to the bills-to-bonds ratio of its ASEAN neighbors, the
Philippines appears to be at par with the rest. All the countries, except for
Hong Kong and Singapore, have debt markets heavily characterized by
long-term bonds. Indonesia, Korea, and Philippines have comparatively
similar bills-to-bonds ratio at 0.1, with total outstanding bonds larger than
bills. In the case of the Philippines, the size of total bonds is 12.5 times
greater than the size of bills, while Indonesia and Korea have long-term
debts 10.6 times and 7.8 times larger than their bills market, respectively.
Japan’s total outstanding bonds is 29.8 times its bills, thus having a 0.03
ratio. Hong Kong and Singapore, on the other hand, have debt markets
“Republic of the Philippines Launches Domestic Liability Management Exercise”, Bureau of
the Treasury, http://www.treasury.gov.ph/wp-content/uploads/2014/08/press-release.pdf (accessed
April 6, 2015).
98
84
immensely composed of bills than bonds. This may imply that the two
countries are contemporaneously liquid to have financed a big volume of
short-term debts.
5.0
4.1
Bills-toBonds Ratio
4.0
3.0
2.0
1.2
1.0
0.0
0.1
0.0
0.1
ID
JP
KR
0.2
0.1
0.3
0.3
TH
VN
0.0
CN*
HK
MY
PH
SG
Figure 18. Bills-to-Bonds Ratio of ASEAN +3 (as of December 2014)
Source of Basic Data: Asian Development Bank, Asian Bonds Online
Note: Latest data for China is as of June 2014
2. Liquidity
Two indicators are used to measure the liquidity of a country’s debt
market. These are the trading volume and the bonds turnover ratio. The
trading volume pertains to the degree of market activity in a country using
the value of local currency government bonds traded in the secondary
market, while the bonds turnover ratio also indicates the extent of trading in
the secondary market but relative to the amount of outstanding bonds.
Figure 19 shows that the growth of the average value of government
bonds being transacted in the secondary market has been accelerating since
2006. As of June 2013, the average trading in the secondary market already
85
reached US $59.8 B. Compared to the ASEAN +3 market, the country still
has one of the smallest secondary bond markets with a volume slightly
higher than Indonesia, but trails behind the rest of its neighbors (as seen in
Figure 20). The largest secondary bond markets can be found in China and
Korea with an average value reaching US $1.2 T and US $652.3 B,
respectively.
For the bonds turnover ratio, Figure 21 illustrates that the share of
the traded bonds in the secondary market is increasing, thereby signaling
increased liquidity throughout the years. However, the market liquidity of
the country is still behind other ASEAN countries. The Philippines, with a
turnover ratio of 0.49, is way behind the liquidity of six other ASEAN
neighbors (Hong Kong, Japan, Korea, Malaysia, Singapore, and Thailand)
with Hong Kong leading the pack with a turnover ratio at 1.46 (which
further justifies Hong Kong’s heightened bills-to-bonds ratio). The liquidity
of the country, nevertheless, still performs better than China and Indonesia,
signifying increased efforts to improve the country’s bond trading activities.
86
70.00
59.80
60.00
50.00
38.95
37.14
40.00
33.40
30.00
20.00
19.08
17.32
16.90
15.77
2006
2007
2008
10.00
0.00
2009
2010
2011
2012
2013
Figure 19. Trading Volume of Philippine Government Bonds
(2013 Average)
Source of Basic Data: Asian Development Bank, Asian Bonds Online
1400.0
1228.2
Government Bonds
1200.0
in USD Billions
1000.0
800.0
652.3
600.0
400.0
193.0
151.3
200.0
123.0
23.7
59.8
73.6
PH
SG
0.0
CN
HK
ID
KR
MY
TH
Figure 20. Trading Volume of Government Bonds in the
ASEAN Market +3 (2013 Average)
Source of Basic Data: Asian Development Bank, Asian Bonds Online
87
0.80
0.73
Government Bonds
0.70
0.64
Bonds Turnover Ratio
0.60
0.54
0.53
2011
2012
0.50
0.41
0.40
0.38
0.35
0.31
0.30
0.20
0.10
0.00
2006
2007
2008
2009
2010
2013
Figure 21. Turnover Ratio of Philippine Government Bonds
(Yearly Average)
Source of Basic Data: Asian Development Bank, Asian Bonds Online
1.60
1.46
Government Bonds
1.40
1.25
1.27
Bonds Turnover Ratio
1.20
1.00
0.84
0.80
0.70
0.60
0.40
0.70
0.49
0.31
0.30
0.20
0.00
CN
HK
ID
JP
KR
MY
PH
SG
TH
Figure 22. Bonds Turnover Ratio in ASEAN Market +4 (as of June 2013)
Source of Basic Data: Asian Development Bank, Asian Bonds Online
In terms of liquidity, the Philippines seems to be improving its stand
among its peers with the gradual acceleration of its bonds turnover ratio. It
88
is also worth noting that the country is working its way to expand the debt
market and enhance its pricing efficiency as evidenced by its liability
management programs. The country also aspires to increase its participation
in the world capital markets as demonstrated by its successful issuance of
US $2 B worth of 25-year dollar-denominated bonds (ROPs) last January
2015.99 These initiatives only reflect the strength of the country’s economy
that allowed the bond market to gain a strong reputation in the international
scene. With these, we cannot but hope for bigger and better developments
in the bond market in the near future.
Overall, it can be inferred that relative to its ASEAN neighbors, the debt
market of the Philippines is still part of the emerging ones because of its relatively
small yet growing bond market, both for government securities and corporate
bonds. In terms of size and composition, the country generally lags behind the GS
volumes of other countries, but at par with the rest as it is characterized by longterm debts than short-term bills.
C. Expectations Hypothesis Tests using Term Spread Models
Empirical data must satisfy three specific assumptions under the
Expectations Hypothesis (EH) for the theory to hold. The first assumption is: The
term spread model must predict future changes in the short rate. The second one is:
“Republic of the Philippines Starts Year Blazing a Trail in International Capital Markets”,
Bureau of the Treasury, http://www.treasury.gov.ph/wp-content/uploads/2015/01/Press-ReleaseRP-Starts-Year-Blazing-a-Trail-in-Intl-Capital-Markets.pdf (accessed April 6, 2015).
99
89
The term spread must predict future changes in the long rate; and lastly: The term
spread must not predict excess bond returns.
For the first assumption, three pairs of short rates and long rates were tested
which were the 3-month and 6-month bond yields, 6-month and 1-year bond yields,
and 1-year and 2-year bond yields. This employed McCallum’s two-period case
method. For the second assumption, this study considered the 1-year bond yields
as the short rate, while the 2-year, 5-year and 10-year bonds yields were the long
rates.
All of the bond yields were tested for unit root using the Correlogram
Specification and Augmented Dickey-Fuller (ADF) Tests. Results showed that the
elements used for all the term spread regressions (both the left-hand side and righthand side of the equations) did not possess any unit root, signifying that the data
distribution are stationary. Stationary data are necessary to avoid spurious
regressions, and thus, the estimates obtained from the regressions can be considered
correct and valid. Additionally, due unstable/auto-correlated nature of the residuals
of the regressors, Heteroskedasticity and Autocorrelation Consistent (HAC)
Newey-West Test was employed instead of using the ordinary least squares (OLS)
method.
Table 8 shows the test results for the first assumption using McCallum’s
two-period case model. For the EH to hold, the 𝛼 coefficient must have a value of
zero while the 𝛽 coefficient must have a value of one. The test results show that the
𝛼 coefficients were all significantly negative, while the
𝛽 coefficients were
significantly below unity.
90
The pair that were closest to the ideal results was the 6-month and 1-year
bonds, with a 𝛽 coefficient at 0.46 and a relatively high predictive power (R2 =
25%). The results for the 3-month and 6-month and 1-year and 2-year, on the other
hand, were significantly different from the desired results with very low predictive
powers. These findings suggest that a one percentage point increase in the spread
between the short rate and the long rate raises the short rate by less than one
percentage point. This result implies that the spread does not provide a “perfect”
forecast of the change in the short rates. Nevertheless, as theory suggests, the term
spread still signaled increases in the short rate, as denoted by the positive 𝛽
coefficients.
Table 8. Term Spread Prediction of Future Changes in the Short Rate
Regression Model: 0.5 (𝑟𝑡 − 𝑟𝑡−1 ) = 𝛼 + 𝛽 (𝑅𝑡−1 −
Short Rate
Long Rate
Period
α
(𝒓𝒕 )
(𝑹𝒕 )
-0.09***
3-month
6-month
2006 – 2014
(0.03)
-0.22***
6-month
1-year
2006 – 2014
(0.05)
-0.13***
1-year
2-year
2006 – 2014
(0.04)
𝑟𝑡−1 ) + 𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑎𝑛𝑐𝑒 𝑡𝑒𝑟𝑚
β
0.21***
(0.07)
0.46***
(0.11)
0.14***
(0.05)
R2
DW
0.06
2.28
0.25
1.96
0.07
1.84
Source of Basic Data: Bloomberg, First Metro Investment Corporation (FMIC)
Notes: Standard errors are placed in parentheses.
* = significant at 10% level
** = significant at 5% level
*** = significant at 1% level
To test the second assumption, McCallum’s n-period case applied using the
following pairs: 1-year and 3-year, 1-year and 5-year, and 1-year and 10-year bond
yields. In a similar way, for the EH to hold, the 𝛼 coefficient must have a value of
zero while the 𝛽 coefficient must have a value of one.
91
Table 9 shows that the term spread tests for changes in future long rates also
did not produce the desired results as theory suggested. The 𝛼 coefficients,
compared to the two-period case, are now positively related to the term spread with
values reaching as high as 2.08 percentage points. The 𝛽 results, on the other hand,
show significantly negative coefficients which suggests that the term spread
forecasts the long rate in the opposite direction. The same results were also
experienced by Mankiw, Goldfeld, and Shiller (1986), McCallum (1994),
Campbell (1997), Dai and Singleton (2002), and several others.
Geiger (2011) asserted that the change in the long rates fall (or become more
negative) monotonically with the maturity of the bond which indicates a strong
positive relationship between yield spreads and excess returns on long-term
bonds.100 This can also be said for the Philippine case, since the term spread and
the changes in the long rate have an inverse relationship. In order to verify this
conclusion, the relationship between excess returns and the term spread must be
tested as the EH’s third assumption.
Table 9. Term Spread Prediction of Future Changes in the Long Rate
Regression Model: 𝑁(𝑅𝑡 − 𝑅𝑡−1 ) = 𝛼 + 𝛽(𝑅𝑡−1 − 𝑟𝑡−1 ) + 𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑎𝑛𝑐𝑒 𝑡𝑒𝑟𝑚
Short Rate Long Rate
Period
α
β
R2
DW
(𝒓𝒕 )
(𝑹𝒕 )
0.61*
-0.71***
1-year
3-year
2006 – 2014
0.06
2.04
(0.37)
(0.34)
2.08***
-1.34***
1-year
5-year
2006 – 2014
0.09
2.13
(0.70)
(0.33)
1.90
-0.88**
1-year
10-year
2006 – 2014
0.02
1.74
(1.45)
(0.44)
Source of Basic Data: Bloomberg, First Metro Investment Corporation (FMIC)
Notes: Standard errors are placed in parentheses.
* = significant at 10% level
** = significant at 5% level
*** = significant at 1% level
Felix Geiger, “The Theory of the Term Structure of Interest Rates,” in the The Yield Curve and
Financial Risk Premia, (Berlin: Springer-Verlag, 2011), 70.
100
92
The third assumption of the EH asserts that the term spread must not predict
the excess bond returns to verify that the term premium is indeed zero. Thus, the
expected value for the coefficient of the term spread must be zero. Excess returns
were calculated using Mankiw, Goldfeld, and Shiller’s (1986) formula and were
regressed against the yield spread for both the two-period case and n-period case.
However, contrary to what the EH says, the results suggest that for the twoperiod and n-period case, the excess returns can be clearly predicted by the term
spread. The 𝛽 coefficients are significantly greater than zero and are noticeably
increasing as the predictive horizon lengthens. The estimated R2 also escalates,
signaling the increased power of the term spread to predict excess returns as bond
maturity increases. This finding confirms Geiger’s (2011) assertion that the term
spread is unable to predict changes in the long rate due to the strong positive
relationship of the term spread with excess returns.
Table 10. Term Spread Prediction of Excess Returns
Regression Model: 𝐸𝐻𝑅𝑟,𝑅 = 𝛼 + 𝛽(𝑅𝑡 − 𝑟𝑡 ) + 𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑎𝑛𝑐𝑒 𝑡𝑒𝑟𝑚
Two-Period Case
Short Rate Long Rate
Period
α
β
R2
(𝒓𝒕 )
(𝑹𝒕 )
0.27***
0.07
3-month
6-month
2006 – 2014
0.00
(0.02)
(0.02)
0.34***
0.22*
6-month
1-year
2006 – 2014
0.04
(0.04)
(0.12)
0.43***
0.42***
1-year
2-year
2006 – 2014
0.16
(0.13)
(0.16)
N-Period Case
Short Rate Long Rate
Period
α
β
R2
(𝒓𝒕 )
(𝑹𝒕 )
0.42***
0.63***
1-year
3-year
2006 – 2014
0.35
(0.12)
(0.11)
0.64***
0.65***
1-year
5-year
2006 – 2014
0.37
(0.22)
(0.13)
0.50***
0.83***
1-year
10-year
2006 – 2014
0.67
(0.18)
(0.05)
DW
2.18
2.00
2.44
DW
2.35
2.35
2.08
Source of Basic Data: Bloomberg, First Metro Investment Corporation (FMIC)
Notes: Standard errors are placed in parentheses.
93
* = significant at 10% level
** = significant at 5% level
*** = significant at 1% level
D. Expectations Hypothesis Tests using Forward Spread Models
Apart from using the yield/term spread, the Expectations Hypothesis can
also be tested using forward spreads. To verify and to compare the results obtained
from the term spread models, forward spread models were also done for forecasting
changes in the short rate, in the long rate, and of excess returns.
Results showed that the forward rates’ predictions for changes in the short
were closely at par with the results from the term spread model. The 𝛼 coefficients
were significantly and consistently zero compared to negative results of the term
spread regressions. The 𝛽 coefficients were also significant and consistent with the
results of the term spread regressions (with a slight 1% difference from the 𝛽
coefficient of the 6-month and 1-year bond pair. Nonetheless, all estimates were
still far below the desired 𝛽 coefficient of one. The predictive power of the term
spread indicated by the R2 were also similar to the results of the term spread tests.
In contrast, the results for the changes in the long rate show that forward
spreads are very poor predictors compared to term spread models. The 𝛼 and 𝛽
coefficients were consistently and significantly zero across the samples. This stark
difference suggests that forward rates work as best predictors of interest rates for
very short horizons, specifically, less than one year. For longer horizons, the
predictive power of forward spreads already deteriorates. This assertion can also be
confirmed by the results of Mishkin (1988) in Table 3.
94
Table 11. Forward Spread Prediction of Changes in Short Rate and Long Rate
Regression Model: (𝑟𝑡+1 − 𝑟𝑡 ) = 𝛼 + 𝛽 (𝑓𝑟→𝑅 −
Two-Period Case
Short Rate Long Rate
Period
α
(𝒓𝒕 )
(𝑹𝒕 )
0.00***
3-month
6-month
2006 – 2014
(0.00)
0.00***
6-month
1-year
2006 – 2014
(0.00)
0.00***
1-year
2-year
2006 – 2014
(0.00)
Regression Model: (𝑅𝑡+1 − 𝑅𝑡 ) = 𝛼 + 𝛽(𝑓𝑟→𝑅 −
N-Period Case
Short Rate Long Rate
Period
α
(𝒓𝒕 )
(𝑹𝒕 )
0.00
1-year
3-year
2006 – 2014
(0.00)
0.00
1-year
5-year
2006 – 2014
(0.00)
0.00
1-year
10-year
2006 – 2014
(0.00)
𝑟𝑡 ) + 𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑎𝑛𝑐𝑒 𝑡𝑒𝑟𝑚
β
R2
DW
0.20***
0.06
2.28
(0.09)
0.46***
0.25
1.95
(0.11)
0.14***
0.07
1.84
(0.05)
𝑟𝑡 ) + 𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑎𝑛𝑐𝑒 𝑡𝑒𝑟𝑚
β
0.00
(0.01)
-0.01
(0.00)
0.00
(0.00)
R2
DW
0.00
1.97
0.00
1.97
0.01
1.96
Source of Basic Data: Bloomberg, First Metro Investment Corporation (FMIC)
Notes: Standard errors are placed in parentheses.
* = significant at 10% level
** = significant at 5% level
*** = significant at 1% level
Excess returns as a function of forward spreads were also tested. If the latter
predicts the former, then it would be a clear rejection of the EH. Results in Table
12 show that, indeed, excess returns can be predicted by the forward rate spread,
especially for the short rates. The 𝛽 coefficients under the two-period case, along
with the R2, signal the potential forecasting power of the forward spread. For the nperiod case, on the other hand, only the 1-year and 3-year bonds showed that the
forward spread can forecast excess returns. The rest of the n-period case sample
results can be considered negligible. In any case, however, we can declare that the
third assumption of the EH was not fulfilled, as well, using forward spreads.
95
Table 12. Forward Spread Prediction of Excess Returns
Regression Model: 𝐸𝐻𝑅𝑟,𝑅 = 𝛼 + 𝛽(𝑓𝑟→𝑅 − 𝑟𝑡 ) + 𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑎𝑛𝑐𝑒 𝑡𝑒𝑟𝑚
Two-Period Case
Short Rate Long Rate
Period
α
β
R2
(𝒓𝒕 )
(𝑹𝒕 )
0.27***
3.47
3-month
6-month
2006 – 2014
0.00
(0.04)
(3.83)
0.34***
10.80*
6-month
1-year
2006 – 2014
0.04
(0.04)
(5.96)
0.43***
20.89***
1-year
2-year
2006 – 2014
0.16
(0.13)
(8.07)
N-Period Case
Short Rate Long rate
Period
α
β
R2
(𝒓𝒕 )
(𝑹𝒕 )
0.74***
5.08***
1-year
3-year
2006 – 2014
0.03
(0.17)
(2.50)
1.95***
-0.66
1-year
5-year
2006 – 2014
0.00
(0.40)
(1.36)
2.31***
0.64
1-year
10-year
2006 – 2014
0.04
(0.40)
(0.51)
DW
2.18
2.00
2.44
DW
1.11
0.92
0.46
Source of Basic Data: Bloomberg, First Metro Investment Corporation (FMIC)
Notes: Standard errors are placed in parentheses.
* = significant at 10% level
** = significant at 5% level
*** = significant at 1% level
From all the term spread models and forward spread models used to test the
EH, we can conclude that the three assumptions were hardly satisfied. The term
spread and forward spread models in predicting future short rates had positive 𝛽
coefficients, suggesting that yield spreads can capture the movement of the short
rates. However, when it comes to the prediction of long rates, results showed zero
to negative 𝛽 coefficients, suggesting that an increase in the term spread has no
effect at all or portends a fall in the long rates – a big contrast from what theory
says. Lastly, instead of losing explanatory powers, test results showed that the term
spread can somehow predict excess returns. This also goes against the third
assumption of the EH.
96
Hence, we can conclude that the EH was not empirically verified using
Philippine bond yields. From the vast literature surveyed in this study, the failure
of the EH does not mean that future interest rates cannot be inferred from the term
structure. The inference power is present but still poor. It should be noted that we
are just tackling interest rates via one approach – the expectations approach. This
rather reflects that the EH can only predict future yield levels up to a limited
extent.101
The failure of the EH, however, can be remedied; and from the vast
literature explored in this study, the distortion of empirical tests point to the failure
of including a bond risk premium (BRP), or more specifically, a time-varying risk
premium. Thus, a major assumption made in this study was that the failure of the
EH is attributed to the omission of the BRP. We, therefore, need to measure the
BRP and redo the EH term spread tests to see if the models can improve or not. In
any case, the estimation of the BRP for Philippine bond yields may have very
informative implications about the bond market helpful for investors,
policymakers, and researchers, alike.
E. Estimation of the Bond Risk Premium
For the estimation of the bond risk premium (BRP), this study adopted the
methodologies of Boero and Torricelli (2000). The main assumption made was that
a higher BRP is associated with higher risk, and risk was represented by higher
interest rate volatility. Interest rate volatility was, therefore, measured using three
Felix Geiger, “The Theory of the Term Structure of Interest Rates,” in the The Yield Curve and
Financial Risk Premia, (Berlin: Springer-Verlag, 2011), 71.
101
97
different estimation methods. These are the: 1) moving average of absolute changes
of the short rates computed over the previous 6 periods; 2) square of the expected
excess holding period return; and 3) estimates of conditional variances and
conditional standard deviations from the univariate GARCH (1,1) model. The
following BRP estimates are shown in the figures below.
Using the moving average method, it can be observed that the estimated
bond risk premium for all bond pairs are time-varying. The BRP of the short rate
pairs are greater than and more volatile than the long rate pairs – which is consistent
with the increased volatility observed from Philippine short-term bonds than longterm ones. Long rate BRP are more stable, nonetheless. The mean BRP for the short
rates was at 0.16% while the long rate BRP averages to 0.03%. This method may
imply that investors are more reactive and demand more compensation for risk in
the short run.
The squared excess returns method also shows a time-varying risk
premium; but, in contrast with moving average estimates, this method implies that
investors required a greater bond risk premium as maturity increases. The mean of
the squared excess returns for the 3-month and 6-month, 6-month and 1-year, and
1-year and 2-year were 0.40%, 0.35%, ad 0.82%, respectively. For the long rates,
the 1-year and 3-year bonds had a mean of squared excess returns of 1.70%, 3.89%
for the 1-year and 5-year bonds, and 9.02% for the 1-year and 10-year bonds.
From the bond risk premium estimated via univariate GARCH (1,1), two
kinds of estimates can be used to improve the EH tests – the conditional standard
deviations and the conditional variances (which are just squared values of the
98
conditional standard deviations). These measures pertain to the volatility of the
excess returns of the bond pairs. Both Figure 9 and 10 show that the bond risk
premium estimates and its volatility increase with maturity. Similar to the results
of the squares excess returns, this suggests that investors require more cushion for
risk as the investment horizon lengthens.
0.80
0.70
PERCENT
0.60
0.50
0.40
0.30
0.20
0.10
2006M01
2006M05
2006M09
2007M01
2007M05
2007M09
2008M01
2008M05
2008M09
2009M01
2009M05
2009M09
2010M01
2010M05
2010M09
2011M01
2011M05
2011M09
2012M01
2012M05
2012M09
2013M01
2013M05
2013M09
2014M01
2014M05
2014M09
0.00
m3m6
m6my1
y1y2
y1y3
y1y5
y1y10
Figure 23. Estimated Bond Risk Premium Using Moving Average Method
Source of Basic Data: Bloomberg, First Metro Investment Corporation (FMIC)
30.00
25.00
15.00
10.00
5.00
0.00
2006M01
2006M05
2006M09
2007M01
2007M05
2007M09
2008M01
2008M05
2008M09
2009M01
2009M05
2009M09
2010M01
2010M05
2010M09
2011M01
2011M05
2011M09
2012M01
2012M05
2012M09
2013M01
2013M05
2013M09
2014M01
2014M05
2014M09
PERCENT
20.00
m3m6
m6y1
y1y2
y1y3
y1y5
y1y10
Figure 24. Estimated Bond Risk Premium Using Squared Excess Returns
Source of Basic Data: Bloomberg, First Metro Investment Corporation (FMIC)
99
5.0
4.5
4.0
PERCENT
3.5
3.0
2.5
2.0
1.5
1.0
0.5
2006M01
2006M05
2006M09
2007M01
2007M05
2007M09
2008M01
2008M05
2008M09
2009M01
2009M05
2009M09
2010M01
2010M05
2010M09
2011M01
2011M05
2011M09
2012M01
2012M05
2012M09
2013M01
2013M05
2013M09
2014M01
2014M05
2014M09
0.0
m3m6
m6my1
y1y2
y1y3
y1y5
y1y10
Figure 25. Conditional Standard Deviation of Excess Returns from GARCH (1,1)
Source of Basic Data: Bloomberg, First Metro Investment Corporation (FMIC)
25.0
PERCENT
20.0
15.0
10.0
5.0
2006M01
2006M05
2006M09
2007M01
2007M05
2007M09
2008M01
2008M05
2008M09
2009M01
2009M05
2009M09
2010M01
2010M05
2010M09
2011M01
2011M05
2011M09
2012M01
2012M05
2012M09
2013M01
2013M05
2013M09
2014M01
2014M05
2014M09
0.0
m3m6
m6my1
y1y2
y1y3
y1y5
y1y10
Figure 26. Conditional Variance of Excess Returns from GARCH (1,1)
Source of Basic Data: Bloomberg, First Metro Investment Corporation (FMIC)
These BRP measures were inserted into the term spread models to identify
which estimate went closest to the desired results. In order to select the best BRP
proxy, goodness of fit evaluations were done. This study adopted the four criteria
suggested by Gujarati (2011) and used by Bico (2010) which are the Adjusted R2,
100
F-statistic, Akaike Information Criterion (AIC), and Schwarz Information Criterion
(SIC). The improvement of the 𝛼 and 𝛽 coefficients were also considered.
For the short rate regressions, the conditional variance estimation of the
BRP outperformed the rest of the estimates. This was shown in the minimal 1% to
2% change in the Adjusted R2, in the high F-Statistic values, and in the smaller AIC
and SIC values. The 𝛼 and 𝛽 coefficients also improved and were all statistically
significant from the previous HAC Newey-West tests.
Table 13. Term Spread Prediction of Future Changes in the Short Rate with Bond
Risk Premium
Short Rate Regression: 0.5 (𝑟𝑡 − 𝑟𝑡−1 ) = 𝛼1 + 𝛽1 (𝑅𝑡−1 − 𝑟𝑡−1 ) + 𝛾𝐵𝑅𝑃 + 𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑎𝑛𝑐𝑒 𝑡𝑒𝑟𝑚
3-month and 6-month
OLS
(HAC NeweyWest Test)
𝛽1
-0.09***
(0.03)
0.21***
(0.07)
𝛾
--
𝛼1
R2
0.06
DW
2.28
Adjusted R2
-F-Statistic
-AIC
-SIC
-6-month and 1-year
-0.22***
𝛼1
(0.05)
0.46***
𝛽1
(0.11)
Square of
Excess
Returns BRP
Conditional
Variance
-0.04
(0.05)
0.20***
(0.08)
-0.27
(0.33)
0.07
2.99
0.05
3.72
0.98
1.06
-0.09***
(0.02)
0.21***
(0.05)
0.00
(0.01)
0.06
2.28
0.04
3.16
1.00
1.07
-0.06
(0.03)
0.24***
(0.05)
-0.13***
(0.04)
0.08
2.36
0.06
4.62
0.98
1.05
Conditional
Standard
Deviation
0.00
(0.03)
0.24***
(0.06)
-0.20***
(0.06)
0.08
2.33
0.06
4.20
0.98
1.06
-0.21***
(0.03)
0.52***
(0.04)
-0.12
(0.08)
0.28
2.07
0.27
20.26
0.57
0.65
-0.13***
(0.03)
0.50***
(0.03)
-0.29***
(0.05)
0.29
1.92
0.28
21.41
0.56
0.64
0.00
(0.05)
0.52***
(0.03)
-0.44***
(0.08)
0.30
1.92
0.28
21.87
0.56
0.63
-0.13***
(0.04)
-0.11***
(0.04)
0.06
(0.07)
R
DW
Adjusted R2
F-Statistic
AIC
SIC
0.25
1.96
-----
-0.13***
(0.06)
0.46***
(0.08)
-0.55
(0.41)
0.29
2.01
0.28
21.29
0.56
0.63
𝛼1
-0.13***
(0.04)
-0.07
(0.04)
𝛾
2
--
GARCH (1,1) BRP
Moving
Average BRP
101
0.15***
0.14***
0.27***
0.28***
(0.04)
(0.05)
(0.07)
(0.07)
-0.34***
-0.46
0.00
-0.14***
-𝛾
(0.11)
(0.22)**
(0.04)
(0.05)
R2
0.07
0.12
0.07
0.11
0.12
DW
1.84
1.89
1.84
1.79
1.81
0.11
Adjusted R2
-0.10
0.05
0.09
7.19
F-Statistic
-6.77
3.77
6.33
0.12
AIC
-0.12
0.18
0.14
0.20
SIC
-0.20
0.25
0.21
Source of Basic Data: Bloomberg, First Metro Investment Corporation (FMIC), Author’s
computations
Notes: Standard errors are placed in parentheses.
* = significant at 10% level
** = significant at 5% level
*** = significant at 1% level
𝛽1
0.14***
(0.05)
Table 13, on the other hand, shows that the conditional standard deviation
from the univariate GARCH (1,1) model dominated the other BRP proxies for the
long rate regressions. The Adjusted R2 barely differed from their original R2, FStatistic values were also greater than the rest, and the AIC and SIC criteria were
the lowest. Majority of the 𝛼 and 𝛽 coefficients, however, did not show the desired
results under the EH’s assumption. Instead of converging to zero, the 𝛼 values
became higher and more positive. The 𝛽 coefficients barely improved as well, as
they did not converge to unity but sky-rocketed to as high as 31.38 points (for 1year and 10-year bonds). Although 1-year and 3-year and the 1-year and 10-year
bonds now have positive 𝛽 coefficients, the 𝛽 of the 1-year and 5-year bonds was
left at the negative territory.
102
Table 14. Term Spread Prediction of Future Changes in the Long Rate with Bond
Risk Premium
Long Rate Regression 𝑁(𝑅𝑡 − 𝑅𝑡−1 ) = 𝛼2 + 𝛽2 (𝑅𝑡−1 − 𝑟𝑡−1 ) + 𝛾𝐵𝑅𝑃 + 𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑎𝑛𝑐𝑒 𝑡𝑒𝑟𝑚
1-year and 3-year
OLS
GARCH (1,1) BRP
Moving
Square of
(HAC
Conditional
Average
Excess
Newey-West
Conditional
Standard
BRP
Returns
BRP
Test)
Variance
Deviation
0.61
0.97***
0.79***
0.00
5.44***
𝛼2
(0.37)
(0.39)
(0.31)
(0.32)
(1.21)
-0.71***
-0.77**
-1.56***
2.69***
3.92***
𝛽2
(0.34)
(0.39)
(0.46)
(0.60)
(0.63)
-11.49***
0.46***
-1.85***
-7.95***
-𝛾
(3.81)
(0.11)
(0.40)
(1.40)
R2
0.06
0.08
0.29
0.31
0.33
DW
2.04
2.10
1.59
2.11
2.30
Adjusted R2
-0.07
0.27
0.30
0.32
F-Statistic
-4.81
20.78
23.49
25.68
AIC
-4.02
3.77
3.73
3.71
SIC
-4.09
3.84
3.77
3.78
1-year and 5-year
2.08***
4.20***
2.39**
2.02
3.76*
𝛼2
(0.70)
(0.78)
(1.23)
(1.55)
(1.94)
-1.34***
-1.69***
-2.98***
0.04
-0.37
𝛽2
(0.33)
(0.33)
(0.88)
(0.68)
(1.04)
-56.19***
0.67***
-0.61***
-1.77***
-𝛾
(12.63)
(0.14)
(0.28)
(0.89)
R2
0.09
0.25
0.42
0.12
0.10
DW
2.13
2.05
1.51
2.18
2.18
Adjusted R2
-0.24
0.40
0.10
0.09
F-Statistic
-17.74
36.93
7.04
5.88
AIC
-5.13
4.89
5.31
5.33
SIC
-5.21
4.96
5.34
5.40
1-year and 10-year
1.90
4.22***
5.93***
-4.63
44.48***
𝛼2
(1.45)
(1.61)
(2.01)
(3.38)
(6.37)
-0.88**
-1.32***
-5.10***
8.62***
31.38***
𝛽2
(0.44)
(0.45)
(1.40)
(3.00)
(4.64)
-36.36**
0.88***
-2.26***
-45.95***
-𝛾
(15.34)
(0.28)
(0.65)
(6.64)
2
0.40
R
0.02
0.05
0.28
0.12
DW
1.74
1.75
1.57
1.59
1.35
Adjusted R2
-0.03
0.26
0.10
0.39
F-Statistic
-2.67
19.92
6.88
35.02
AIC
-6.46
6.19
6.39
6.00
SIC
-6.54
6.26
6.47
6.03
Source of Basic Data: Bloomberg, First Metro Investment Corporation (FMIC), Author’s
computations
Notes: Standard errors are placed in parentheses.
* = significant at 10% level
** = significant at 5% level
*** = significant at 1% level
103
The option of the conditional variance values as the bond risk premium for
the short rate regressions and the conditional standard deviation for the long rate
regressions just confirms that short-term yields are more volatile than long-term
yields. Due to the “squared” nature of the conditional variance, it better captures
the volatility or variance of the excess returns among the short rates. The
conditional standard deviation, on the other hand, is a toned down measure of the
conditional variance (as it is just the square root of the conditional variance); and
since long-term rates are less volatile, the conditional standard deviations were
enough in grasping the long rates’ excess returns volatility.
However, we cannot say that the BRP proxies of the univariate GARCH
model are the best estimates that improved the term spread models of the EH tests.
The results of the GARCH model, especially for the long rate regressions, were still
far from the desired 𝛼 and 𝛽 values.
The rejection of the EH, even after including the best BRP proxy among the
estimates done in this study, does not mean that the Philippine term spread is useless
in predicting future movements of interest rates. The direction and magnitude of
the 𝛽 coefficients, for both short rates and long rates, still have some important
implications.
One implication is that the term spread is able to positively portend future
changes in interest rates to a limited extent. The bond risk premium proxies for the
short rates also improved the EH tests, implying that the GARCH estimation is
consistent enough to capture the volatility of the short rates’ excess returns. For the
long rates, on the other hand, the conditional standard deviations of the excess
104
returns were able to reverse the negative signs of the 𝛽 coefficients, making it
consistent with theory. The 𝛽 coefficient for the 1-year and 5-year may still be
negative, but this result can still be discounted since it is not considered statistically
significant.
F. Macroeconomic Variables and the Bond Risk Premium
The fourth objective in this study is to identify certain macroeconomic
variables that highly influence the estimated bond risk premium. To achieve this, a
panel regression model, with the BRP as the dependent variable, was done. Fixed
effects specification of the panel regression was employed to consider the effects
of the explanatory variables that are time-varying.
From the results of the BRP tests, the selected BRP proxies for the twoperiod case (i.e., between one-period and two-period bonds) are the GARCHgenerated measures of conditional variances, while the best BRP proxies for the nperiod case (i.e., between one-period and n-period bonds) are the GARCHgenerated measures of conditional standard deviations. These BRP measures
proved to be the best among the three methods presented, as shown in the
improvement of the goodness-of-fit evaluations and term spread regression
coefficients.
The analysis have the following variations – whole sample test, short rate
tests, long rate tests, and analysis according to two periods (2006 – 2010 and 2011
– 2014) for both the short rate and long rate.
105
The whole sample test includes the bond risk premium estimates for both
the two-period case (which are the BRPs for the 3-month and 6-month, 6-month
and 1-year, and 1-year and 2-year bonds) and the n-period case (which are the 1year and 3-year, 1-year and 5-year, and 1-year and 10-year bonds) as the dependent
variables, together with all of the 12 macroeconomic variables with the lagged
values of the BRP and the bond spread as the explanatory variables. All of the data
are transformed to monthly growth rates from 2006 to 2014.
The short rate tests, on the other hand, only include the BRPs estimated
under the two-period case (which are the BRPs for the 3-month and 6-month, 6month and 1-year, and 1-year and 2-year bonds) as the dependent variables,
together with all of the 12 macroeconomic variables with the lagged values of the
BRP and the bond spread as the explanatory variables. All of the data are
transformed to monthly growth rates from 2006 to 2014.
The long rate tests, in the same way, include BRPs estimated under the nperiod case (which are the 1-year and 3-year, 1-year and 5-year, and 1-year and 10year bonds) as the dependent variables, with all of the 12 macroeconomic variables,
the lagged values of the BRP, and the bond spread as explanatory variables. All of
the data are transformed to monthly growth rates from 2006 to 2014.
For the periodical analysis, the data sample will be divided into two subperiods: 2006 to 2010 and 2011 to 2014.
106
1. Whole Sample Test
The whole sample test (which includes both the short rate and long rate
bond risk premium with all the macroeconomic variables from 2006 to 2014) show
that four variables out of the 12 regressors significantly affect the bond risk
premium. The most significant of them is the lagged values of the BRP, with a
minimal standard error, and a p-value nearly zero. An increase in the lagged BRP
by 1% or 100 basis points (bps) would induce the current BRP to increase by 77
bps.
Among the macroeconomic variables, Meralco sales (𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠) (as a
proxy for economic growth) and the lagged values of the growth rate of the federal
funds rate (𝑔𝑓𝑒𝑑𝑟𝑎𝑡𝑒(−1)) are observed to be the most significant determinants
of the BRP, having one of the highest t-statistics at 2.83 and 2.63, respectively. The
impact of Meralco sales, however, is very minimal at -0.7 bps, compared to federal
funds rate at 21 bps. This signifies that for every 100 bps change in economic
growth and in the past growth rate of monetary policy in the US, the BRP will
change by -0.7 bps and 21 bps, respectively.
Excess liquidity (𝑔𝑚2) and the lagged values of the growth rate of foreign
exchange rate (𝑔𝑓𝑜𝑟𝑒𝑥(−1)) followed suit as important determinants of the BRP.
Similarly, the former seems to have a very small impact to the BRP at -0.3 bps than
the relatively larger effect of foreign exchange rate at 171 bps. With the latter’s
standard error at ±79 bps, the effect of the foreign exchange rate on the BRP can
fluctuate from 92 bps to 250 bps, which can be quite volatile than the rest.
107
As we can see, the impact of the domestic variables are overpowered by the
large 𝛽 coefficients of the lagged values of the world macroeconomic factors. The
minute effects of economic growth (𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠) and excess liquidity (𝑔𝑚2) seem
negligible compared to the immense impacts of the lagged values of the foreign
exchange rate (𝑔𝑓𝑜𝑟𝑒𝑥(−1)) and the Fed’s policy rate (𝑔𝑓𝑒𝑑𝑟𝑎𝑡𝑒(−1)). The
observed significance of the current domestic data than the one-period lag in
foreign factors signify that information delay could exist. Thus, the effects of the
past peso-dollar exchange rate and the federal funds rate may ensue until the
present.
Table 15. Regression Results of Whole Sample
Variable
Coefficient
Standard Error
0.37
0.04
𝑐
0.77
0.02
𝐵𝑅𝑃(−1)
-0.007
0.002
𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠
1.71
0.79
𝑔𝑓𝑜𝑟𝑒𝑥(−1)
-0.003
0.001
𝑔𝑚2
0.21
0.08
𝑔𝑓𝑒𝑑𝑟𝑎𝑡𝑒(−1)
2
R = 0.920823
DW = 2.075503, Durbin’s h = -1.182402
t-Statistic
8.44***
32.12***
2.83***
2.15**
1.95**
2.63***
(no serial correlation among the variables)
Source of Basic Data: Author’s computations
Notes: * = significant at 10% level
** = significant at 5% level
*** = significant at 1% level
2. Periodical Sample Test (Crisis and Post-Crisis Periods)
A periodical analysis was also done to observe the behavior of the BRP and
its interaction with macroeconomic variables during and after the global financial
crisis. Results show that during the crisis period, from 2006 to 2010, the most
important determinants of the BRP are its lagged values (𝐵𝑅𝑃(−1)), the bond
108
spread (𝑠𝑝𝑟𝑒𝑎𝑑), the growth rate of the gross international reserves (𝑔𝑔𝑖𝑟), and the
growth rate of the US inflation (𝑔𝑢𝑠𝑐𝑝𝑖).
We can see here that the country’s BRP is prominently affected by world
macroeconomic variables (such as the gross international reserves and the US
inflation) than domestic factors. This suggests that despite our known resilience
during the global financial crisis, investors still took into consideration the possible
consequences of the crisis to the country’s financial market. The effect of GIR on
BRP, however, is relatively small (at 0.2 bps) compared to the immense effect of
US inflation – such that for every 1% change in the growth rate of US inflation, the
BRP may change by 202 bps. The latter, nevertheless, should be considered with
caution due to its relatively high standard error (at ±92 bps).
The finding that the lagged values of the BRP and the current bond spread
are among the most important determinants of the BRP only shows the great
relationship between the past values of the BRP and the slope of the yield curve to
the current BRP. This also signals the great relevance of these factors to the current
condition of interest rates. This may imply that investors were already watchful
about the movement of interest rates during the crisis, taking into account the
direction of past data and direction of long-term interest rates relative to the shortterm rates.
For the periods after the financial crisis, it can be observed that the world
macroeconomic effects have died down, and domestic factors took the role. These
country variables are the lagged values of the BRP (𝐵𝑅𝑃(−1)), lagged values of
the bond spread (𝑠𝑝𝑟𝑒𝑎𝑑(−1)), and the growth rate of BSP’s monetary stance
109
(𝑔𝑟𝑟𝑝). Among these, BSP’s policy rate has the highest impact on BRP at 129 bps
(with a standard error of ±53 bps). This highlights the increased importance of the
reverse repurchase rate (𝑟𝑟𝑝) at present as the primary reference for interest rates
monitored by investors. This finding also suggests that the BSP must remain
attentive to the effects of its monetary policy rate decisions as the BRP is shown to
be very reactive to the 𝑟𝑟𝑝’s movements.
Table 16. Regression Results of Periodical Sample
2006 to 2010
2011 to 2014
Variable
Coefficient
Standard
Error
tStatistic
Variable
Coefficient
Standard
Error
tStatistic
𝑐
0.20
0.05
3.93***
𝑐
0.32
0.05
5.91***
𝐵𝑅𝑃(−1)
0.52
0.03
17.24***
𝐵𝑅𝑃(−1)
0.58
0.08
7.50***
𝑠𝑝𝑟𝑒𝑎𝑑
0.36
0.02
14.98***
𝑠𝑝𝑟𝑒𝑎𝑑(−1)
0.18
0.06
3.22***
𝑔𝑟𝑟𝑝
1.29
0.53
2.43**
𝑔𝑔𝑖𝑟
𝑔𝑢𝑠𝑐𝑝𝑖
-0.002
0.001
1.70*
2.02
0.92
2.19**
R2 = 0.923858
DW = 2.064108, Durbin’s h = -0.731383
(no serial correlation among the variables)
Source of Basic Data: Author’s computations
Notes: * = significant at 10% level
** = significant at 5% level
*** = significant at 1% level
R2 = 0.953200
DW = 1.829008, Durbin’s h = 1.760418
(no serial correlation among the variables)
3. Short Rate Bond Risk Premium and Macroeconomic Variables
The effect of macroeconomic variables on the short rate BRP (3-month and
6-month, 6-month and 1-year, and 1-year and 2-year bonds) were also studied,
along with some periodical analyses.
Using the whole sample period (2006 to 2014), it is observed none of the
12 macroeconomic variables was significant at the 95% and 90% confidence level.
The only factors that proved to be significant are the lagged values of the BRP
(𝐵𝑅𝑃(−1)) and the bond spread (𝑠𝑝𝑟𝑒𝑎𝑑). This finding may suggest that when
110
investors trade short-term investment instruments, they tend to focus more on the
available information in the bond market than consider other macroeconomic
variables in their decision-making process. The results are a sign that investors may
base their current decisions on the outcome of past data. This may also explain why
volatility clustering is present, especially in short rates – where periods of high
volatility are followed by periods of high volatility, and periods of low volatility
are trailed by periods of low volatility.
Table 17. Regression Results of Short Rates (2006 to 2014)
Variable
Coefficient
Standard Error
t-Statistic
0.03
0.02
1.52
𝑐
0.72
0.03
24.07***
𝐵𝑅𝑃(−1)
0.20
0.03
6.57***
𝑠𝑝𝑟𝑒𝑎𝑑
2
R = 0.793214
DW = 2.181456 , Durbin’s h = -1.900565
(no serial correlation among the variables)
Source of Basic Data: Author’s computations
Notes: * = significant at 10% level
** = significant at 5% level
*** = significant at 1% level
When the sample was divided into two time periods, 2006 to 2010 and 2011
to 2014, the BRP determinants has been clear cut. Apart from the usual determinant
of the BRP (which is the lagged values of BRP), US inflation (𝑔𝑢𝑠𝑐𝑝𝑖) prevailed
over the rest and is deemed statistically significant in affecting the BRP. A 100 bps
change in the growth rate of US inflation may induce an increase in the BRP by
208 bps. Inflationary pressures abroad may have heavily affected the decision of
domestic investors to increase their short-term BRP outlook due to the worsening
US economy when the crisis hit. We should note here that none of the domestic
variables heavily affected the BRP of the short rates during the crisis period.
111
But now, after the crisis years, it is observed that the short BRP have
become highly relevant to a domestic factor, which is the economic growth
indicator (𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠). The effect on BRP, however, is very minimal at -0.7 bps for
every 100 bps change in the growth rate of Meralco sales. This suggests that
investors who are heavily invested in short maturity debt instruments may
immediately decide based on the current performance of the economy. Hence, the
announcement of the quarterly GDP figures may be crucial to the bond market. Of
course, the lagged values of the BRP (𝐵𝑅𝑃(−1)) and lagged values of the bond
spread (𝑠𝑝𝑟𝑒𝑎𝑑(−1)) still prevailed to be significant indicators due to their high
correlation with the estimates of BRP.
Table 18. Regression Results of Short Rates (2006 to 2010 and 2011 to 2014)
Variable
𝑐
𝐵𝑅𝑃(−1)
𝑔𝑢𝑠𝑐𝑝𝑖
2006 to 2010
Standard
Coefficient
Error
0.07
0.04
0.73
0.04
2.08
1.25
tStatistic
1.98**
16.49***
1.67*
R2 = 0.681370
DW = 2.191396, Durbin’s h = -1.571606
(no serial correlation among the variables)
Variable
𝑐
𝐵𝑅𝑃(−1)
𝑠𝑝𝑟𝑒𝑎𝑑(−1)
𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠
2011 to 2014
Standard
Coefficient
Error
0.10
0.03
0.71
0.06
0.14
0.05
-0.007
0.003
R2 = 0.906905
tStatistic
2.92***
11.64***
2.90***
2.26**
DW = 1.90551, Durbin’s h = 0.789445
(no serial correlation among the variables)
Source of Basic Data: Author’s computations
Notes: * = significant at 10% level
** = significant at 5% level
*** = significant at 1% level
4. Long Rate Bond Risk Premium and Macroeconomic Variables
For the tests of the BRP of the long rates from 2006 to 2014, results show
there are five factors (that is, a mixture of domestic and world macroeconomic
variables) highly affecting the BRP (apart from the lagged values of the BRP).
These are Meralco sales (𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠), the growth rate of the foreign exchange rate
112
(𝑔𝑓𝑜𝑟𝑒𝑥), excess liquidity (𝑔𝑚2), the lagged values of the growth rate of the
federal funds rate (𝑔𝑓𝑒𝑑𝑟𝑎𝑡𝑒(−1)), and the growth rate of the Philippine Stock
Exchange index (𝑔𝑝𝑠𝑒𝑖). All of them are statistically significant at the 5% to 1%
significance level.
The effect, however, of excess liquidity and economic growth on BRP are
very minimal at -0.5 bps and -0.8 bps, respectively for every 100 bps change of the
two variables. Investors, nevertheless, are more reactive when foreign exchange
rate, the lagged values of the federal funds rate, and the Philippine Stock Exchange
index grow. For every 100 bps change in the growth rate of these variables,
investors may increase the BRP by 269 bps, 26 bps, and 85 bps, respectively.
It can also be noticed that more macroeconomic variables significantly
affect the long rate BRP than the short rate BRP. Additionally, the factors that
significantly affect the BRP of the whole sample data (2006 to 2014) are greatly
similar to the variables that affect the long rate BRP. This signifies that the effect
of macroeconomic variables on the long rate BRP prevail over their effect on the
short rate BRP. Furthermore, this gives us the impression that long maturity rates
are more rooted on macroeconomic conditions than short rates. Remember that only
the past values of the BRP and the bond spread affect the current BRP of the short
rates. This may suggest that when it comes to trading short maturity bonds,
investors are more adaptive or backward-looking. Thus, the outcome of the past
BRP values may heavily influence investors’ current BRP decision.
113
Table 19. Regression Results of Long Rates (2006 to 2014)
Variable
Coefficient
Standard Error
t-Statistic
0.62
0.09
6.56***
𝑐
0.75
0.04
19.94***
𝐵𝑅𝑃(−1)
-0.008
0.004
2.12***
𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠
2.69
1.36
1.98**
𝑔𝑓𝑜𝑟𝑒𝑥
-0.005
0.002
2.13***
𝑔𝑚2
0.26
0.13
2.00**
𝑔𝑓𝑒𝑑𝑟𝑎𝑡𝑒(−1)
0.85
0.37
2.29***
𝑔𝑝𝑠𝑒𝑖
R2 = 0.850545
DW = 2.003696, Durbin’s h = -0.134421 (no serial correlation among the variables)
Source of Basic Data: Author’s computations
Notes: * = significant at 10% level
** = significant at 5% level
*** = significant at 1% level
On the other hand, the results for the sample during the crisis period show
that the most significant determinants of BRP are dominated by world
macroeconomic factors (similar to the case of the whole sample and short rate
BRP). These variables are the growth of gross international reserves (𝑔𝑔𝑖𝑟) and the
lagged values the foreign exchange rate (𝑔𝑓𝑜𝑟𝑒𝑥(−1)).
A 1% or 100 bps change in the growth rate of the GIR may induce investors
to change their BRP by -0.7 bps, while the peso-dollar rate may prompt the BRP to
change by as much as 322 bps. It can be noticed that the effect of the exchange rate
has been relatively high throughout the other sample regressions at levels reaching
more than 170 bps, and now reaching as high as 300 bps for the long rate BRP
during the crisis years. This observation may highlight the big impact of peso
appreciation or depreciation to the country’s bond market as the size of foreigncurrency bonds have been growing until now.
114
The growth of inflation followed suit as the next significant factor in
determining the BRP with an impact of 91 bps. This figure may still fluctuate from
38 bps to 144 bps which can be quite volatile and risky. Also, we can notice that
Philippine inflation took over the role of US inflation from the whole sample and
short rate regressions. Hence, we can say that Philippine economic data has become
more relevant for the long-end during the crisis years. Investors were already wary
about the increased risk from inflation, as price uncertainties also heightened during
the global financial crisis. It is, therefore, noticed that not only world
macroeconomic conditions significantly affected investment decisions during the
crisis periods, but also domestic factors such as the country’s elevated inflation that
may have readily provoked investors to require higher BRP returns.
For the post-crisis years, the relationship between the estimated BRP and
macroeconomic variables suddenly paint a unique picture. The whole sample and
short rate BRP regressions show that the BSP’s policy rate (𝑔𝑟𝑟𝑝) and economic
growth (𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠), respectively, emerged to be the only variables affecting the
BRP. For the long rate BRP, however, both the reverse repurchase rate (𝑔𝑟𝑟𝑝) and
the excess liquidity (𝑔𝑚2) proved to be the most relevant variables. The effect of
the former is quite large than the latter – such that for every 100 bps or 1% change
in the growth of BSP’s policy rate, the BRP may change by 236 bps (and this may
still fluctuate between 142 bps and 330 bps given its standard error). On the other
hand, the effect of excess liquidity on the BRP seems to be more subdued at only 0.8 bps, but statistically, excess liquidity is a better BRP predictor than the reverse
repurchase rate.
115
Moreover, compared to the post-crisis regressions of the whole sample and
short rate BRP data, which required the lagged values of the bond spread, long rates
demanded future values of the bond spread. To prevent serial correlation among the
variables in the regression, the “one-period ahead” figure of the bond spread
(𝑠𝑝𝑟𝑒𝑎𝑑 (+1)) must be inputted into the model. This result implies that there is a
possibility that investors now rely on the expected movement of the slope of the
yield curve when trading long-term debt instruments.
Table 20. Regression Results of Long Rates (2006 – 2010 and 2011 – 2014)
2006 to 2010
Standard
tVariable
Coefficient
Error
Statistic
0.79
0.14
5.46***
𝑐
0.65
0.06
11.40***
𝐵𝑅𝑃(−1)
-0.007
0.003
2.31**
𝑔𝑔𝑖𝑟
0.91
0.53
1.72*
𝑔𝑖𝑛𝑓
3.22
1.61
2.00**
𝑔𝑓𝑜𝑟𝑒𝑥(−1)
R2 = 0.835654
DW = 2.154323, Durbin’s h = -1.581699
(no serial correlation among the variables)
Source of Basic Data: Author’s computations
Notes: * = significant at 10% level
** = significant at 5% level
*** = significant at 1% level
2011 to 2014
Standard
tVariable
Coefficient
Error
Statistic
0.76
0.17
4.39***
𝑐
0.69
0.06
11.04***
𝐵𝑅𝑃(−1)
0.15
0.07
2.15**
𝑠𝑝𝑟𝑒𝑎𝑑(+1)
2.36
0.94
2.52**
𝑔𝑟𝑟𝑝
-0.008
0.003
2.85***
𝑔𝑚2
R2 = 0.874554
DW = 1.769473, Durbin’s h = 1.939539
(no serial correlation among the variables)
G. Economic Implications of Macro-BRP Relationship
The tests regarding the relationship of macroeconomic variables on the BRP
showed that a varied set of macroeconomic variables highly affect the estimated
BRP, and these relationships change through time.
Based on the estimation methods for the bond risk premium of different
maturities (short rate or long rate), the most persistent and highly significant
variable that is consistent through time is the lagged values of the BRP. For every
100 bps change in the lagged values of the estimated BRP, current BRP may change
116
by 52 bps (from the 2006 to 2010 regressions of the whole sample data) to as high
as 77 bps (from the 2006 to 2014 regressions of the whole sample data).
This indicator of interest rates heavily affects both the BRP of the short rates
and the BRP of the long rates – but the impact is more distinct for the short rates.
This denotes that investors, especially those in the short-term debt market, are
highly sensitive to the past condition of bond rates and not on economic factors;
thus, explaining the more volatile nature of short-term bonds than long-term bonds.
Investors closely watch the situation of the financial market in requiring respective
BRPs. This behavior is highlighted by the so called adaptive expectations, which
states that people form their current decisions from the direction of past data.102
The bond spread or the slope of the yield curve was also used as one of the
basic indicators of the estimated BRP. Regression results show that the bond spread
was only relevant in the periodical analysis. The current spread was a good
predictor of the BRP during the crisis years, specifically for the short rate BRP; but
the lagged values of the spread were more effective during the post-global financial
crisis, especially for the long rate BRP. This finding implies that the relationship of
short-term rates and long-term rates may be one of the factors that investors
consider when assigning respective risk premiums for their bonds. Even though the
movement of the long rates did not perfectly translate to the changes of the short
rates, the large effect of the bond spread on the BRP indicates that the slope of the
yield curve can be a good predictor of the BRP when properly used in regression
tests.
“Adaptive Expectations Hypothesis,” Investopedia,
http://www.investopedia.com/terms/a/adaptiveexpthyp.asp (accessed April 20, 2015).
102
117
The macro-BRP relationship tests done, however, did not produce
conclusive and consistent results. Various macroeconomic variables affect the
estimated BRP differently according to maturity and time. Several variables,
however, proved to be recurring than the rest. These factors are summarized in the
whole sample results.
Using the data from 2006 to 2014, the most persistent factors are the annual
growth rate of Meralco sales (𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠, an indicator of economic growth),
excess liquidity (𝑔𝑚2), foreign exchange rate (𝑔𝑓𝑜𝑟𝑒𝑥 (−1) or simply 𝑔𝑓𝑜𝑟𝑒𝑥),
and the federal funds rate (𝑔𝑓𝑒𝑑𝑟𝑎𝑡𝑒(−1) or 𝑔𝑓𝑒𝑑𝑟𝑎𝑡𝑒). We can notice that these
are a mixture of both domestic and world macroeconomic variables. The impact of
the foreign factors, however, have exceeded the effect of the domestic factors. This
may signify that even after the global financial crisis, the country is still vulnerable
to impacts abroad. Hence, the Philippine bond market’s move towards global
integration and increased participation in the international market must be closely
supervised and monitored, as any global shock may cause immense changes to the
country’s financial system.
Additionally, it is observed that the whole sample results (from 2006 to
2014) resemble the results of the long rate tests (from 2006 to 2014). This tells us
that the long rate BRPs may be more grounded on macroeconomic data than short
rates, and the effect of these macroeconomic variables last through the crisis and
post-crisis years. This inference is also confirmed by the results for the short rate
BRP – which shows that the only persistent predictors of the short rate BRP are its
lagged values and the bond spread.
118
The effect of these world macroeconomic variables also varies through
time. For instance, the effect of the foreign exchange rate has been more prominent
from 2006 to 2010. Additionally, Bico (2010) noted that since short-term maturity
bonds (such as the 91-day T-Bill) do not have a dollar substitutes compared to longterm bonds, they are not sensitive to changes in the peso-dollar exchange rate.103
Hence, the exchange rate remains to be one of the strongest determinants of longterm yields and consequently of long rate BRPs.
In contrast to exchange rate, the effect of the federal funds rate was only
evident through the crisis and post-crisis periods (2006 to 2014). However, contrary
to conventional thinking, the impact of the federal funds rate is observed to be more
evident on the long rate BRP than the short rate BRP. The same situation applies
for BSP’s monetary stance. It is seen that the reverse repurchase facility and the
federal funds rate have been more effective in determining the BRP of long-term
bonds than short-term ones, especially during the post-crisis periods. These
findings may suggest that long-term bond yields are more sensitive to changes in
the domestic and foreign factors, giving policymakers a possible strategy when they
want to influence the long end of the country’s yield curve.
Meralco sales (𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠, as a proxy for productivity) and excess liquidity
(𝑚2), nevertheless, are also significant determinants of the BRP, but only have very
small impacts on it. The former seems to be more relevant to the short-term BRP
than the latter (which affects the long rate BRP more). This finding implies that
short-term investors can be more reactive to the regular announcement of the
C. Bico, “Estimating and Forecasting the Philippines Zero-Coupon Yield Curve: A
Multimethod Approach” (Thesis, University of Asia and the Pacific, 2010), 75-76.
103
119
country’s GDP figures in making their short-term investment decisions. One factor
that may have invited this behavior is the fact that the country’s economic growth
is readily publicized for the financial market to consider. The quarterly
announcement of the GDP figures are much anticipated for compared to the
measure of the country’s broad money – which can only be relevant on the part of
policymakers.
When the analysis was divided into crisis and post-crisis periods, the effect
of the macroeconomic variables have been more distinct. For the periods 2006 to
2010, world factors dominated the effect of domestic factors on the estimated BRP.
For the short rate, US inflation was the only statistically significant variable; while
for the long rate, gross international reserves and the peso-dollar rate prevailed
among the rest.
These results imply that bond yields were more sensitive to global jolts
during the crisis. Despite reports saying that the country was not badly hit during
the global financial crisis, the findings of this study shows that the Philippine bond
market has been greatly affected as well, to a limited extent (as the effects did not
ensue anymore to the present). This is not to forget, however, that domestic
inflation was also one of the factors that highly influence the BRP. Obviously, price
anxieties abroad shook domestic prices, as supplies abroad suffered from the tight
financial system in the US.
Another noticeable finding from the crisis period results is that, money
demand variables (inflation and foreign exchange rate) are more dominant than
money supply variables (gross international reserves). This simply confirms that,
120
when the crisis hit, the financial market’s appetite has been distressed. The market’s
momentum halted thereby encouraging investors to put a higher risk premium on
their debt instruments.
On the other hand, the results for the post-crisis periods show that the
influence of world macroeconomic variables have gradually receded and domestic
factors have become more effective. It can be noticed in the short rate results,
Meralco sales (𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠) emerged to be the only effective factor while for the
long rate, BSP’s monetary policy (𝑔𝑟𝑟𝑝) and excess liquidity (𝑔𝑚2) were the most
significant predictors. Among these variables, the impact of BSP’s reverse
repurchase rate (rrp) dominated in the whole sample results. The effect of BSP’s
rrp on the BRP can range from 129 bps (in the whole sample results) to 236 bps (in
the long rate results).
The result for the long rate BRP are very similar to the whole sample results
except for an addition. The condition of the Philippine Stock exchange index is also
observed to be one of the most significant determinants of the long rate BRP. This
means that when stock returns are higher, bond investors would expected a higher
compensation for the risk of shifting investment markets. This is due to the
observed negative correlation of stock and bond returns, making government bonds
the “ultimate safe-haven assets”.104
Overall, these findings imply that the Philippine BRP, both short rates and
long rates, is mostly dependent on domestic short-term indicators than world
macroeconomic variables. This is perhaps because of the increased resiliency of the
104
Antti Ilmanen, Expected Returns on Major Asset Classes (Research Foundation of CFA
Institute: John Wiley & Sons, Inc., 2012), 68.
121
country’s financial markets from external shocks and persistent economic growth
brought about by the large domestic savings from OFW and BPO remittances.
Macroprudential measures have been strictly put in place so that risks may be
mitigated.
Another reason that may have added to the protection of the bond market is
its innate characteristic itself. The Philippine bond market is still relatively small
and young compared to its neighboring countries. The government debt market is
also less integrated into the international arena, making it more “resistant” and less
affected by external macroeconomic events and shocks. And unlike the interest
rates of developed markets, Philippine interest rates (especially at the short-end)
dramatically fluctuate, and hence, very hard to predict. This observation further
supports the implication of this study – that Philippine bond yields (especially, the
short rates) are not yet strongly anchored on macroeconomic variables relative to
the bond markets of developed countries.
The Philippine bond market, however, is gradually growing and is slowly
tapping the international market, so developments in the future must be closely
monitored. These advancements must translate to a more efficient bond market and
must result to well-anchored trading decisions to facilitate predictability of the bond
risk premium.
122
Table 21. Summary of Macro-BRP Regressions
Whole
Sample
20062010
20112014
𝑐
𝐵𝑅𝑃(−1)
𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠
𝑔𝑓𝑜𝑟𝑒𝑥(−1)
𝑔𝑚2
𝑔𝑓𝑒𝑑𝑟𝑎𝑡𝑒(−1)
𝑐
𝐵𝑅𝑃(−1)
𝑠𝑝𝑟𝑒𝑎𝑑
𝑔𝑔𝑖𝑟
𝑔𝑢𝑠𝑐𝑝𝑖
𝑐
𝐵𝑅𝑃(−1)
𝑠𝑝𝑟𝑒𝑎𝑑(−1)
𝑔𝑟𝑟𝑝
Short
Rate
(20062014)
Short
Rate
(20062010)
Short
Rate
(20112014)
𝑐
𝐵𝑅𝑃(−1)
𝑠𝑝𝑟𝑒𝑎𝑑
𝑐
𝐵𝑅𝑃(−1)
𝑢𝑠𝑐𝑝𝑖
𝑐
𝐵𝑅𝑃(−1)
𝑠𝑝𝑟𝑒𝑎𝑑(−1)
𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠
Long Rate
(20062010)
Long Rate
(20112014)
𝑐
𝑐
𝐵𝑅𝑃(−1)
𝐵𝑅𝑃(−1)
𝑔𝑚𝑒𝑟𝑠𝑎𝑙𝑒𝑠
𝑔𝑔𝑖𝑟
𝑔𝑓𝑜𝑟𝑒𝑥
𝑔𝑓𝑜𝑟𝑒𝑥(−1)
𝑔𝑚2
𝑔𝑖𝑛𝑓
𝑔𝑓𝑒𝑑𝑟𝑎𝑡𝑒(−1)
𝑔𝑝𝑠𝑒𝑖
𝑐
𝐵𝑅𝑃(−1)
𝑠𝑝𝑟𝑒𝑎𝑑(+1)
𝑔𝑟𝑟𝑝
𝑔𝑚2
Long Rate
(2006-2014)
Source: Author’s compilation
123
CHAPTER V
SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS
This study aims to test the correspondence of Philippine bond yields to the
Expectations Hypothesis (EH), and consequently measure the bond risk premium
of Philippine bond rates. This study is motivated by the developing government
debt market in the country, the growing importance of term spreads in investment
and trading decisions, and the flourishing potential of the EH as a framework in
monitoring interest rates.
This study has five major objectives to fulfill. These are: 1) to empirically
test the validity of the Expectations Hypothesis via term spread models; 2) to
estimate the bond risk premium (BRP) of Philippine bond yields; 3) to test again
the EH using the term spread models with the estimated BRP; 4) to identify the
macroeconomic variables that highly affect the estimated the BRP; and 5) to
explain the implications of the findings of the study on the Philippine bond market.
A. Summary of Results and Conclusions
Results are discussed according to the objectives posed in this study:
The first objective is to empirically test the validity of the assumptions
under the Expectations Hypothesis (EH) via term spread models using the
Philippine bond yields. To do this, the future changes in the short-term yields,
future changes in the long-term yields, and excess returns were regressed against
their corresponding term spreads. The discussion was divided into the two-period
124
case (3-month and 6-month, 6-month and 1-year, and 1-year and 2-year bond
yields) and the n-period case (1-year and 3-year, 1-year and 5-year, and 1-year and
10-year bond yields). The desired 𝛼 coefficient must be zero and the 𝛽 coefficient
must be one.
The results of the term spread regression models highly affirm the rejection
of the assumptions of the Expectations Hypothesis (EH). Firstly, the term spread
models did not “perfectly” forecast the future changes in the short rate. The 𝛼
coefficients were below zero while the 𝛽 coefficients were far from unity –
although the direction of the forecast was right (positive).
Secondly, the term spread did not “perfectly” forecast the future changes in
the long rate, and the results showed that the 𝛼 coefficients were highly positive
while the direction of the forecast was contrary to theory as the 𝛽 coefficients were
significantly negative.
Lastly, the term spread models were able to positively, consistently (across
all maturities), and strongly (high 𝛽 coefficients) forecast the excess returns of bond
rates, which it was not supposed to do. The additional tests using forward spread
models also confirmed that the EH did not hold true for Philippine bond yields.
Due to the failure of the assumptions of the EH, this study assumed right
away that the rejection of the tests was due to the omission for the bond risk
premium (BRP) as suggested by various literature. Hence, the second objective
was to have an estimate of the bond risk premium to be plugged in into the
term spread models.
125
In this study, the BRP was associated with interest rate volatility. Three
measures of volatility were obtained. These were the: 1) moving average of the
absolute changes in the short rate and long rate computed over the previous six
periods; 2) square of the expected excess holding period return; and the estimates
of conditional standard deviations and variances from the univariate GARCH (1,1)
model.
To select which BRP estimate is the best, each of them were inputted
into the term spread models and improvement indicators were monitored as
indicated by the third objective. These indicators are the: 1) Adjusted R2 which
must not be far away from the original R2; 2) F-statistic which must have a large
value; 3) Akaike Information Criterion; and the 4) Schwarz Information Criterion
(SIC) which should both be at a minimum value. The improvement of the 𝛼 and 𝛽
coefficients were also considered.
From the criteria above, the best BRP proxy estimates were obtained from
the GARCH (1,1) model that measured the volatility of the monthly excess returns
of bond yields. Based on the assessment, the best BRP for the short rates were the
conditional variances, while the best BRP for the long rates were the conditional
standard deviations. This only affirms that the short rates are more volatile than the
long rates; hence, variances must be used for the former, while a more stable proxy
can be used to capture the volatility of the latter.
Nevertheless, despite producing the best BRP estimates among the methods
tested, the conditional standard deviations and conditional variances did not
achieve the theoretical values of the 𝛼 and 𝛽 coefficients. In the case of the short
126
rates, the conditional variances enhanced the 𝛼 coefficients by making it less
negative than the original test, and by adding more points to the 𝛽 coefficient
making it closer to one. This implies that the conditional variances are good proxies
for the BRP, making them close to the real BRP required by investors in the
Philippine bond market.
In the case of the long rate regressions, the conditional standard deviations
somehow improved the results of the tests, although still far from the desired
results. The 𝛼 coefficients had large positive values which were still far away from
zero. The 𝛽 coefficients, on the other hand, now became positive which is big
change from the negative 𝛽s in the original term spread model. With this, empirical
results already correspond to what theory says – an increase in the term spread does
signal a positive change of future long rates.
From these findings, we can say that the BRP estimates from the univariate
GARCH (1,1) model are still good BRP proxies. However, the estimation model
can be further improved to achieve the desired 𝛼 and 𝛽 coefficients.
Now that the BRP proxy has been selected and tested, the fourth
objective of this study was to identify the various macroeconomic variables
that highly affect the BRP. To achieve this, a fixed effects panel regression model
was used to test the relationship of 14 macroeconomic variables (independent
variables), together with the lagged values of the BRP and the bond spread, and the
estimated BRP (dependent variable), both for the short rate and the long rate. The
following variables are classified into macroeconomic variables, government/fiscal
variables, institutional variables, and additional variables derived from the yield
127
curve. They are as follows: annual growth rate of Meralco sales (as a proxy for
economic growth), inflation, peso-dollar rate, excess liquidity, OFW remittances,
BSP monetary stance, US prices, federal funds rate, gross international reserves,
budget deficit as a percent of GDP, government debt as a percent of GDP,
Philippines stock market index, the lagged values of the BRP, and the bond spread.
Periodical analyses were also done to deepen the discussion of the results.
The regression results showed that the various macroeconomic variables
affect the estimated BRP differently according to maturity and time. It was,
therefore, hard to pinpoint which variables consistently and significantly affect the
estimated BRP. The most persistent factor throughout the tests, however, was the
lagged values of the BRP and the bond spread. This implies that investors highly
rely on the past conditions of the market and the movement of long-term rates
relative to the short-term rates to peg their assigned BRP. They closely watch the
movement of interest rates to make their next trading or investment move. This
behavior suggests that investors follow more the assumptions of the Adaptive
Expectations Hypothesis (AEH) (i.e., being more backward-looking) than the
Rational Expectations Hypothesis (REH) (i.e., being more forward-looking).
For the macroeconomic variables, the most insistent and statistically
significant factors were shown in the whole sample results which were which were
the annual growth rate of Meralco sales, excess liquidity, peso-dollar exchange rate,
and the federal funds rate. Other variables not in the whole sample results, such as
BSP’s monetary stance and the growth rate of the Philippine Stock Exchange index,
were also observed to be some of the most important determinants of the BRP. This
128
finding suggests that investors also take into account the effect of various
macroeconomic variables on their investment instruments.
Among these macroeconomic variables, the short rate BRP is observed to
be more responsive to the lagged values of the BRP, while the long rate is observed
to be more anchored on economic factors, both domestic and foreign variables. This
finding confirms that expectations of investors in the short-term debt market may
still be based on adaptive sentiments (i.e., on what they feel or believe will happen
based on the previous direction of the data). Hence, trading decisions may be
temporary and fleeting – giving the BSP and the PDS Group more ways to deviate
or correct the market’s prospects.
The long rate BRP, on the other hand, are more grounded on economic
variables and their effects have been varied. Meralco sales (as a proxy for economic
growth) and excess liquidity, for instance, have very minute yet significant effects
on BRP. The financial market may, therefore, expect small impacts on the BRP
when measures of economic growth and liquidity change. On the other hand, when
shocks to the peso-dollar rate, BSP’s policy rate, federal funds rate, and stock
market activity transpire, the bond market can expect the BRP and, consequently,
yields to strongly react. Hence, these macroeconomic variables must be closely
monitored to maintain stability of long-term maturity bonds.
As a response to the fifth objective, the findings of the study has several
implications especially about the bond market of the country. First and
foremost, the Philippine bond market is still young and small, compared to the
government debt market of other developing countries (especially, its ASEAN
129
neighbors), which still needs a lot of improvement in terms of efficiency. The bond
market is not yet very competitive enough to meet the rigid assumptions of the
Expectations Hypothesis (EH). This just shows that our country’s interest rates are
not purely dependent on the expectations of investors as theory dictates, but also on
other factors. The nature of these factors that significantly affect the BRP and,
consequently, the bond yields, confirm the country’s resistance to external shocks
after the crisis period; hence, pointing our direction to domestic economic variables
as reliable predictors of the current BRP and bond yields.
Secondly, the lack of studies about frameworks regarding the term structure
of interest rates only highlights the fact that the market is not yet well-structured
enough. The academe nor financial analysts are not yet deep into analyzing the
motivations behind the movements of interest rates. This makes investment or
trading decisions loosely grounded on macroeconomic activities and more rooted
on sentiments or mere expectations.
Unlike in developed countries, several studies have been done already to
estimate interest rate expectations and the BRP so that forecasts may have a
framework. In the Philippines, however, decisions are not yet well-supported by
macroeconomic forces and policymakers do not have yet a concrete framework to
follow when it comes to interest-rate monitoring, making it hard to predict the
movement of interest rates and the BRP.
Nevertheless, the macro-BRP relationship tests done in this study show that
the estimated BRP of the Philippines is, in one way or another, related to various
macroeconomic variables. This is a good indication that the debt market is
130
gradually being characterized by rational market players as decisions are becoming
more based on analyzed facts and more informed choices. Furthermore, as the
Philippine
bond
market
moves
towards
advancements,
corresponding
developments may translate to a more competitive and efficient debt market. A
more feasible interest rate framework is, therefore, not too distant to be achieved.
B. Limits of the Study and Recommendations
Future researchers can explore more on the limitations of this study. Since
this study only discussed the single-equation approach in the empirical testing of
the Expectations Hypothesis, other estimation methods can be done. One example
is the affine term structure representations, which includes the Stochastic Discount
Factor (SDF) model or the capital asset pricing model (CAPM). Other studies may
also extend the bond maturities of this study by computing for the zero-coupon
bonds of consecutive tenors via bootstrapping.
It is also suggested to make use of benchmark bonds – bonds that are
actively traded in the secondary market and proven to be more liquid. This is
because the yields of these bonds efficiently reflect the true yields made by the
market; hence, benchmark bonds will serve as more accurate indicators of
Philippine’s interest rates.
There are also a number of ways to estimate the bond risk premium (BRP)
as discussed in the related literature of this study. Instead of using the observable
proxy method, the term premium specification model from the SDF and CAPM
methods can used. The survey method can also be done if possible.
131
Lastly, since this study only analyzed the relationship of the estimated BRP
with a limited number of macroeconomic variables, more econometric models can
be developed and more macroeconomic variables can be added to come up with a
very robust model useful for forecasting. With this, the BRP can be efficiently
predicted that may be helpful for investors and policymakers.
132
APPENDIX A:
ZERO COUPON BOND YIELDS OBTAINED FROM THE BLOOMBERG TERMINAL
(TENORS: 3-MONTH, 6-MONTH, 1-YEAR, 2-YEAR, 3-YEAR, 5-YEAR, AND 10-YEAR)
PHP Philippine
Government Zero
Coupon Yield 3
Month
Security
Start Date
End Date
Period
Currency
Date
11/30/2014
10/31/2014
9/30/2014
8/29/2014
7/31/2014
6/30/2014
5/30/2014
4/30/2014
3/31/2014
2/28/2014
1/31/2014
12/31/2013
11/29/2013
10/31/2013
9/30/2013
8/30/2013
7/31/2013
6/28/2013
5/31/2013
4/30/2013
I10503M Index
2/26/2004
12/30/2014
M
PHP
PX_LAST
1.5
1.4
1.5
1.25
1.375
1.15
1.07
1.3
1.5
1
1.2
0.325
0.175
0.095
0.476
1.25
1.049
1.75
2
0.2
PHP Philippine
Government Zero
Coupon Yield 6
Month
Security
Start Date
End Date
Period
Currency
Date
11/30/2014
10/31/2014
9/30/2014
8/29/2014
7/31/2014
6/30/2014
5/30/2014
4/30/2014
3/31/2014
2/28/2014
1/31/2014
12/31/2013
11/29/2013
10/31/2013
9/30/2013
8/30/2013
7/31/2013
6/28/2013
5/31/2013
4/30/2013
I10506M Index
2/26/2004
12/30/2014
M
PHP
PX_LAST
1.738
1.464
1.737
1.613
1.663
1.29
1.789
1.96
1.321
1.481
1.947
0.425
0.299
0.184
0.896
1.35
0.847
1.802
2.025
0.3
PHP Philippine
Government Zero
Coupon Yield 1
Year
Security
Start Date
End Date
Period
Currency
Date
11/30/2014
10/31/2014
9/30/2014
8/29/2014
7/31/2014
6/30/2014
5/30/2014
4/30/2014
3/31/2014
2/28/2014
1/31/2014
12/31/2013
11/29/2013
10/31/2013
9/30/2013
8/30/2013
7/31/2013
6/28/2013
5/31/2013
4/30/2013
I10501Y Index
2/26/2004
12/30/2014
M
PHP
PX_LAST
2.033
1.742
1.754
1.9
1.92
1.753
2
2.255
1.399
1.923
2.044
0.922
0.754
0.409
1.077
1.573
1.422
2.037
2.016
0.454
133
3/29/2013
2/28/2013
1/31/2013
12/31/2012
11/30/2012
10/31/2012
9/28/2012
8/31/2012
7/31/2012
6/29/2012
5/31/2012
4/30/2012
3/30/2012
2/29/2012
1/31/2012
12/30/2011
11/30/2011
10/31/2011
9/30/2011
8/31/2011
7/29/2011
6/30/2011
5/31/2011
4/29/2011
3/31/2011
2/28/2011
1/31/2011
12/31/2010
11/30/2010
10/29/2010
9/30/2010
8/31/2010
7/30/2010
6/30/2010
5/31/2010
0.25
0.35
0.151
0.3
0.611
0.3
0.625
1.382
1.84
2.195
2.2
2.15
2.3
1.889
1.625
1.375
2.165
1.115
2.745
0.951
2.425
2.852
2.189
0.607
1.042
1.65
3.2
1.195
1.5
3.749
4.103
4.1
4.066
3.951
4.15
3/29/2013
2/28/2013
1/31/2013
12/31/2012
11/30/2012
10/31/2012
9/28/2012
8/31/2012
7/31/2012
6/29/2012
5/31/2012
4/30/2012
3/30/2012
2/29/2012
1/31/2012
12/30/2011
11/30/2011
10/31/2011
9/30/2011
8/31/2011
7/29/2011
6/30/2011
5/31/2011
4/29/2011
3/31/2011
2/28/2011
1/31/2011
12/31/2010
11/30/2010
10/29/2010
9/30/2010
8/31/2010
7/30/2010
6/30/2010
5/31/2010
0.321
0.35
0.387
0.575
0.646
0.488
0.973
1.669
2.091
2.277
2.321
2.162
2.313
2.31
1.786
1.536
1.51
1.445
2.039
0.992
2.63
2.982
2.376
0.882
1.215
2.062
3.218
1.465
1.82
4.055
4.313
4.306
4.249
4.226
4.332
3/29/2013
2/28/2013
1/31/2013
12/31/2012
11/30/2012
10/31/2012
9/28/2012
8/31/2012
7/31/2012
6/29/2012
5/31/2012
4/30/2012
3/30/2012
2/29/2012
1/31/2012
12/30/2011
11/30/2011
10/31/2011
9/30/2011
8/31/2011
7/29/2011
6/30/2011
5/31/2011
4/29/2011
3/31/2011
2/28/2011
1/31/2011
12/31/2010
11/30/2010
10/29/2010
9/30/2010
8/31/2010
7/30/2010
6/30/2010
5/31/2010
0.822
1.034
1.245
0.929
0.754
0.83
1.475
2.114
2.297
2.457
2.579
2.556
2.999
2.563
2.232
1.678
1.613
1.607
1.531
1.576
3.1
3.131
2.809
2.18
2.305
3.34
3.807
2.548
2.555
4.129
4.568
4.54
4.609
4.607
4.625
134
4/30/2010
3/31/2010
2/26/2010
1/29/2010
12/31/2009
11/30/2009
10/30/2009
9/30/2009
8/31/2009
7/31/2009
6/30/2009
5/29/2009
4/30/2009
3/31/2009
2/27/2009
1/30/2009
12/31/2008
11/28/2008
10/31/2008
9/30/2008
8/29/2008
7/31/2008
6/30/2008
5/30/2008
4/30/2008
3/31/2008
2/29/2008
1/31/2008
12/31/2007
11/30/2007
10/31/2007
9/28/2007
8/31/2007
7/31/2007
6/29/2007
4.056
3.9
4.015
3.805
4.067
3.647
4.005
4.052
3.751
3.688
4.319
4.355
4.353
4.293
4.556
4.282
5.626
6.375
6.75
6.5
6.185
6.082
5.116
6.061
5.087
4.375
4.6
4
4.22
4.022
4
4.062
4.525
4.25
4.66
4/30/2010
3/31/2010
2/26/2010
1/29/2010
12/31/2009
11/30/2009
10/30/2009
9/30/2009
8/31/2009
7/31/2009
6/30/2009
5/29/2009
4/30/2009
3/31/2009
2/27/2009
1/30/2009
12/31/2008
11/28/2008
10/31/2008
9/30/2008
8/29/2008
7/31/2008
6/30/2008
5/30/2008
4/30/2008
3/31/2008
2/29/2008
1/31/2008
12/31/2007
11/30/2007
10/31/2007
9/28/2007
8/31/2007
7/31/2007
6/29/2007
4.16
4.028
4.139
4.243
4.314
4.142
4.191
4.17
3.997
3.828
4.567
4.552
4.586
4.462
4.777
4.511
6.002
6.426
6.971
6.222
6.781
6.049
5.558
5.842
6.172
5.129
5.424
4.819
4.835
4.844
4.733
4.813
5.503
4.944
4.784
4/30/2010
3/31/2010
2/26/2010
1/29/2010
12/31/2009
11/30/2009
10/30/2009
9/30/2009
8/31/2009
7/31/2009
6/30/2009
5/29/2009
4/30/2009
3/31/2009
2/27/2009
1/30/2009
12/31/2008
11/28/2008
10/31/2008
9/30/2008
8/29/2008
7/31/2008
6/30/2008
5/30/2008
4/30/2008
3/31/2008
2/29/2008
1/31/2008
12/31/2007
11/30/2007
10/31/2007
9/28/2007
8/31/2007
7/31/2007
6/29/2007
4.514
4.414
4.393
4.773
4.791
4.53
4.454
4.399
4.434
4.252
4.792
4.665
4.757
4.787
4.943
4.637
6.083
6.839
7.227
6.503
6.657
7.269
6.709
6.824
6.595
5.521
5.906
5.21
5.595
5.652
5.72
5.717
5.742
5.716
5.296
135
5/31/2007
4/30/2007
3/30/2007
2/28/2007
1/31/2007
12/29/2006
11/30/2006
10/31/2006
9/29/2006
8/31/2006
7/31/2006
6/30/2006
5/31/2006
4/28/2006
3/31/2006
2/28/2006
1/31/2006
12/30/2005
11/30/2005
10/31/2005
9/30/2005
8/31/2005
7/29/2005
6/30/2005
5/31/2005
4/29/2005
3/31/2005
2/28/2005
1/31/2005
12/31/2004
11/30/2004
10/29/2004
9/30/2004
8/31/2004
7/30/2004
4.567
3
4.023
3.538
3.643
4.885
5.212
5.725
5.724
5.917
6.332
8.906
5.736
5.058
5.389
5.756
5.732
7.769
5.878
6.265
6.259
6.08
6.041
6.216
5.946
6.591
6.694
7.497
8.008
8.084
8.002
7.978
7.821
7.561
7.33
5/31/2007
4/30/2007
3/30/2007
2/28/2007
1/31/2007
12/29/2006
11/30/2006
10/31/2006
9/29/2006
8/31/2006
7/31/2006
6/30/2006
5/31/2006
4/28/2006
3/31/2006
2/28/2006
1/31/2006
12/30/2005
11/30/2005
10/31/2005
9/30/2005
8/31/2005
7/29/2005
6/30/2005
5/31/2005
4/29/2005
3/31/2005
2/28/2005
1/31/2005
12/31/2004
11/30/2004
10/29/2004
9/30/2004
8/31/2004
7/30/2004
4.1
3.839
4.307
3.926
4.271
4.885
5.219
6.238
6.282
6.383
6.883
7.161
6.173
5.499
8.692
6.359
6.329
8.295
7.64
7.953
8.05
7.635
7.413
6.983
6.87
7.659
7.789
7.497
8.008
9.17
8.916
9.107
8.605
8.428
8.258
5/31/2007
4/30/2007
3/30/2007
2/28/2007
1/31/2007
12/29/2006
11/30/2006
10/31/2006
9/29/2006
8/31/2006
7/31/2006
6/30/2006
5/31/2006
4/28/2006
3/31/2006
2/28/2006
1/31/2006
12/30/2005
11/30/2005
10/31/2005
9/30/2005
8/31/2005
7/29/2005
6/30/2005
5/31/2005
4/29/2005
3/31/2005
2/28/2005
1/31/2005
12/31/2004
11/30/2004
10/29/2004
9/30/2004
8/31/2004
7/30/2004
5.131
5.029
4.763
4.382
4.572
5.23
5.366
6.798
6.652
7.322
7.371
7.794
6.97
5.935
6.647
7.315
7.304
8.236
8.175
8.99
9.059
8.65
8.409
8.193
7.99
8.559
8.752
8.345
8.682
10.081
9.803
9.715
9.718
9.801
9.386
136
6/30/2004
5/31/2004
4/30/2004
3/31/2004
2/27/2004
7.437
7.141
7.126
7.994
6.483
6/30/2004
5/31/2004
4/30/2004
3/31/2004
2/27/2004
PHP Philippine
Government Zero
Coupon Yield 2
Year
Security
Start Date
End Date
Period
Currency
Date
11/30/2014
10/31/2014
9/30/2014
8/29/2014
7/31/2014
6/30/2014
5/30/2014
4/30/2014
3/31/2014
2/28/2014
1/31/2014
12/31/2013
11/29/2013
10/31/2013
9/30/2013
8/30/2013
7/31/2013
6/28/2013
I10502Y Index
2/26/2004
12/30/2014
M
PHP
PX_LAST
2.508
2.321
2.145
2.455
2.497
2.378
2.346
2.727
2.404
2.247
2.705
2.151
1.925
1.953
2.045
2.647
2.267
2.553
8.603
8.505
8.093
8.742
7.925
6/30/2004
5/31/2004
4/30/2004
3/31/2004
2/27/2004
PHP Philippine
Government Zero
Coupon Yield 3
Year
Security
Start Date
End Date
Period
Currency
Date
11/30/2014
10/31/2014
9/30/2014
8/29/2014
7/31/2014
6/30/2014
5/30/2014
4/30/2014
3/31/2014
2/28/2014
1/31/2014
12/31/2013
11/29/2013
10/31/2013
9/30/2013
8/30/2013
7/31/2013
6/28/2013
I10503Y Index
2/26/2004
12/30/2014
M
PHP
PX_LAST
2.829
2.442
2.672
2.66
2.751
2.685
2.671
2.954
2.932
2.663
2.935
2.264
2.111
2.021
2.356
2.438
2.135
2.883
9.613
9.125
8.835
9.647
9.182
PHP Philippine
Government Zero
Coupon Yield 5
Year
Security
Start Date
End Date
Period
Currency
Date
11/30/2014
10/31/2014
9/30/2014
8/29/2014
7/31/2014
6/30/2014
5/30/2014
4/30/2014
3/31/2014
2/28/2014
1/31/2014
12/31/2013
11/29/2013
10/31/2013
9/30/2013
8/30/2013
7/31/2013
6/28/2013
I10505Y Index
2/26/2004
12/30/2014
M
PHP
PX_LAST
3.331
3.599
4.153
3.873
3.596
3.606
3.337
3.901
3.463
3.593
3.414
3
2.786
2.898
3.115
2.841
2.504
2.875
137
5/31/2013
4/30/2013
3/29/2013
2/28/2013
1/31/2013
12/31/2012
11/30/2012
10/31/2012
9/28/2012
8/31/2012
7/31/2012
6/29/2012
5/31/2012
4/30/2012
3/30/2012
2/29/2012
1/31/2012
12/30/2011
11/30/2011
10/31/2011
9/30/2011
8/31/2011
7/29/2011
6/30/2011
5/31/2011
4/29/2011
3/31/2011
2/28/2011
1/31/2011
12/31/2010
11/30/2010
10/29/2010
9/30/2010
8/31/2010
7/30/2010
2.266
2.02
2.186
2.338
2.64
2.864
2.452
2.698
2.299
2.658
2.674
3.085
2.987
2.907
3.197
3.07
2.788
2.362
2.431
2.483
2.622
2.643
3.572
3.914
4.419
3.272
4.28
4.74
4.719
3.564
3.834
4.434
5.015
5.105
5.164
5/31/2013
4/30/2013
3/29/2013
2/28/2013
1/31/2013
12/31/2012
11/30/2012
10/31/2012
9/28/2012
8/31/2012
7/31/2012
6/29/2012
5/31/2012
4/30/2012
3/30/2012
2/29/2012
1/31/2012
12/30/2011
11/30/2011
10/31/2011
9/30/2011
8/31/2011
7/29/2011
6/30/2011
5/31/2011
4/29/2011
3/31/2011
2/28/2011
1/31/2011
12/31/2010
11/30/2010
10/29/2010
9/30/2010
8/31/2010
7/30/2010
2.289
1.978
2.537
2.791
3.206
3.285
3.413
3.683
3.281
3.828
3.609
3.654
3.588
3.749
3.613
3.509
3.758
3.432
3.517
3.757
3.308
3.224
3.963
4.486
5.082
4.643
5.197
5.433
4.951
4.237
4.337
4.534
5.098
5.123
5.373
5/31/2013
4/30/2013
3/29/2013
2/28/2013
1/31/2013
12/31/2012
11/30/2012
10/31/2012
9/28/2012
8/31/2012
7/31/2012
6/29/2012
5/31/2012
4/30/2012
3/30/2012
2/29/2012
1/31/2012
12/30/2011
11/30/2011
10/31/2011
9/30/2011
8/31/2011
7/29/2011
6/30/2011
5/31/2011
4/29/2011
3/31/2011
2/28/2011
1/31/2011
12/31/2010
11/30/2010
10/29/2010
9/30/2010
8/31/2010
7/30/2010
2.163
2.448
2.974
3.318
3.459
3.798
3.844
4.323
4.524
4.558
4.617
4.883
4.975
4.888
4.606
4.406
4.403
4.367
4.981
4.764
5.25
4.598
4.947
5.129
5.436
5.03
5.887
6.486
5.486
4.926
4.836
4.782
5.397
5.585
6.328
138
6/30/2010
5/31/2010
4/30/2010
3/31/2010
2/26/2010
1/29/2010
12/31/2009
11/30/2009
10/30/2009
9/30/2009
8/31/2009
7/31/2009
6/30/2009
5/29/2009
4/30/2009
3/31/2009
2/27/2009
1/30/2009
12/31/2008
11/28/2008
10/31/2008
9/30/2008
8/29/2008
7/31/2008
6/30/2008
5/30/2008
4/30/2008
3/31/2008
2/29/2008
1/31/2008
12/31/2007
11/30/2007
10/31/2007
9/28/2007
8/31/2007
5.208
5.195
4.898
4.848
4.672
5.019
5.352
4.672
4.658
4.795
4.743
4.722
5.296
4.941
4.984
5.232
5.405
5.561
6.592
7.674
7.672
7.464
7.163
7.137
7.146
7.679
7.528
6.202
6.099
5.43
5.713
6.22
6.243
6.265
6.581
6/30/2010
5/31/2010
4/30/2010
3/31/2010
2/26/2010
1/29/2010
12/31/2009
11/30/2009
10/30/2009
9/30/2009
8/31/2009
7/31/2009
6/30/2009
5/29/2009
4/30/2009
3/31/2009
2/27/2009
1/30/2009
12/31/2008
11/28/2008
10/31/2008
9/30/2008
8/29/2008
7/31/2008
6/30/2008
5/30/2008
4/30/2008
3/31/2008
2/29/2008
1/31/2008
12/31/2007
11/30/2007
10/31/2007
9/28/2007
8/31/2007
5.356
5.362
5.45
5.181
5.423
5.419
5.673
5.38
5.436
5.261
5.421
5.222
5.504
5.151
5.395
5.881
5.772
5.927
6.252
7.98
7.777
7.009
7.038
7.831
8.225
8.27
7.663
6.347
6.371
5.487
5.698
6.314
6.39
6.427
7.031
6/30/2010
5/31/2010
4/30/2010
3/31/2010
2/26/2010
1/29/2010
12/31/2009
11/30/2009
10/30/2009
9/30/2009
8/31/2009
7/31/2009
6/30/2009
5/29/2009
4/30/2009
3/31/2009
2/27/2009
1/30/2009
12/31/2008
11/28/2008
10/31/2008
9/30/2008
8/29/2008
7/31/2008
6/30/2008
5/30/2008
4/30/2008
3/31/2008
2/29/2008
1/31/2008
12/31/2007
11/30/2007
10/31/2007
9/28/2007
8/31/2007
6.522
6.61
6.67
6.509
6.483
6.624
6.553
6.542
6.567
6.432
6.546
6.49
6.526
6.261
6.426
6.545
6.541
6.295
6.704
8.54
7.864
7.673
7.354
8.526
8.955
8.631
8.153
6.56
6.554
5.603
5.814
6.48
6.552
6.661
7.305
139
7/31/2007
6/29/2007
5/31/2007
4/30/2007
3/30/2007
2/28/2007
1/31/2007
12/29/2006
11/30/2006
10/31/2006
9/29/2006
8/31/2006
7/31/2006
6/30/2006
5/31/2006
4/28/2006
3/31/2006
2/28/2006
1/31/2006
12/30/2005
11/30/2005
10/31/2005
9/30/2005
8/31/2005
7/29/2005
6/30/2005
5/31/2005
4/29/2005
3/31/2005
2/28/2005
1/31/2005
12/31/2004
11/30/2004
10/29/2004
9/30/2004
6.781
6.158
5.864
5.614
5.295
5.173
5.418
5.56
5.793
7.003
7.489
7.78
8.359
8.551
10.242
6.314
7.079
8.067
8.349
10.038
9.27
9.786
9.7
9.586
9.582
9.343
9.289
9.784
10.091
10.106
10.077
11.532
11
10.425
10.94
7/31/2007
6/29/2007
5/31/2007
4/30/2007
3/30/2007
2/28/2007
1/31/2007
12/29/2006
11/30/2006
10/31/2006
9/29/2006
8/31/2006
7/31/2006
6/30/2006
5/31/2006
4/28/2006
3/31/2006
2/28/2006
1/31/2006
12/30/2005
11/30/2005
10/31/2005
9/30/2005
8/31/2005
7/29/2005
6/30/2005
5/31/2005
4/29/2005
3/31/2005
2/28/2005
1/31/2005
12/31/2004
11/30/2004
10/29/2004
9/30/2004
6.907
6.555
5.913
5.784
5.541
5.355
5.671
5.707
5.912
7.073
7.491
10.724
8.681
9.205
8.52
6.478
7.133
8.232
8.601
9.549
9.736
10.304
10.221
10.22
10.144
9.899
9.907
10.703
10.724
10.731
10.404
11.951
11.53
11.586
11.422
7/31/2007
6/29/2007
5/31/2007
4/30/2007
3/30/2007
2/28/2007
1/31/2007
12/29/2006
11/30/2006
10/31/2006
9/29/2006
8/31/2006
7/31/2006
6/30/2006
5/31/2006
4/28/2006
3/31/2006
2/28/2006
1/31/2006
12/30/2005
11/30/2005
10/31/2005
9/30/2005
8/31/2005
7/29/2005
6/30/2005
5/31/2005
4/29/2005
3/31/2005
2/28/2005
1/31/2005
12/31/2004
11/30/2004
10/29/2004
9/30/2004
7.175
6.92
6.152
6.149
6.036
5.743
6.123
5.89
6.094
7.259
7.687
8.137
9.248
9.766
8.772
6.745
7.289
11.418
8.674
9.705
10.13
11.05
11.14
11.138
11.128
11.268
11.052
11.659
11.472
11.592
11.436
13.124
12.846
12.837
12.526
140
8/31/2004
7/30/2004
6/30/2004
5/31/2004
4/30/2004
3/31/2004
2/27/2004
10.73
10.29
10.486
10.261
9.878
10.795
10.869
8/31/2004
7/30/2004
6/30/2004
5/31/2004
4/30/2004
3/31/2004
2/27/2004
11.611
11.033
11.223
11.011
10.478
11.555
11.518
8/31/2004
7/30/2004
6/30/2004
5/31/2004
4/30/2004
3/31/2004
2/27/2004
12.818
11.51
12.394
12.045
11.015
12.296
12.501
PHP Philippine Government Zero Coupon Yield 10 Year
Security Index
Date
11/30/2014
10/31/2014
9/30/2014
8/29/2014
7/31/2014
6/30/2014
5/30/2014
4/30/2014
3/31/2014
2/28/2014
1/31/2014
12/31/2013
11/29/2013
10/31/2013
9/30/2013
8/30/2013
7/31/2013
6/28/2013
5/31/2013
4/30/2013
3/29/2013
2/28/2013
PX_LAST
3.851
4.157
4.361
4.306
4.195
4.043
4.118
4.36
4.454
4.182
4.296
3.73
3.544
3.499
3.608
3.498
3.375
3.856
3.369
2.905
3.024
3.607
I10510Y Index
Date
1/31/2013
12/31/2012
11/30/2012
10/31/2012
9/28/2012
8/31/2012
7/31/2012
6/29/2012
5/31/2012
4/30/2012
3/30/2012
2/29/2012
1/31/2012
12/30/2011
11/30/2011
10/31/2011
9/30/2011
8/31/2011
7/29/2011
6/30/2011
5/31/2011
4/29/2011
PX_LAST
4.072
4.299
4.604
4.877
4.841
5.038
5.12
5.529
5.838
5.523
5.599
5.179
5.393
5.355
6.044
5.973
6.346
6.246
6.555
6.77
6.624
6.518
Date
3/31/2011
2/28/2011
1/31/2011
12/31/2010
11/30/2010
10/29/2010
9/30/2010
8/31/2010
7/30/2010
6/30/2010
5/31/2010
4/30/2010
3/31/2010
2/26/2010
1/29/2010
12/31/2009
11/30/2009
10/30/2009
9/30/2009
8/31/2009
7/31/2009
6/30/2009
PX_LAST
7.293
7.551
6.563
6.326
6.17
5.913
6.346
7.042
8.168
8.288
8.568
8.628
8.735
8.447
8.515
8.654
8.567
8.627
8.762
8.514
8.538
8.774
Start Date
Period
Date
5/29/2009
4/30/2009
3/31/2009
2/27/2009
1/30/2009
12/31/2008
11/28/2008
10/31/2008
9/30/2008
8/29/2008
7/31/2008
6/30/2008
5/30/2008
4/30/2008
3/31/2008
2/29/2008
1/31/2008
12/31/2007
11/30/2007
10/31/2007
9/28/2007
8/31/2007
2/26/2004
M
PX_LAST
8.272
8.953
8.509
8.652
7.957
7.614
9.138
10.202
8.502
8.535
10.236
9.69
9.302
8.621
7.546
7.254
6.136
6.723
7.242
7.281
7.372
8.123
Date
7/31/2007
6/29/2007
5/31/2007
4/30/2007
3/30/2007
2/28/2007
1/31/2007
12/29/2006
11/30/2006
10/31/2006
9/29/2006
8/31/2006
7/31/2006
6/30/2006
5/31/2006
4/28/2006
3/31/2006
2/28/2006
1/31/2006
12/30/2005
11/30/2005
10/31/2005
End Date
Currency
PX_LAST
7.456
7.195
7.298
7.495
7.396
7.197
6.991
6.498
6.641
7.883
8.549
9.171
10.57
10.692
10.396
7.35
7.704
8.682
9.838
10.061
11.915
12.672
12/30/2014
PHP
Date
9/30/2005
8/31/2005
7/29/2005
6/30/2005
5/31/2005
4/29/2005
3/31/2005
2/28/2005
1/31/2005
12/31/2004
11/30/2004
10/29/2004
9/30/2004
8/31/2004
7/30/2004
6/30/2004
5/31/2004
4/30/2004
3/31/2004
2/27/2004
PX_LAST
12.69
12.823
13.118
12.71
12.628
12.631
12.932
13.278
13.214
14.533
14.431
14.283
13.764
13.863
13.316
13.025
13.06
12.524
12.991
13.471
141
APPENDIX B:
DATA FOR TWO-PERIOD CASE
m3
m6
m3m3
2005M11
5.87800
2005M12
7.76900
2006M01
5.73200
6.32900
-1.01850
2006M02
5.75600
6.35900
2006M03
5.38900
2006M04
m3m6
m6
y1
m6m6
m6y1
y1
y2
y1y1
y1y2
7.64000
7.64000
8.17500
8.17500
9.27000
8.29500
8.29500
8.23600
8.23600
10.03800
0.52600
6.32900
7.30400
-0.98300
-0.05900
7.30400
8.34900
-0.46600
1.80200
0.01200
0.59700
6.35900
7.31500
0.01500
0.97500
7.31500
8.06700
0.00550
1.04500
8.69200
-0.18350
0.60300
8.69200
6.64700
1.16650
0.95600
6.64700
7.07900
-0.33400
0.75200
5.05800
5.49900
-0.16550
3.30300
5.49900
5.93500
-1.59650
-2.04500
5.93500
6.31400
-0.35600
0.43200
2006M05
5.73600
6.17300
0.33900
0.44100
6.17300
6.97000
0.33700
0.43600
6.97000
10.24200
0.51750
0.37900
2006M06
8.90600
7.16100
1.58500
0.43700
7.16100
7.79400
0.49400
0.79700
7.79400
8.55100
0.41200
3.27200
2006M07
6.33200
6.88300
-1.28700
2006M08
5.91700
6.38300
-0.20750
-1.74500
6.88300
7.37100
-0.13900
0.63300
7.37100
8.35900
-0.21150
0.75700
0.55100
6.38300
7.32200
-0.25000
0.48800
7.32200
7.78000
-0.02450
0.98800
2006M09
5.72400
6.28200
-0.09650
0.46600
6.28200
6.65200
-0.05050
0.93900
6.65200
7.48900
-0.33500
0.45800
2006M10
5.72500
6.23800
0.00050
0.55800
6.23800
6.79800
-0.02200
0.37000
6.79800
7.00300
0.07300
0.83700
2006M11
5.21200
5.21900
-0.25650
0.51300
5.21900
5.36600
-0.50950
0.56000
5.36600
5.79300
-0.71600
0.20500
2006M12
4.88500
4.88500
-0.16350
0.00700
4.88500
5.23000
-0.16700
0.14700
5.23000
5.56000
-0.06800
0.42700
2007M01
3.64300
4.27100
-0.62100
0.00000
4.27100
4.57200
-0.30700
0.34500
4.57200
5.41800
-0.32900
0.33000
2007M02
3.53800
3.92600
-0.05250
0.62800
3.92600
4.38200
-0.17250
0.30100
4.38200
5.17300
-0.09500
0.84600
2007M03
4.02300
4.30700
0.24250
0.38800
4.30700
4.76300
0.19050
0.45600
4.76300
5.29500
0.19050
0.79100
2007M04
3.00000
3.83900
-0.51150
0.28400
3.83900
5.02900
-0.23400
0.45600
5.02900
5.61400
0.13300
0.53200
2007M05
4.56700
4.10000
0.78350
0.83900
4.10000
5.13100
0.13050
1.19000
5.13100
5.86400
0.05100
0.58500
2007M06
4.66000
4.78400
0.04650
-0.46700
4.78400
5.29600
0.34200
1.03100
5.29600
6.15800
0.08250
0.73300
2007M07
4.25000
4.94400
-0.20500
0.12400
4.94400
5.71600
0.08000
0.51200
5.71600
6.78100
0.21000
0.86200
2007M08
4.52500
5.50300
0.13750
0.69400
5.50300
5.74200
0.27950
0.77200
5.74200
6.58100
0.01300
1.06500
2007M09
4.06200
4.81300
-0.23150
0.97800
4.81300
5.71700
-0.34500
0.23900
5.71700
6.26500
-0.01250
0.83900
2007M10
4.00000
4.73300
-0.03100
0.75100
4.73300
5.72000
-0.04000
0.90400
5.72000
6.24300
0.00150
0.54800
2007M11
4.02200
4.84400
0.01100
0.73300
4.84400
5.65200
0.05550
0.98700
5.65200
6.22000
-0.03400
0.52300
2007M12
4.22000
4.83500
0.09900
0.82200
4.83500
5.59500
-0.00450
0.80800
5.59500
5.71300
-0.02850
0.56800
142
2008M01
4.00000
4.81900
-0.11000
0.61500
4.81900
5.21000
-0.00800
0.76000
5.21000
5.43000
-0.19250
0.11800
2008M02
4.60000
5.42400
0.30000
0.81900
5.42400
5.90600
0.30250
0.39100
5.90600
6.09900
0.34800
0.22000
2008M03
4.37500
5.12900
-0.11250
0.82400
5.12900
5.52100
-0.14750
0.48200
5.52100
6.20200
-0.19250
0.19300
2008M04
5.08700
6.17200
0.35600
0.75400
6.17200
6.59500
0.52150
0.39200
6.59500
7.52800
0.53700
0.68100
2008M05
6.06100
5.84200
0.48700
1.08500
5.84200
6.82400
-0.16500
0.42300
6.82400
7.67900
0.11450
0.93300
2008M06
5.11600
5.55800
-0.47250
-0.21900
5.55800
6.70900
-0.14200
0.98200
6.70900
7.14600
-0.05750
0.85500
2008M07
6.08200
6.04900
0.48300
0.44200
6.04900
7.26900
0.24550
1.15100
7.26900
7.13700
0.28000
0.43700
2008M08
6.18500
6.78100
0.05150
-0.03300
6.78100
6.65700
0.36600
1.22000
6.65700
7.16300
-0.30600
-0.13200
2008M09
6.50000
6.22200
0.15750
0.59600
6.22200
6.50300
-0.27950
-0.12400
6.50300
7.46400
-0.07700
0.50600
2008M10
6.75000
6.97100
0.12500
-0.27800
6.97100
7.22700
0.37450
0.28100
7.22700
7.67200
0.36200
0.96100
2008M11
6.37500
6.42600
-0.18750
0.22100
6.42600
6.83900
-0.27250
0.25600
6.83900
7.67400
-0.19400
0.44500
2008M12
5.62600
6.00200
-0.37450
0.05100
6.00200
6.08300
-0.21200
0.41300
6.08300
6.59200
-0.37800
0.83500
2009M01
4.28200
4.51100
-0.67200
0.37600
4.51100
4.63700
-0.74550
0.08100
4.63700
5.56100
-0.72300
0.50900
2009M02
4.55600
4.77700
0.13700
0.22900
4.77700
4.94300
0.13300
0.12600
4.94300
5.40500
0.15300
0.92400
2009M03
4.29300
4.46200
-0.13150
0.22100
4.46200
4.78700
-0.15750
0.16600
4.78700
5.23200
-0.07800
0.46200
2009M04
4.35300
4.58600
0.03000
0.16900
4.58600
4.75700
0.06200
0.32500
4.75700
4.98400
-0.01500
0.44500
2009M05
4.35500
4.55200
0.00100
0.23300
4.55200
4.66500
-0.01700
0.17100
4.66500
4.94100
-0.04600
0.22700
2009M06
4.31900
4.56700
-0.01800
0.19700
4.56700
4.79200
0.00750
0.11300
4.79200
5.29600
0.06350
0.27600
2009M07
3.68800
3.82800
-0.31550
0.24800
3.82800
4.25200
-0.36950
0.22500
4.25200
4.72200
-0.27000
0.50400
2009M08
3.75100
3.99700
0.03150
0.14000
3.99700
4.43400
0.08450
0.42400
4.43400
4.74300
0.09100
0.47000
2009M09
4.05200
4.17000
0.15050
0.24600
4.17000
4.39900
0.08650
0.43700
4.39900
4.79500
-0.01750
0.30900
2009M10
4.00500
4.19100
-0.02350
0.11800
4.19100
4.45400
0.01050
0.22900
4.45400
4.65800
0.02750
0.39600
2009M11
3.64700
4.14200
-0.17900
0.18600
4.14200
4.53000
-0.02450
0.26300
4.53000
4.67200
0.03800
0.20400
2009M12
4.06700
4.31400
0.21000
0.49500
4.31400
4.79100
0.08600
0.38800
4.79100
5.35200
0.13050
0.14200
2010M01
3.80500
4.24300
-0.13100
0.24700
4.24300
4.77300
-0.03550
0.47700
4.77300
5.01900
-0.00900
0.56100
2010M02
4.01500
4.13900
0.10500
0.43800
4.13900
4.39300
-0.05200
0.53000
4.39300
4.67200
-0.19000
0.24600
2010M03
3.90000
4.02800
-0.05750
0.12400
4.02800
4.41400
-0.05550
0.25400
4.41400
4.84800
0.01050
0.27900
2010M04
4.05600
4.16000
0.07800
0.12800
4.16000
4.51400
0.06600
0.38600
4.51400
4.89800
0.05000
0.43400
2010M05
4.15000
4.33200
0.04700
0.10400
4.33200
4.62500
0.08600
0.35400
4.62500
5.19500
0.05550
0.38400
2010M06
3.95100
4.22600
-0.09950
0.18200
4.22600
4.60700
-0.05300
0.29300
4.60700
5.20800
-0.00900
0.57000
143
2010M07
4.06600
4.24900
0.05750
0.27500
4.24900
4.60900
0.01150
0.38100
4.60900
5.16400
0.00100
0.60100
2010M08
4.10000
4.30600
0.01700
0.18300
4.30600
4.54000
0.02850
0.36000
4.54000
5.10500
-0.03450
0.55500
2010M09
4.10300
4.31300
0.00150
0.20600
4.31300
4.56800
0.00350
0.23400
4.56800
5.01500
0.01400
0.56500
2010M10
3.74900
4.05500
-0.17700
0.21000
4.05500
4.12900
-0.12900
0.25500
4.12900
4.43400
-0.21950
0.44700
2010M11
1.50000
1.82000
-1.12450
0.30600
1.82000
2.55500
-1.11750
0.07400
2.55500
3.83400
-0.78700
0.30500
2010M12
1.19500
1.46500
-0.15250
0.32000
1.46500
2.54800
-0.17750
0.73500
2.54800
3.56400
-0.00350
1.27900
2011M01
3.20000
3.21800
1.00250
0.27000
3.21800
3.80700
0.87650
1.08300
3.80700
4.71900
0.62950
1.01600
2011M02
1.65000
2.06200
-0.77500
0.01800
2.06200
3.34000
-0.57800
0.58900
3.34000
4.74000
-0.23350
0.91200
2011M03
1.04200
1.21500
-0.30400
0.41200
1.21500
2.30500
-0.42350
1.27800
2.30500
4.28000
-0.51750
1.40000
2011M04
0.60700
0.88200
-0.21750
0.17300
0.88200
2.18000
-0.16650
1.09000
2.18000
3.27200
-0.06250
1.97500
2011M05
2.18900
2.37600
0.79100
0.27500
2.37600
2.80900
0.74700
1.29800
2.80900
4.41900
0.31450
1.09200
2011M06
2.85200
2.98200
0.33150
0.18700
2.98200
3.13100
0.30300
0.43300
3.13100
3.91400
0.16100
1.61000
2011M07
2.42500
2.63000
-0.21350
0.13000
2.63000
3.10000
-0.17600
0.14900
3.10000
3.57200
-0.01550
0.78300
2011M08
0.95100
0.99200
-0.73700
0.20500
0.99200
1.57600
-0.81900
0.47000
1.57600
2.64300
-0.76200
0.47200
2011M09
2.74500
2.03900
0.89700
0.04100
2.03900
1.53100
0.52350
0.58400
1.53100
2.62200
-0.02250
1.06700
2011M10
1.11500
1.44500
-0.81500
-0.70600
1.44500
1.60700
-0.29700
-0.50800
1.60700
2.48300
0.03800
1.09100
2011M11
2.16500
1.51000
0.52500
0.33000
1.51000
1.61300
0.03250
0.16200
1.61300
2.43100
0.00300
0.87600
2011M12
1.37500
1.53600
-0.39500
-0.65500
1.53600
1.67800
0.01300
0.10300
1.67800
2.36200
0.03250
0.81800
2012M01
1.62500
1.78600
0.12500
0.16100
1.78600
2.23200
0.12500
0.14200
2.23200
2.78800
0.27700
0.68400
2012M02
1.88900
2.31000
0.13200
0.16100
2.31000
2.56300
0.26200
0.44600
2.56300
3.07000
0.16550
0.55600
2012M03
2.30000
2.31300
0.20550
0.42100
2.31300
2.99900
0.00150
0.25300
2.99900
3.19700
0.21800
0.50700
2012M04
2.15000
2.16200
-0.07500
0.01300
2.16200
2.55600
-0.07550
0.68600
2.55600
2.90700
-0.22150
0.19800
2012M05
2.20000
2.32100
0.02500
0.01200
2.32100
2.57900
0.07950
0.39400
2.57900
2.98700
0.01150
0.35100
2012M06
2.19500
2.27700
-0.00250
0.12100
2.27700
2.45700
-0.02200
0.25800
2.45700
3.08500
-0.06100
0.40800
2012M07
1.84000
2.09100
-0.17750
0.08200
2.09100
2.29700
-0.09300
0.18000
2.29700
2.67400
-0.08000
0.62800
2012M08
1.38200
1.66900
-0.22900
0.25100
1.66900
2.11400
-0.21100
0.20600
2.11400
2.65800
-0.09150
0.37700
2012M09
0.62500
0.97300
-0.37850
0.28700
0.97300
1.47500
-0.34800
0.44500
1.47500
2.29900
-0.31950
0.54400
2012M10
0.30000
0.48800
-0.16250
0.34800
0.48800
0.83000
-0.24250
0.50200
0.83000
2.69800
-0.32250
0.82400
2012M11
0.61100
0.64600
0.15550
0.18800
0.64600
0.75400
0.07900
0.34200
0.75400
2.45200
-0.03800
1.86800
2012M12
0.30000
0.57500
-0.15550
0.03500
0.57500
0.92900
-0.03550
0.10800
0.92900
2.86400
0.08750
1.69800
144
2013M01
0.15100
0.38700
-0.07450
0.27500
0.38700
1.24500
-0.09400
0.35400
1.24500
2.64000
0.15800
1.93500
2013M02
0.35000
0.35000
0.09950
0.23600
0.35000
1.03400
-0.01850
0.85800
1.03400
2.33800
-0.10550
1.39500
2013M03
0.25000
0.32100
-0.05000
0.00000
0.32100
0.82200
-0.01450
0.68400
0.82200
2.18600
-0.10600
1.30400
2013M04
0.20000
0.30000
-0.02500
0.07100
0.30000
0.45400
-0.01050
0.50100
0.45400
2.02000
-0.18400
1.36400
2013M05
2.00000
2.02500
0.90000
0.10000
2.02500
2.01600
0.86250
0.15400
2.01600
2.26600
0.78100
1.56600
2013M06
1.75000
1.80200
-0.12500
0.02500
1.80200
2.03700
-0.11150
-0.00900
2.03700
2.55300
0.01050
0.25000
2013M07
1.04900
0.84700
-0.35050
0.05200
0.84700
1.42200
-0.47750
0.23500
1.42200
2.26700
-0.30750
0.51600
2013M08
1.25000
1.35000
0.10050
-0.20200
1.35000
1.57300
0.25150
0.57500
1.57300
2.64700
0.07550
0.84500
2013M09
0.47600
0.89600
-0.38700
0.10000
0.89600
1.07700
-0.22700
0.22300
1.07700
2.04500
-0.24800
1.07400
2013M10
0.09500
0.18400
-0.19050
0.42000
0.18400
0.40900
-0.35600
0.18100
0.40900
1.95300
-0.33400
0.96800
2013M11
0.17500
0.29900
0.04000
0.08900
0.29900
0.75400
0.05750
0.22500
0.75400
1.92500
0.17250
1.54400
2013M12
0.32500
0.42500
0.07500
0.12400
0.42500
0.92200
0.06300
0.45500
0.92200
2.15100
0.08400
1.17100
2014M01
1.20000
1.94700
0.43750
0.10000
1.94700
2.04400
0.76100
0.49700
2.04400
2.70500
0.56100
1.22900
2014M02
1.00000
1.48100
-0.10000
0.74700
1.48100
1.92300
-0.23300
0.09700
1.92300
2.24700
-0.06050
0.66100
2014M03
1.50000
1.32100
0.25000
0.48100
1.32100
1.39900
-0.08000
0.44200
1.39900
2.40400
-0.26200
0.32400
2014M04
1.30000
1.96000
-0.10000
-0.17900
1.96000
2.25500
0.31950
0.07800
2.25500
2.72700
0.42800
1.00500
2014M05
1.07000
1.78900
-0.11500
0.66000
1.78900
2.00000
-0.08550
0.29500
2.00000
2.34600
-0.12750
0.47200
2014M06
1.15000
1.29000
0.04000
0.71900
1.29000
1.75300
-0.24950
0.21100
1.75300
2.37800
-0.12350
0.34600
2014M07
1.37500
1.66300
0.11250
0.14000
1.66300
1.92000
0.18650
0.46300
1.92000
2.49700
0.08350
0.62500
2014M08
1.25000
1.61300
-0.06250
0.28800
1.61300
1.90000
-0.02500
0.25700
1.90000
2.45500
-0.01000
0.57700
2014M09
1.50000
1.73700
0.12500
0.36300
1.73700
1.75400
0.06200
0.28700
1.75400
2.14500
-0.07300
0.55500
2014M10
1.40000
1.46400
-0.05000
0.23700
1.46400
1.74200
-0.13650
0.01700
1.74200
2.32100
-0.00600
0.39100
2014M11
1.50000
1.73800
0.05000
0.06400
1.73800
2.03300
0.13700
0.27800
2.03300
2.50800
0.14550
0.57900
where:
m3 = 3-month bond yield, m6 = 6-month bond yield, y1 = 1-year bond yield, y2 = 2-year bond yield
m3m3 = average change in 3-month bond yield, m6m6 = average change in 6-month bond yield, y1y1 = average change in 1-year bond yield
m3m6 = 3-month & 6-month bond spread, m6y1= 6-month & 1-year bond spread, y1y2 = 1-year & 2-year bond spread
145
APPENDIX C:
DATA FOR N-PERIOD CASE
y1
y3
y3y3
2005M11
8.17500
2005M12
8.23600
2006M01
7.30400
8.60100
-2.84400
2006M02
7.31500
8.23200
2006M03
6.64700
2006M04
y1y3
y1
y5
y5y5
9.73600
8.17500
9.54900
8.23600
1.31300
7.30400
8.67400
-5.15500
-1.10700
1.29700
7.31500
11.41800
7.13300
-3.29700
0.91700
6.64700
5.93500
6.47800
-1.96500
0.48600
2006M05
6.97000
8.52000
6.12600
2006M06
7.79400
9.20500
2006M07
7.37100
2006M08
7.32200
2006M09
6.65200
2006M10
y1y5
y1
y10
y10y10
y1y10
10.13000
8.17500
11.91500
9.70500
8.23600
10.06100
1.46900
7.30400
9.83800
-2.23000
1.82500
13.72000
1.37000
7.31500
8.68200
-11.56000
2.53400
7.28900
-20.64500
4.10300
6.64700
7.70400
-9.78000
1.36700
5.93500
6.74500
-2.72000
0.64200
5.93500
7.35000
-3.54000
1.05700
0.54300
6.97000
8.77200
10.13500
0.81000
6.97000
10.39600
30.46000
1.41500
2.05500
1.55000
7.79400
9.76600
4.97000
1.80200
7.79400
10.69200
2.96000
3.42600
8.68100
-1.57200
10.72400
6.12900
1.41100
7.37100
9.24800
-2.59000
1.97200
7.37100
10.57000
-1.22000
2.89800
1.31000
7.32200
8.13700
-5.55500
1.87700
7.32200
9.17100
-13.99000
3.19900
7.49100
-9.69900
3.40200
6.65200
7.68700
-2.25000
0.81500
6.65200
8.54900
-6.22000
1.84900
6.79800
7.07300
-1.25400
0.83900
6.79800
7.25900
-2.14000
1.03500
6.79800
7.88300
-6.66000
1.89700
2006M11
5.36600
5.91200
-3.48300
0.27500
5.36600
6.09400
-5.82500
0.46100
5.36600
6.64100
-12.42000
1.08500
2006M12
5.23000
5.70700
-0.61500
0.54600
5.23000
5.89000
-1.02000
0.72800
5.23000
6.49800
-1.43000
1.27500
2007M01
4.57200
5.67100
-0.10800
0.47700
4.57200
6.12300
1.16500
0.66000
4.57200
6.99100
4.93000
1.26800
2007M02
4.38200
5.35500
-0.94800
1.09900
4.38200
5.74300
-1.90000
1.55100
4.38200
7.19700
2.06000
2.41900
2007M03
4.76300
5.54100
0.55800
0.97300
4.76300
6.03600
1.46500
1.36100
4.76300
7.39600
1.99000
2.81500
2007M04
5.02900
5.78400
0.72900
0.77800
5.02900
6.14900
0.56500
1.27300
5.02900
7.49500
0.99000
2.63300
2007M05
5.13100
5.91300
0.38700
0.75500
5.13100
6.15200
0.01500
1.12000
5.13100
7.29800
-1.97000
2.46600
2007M06
5.29600
6.55500
1.92600
0.78200
5.29600
6.92000
3.84000
1.02100
5.29600
7.19500
-1.03000
2.16700
2007M07
5.71600
6.90700
1.05600
1.25900
5.71600
7.17500
1.27500
1.62400
5.71600
7.45600
2.61000
1.89900
2007M08
5.74200
7.03100
0.37200
1.19100
5.74200
7.30500
0.65000
1.45900
5.74200
8.12300
6.67000
1.74000
2007M09
5.71700
6.42700
-1.81200
1.28900
5.71700
6.66100
-3.22000
1.56300
5.71700
7.37200
-7.51000
2.38100
2007M10
5.72000
6.39000
-0.11100
0.71000
5.72000
6.55200
-0.54500
0.94400
5.72000
7.28100
-0.91000
1.65500
2007M11
5.65200
6.31400
-0.22800
0.67000
5.65200
6.48000
-0.36000
0.83200
5.65200
7.24200
-0.39000
1.56100
2007M12
5.59500
5.69800
-1.84800
0.66200
5.59500
5.81400
-3.33000
0.82800
5.59500
6.72300
-5.19000
1.59000
146
2008M01
5.21000
5.48700
-0.63300
0.10300
5.21000
5.60300
-1.05500
0.21900
5.21000
6.13600
-5.87000
1.12800
2008M02
5.90600
6.37100
2.65200
0.27700
5.90600
6.55400
4.75500
0.39300
5.90600
7.25400
11.18000
0.92600
2008M03
5.52100
6.34700
-0.07200
0.46500
5.52100
6.56000
0.03000
0.64800
5.52100
7.54600
2.92000
1.34800
2008M04
6.59500
7.66300
3.94800
0.82600
6.59500
8.15300
7.96500
1.03900
6.59500
8.62100
10.75000
2.02500
2008M05
6.82400
8.27000
1.82100
1.06800
6.82400
8.63100
2.39000
1.55800
6.82400
9.30200
6.81000
2.02600
2008M06
6.70900
8.22500
-0.13500
1.44600
6.70900
8.95500
1.62000
1.80700
6.70900
9.69000
3.88000
2.47800
2008M07
7.26900
7.83100
-1.18200
1.51600
7.26900
8.52600
-2.14500
2.24600
7.26900
10.23600
5.46000
2.98100
2008M08
6.65700
7.03800
-2.37900
0.56200
6.65700
7.35400
-5.86000
1.25700
6.65700
8.53500
-17.01000
2.96700
2008M09
6.50300
7.00900
-0.08700
0.38100
6.50300
7.67300
1.59500
0.69700
6.50300
8.50200
-0.33000
1.87800
2008M10
7.22700
7.77700
2.30400
0.50600
7.22700
7.86400
0.95500
1.17000
7.22700
10.20200
17.00000
1.99900
2008M11
6.83900
7.98000
0.60900
0.55000
6.83900
8.54000
3.38000
0.63700
6.83900
9.13800
-10.64000
2.97500
2008M12
6.08300
6.25200
-5.18400
1.14100
6.08300
6.70400
-9.18000
1.70100
6.08300
7.61400
-15.24000
2.29900
2009M01
4.63700
5.92700
-0.97500
0.16900
4.63700
6.29500
-2.04500
0.62100
4.63700
7.95700
3.43000
1.53100
2009M02
4.94300
5.77200
-0.46500
1.29000
4.94300
6.54100
1.23000
1.65800
4.94300
8.65200
6.95000
3.32000
2009M03
4.78700
5.88100
0.32700
0.82900
4.78700
6.54500
0.02000
1.59800
4.78700
8.50900
-1.43000
3.70900
2009M04
4.75700
5.39500
-1.45800
1.09400
4.75700
6.42600
-0.59500
1.75800
4.75700
8.95300
4.44000
3.72200
2009M05
4.66500
5.15100
-0.73200
0.63800
4.66500
6.26100
-0.82500
1.66900
4.66500
8.27200
-6.81000
4.19600
2009M06
4.79200
5.50400
1.05900
0.48600
4.79200
6.52600
1.32500
1.59600
4.79200
8.77400
5.02000
3.60700
2009M07
4.25200
5.22200
-0.84600
0.71200
4.25200
6.49000
-0.18000
1.73400
4.25200
8.53800
-2.36000
3.98200
2009M08
4.43400
5.42100
0.59700
0.97000
4.43400
6.54600
0.28000
2.23800
4.43400
8.51400
-0.24000
4.28600
2009M09
4.39900
5.26100
-0.48000
0.98700
4.39900
6.43200
-0.57000
2.11200
4.39900
8.76200
2.48000
4.08000
2009M10
4.45400
5.43600
0.52500
0.86200
4.45400
6.56700
0.67500
2.03300
4.45400
8.62700
-1.35000
4.36300
2009M11
4.53000
5.38000
-0.16800
0.98200
4.53000
6.54200
-0.12500
2.11300
4.53000
8.56700
-0.60000
4.17300
2009M12
4.79100
5.67300
0.87900
0.85000
4.79100
6.55300
0.05500
2.01200
4.79100
8.65400
0.87000
4.03700
2010M01
4.77300
5.41900
-0.76200
0.88200
4.77300
6.62400
0.35500
1.76200
4.77300
8.51500
-1.39000
3.86300
2010M02
4.39300
5.42300
0.01200
0.64600
4.39300
6.48300
-0.70500
1.85100
4.39300
8.44700
-0.68000
3.74200
2010M03
4.41400
5.18100
-0.72600
1.03000
4.41400
6.50900
0.13000
2.09000
4.41400
8.73500
2.88000
4.05400
2010M04
4.51400
5.45000
0.80700
0.76700
4.51400
6.67000
0.80500
2.09500
4.51400
8.62800
-1.07000
4.32100
2010M05
4.62500
5.36200
-0.26400
0.93600
4.62500
6.61000
-0.30000
2.15600
4.62500
8.56800
-0.60000
4.11400
2010M06
4.60700
5.35600
-0.01800
0.73700
4.60700
6.52200
-0.44000
1.98500
4.60700
8.28800
-2.80000
3.94300
147
2010M07
4.60900
5.37300
0.05100
0.74900
4.60900
6.32800
-0.97000
1.91500
4.60900
8.16800
-1.20000
3.68100
2010M08
4.54000
5.12300
-0.75000
0.76400
4.54000
5.58500
-3.71500
1.71900
4.54000
7.04200
-11.26000
3.55900
2010M09
4.56800
5.09800
-0.07500
0.58300
4.56800
5.39700
-0.94000
1.04500
4.56800
6.34600
-6.96000
2.50200
2010M10
4.12900
4.53400
-1.69200
0.53000
4.12900
4.78200
-3.07500
0.82900
4.12900
5.91300
-4.33000
1.77800
2010M11
2.55500
4.33700
-0.59100
0.40500
2.55500
4.83600
0.27000
0.65300
2.55500
6.17000
2.57000
1.78400
2010M12
2.54800
4.23700
-0.30000
1.78200
2.54800
4.92600
0.45000
2.28100
2.54800
6.32600
1.56000
3.61500
2011M01
3.80700
4.95100
2.14200
1.68900
3.80700
5.48600
2.80000
2.37800
3.80700
6.56300
2.37000
3.77800
2011M02
3.34000
5.43300
1.44600
1.14400
3.34000
6.48600
5.00000
1.67900
3.34000
7.55100
9.88000
2.75600
2011M03
2.30500
5.19700
-0.70800
2.09300
2.30500
5.88700
-2.99500
3.14600
2.30500
7.29300
-2.58000
4.21100
2011M04
2.18000
4.64300
-1.66200
2.89200
2.18000
5.03000
-4.28500
3.58200
2.18000
6.51800
-7.75000
4.98800
2011M05
2.80900
5.08200
1.31700
2.46300
2.80900
5.43600
2.03000
2.85000
2.80900
6.62400
1.06000
4.33800
2011M06
3.13100
4.48600
-1.78800
2.27300
3.13100
5.12900
-1.53500
2.62700
3.13100
6.77000
1.46000
3.81500
2011M07
3.10000
3.96300
-1.56900
1.35500
3.10000
4.94700
-0.91000
1.99800
3.10000
6.55500
-2.15000
3.63900
2011M08
1.57600
3.22400
-2.21700
0.86300
1.57600
4.59800
-1.74500
1.84700
1.57600
6.24600
-3.09000
3.45500
2011M09
1.53100
3.30800
0.25200
1.64800
1.53100
5.25000
3.26000
3.02200
1.53100
6.34600
1.00000
4.67000
2011M10
1.60700
3.75700
1.34700
1.77700
1.60700
4.76400
-2.43000
3.71900
1.60700
5.97300
-3.73000
4.81500
2011M11
1.61300
3.51700
-0.72000
2.15000
1.61300
4.98100
1.08500
3.15700
1.61300
6.04400
0.71000
4.36600
2011M12
1.67800
3.43200
-0.25500
1.90400
1.67800
4.36700
-3.07000
3.36800
1.67800
5.35500
-6.89000
4.43100
2012M01
2.23200
3.75800
0.97800
1.75400
2.23200
4.40300
0.18000
2.68900
2.23200
5.39300
0.38000
3.67700
2012M02
2.56300
3.50900
-0.74700
1.52600
2.56300
4.40600
0.01500
2.17100
2.56300
5.17900
-2.14000
3.16100
2012M03
2.99900
3.61300
0.31200
0.94600
2.99900
4.60600
1.00000
1.84300
2.99900
5.59900
4.20000
2.61600
2012M04
2.55600
3.74900
0.40800
0.61400
2.55600
4.88800
1.41000
1.60700
2.55600
5.52300
-0.76000
2.60000
2012M05
2.57900
3.58800
-0.48300
1.19300
2.57900
4.97500
0.43500
2.33200
2.57900
5.83800
3.15000
2.96700
2012M06
2.45700
3.65400
0.19800
1.00900
2.45700
4.88300
-0.46000
2.39600
2.45700
5.52900
-3.09000
3.25900
2012M07
2.29700
3.60900
-0.13500
1.19700
2.29700
4.61700
-1.33000
2.42600
2.29700
5.12000
-4.09000
3.07200
2012M08
2.11400
3.82800
0.65700
1.31200
2.11400
4.55800
-0.29500
2.32000
2.11400
5.03800
-0.82000
2.82300
2012M09
1.47500
3.28100
-1.64100
1.71400
1.47500
4.52400
-0.17000
2.44400
1.47500
4.84100
-1.97000
2.92400
2012M10
0.83000
3.68300
1.20600
1.80600
0.83000
4.32300
-1.00500
3.04900
0.83000
4.87700
0.36000
3.36600
2012M11
0.75400
3.41300
-0.81000
2.85300
0.75400
3.84400
-2.39500
3.49300
0.75400
4.60400
-2.73000
4.04700
2012M12
0.92900
3.28500
-0.38400
2.65900
0.92900
3.79800
-0.23000
3.09000
0.92900
4.29900
-3.05000
3.85000
148
2013M01
1.24500
3.20600
-0.23700
2.35600
1.24500
3.45900
-1.69500
2.86900
1.24500
4.07200
-2.27000
3.37000
2013M02
1.03400
2.79100
-1.24500
1.96100
1.03400
3.31800
-0.70500
2.21400
1.03400
3.60700
-4.65000
2.82700
2013M03
0.82200
2.53700
-0.76200
1.75700
0.82200
2.97400
-1.72000
2.28400
0.82200
3.02400
-5.83000
2.57300
2013M04
0.45400
1.97800
-1.67700
1.71500
0.45400
2.44800
-2.63000
2.15200
0.45400
2.90500
-1.19000
2.20200
2013M05
2.01600
2.28900
0.93300
1.52400
2.01600
2.16300
-1.42500
1.99400
2.01600
3.36900
4.64000
2.45100
2013M06
2.03700
2.88300
1.78200
0.27300
2.03700
2.87500
3.56000
0.14700
2.03700
3.85600
4.87000
1.35300
2013M07
1.42200
2.13500
-2.24400
0.84600
1.42200
2.50400
-1.85500
0.83800
1.42200
3.37500
-4.81000
1.81900
2013M08
1.57300
2.43800
0.90900
0.71300
1.57300
2.84100
1.68500
1.08200
1.57300
3.49800
1.23000
1.95300
2013M09
1.07700
2.35600
-0.24600
0.86500
1.07700
3.11500
1.37000
1.26800
1.07700
3.60800
1.10000
1.92500
2013M10
0.40900
2.02100
-1.00500
1.27900
0.40900
2.89800
-1.08500
2.03800
0.40900
3.49900
-1.09000
2.53100
2013M11
0.75400
2.11100
0.27000
1.61200
0.75400
2.78600
-0.56000
2.48900
0.75400
3.54400
0.45000
3.09000
2013M12
0.92200
2.26400
0.45900
1.35700
0.92200
3.00000
1.07000
2.03200
0.92200
3.73000
1.86000
2.79000
2014M01
2.04400
2.93500
2.01300
1.34200
2.04400
3.41400
2.07000
2.07800
2.04400
4.29600
5.66000
2.80800
2014M02
1.92300
2.66300
-0.81600
0.89100
1.92300
3.59300
0.89500
1.37000
1.92300
4.18200
-1.14000
2.25200
2014M03
1.39900
2.93200
0.80700
0.74000
1.39900
3.46300
-0.65000
1.67000
1.39900
4.45400
2.72000
2.25900
2014M04
2.25500
2.95400
0.06600
1.53300
2.25500
3.90100
2.19000
2.06400
2.25500
4.36000
-0.94000
3.05500
2014M05
2.00000
2.67100
-0.84900
0.69900
2.00000
3.33700
-2.82000
1.64600
2.00000
4.11800
-2.42000
2.10500
2014M06
1.75300
2.68500
0.04200
0.67100
1.75300
3.60600
1.34500
1.33700
1.75300
4.04300
-0.75000
2.11800
2014M07
1.92000
2.75100
0.19800
0.93200
1.92000
3.59600
-0.05000
1.85300
1.92000
4.19500
1.52000
2.29000
2014M08
1.90000
2.66000
-0.27300
0.83100
1.90000
3.87300
1.38500
1.67600
1.90000
4.30600
1.11000
2.27500
2014M09
1.75400
2.67200
0.03600
0.76000
1.75400
4.15300
1.40000
1.97300
1.75400
4.36100
0.55000
2.40600
2014M10
1.74200
2.44200
-0.69000
0.91800
1.74200
3.59900
-2.77000
2.39900
1.74200
4.15700
-2.04000
2.60700
2014M11
2.03300
2.82900
1.16100
0.70000
2.03300
3.33100
-1.34000
1.85700
2.03300
3.85100
-3.06000
2.41500
where:
y1 = 1-year bond yield, y3 = 3-year bond yield, y5 = 5-year bond yield, y10 = 10-year bond yield
y3y3 = maturity times change in 3-year bond yield, y5y5 = maturity times change in 5-year bond yield, y10y10 = maturity times change in 10year bond yield
y1y3 = 1-year & 3-year bond spread, y1y5 = 1-year & 5-year bond spread, y1y10 = 1-year & 10-year bond spread
149
APPENDIX D:
TWO-PERIOD CASE TERM SPREAD REGRESSION MODEL RESULTS USING
HETEROSKEDASTICITY-AUTOCORRELATION CONSISTENT (HAC) NEWEY-WEST TEST
3-month & 6-month Regression using HAC Newey-West Test
6-month & 1-year Regression using HAC Newey-West Test
Dependent Variable: M3M3
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Dependent Variable: M6M6
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
M3M6SPREAD
-0.0872
0.2056
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0572
0.0482
0.3901
15.9808
-50.0992
6.3700
0.0131
0.0037
Std.
Error
0.0272
0.0693
t-Statistic
Prob.
Variable
Coefficient
-3.2043
2.9664
0.0018
0.0037
C
M6Y1SPREAD
-0.2213
0.4621
-0.0293
0.3999
0.9738
1.0238
0.9941
2.2792
8.7997
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.2538
0.2467
0.3221
10.8947
-29.6030
35.7208
0.0000
0.0001
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
Std.
Error
0.0512
0.1113
t-Statistic
Prob.
-4.3199
4.1521
0.0000
0.0001
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.0306
0.3711
0.5907
0.6407
0.6110
1.9555
17.2399
150
1-year & 2-year Regression using HAC Newey-West Test
Dependent Variable: Y1Y1
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
Y1Y2SPREAD
-0.1327
0.1402
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0673
0.0584
0.2594
7.0629
-6.4148
7.5769
0.0070
0.0048
Std.
Error
0.0441
0.0487
t-Statistic
Prob.
-3.0078
2.8790
0.0033
0.0048
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.0290
0.2673
0.1573
0.2072
0.1775
1.8412
8.2889
151
APPENDIX E:
N-PERIOD CASE TERM SPREAD REGRESSION MODEL RESULTS USING
HETEROSKEDASTICITY-AUTOCORRELATION CONSISTENT (HAC) NEWEY-WEST TEST
1-year & 3-year Regression using HAC Newey-West Test
1-year & 5-year Regression using HAC Newey-West Test
Dependent Variable: Y3Y3
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Dependent Variable: Y5Y5
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
Y1Y3
0.6128
-0.7134
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0572
0.0482
1.7964
338.8351
-213.4951
6.3698
0.0131
0.0391
Std.
Error
0.3741
0.3414
t-Statistic
Prob.
Variable
Coefficient
1.6380
-2.0896
0.1044
0.0391
C
Y1Y5
2.0837
-1.3357
-0.1884
1.8413
4.0279
4.0779
4.0482
2.0380
4.3666
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0883
0.0796
3.4193
1227.6010
-282.3658
10.1682
0.0019
0.0001
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
Std.
Error
0.7031
0.3277
t-Statistic
Prob.
2.9636
-4.0757
0.0038
0.0001
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.2979
3.5641
5.3152
5.3652
5.3355
2.1337
16.6113
152
1-year & 10-year Regression using HAC Newey-West Test
Dependent Variable: Y10Y10
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
Y1Y5
1.8975
-0.8764
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0201
0.0107
6.0973
3903.6240
-344.2569
2.1516
0.1454
0.0471
Std.
Error
1.4491
0.4362
t-Statistic
Prob.
1.3094
-2.0091
0.1933
0.0471
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.5804
6.1304
6.4721
6.5221
6.4923
1.7391
4.0366
153
APPENDIX F:
COMPUTED EXCESS HOLDING RETURNS OF BOND YIELDS UNDER THE TWO-PERIOD CASE
m3
m6
m3m6hr
m3m6ehr
m6
y1
m6y1hr
m6y1ehr
y1
y2
y1y2hr
y1y2ehr
2006M01
5.73200
6.32900
6.32031
0.58831
6.32900
7.3040
7.30116
0.97216
7.3040
8.3490
8.41034
1.10634
2006M02
5.75600
6.35900
5.68344
-0.07256
6.35900
7.3150
7.48764
1.12864
7.3150
8.0670
8.28192
0.96692
2006M03
5.38900
8.69200
9.61659
4.22759
8.69200
6.6470
6.83101
-1.86099
6.6470
7.0790
7.24541
0.59841
2006M04
5.05800
5.49900
5.30383
0.24583
5.49900
5.9350
5.66752
0.16852
5.9350
6.3140
5.45952
-0.47548
2006M05
5.73600
6.17300
5.88691
0.15091
6.17300
6.9700
6.75705
0.58405
6.9700
10.2420
10.60985
3.63985
2006M06
8.90600
7.16100
7.24150
-1.66450
7.16100
7.7940
7.90332
0.74232
7.7940
8.5510
8.59277
0.79877
2006M07
6.33200
6.88300
7.02778
0.69578
6.88300
7.3710
7.38366
0.50066
7.3710
8.3590
8.48495
1.11395
2006M08
5.91700
6.38300
6.41225
0.49525
6.38300
7.3220
7.49515
1.11215
7.3220
7.7800
7.84330
0.52130
2006M09
5.72400
6.28200
6.29474
0.57074
6.28200
6.6520
6.61427
0.33227
6.6520
7.4890
7.59472
0.94272
2006M10
5.72500
6.23800
6.53307
0.80807
6.23800
6.7980
7.16808
0.93008
6.7980
7.0030
7.26622
0.46822
2006M11
5.21200
5.21900
5.31572
0.10372
5.21900
5.3660
5.40115
0.18215
5.3660
5.7930
5.84369
0.47769
2006M12
4.88500
4.88500
5.06279
0.17779
4.88500
5.2300
5.40005
0.51505
5.2300
5.5600
5.59089
0.36089
2007M01
3.64300
4.27100
4.37090
0.72790
4.27100
4.5720
4.62110
0.35010
4.5720
5.4180
5.47130
0.89930
2007M02
3.53800
3.92600
3.81567
0.27767
3.92600
4.3820
4.28354
0.35754
4.3820
5.1730
5.14646
0.76446
2007M03
4.02300
4.30700
4.44252
0.41952
4.30700
4.7630
4.69426
0.38726
4.7630
5.2950
5.22561
0.46261
2007M04
3.00000
3.83900
3.76342
0.76342
3.83900
5.0290
5.00264
1.16364
5.0290
5.6140
5.55962
0.53062
2007M05
4.56700
4.10000
3.90194
-0.66506
4.10000
5.1310
5.08836
0.98836
5.1310
5.8640
5.80004
0.66904
2007M06
4.66000
4.78400
4.73767
0.07767
4.78400
5.2960
5.18746
0.40346
5.2960
6.1580
6.02248
0.72648
2007M07
4.25000
4.94400
4.78213
0.53213
4.94400
5.7160
5.70928
0.76528
5.7160
6.7810
6.82451
1.10851
2007M08
4.52500
5.50300
5.70280
1.17780
5.50300
5.7420
5.74846
0.24546
5.7420
6.5810
6.64974
0.90774
2007M09
4.06200
4.81300
4.83617
0.77417
4.81300
5.7170
5.71622
0.90322
5.7170
6.2650
6.26979
0.55279
2007M10
4.00000
4.73300
4.70086
0.70086
4.73300
5.7200
5.73757
1.00457
5.7200
6.2430
6.24800
0.52800
2007M11
4.02200
4.84400
4.84661
0.82461
4.84400
5.6520
5.66673
0.82273
5.6520
6.2200
6.33029
0.67829
2007M12
4.22000
4.83500
4.83963
0.61963
4.83500
5.5950
5.69450
0.85950
5.5950
5.7130
5.77456
0.17956
2008M01
4.00000
4.81900
4.64381
0.64381
4.81900
5.2100
5.03013
0.21113
5.2100
5.4300
5.28447
0.07447
2008M02
4.60000
5.42400
5.50942
0.90942
5.42400
5.9060
6.00550
0.58150
5.9060
6.0990
6.07659
0.17059
154
2008M03
4.37500
5.12900
4.82698
0.45198
5.12900
5.5210
5.24344
0.11444
5.5210
6.2020
5.91355
0.39255
2008M04
5.08700
6.17200
6.26756
1.18056
6.17200
6.5950
6.53582
0.36382
6.5950
7.5280
7.49515
0.90015
2008M05
6.06100
5.84200
5.92424
-0.13676
5.84200
6.8240
6.85372
1.01172
6.8240
7.6790
7.79495
0.97095
2008M06
5.11600
5.55800
5.41582
0.29982
5.55800
6.7090
6.56428
1.00628
6.7090
7.1460
7.14796
0.43896
2008M07
6.08200
6.04900
5.83704
-0.24496
6.04900
7.2690
7.42716
1.37816
7.2690
7.1370
7.13134
-0.13766
2008M08
6.18500
6.78100
6.94287
0.75787
6.78100
6.6570
6.69680
-0.08420
6.6570
7.1630
7.09752
0.44052
2008M09
6.50000
6.22200
6.00511
-0.49489
6.22200
6.5030
6.31589
0.09389
6.5030
7.4640
7.41875
0.91575
2008M10
6.75000
6.97100
7.12881
0.37881
6.97100
7.2270
7.32727
0.35627
7.2270
7.6720
7.67156
0.44456
2008M11
6.37500
6.42600
6.54878
0.17378
6.42600
6.8390
7.03438
0.60838
6.8390
7.6740
7.90937
1.07037
2008M12
5.62600
6.00200
6.43374
0.80774
6.00200
6.0830
6.45670
0.45470
6.0830
6.5920
6.81628
0.73328
2009M01
4.28200
4.51100
4.43398
0.15198
4.51100
4.6370
4.55792
0.04692
4.6370
5.5610
5.59494
0.95794
2009M02
4.55600
4.77700
4.86821
0.31221
4.77700
4.9430
4.98332
0.20632
4.9430
5.4050
5.44263
0.49963
2009M03
4.29300
4.46200
4.42609
0.13309
4.46200
4.7870
4.79475
0.33275
4.7870
5.2320
5.28595
0.49895
2009M04
4.35300
4.58600
4.59585
0.24285
4.58600
4.7570
4.78078
0.19478
4.7570
4.9840
4.99335
0.23635
2009M05
4.35500
4.55200
4.54766
0.19266
4.55200
4.6650
4.63218
0.08018
4.6650
4.9410
4.86377
0.19877
2009M06
4.31900
4.56700
4.78099
0.46199
4.56700
4.7920
4.93156
0.36456
4.7920
5.2960
5.42087
0.62887
2009M07
3.68800
3.82800
3.77906
0.09106
3.82800
4.2520
4.20496
0.37696
4.2520
4.7220
4.71743
0.46543
2009M08
3.75100
3.99700
3.94690
0.19590
3.99700
4.4340
4.44305
0.44605
4.4340
4.7430
4.73169
0.29769
2009M09
4.05200
4.17000
4.16392
0.11192
4.17000
4.3990
4.38479
0.21479
4.3990
4.7950
4.82480
0.42580
2009M10
4.00500
4.19100
4.20519
0.20019
4.19100
4.4540
4.43436
0.24336
4.4540
4.6580
4.65495
0.20095
2009M11
3.64700
4.14200
4.09219
0.44519
4.14200
4.5300
4.46255
0.32055
4.5300
4.6720
4.52408
-0.00592
2009M12
4.06700
4.31400
4.33456
0.26756
4.31400
4.7910
4.79565
0.48165
4.7910
5.3520
5.42444
0.63344
2010M01
3.80500
4.24300
4.27311
0.46811
4.24300
4.7730
4.87121
0.62821
4.7730
5.0190
5.09448
0.32148
2010M02
4.01500
4.13900
4.17114
0.15614
4.13900
4.3930
4.38757
0.24857
4.3930
4.6720
4.63371
0.24071
2010M03
3.90000
4.02800
3.98978
0.08978
4.02800
4.4140
4.38816
0.36016
4.4140
4.8480
4.83712
0.42312
2010M04
4.05600
4.16000
4.11019
0.05419
4.16000
4.5140
4.48531
0.32531
4.5140
4.8980
4.83339
0.31939
2010M05
4.15000
4.33200
4.36269
0.21269
4.33200
4.6250
4.62965
0.29765
4.6250
5.1950
5.19217
0.56717
2010M06
3.95100
4.22600
4.21934
0.26834
4.22600
4.6070
4.60648
0.38048
4.6070
5.2080
5.21757
0.61057
2010M07
4.06600
4.24900
4.23249
0.16649
4.24900
4.6090
4.62683
0.37783
4.6090
5.1640
5.17683
0.56783
2010M08
4.10000
4.30600
4.30397
0.20397
4.30600
4.5400
4.53276
0.22676
4.5400
5.1050
5.12458
0.58458
155
2010M09
4.10300
4.31300
4.38771
0.28471
4.31300
4.5680
4.68145
0.36845
4.5680
5.0150
5.14139
0.57339
2010M10
3.74900
4.05500
4.70218
0.95318
4.05500
4.1290
4.53578
0.48078
4.1290
4.4340
4.56452
0.43552
2010M11
1.50000
1.82000
1.92280
0.42280
1.82000
2.5550
2.55681
0.73681
2.5550
3.8340
3.89273
1.33773
2010M12
1.19500
1.46500
0.95739
-0.23761
1.46500
2.5480
2.22263
0.75763
2.5480
3.5640
3.31275
0.76475
2011M01
3.20000
3.21800
3.55274
0.35274
3.21800
3.8070
3.92769
0.70969
3.8070
4.7190
4.71443
0.90743
2011M02
1.65000
2.06200
2.30726
0.65726
2.06200
3.3400
3.60748
1.54548
3.3400
4.7400
4.84007
1.50007
2011M03
1.04200
1.21500
1.31143
0.26943
1.21500
2.3050
2.33730
1.12230
2.3050
4.2800
4.49928
2.19428
2011M04
0.60700
0.88200
0.44939
-0.15761
0.88200
2.1800
2.01744
1.13544
2.1800
3.2720
3.02249
0.84249
2011M05
2.18900
2.37600
2.20052
0.01152
2.37600
2.8090
2.72578
0.34978
2.8090
4.4190
4.52886
1.71986
2011M06
2.85200
2.98200
3.08393
0.23193
2.98200
3.1310
3.13901
0.15701
3.1310
3.9140
3.98840
0.85740
2011M07
2.42500
2.63000
3.10431
0.67931
2.63000
3.1000
3.49386
0.86386
3.1000
3.5720
3.77409
0.67409
2011M08
0.95100
0.99200
0.68882
-0.26218
0.99200
1.5760
1.58763
0.59563
1.5760
2.6430
2.64757
1.07157
2011M09
2.74500
2.03900
2.21100
-0.53400
2.03900
1.5310
1.51136
-0.52764
1.5310
2.6220
2.65224
1.12124
2011M10
1.11500
1.44500
1.42618
0.31118
1.44500
1.6070
1.60545
0.16045
1.6070
2.4830
2.49431
0.88731
2011M11
2.16500
1.51000
1.50247
-0.66253
1.51000
1.6130
1.59620
0.08620
1.6130
2.4310
2.44601
0.83301
2011M12
1.37500
1.53600
1.46361
0.08861
1.53600
1.6780
1.53483
-0.00117
1.6780
2.3620
2.26933
0.59133
2012M01
1.62500
1.78600
1.63427
0.00927
1.78600
2.2320
2.14646
0.36046
2.2320
2.7880
2.72666
0.49466
2012M02
1.88900
2.31000
2.30913
0.42013
2.31000
2.5630
2.45032
0.14032
2.5630
3.0700
3.04237
0.47937
2012M03
2.30000
2.31300
2.35672
0.05672
2.31300
2.9990
3.11349
0.80049
2.9990
3.1970
3.26009
0.26109
2012M04
2.15000
2.16200
2.11596
-0.03404
2.16200
2.5560
2.55006
0.38806
2.5560
2.9070
2.88960
0.33360
2012M05
2.20000
2.32100
2.33374
0.13374
2.32100
2.5790
2.61053
0.28953
2.5790
2.9870
2.96568
0.38668
2012M06
2.19500
2.27700
2.33086
0.13586
2.27700
2.4570
2.49835
0.22135
2.4570
3.0850
3.17441
0.71741
2012M07
1.84000
2.09100
2.21320
0.37320
2.09100
2.2970
2.34429
0.25329
2.2970
2.6740
2.67748
0.38048
2012M08
1.38200
1.66900
1.87054
0.48854
1.66900
2.1140
2.27914
0.61014
2.1140
2.6580
2.73610
0.62210
2012M09
0.62500
0.97300
1.11344
0.48844
0.97300
1.4750
1.64169
0.66869
1.4750
2.2990
2.21220
0.73720
2012M10
0.30000
0.48800
0.44225
0.14225
0.48800
0.8300
0.84964
0.36164
0.8300
2.6980
2.75151
1.92151
2012M11
0.61100
0.64600
0.66656
0.05556
0.64600
0.7540
0.70877
0.06277
0.7540
2.4520
2.36238
1.60838
2012M12
0.30000
0.57500
0.62944
0.32944
0.57500
0.9290
0.84733
0.27233
0.9290
2.8640
2.91273
1.98373
2013M01
0.15100
0.38700
0.39771
0.24671
0.38700
1.2450
1.29953
0.91253
1.2450
2.6400
2.70570
1.46070
2013M02
0.35000
0.35000
0.35840
0.00840
0.35000
1.0340
1.08879
0.73879
1.0340
2.3380
2.37107
1.33707
156
2013M03
0.25000
0.32100
0.32708
0.07708
0.32100
0.8220
0.91710
0.59610
0.8220
2.1860
2.22211
1.40011
2013M04
0.20000
0.30000
-0.19950
-0.39950
0.30000
0.4540
0.05032
-0.24968
0.4540
2.0200
1.96649
1.51249
2013M05
2.00000
2.02500
2.08957
0.08957
2.02500
2.0160
2.01057
-0.01443
2.0160
2.2660
2.20357
0.18757
2013M06
1.75000
1.80200
2.07854
0.32854
1.80200
2.0370
2.19594
0.39394
2.0370
2.5530
2.61522
0.57822
2013M07
1.04900
0.84700
0.70135
-0.34765
0.84700
1.4220
1.38298
0.53598
1.4220
2.2670
2.18434
0.76234
2013M08
1.25000
1.35000
1.48146
0.23146
1.35000
1.5730
1.70118
0.35118
1.5730
2.6470
2.77796
1.20496
2013M09
0.47600
0.89600
1.10217
0.62617
0.89600
1.0770
1.24964
0.35364
1.0770
2.0450
2.06501
0.98801
2013M10
0.09500
0.18400
0.15070
0.05570
0.18400
0.4090
0.31984
0.13584
0.4090
1.9530
1.95909
1.55009
2013M11
0.17500
0.29900
0.26251
0.08751
0.29900
0.7540
0.71058
0.41158
0.7540
1.9250
1.87584
1.12184
2013M12
0.32500
0.42500
-0.01572
-0.34072
0.42500
0.9220
0.63203
0.20703
0.9220
2.1510
2.03049
1.10849
2014M01
1.20000
1.94700
2.08194
0.88194
1.94700
2.0440
2.07527
0.12827
2.0440
2.7050
2.80463
0.76063
2014M02
1.00000
1.48100
1.52733
0.52733
1.48100
1.9230
2.05842
0.57742
1.9230
2.2470
2.21285
0.28985
2014M03
1.50000
1.32100
1.13597
-0.36403
1.32100
1.3990
1.17778
-0.14322
1.3990
2.4040
2.33374
0.93474
2014M04
1.30000
1.96000
2.00952
0.70952
1.96000
2.2550
2.32090
0.36090
2.2550
2.7270
2.80988
0.55488
2014M05
1.07000
1.78900
1.93349
0.86349
1.78900
2.0000
2.06383
0.27483
2.0000
2.3460
2.33904
0.33904
2014M06
1.15000
1.29000
1.18199
0.03199
1.29000
1.7530
1.70984
0.41984
1.7530
2.3780
2.35211
0.59911
2014M07
1.37500
1.66300
1.67748
0.30248
1.66300
1.9200
1.92517
0.26217
1.9200
2.4970
2.50614
0.58614
2014M08
1.25000
1.61300
1.57709
0.32709
1.61300
1.9000
1.93773
0.32473
1.9000
2.4550
2.52244
0.62244
2014M09
1.50000
1.73700
1.81605
0.31605
1.73700
1.7540
1.75710
0.02010
1.7540
2.1450
2.10671
0.35271
2014M10
1.40000
1.46400
1.38466
-0.01534
1.46400
1.7420
1.66679
0.20279
1.7420
2.3210
2.28032
0.53832
2014M11
1.50000
1.73800
1.73800
2.0330
2.0330
2.5080
where:
m3 = 3-month bond yield, m6 = 6-month bond yield, y1 = 1-year bond yield, y2 = 2-year bond yield
m3m6hr = holding return of 6-month bonds over 3-month bonds, m6y1hr = holding return of 1-year bonds over 6-month bonds, y1y2hr = holding
return of 2-year bonds over 1-year bonds
m3m6ehr = excess holding return of 6-month bonds over 3-month bonds, m6y1ehr = excess holding return of 1-year bonds over 6-month bonds,
y1y2ehr = excess holding return of 2-year bonds over 1-year bonds
157
APPENDIX G:
COMPUTED EXCESS HOLDING RETURNS OF BOND YIELDS UNDER THE N-PERIOD CASE
y1
y3
y1y3hr
y1y3ehr
y1
y5
y1y5hr
y1y5ehr
y1
y10
y1y10hr
y1y10ehr
2006M01
7.3040
8.6010
8.67498
1.37098
7.3040
8.6740
8.18840
0.88440
7.3040
9.8380
10.01063
2.70663
2006M02
7.3150
8.2320
8.45235
1.13735
7.3150
11.4180
12.14869
4.83369
7.3150
8.6820
8.82805
1.51305
2006M03
6.6470
7.1330
7.26433
0.61733
6.6470
7.2890
7.38527
0.73827
6.6470
7.7040
7.75686
1.10986
2006M04
5.9350
6.4780
6.06859
0.13359
5.9350
6.7450
6.38629
0.45129
5.9350
7.3500
6.89514
0.96014
2006M05
6.9700
8.5200
8.38266
1.41266
6.9700
8.7720
8.59610
1.62610
6.9700
10.3960
10.35180
3.38180
2006M06
7.7940
9.2050
9.31006
1.51606
7.7940
9.7660
9.85767
2.06367
7.7940
10.6920
10.71022
2.91622
2006M07
7.3710
8.6810
8.27139
0.90039
7.3710
9.2480
9.44461
2.07361
7.3710
10.5700
10.77891
3.40791
2006M08
7.3220
10.7240
11.37221
4.05021
7.3220
8.1370
8.21663
0.89463
7.3220
9.1710
9.26388
1.94188
2006M09
6.6520
7.4910
7.57481
0.92281
6.6520
7.6870
7.76274
1.11074
6.6520
8.5490
8.64845
1.99645
2006M10
6.7980
7.0730
7.30578
0.50778
6.7980
7.2590
7.46517
0.66717
6.7980
7.8830
8.06847
1.27047
2006M11
5.3660
5.9120
5.95310
0.58710
5.3660
6.0940
6.13010
0.76410
5.3660
6.6410
6.66235
1.29635
2006M12
5.2300
5.7070
5.71422
0.48422
5.2300
5.8900
5.84877
0.61877
5.2300
6.4980
6.42438
1.19438
2007M01
4.5720
5.6710
5.73436
1.16236
4.5720
6.1230
6.19025
1.61825
4.5720
6.9910
6.96024
2.38824
2007M02
4.3820
5.3550
5.31771
0.93571
4.3820
5.7430
5.69115
1.30915
4.3820
7.1970
7.16728
2.78528
2007M03
4.7630
5.5410
5.49228
0.72928
4.7630
6.0360
6.01600
1.25300
4.7630
7.3960
7.38122
2.61822
2007M04
5.0290
5.7840
5.75814
0.72914
5.0290
6.1490
6.14847
1.11947
5.0290
7.4950
7.52442
2.49542
2007M05
5.1310
5.9130
5.78428
0.65328
5.1310
6.1520
6.01609
0.88509
5.1310
7.2980
7.31338
2.18238
2007M06
5.2960
6.5550
6.48443
1.18843
5.2960
6.9200
6.87487
1.57887
5.2960
7.1950
7.15602
1.86002
2007M07
5.7160
6.9070
6.88214
1.16614
5.7160
7.1750
7.15199
1.43599
5.7160
7.4560
7.35640
1.64040
2007M08
5.7420
7.0310
7.15210
1.41010
5.7420
7.3050
7.41897
1.67697
5.7420
8.1230
8.23515
2.49315
2007M09
5.7170
6.4270
6.43442
0.71742
5.7170
6.6610
6.68029
0.96329
5.7170
7.3720
7.38559
1.66859
2007M10
5.7200
6.3900
6.40524
0.68524
5.7200
6.5520
6.56474
0.84474
5.7200
7.2810
7.28682
1.56682
2007M11
5.6520
6.3140
6.43751
0.78551
5.6520
6.4800
6.59786
0.94586
5.6520
7.2420
7.31950
1.66750
2007M12
5.5950
5.6980
5.74030
0.14530
5.5950
5.8140
5.85134
0.25634
5.5950
6.7230
6.81066
1.21566
2008M01
5.2100
5.4870
5.30976
0.09976
5.2100
5.6030
5.43471
0.22471
5.2100
6.1360
5.96905
0.75905
2008M02
5.9060
6.3710
6.37581
0.46981
5.9060
6.5540
6.55294
0.64694
5.9060
7.2540
7.21040
1.30440
158
2008M03
5.5210
6.3470
6.08315
0.56215
5.5210
6.5600
6.27809
0.75709
5.5210
7.5460
7.38547
1.86447
2008M04
6.5950
7.6630
7.54130
0.94630
6.5950
8.1530
8.06841
1.47341
6.5950
8.6210
8.51931
1.92431
2008M05
6.8240
8.2700
8.27902
1.45502
6.8240
8.6310
8.57366
1.74966
6.8240
9.3020
9.24406
2.42006
2008M06
6.7090
8.2250
8.30400
1.59500
6.7090
8.9550
9.03092
2.32192
6.7090
9.6900
9.60847
2.89947
2008M07
7.2690
7.8310
7.98999
0.72099
7.2690
8.5260
8.73340
1.46440
7.2690
10.2360
10.49001
3.22101
2008M08
6.6570
7.0380
7.04381
0.38681
6.6570
7.3540
7.29755
0.64055
6.6570
8.5350
8.53993
1.88293
2008M09
6.5030
7.0090
6.85502
0.35202
6.5030
7.6730
7.63920
1.13620
6.5030
8.5020
8.24814
1.74514
2008M10
7.2270
7.7770
7.73630
0.50930
7.2270
7.8640
7.74437
0.51737
7.2270
10.2020
10.36089
3.13389
2008M11
6.8390
7.9800
8.32646
1.48746
6.8390
8.5400
8.86491
2.02591
6.8390
9.1380
9.36558
2.52658
2008M12
6.0830
6.2520
6.31716
0.23416
6.0830
6.7040
6.77638
0.69338
6.0830
7.6140
7.56278
1.47978
2009M01
4.6370
5.9270
5.95808
1.32108
4.6370
6.2950
6.25147
1.61447
4.6370
7.9570
7.85322
3.21622
2009M02
4.9430
5.7720
5.75015
0.80715
4.9430
6.5410
6.54029
1.59729
4.9430
8.6520
8.67335
3.73035
2009M03
4.7870
5.8810
5.97844
1.19144
4.7870
6.5450
6.56606
1.77906
4.7870
8.5090
8.44270
3.65570
2009M04
4.7570
5.3950
5.44392
0.68692
4.7570
6.4260
6.45520
1.69820
4.7570
8.9530
9.05469
4.29769
2009M05
4.6650
5.1510
5.08022
0.41522
4.6650
6.2610
6.21410
1.54910
4.6650
8.2720
8.19704
3.53204
2009M06
4.7920
5.5040
5.56054
0.76854
4.7920
6.5260
6.53237
1.74037
4.7920
8.7740
8.80924
4.01724
2009M07
4.2520
5.2220
5.18210
0.93010
4.2520
6.4900
6.48009
2.22809
4.2520
8.5380
8.54158
4.28958
2009M08
4.4340
5.4210
5.45308
1.01908
4.4340
6.5460
6.56617
2.13217
4.4340
8.5140
8.47697
4.04297
2009M09
4.3990
5.2610
5.22591
0.82691
4.3990
6.4320
6.40811
2.00911
4.3990
8.7620
8.78216
4.38316
2009M10
4.4540
5.4360
5.44723
0.99323
4.4540
6.5670
6.57142
2.11742
4.4540
8.6270
8.63596
4.18196
2009M11
4.5300
5.3800
5.32125
0.79125
4.5300
6.5420
6.54005
2.01005
4.5300
8.5670
8.55401
4.02401
2009M12
4.7910
5.6730
5.72393
0.93293
4.7910
6.5530
6.54044
1.74944
4.7910
8.6540
8.67476
3.88376
2010M01
4.7730
5.4190
5.41820
0.64520
4.7730
6.6240
6.64895
1.87595
4.7730
8.5150
8.52515
3.75215
2010M02
4.3930
5.4230
5.47152
1.07852
4.3930
6.4830
6.47840
2.08540
4.3930
8.4470
8.40399
4.01099
2010M03
4.4140
5.1810
5.12707
0.71307
4.4140
6.5090
6.48051
2.06651
4.4140
8.7350
8.75098
4.33698
2010M04
4.5140
5.4500
5.46764
0.95364
4.5140
6.6700
6.68062
2.16662
4.5140
8.6280
8.63696
4.12296
2010M05
4.6250
5.3620
5.36320
0.73820
4.6250
6.6100
6.62557
2.00057
4.6250
8.5680
8.60981
3.98481
2010M06
4.6070
5.3560
5.35259
0.74559
4.6070
6.5220
6.55633
1.94933
4.6070
8.2880
8.30592
3.69892
2010M07
4.6090
5.3730
5.42312
0.81412
4.6090
6.3280
6.45949
1.85049
4.6090
8.1680
8.33615
3.72715
2010M08
4.5400
5.1230
5.12801
0.58801
4.5400
5.5850
5.61827
1.07827
4.5400
7.0420
7.14593
2.60593
159
2010M09
4.5680
5.0980
5.21108
0.64308
4.5680
5.3970
5.50583
0.93783
4.5680
6.3460
6.41066
1.84266
2010M10
4.1290
4.5340
4.57350
0.44450
4.1290
4.7820
4.77244
0.64344
4.1290
5.9130
5.87462
1.74562
2010M11
2.5550
4.3370
4.35705
1.80205
2.5550
4.8360
4.82007
2.26507
2.5550
6.1700
6.14670
3.59170
2010M12
2.5480
4.2370
4.09385
1.54585
2.5480
4.9260
4.82690
2.27890
2.5480
6.3260
6.29061
3.74261
2011M01
3.8070
4.9510
4.85436
1.04736
3.8070
5.4860
5.30903
1.50203
3.8070
6.5630
6.41546
2.60846
2011M02
3.3400
5.4330
5.48032
2.14032
3.3400
6.4860
6.59200
3.25200
3.3400
7.5510
7.58953
4.24953
2011M03
2.3050
5.1970
5.30808
3.00308
2.3050
5.8870
6.03866
3.73366
2.3050
7.2930
7.40873
5.10373
2011M04
2.1800
4.6430
4.55498
2.37498
2.1800
5.0300
4.95815
2.77815
2.1800
6.5180
6.50217
4.32217
2011M05
2.8090
5.0820
5.20150
2.39250
2.8090
5.4360
5.49033
2.68133
2.8090
6.6240
6.60220
3.79320
2011M06
3.1310
4.4860
4.59086
1.45986
3.1310
5.1290
5.16121
2.03021
3.1310
6.7700
6.80211
3.67111
2011M07
3.1000
3.9630
4.11117
1.01117
3.1000
4.9470
5.00876
1.90876
3.1000
6.5550
6.60114
3.50114
2011M08
1.5760
3.2240
3.20716
1.63116
1.5760
4.5980
4.48262
2.90662
1.5760
6.2460
6.23107
4.65507
2011M09
1.5310
3.3080
3.21798
1.68698
1.5310
5.2500
5.33601
3.80501
1.5310
6.3460
6.40170
4.87070
2011M10
1.6070
3.7570
3.80512
2.19812
1.6070
4.7640
4.72560
3.11860
1.6070
5.9730
5.96240
4.35540
2011M11
1.6130
3.5170
3.53404
1.92104
1.6130
4.9810
5.08966
3.47666
1.6130
6.0440
6.14689
4.53389
2011M12
1.6780
3.4320
3.36664
1.68864
1.6780
4.3670
4.36063
2.68263
1.6780
5.3550
5.34933
3.67133
2012M01
2.2320
3.7580
3.80792
1.57592
2.2320
4.4030
4.40247
2.17047
2.2320
5.3930
5.42496
3.19296
2012M02
2.5630
3.5090
3.48815
0.92515
2.5630
4.4060
4.37061
1.80761
2.5630
5.1790
5.11628
2.55328
2012M03
2.9990
3.6130
3.58573
0.58673
2.9990
4.6060
4.55610
1.55710
2.9990
5.5990
5.61035
2.61135
2012M04
2.5560
3.7490
3.78128
1.22528
2.5560
4.8880
4.87260
2.31660
2.5560
5.5230
5.47596
2.91996
2012M05
2.5790
3.5880
3.57477
0.99577
2.5790
4.9750
4.99128
2.41228
2.5790
5.8380
5.88414
3.30514
2012M06
2.4570
3.6540
3.66302
1.20602
2.4570
4.8830
4.93007
2.47307
2.4570
5.5290
5.59008
3.13308
2012M07
2.2970
3.6090
3.56509
1.26809
2.2970
4.6170
4.62744
2.33044
2.2970
5.1200
5.13225
2.83525
2012M08
2.1140
3.8280
3.93767
1.82367
2.1140
4.5580
4.56402
2.45002
2.1140
5.0380
5.06742
2.95342
2012M09
1.4750
3.2810
3.20040
1.72540
1.4750
4.5240
4.55957
3.08457
1.4750
4.8410
4.83562
3.36062
2012M10
0.8300
3.6830
3.73713
2.90713
0.8300
4.3230
4.40777
3.57777
0.8300
4.8770
4.91777
4.08777
2012M11
0.7540
3.4130
3.43866
2.68466
0.7540
3.8440
3.85214
3.09814
0.7540
4.6040
4.64955
3.89555
2012M12
0.9290
3.2850
3.30084
2.37184
0.9290
3.7980
3.85799
2.92899
0.9290
4.2990
4.33290
3.40390
2013M01
1.2450
3.2060
3.28921
2.04421
1.2450
3.4590
3.48395
2.23895
1.2450
4.0720
4.14144
2.89644
2013M02
1.0340
2.7910
2.84193
1.80793
1.0340
3.3180
3.37888
2.34488
1.0340
3.6070
3.69406
2.66006
160
2013M03
0.8220
2.5370
2.64908
1.82708
0.8220
2.9740
3.06708
2.24508
0.8220
3.0240
3.04177
2.21977
2013M04
0.4540
1.9780
1.91565
1.46165
0.4540
2.4480
2.49844
2.04444
0.4540
2.9050
2.83571
2.38171
2013M05
2.0160
2.2890
2.16991
0.15391
2.0160
2.1630
2.03700
0.02100
2.0160
3.3690
3.29628
1.28028
2013M06
2.0370
2.8830
3.03297
0.99597
2.0370
2.8750
2.94065
0.90365
2.0370
3.8560
3.92783
1.89083
2013M07
1.4220
2.1350
2.07425
0.65225
1.4220
2.5040
2.44436
1.02236
1.4220
3.3750
3.35663
1.93463
2013M08
1.5730
2.4380
2.45444
0.88144
1.5730
2.8410
2.79251
1.21951
1.5730
3.4980
3.48157
1.90857
2013M09
1.0770
2.3560
2.42317
1.34617
1.0770
3.1150
3.15340
2.07640
1.0770
3.6080
3.62428
2.54728
2013M10
0.4090
2.0210
2.00296
1.59396
0.4090
2.8980
2.91782
2.50882
0.4090
3.4990
3.49228
3.08328
2013M11
0.7540
2.1110
2.08032
1.32632
0.7540
2.7860
2.74813
1.99413
0.7540
3.5440
3.51622
2.76222
2013M12
0.9220
2.2640
2.12947
1.20747
0.9220
3.0000
2.92674
2.00474
0.9220
3.7300
3.64548
2.72348
2014M01
2.0440
2.9350
2.98954
0.94554
2.0440
3.4140
3.38232
1.33832
2.0440
4.2960
4.31302
2.26902
2014M02
1.9230
2.6630
2.60907
0.68607
1.9230
3.5930
3.61601
1.69301
1.9230
4.1820
4.14138
2.21838
2014M03
1.3990
2.9320
2.92759
1.52859
1.3990
3.4630
3.38549
1.98649
1.3990
4.4540
4.46804
3.06904
2014M04
2.2550
2.9540
3.01074
0.75574
2.2550
3.9010
4.00081
1.74581
2.2550
4.3600
4.39614
2.14114
2014M05
2.0000
2.6710
2.66819
0.66819
2.0000
3.3370
3.28940
1.28940
2.0000
4.1180
4.12920
2.12920
2014M06
1.7530
2.6850
2.67177
0.91877
1.7530
3.6060
3.60777
1.85477
1.7530
4.0430
4.02030
2.26730
2014M07
1.9200
2.7510
2.76925
0.84925
1.9200
3.5960
3.54698
1.62698
1.9200
4.1950
4.17842
2.25842
2014M08
1.9000
2.6600
2.65759
0.75759
1.9000
3.8730
3.82345
1.92345
1.9000
4.3060
4.29779
2.39779
2014M09
1.7540
2.6720
2.71811
0.96411
1.7540
4.1530
4.25104
2.49704
1.7540
4.3610
4.39146
2.63746
2014M10
1.7420
2.4420
2.36441
0.62241
1.7420
3.5990
3.64643
1.90443
1.7420
4.1570
4.20270
2.46070
2014M11
2.0330
2.8290
2.0330
3.3310
2.0330
3.8510
where:
y1 = 1-year bond yield, y3 = 3-year bond yield, y5 = 5-year bond yield, y10 = 10-year bond yield
y1y3hr = holding return of 3-year bonds over 1-year bonds, y1y5hr = holding return of 5-year bonds over 1-year bonds, y1y10hr = holding
return of 10-year bonds over 1-year bonds
y1y3ehr = excess holding return of 3-year bonds over 1-year bonds, y1y5ehr = excess holding return of 5-year bonds over 1-year bonds,
y1y10ehr = excess holding return of 10-year bonds over 1-year bonds
161
APPENDIX H:
TERM SPREAD REGRESSION MODEL RESULTS OF PREDICTING EXCESS BOND RETURNS USING
HETEROSKEDASTICITY-AUTOCORRELATION CONSISTENT (HAC) NEWEY-WEST TEST
(TWO-PERIOD & N-PERIOD CASE)
3-month & 6-month Regression using HAC Newey-West Test
6-month & 1-year Regression using HAC Newey-West Test
Dependent Variable: M3M6EHR
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Dependent Variable: M6Y1EHR
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
M3M6SPREAD
0.27230
0.06972
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0033
-0.0062
0.5655
33.2534
-88.9655
0.3481
0.5565
0.3706
Std.
Error
0.04507
0.07753
t-Statistic
Prob.
6.04244
0.89923
0.00000
0.37060
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
0.2921
0.5637
1.7163
1.7666
1.7367
2.1798
0.8086
Variable
Coefficient
C
M6Y1SPREAD
0.3407
0.2156
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0440
0.0349
0.4101
17.4944
-54.9249
4.7918
0.0308
0.0815
Std.
Error
0.0439
0.1225
t-Statistic
Prob.
7.7690
1.7594
0.0000
0.0814
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
0.4300
0.4175
1.0741
1.1243
1.0944
1.9987
3.0955
162
1-year & 2-year Regression using HAC Newey-West Test
1-year & 3-year Regression using HAC Newey-West Test
Dependent Variable: Y1Y2EHR
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Dependent Variable: Y1Y3EHR
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
Y1Y2SPREAD
0.4279
0.4235
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.1583
0.1502
0.4873
24.7001
-73.2061
19.5577
0.0000
0.0106
Std.
Error
0.1269
0.1627
t-Statistic
Prob.
Variable
Coefficient
3.3725
2.6031
0.0010
0.0106
C
Y1Y3SPREAD
0.4207
0.6313
0.7419
0.5287
1.4190
1.4692
1.4394
2.4379
6.7760
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.3506
0.3443
0.5342
29.6834
-82.9464
56.1439
0.0000
0.0000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
Std.
Error
0.1227
0.1143
t-Statistic
Prob.
3.4291
5.5232
0.0009
0.0000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
1.1322
0.6598
1.6028
1.6530
1.6231
2.3501
30.5056
163
1-year & 5-year Regression using HAC Newey-West Test
1-year & 10-year Regression using HAC Newey-West Test
Dependent Variable: Y1Y5EHR
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Dependent Variable: Y1Y10EHR
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
Y1Y5SPREAD
0.6378
0.6492
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.3764
0.3704
0.6688
46.5184
-106.7572
62.7810
0.0000
0.0000
Std.
Error
0.2183
0.1275
t-Statistic
Prob.
Variable
Coefficient
2.9223
5.0911
0.0043
0.0000
C
Y1Y5SPREAD
0.6378
0.6492
1.7949
0.8429
2.0520
2.1023
2.0724
2.3456
25.9194
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.6657
0.6625
0.5859
35.7012
-92.7300
207.0650
0.0000
0.0000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
Std.
Error
0.2183
0.1275
t-Statistic
Prob.
2.9223
5.0911
0.0043
0.0000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
2.8451
1.0085
1.7874
1.8376
1.8077
2.0758
229.3279
164
APPENDIX I:
TWO-PERIOD CASE FORWARD SPREAD REGRESSION MODEL RESULTS USING
HETEROSKEDASTICITY-AUTOCORRELATION CONSISTENT (HAC) NEWEY-WEST TEST
3-month & 6-month Regression using HAC Newey-West Test
6-month & 1-year Regression using HAC Newey-West Test
Dependent Variable: CSRM3
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Dependent Variable: CSRM6
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
FM3M6SPREAD
-0.0017
0.2020
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0560
0.0470
0.0078
0.0064
368.4186
6.2271
0.0141
0.0198
Std.
Error
0.0006
0.0854
t-Statistic
Prob.
Variable
Coefficient
-2.8537
2.3668
0.0052
0.0198
C
FM6Y1SPREAD
-0.0044
0.4608
-0.0006
0.0080
-6.8489
-6.7990
-6.8287
2.2826
5.6018
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.2529
0.2458
0.0064
0.0044
388.9175
35.5472
0.0000
0.0000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
Std.
Error
0.0010
0.1082
t-Statistic
Prob.
-4.4672
4.2606
0.0000
0.0000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.0006
0.0074
-7.2321
-7.1821
-7.2118
1.9571
18.1527
165
1-year & 2-year Regression using HAC Newey-West Test
Dependent Variable: CSRY1
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
FY1Y2SPREAD
-0.0026
0.1385
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0672
0.0583
0.0052
0.0028
412.1673
7.5678
0.0070
0.0056
Std.
Error
0.0008
0.0490
t-Statistic
Prob.
-3.1961
2.8269
0.0018
0.0056
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.0006
0.0053
-7.6667
-7.6167
-7.6464
1.8423
7.9915
166
APPENDIX J:
N-PERIOD CASE FORWARD SPREAD REGRESSION MODEL USING
HETEROSKEDASTICITY-AUTOCORRELATION CONSISTENT (HAC) NEWEY-WEST TEST
1-year & 3-year Regression using HAC Newey-West Test
1-year & 5-year Regression using HAC Newey-West Test
Dependent Variable: CSRY3
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Dependent Variable: CSRY5
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
FY1Y3SPREAD
-0.0002
-0.0040
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0003
-0.0092
0.0053
0.0030
409.5320
0.0335
0.8552
0.7885
Std.
Error
0.0011
0.0147
t-Statistic
Prob.
Variable
Coefficient
-0.2071
-0.2689
0.8364
0.7885
C
FY1Y5SPREAD
0.0011
-0.0075
-0.0005
0.0053
-7.6174
-7.5675
-7.5972
1.9741
0.0723
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0092
-0.0002
0.0054
0.0030
408.7525
0.9787
0.3248
0.0999
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
Std.
Error
0.0011
0.0045
t-Statistic
Prob.
1.0883
-1.6602
0.2789
0.0998
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.0006
0.0054
-7.6029
-7.5529
-7.5826
1.9683
2.7564
167
1-year & 10-year Regression using HAC Newey-West Test
Dependent Variable: CSRY10
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
FY1Y10SPREAD
0.0007
-0.0015
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0068
-0.0026
0.0054
0.0030
408.8107
0.7221
0.3974
0.1729
Std.
Error
0.0010
0.0011
t-Statistic
Prob.
0.6563
-1.3721
0.5131
0.1729
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.0006
0.0053
-7.6039
-7.5540
-7.5837
1.9608
1.8828
168
APPENDIX K:
FORWARD SPREAD REGRESSION MODEL RESULTS OF PREDICTING EXCESS BOND RETURNS USING
HETEROSKEDASTICITY-AUTOCORRELATION CONSISTENT (HAC) NEWEY-WEST TEST
(TWO-PERIOD & N-PERIOD CASE)
3-month & 6-month Regression using HAC Newey-West Test
Dependent Variable: M3M6EHR
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
FM3M6SPREAD
0.2723
3.4684
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0033
-0.0062
0.5655
33.2531
-88.9650
0.3491
0.5559
0.3672
Std.
Error
0.0445
3.8297
t-Statistic
Prob.
6.1184
0.9056
0.0000
0.3672
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
0.2921
0.5637
1.7163
1.7666
1.7367
2.1801
0.8202
6-month & 1-year Regression using HAC Newey-West Test
Dependent Variable: M6Y1EHR
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
FM6Y1SPREAD
0.3402
10.7984
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0443
0.0351
0.4101
17.4902
-54.9122
4.8180
0.0304
0.0728
Std.
Error
0.0409
5.9580
t-Statistic
Prob.
8.3196
1.8124
0.0000
0.0728
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
0.4300
0.4175
1.0738
1.1241
1.0942
1.9996
3.2848
169
1-year & 2-year Regression using HAC Newey-West Test
1-year & 3-year Regression using HAC Newey-West Test
Dependent Variable: Y1Y2EHR
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Dependent Variable: Y1Y3EHR
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
FY1Y2SPREAD
0.4305
20.8889
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.1576
0.1495
0.4875
24.7209
-73.2506
19.4539
0.0000
0.0110
Std.
Error
0.1275
8.0717
t-Statistic
Prob.
Variable
Coefficient
3.3760
2.5879
0.0010
0.0110
C
FY1Y3SPREAD
0.7426
5.0811
0.7419
0.5287
1.4198
1.4701
1.4402
2.4364
6.6974
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0335
0.0242
0.6518
44.1783
-104.0216
3.6008
0.0605
0.0449
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
Std.
Error
0.1702
2.5031
t-Statistic
Prob.
4.3641
2.0299
0.0000
0.0449
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
1.1322
0.6598
2.0004
2.0507
2.0208
1.1120
4.1204
170
1-year & 5-year Regression using HAC Newey-West Test
1-year & 10-year Regression using HAC Newey-West Test
Dependent Variable: Y1Y5EHR
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Dependent Variable: Y1Y10EHR
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
FY1Y5SPREAD
1.9479
-0.6568
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0029
-0.0067
0.8457
74.3843
-131.6352
0.3014
0.5842
0.6308
Std.
Error
0.4034
1.3627
t-Statistic
Prob.
Variable
Coefficient
4.8292
-0.4820
0.0000
0.6308
C
FY1Y10SPREAD
2.3129
0.6351
1.7949
0.8429
2.5214
2.5717
2.5418
0.9231
0.2323
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0353
0.0260
0.9953
103.0146
-148.8934
3.8041
0.0538
0.2159
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
Std.
Error
0.4030
0.5101
t-Statistic
Prob.
5.7388
1.2452
0.0000
0.2159
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
2.8451
1.0085
2.8470
2.8973
2.8674
0.4551
1.5505
171
APPENDIX L:
TERM SPREAD REGRESSION MODEL WITH MOVING AVERAGE BOND RISK PREMIUM RESULTS
USING HETEROSKEDASTICITY-AUTOCORRELATION CONSISTENT (HAC) NEWEY-WEST TEST
(TWO-PERIOD & N-PERIOD CASE)
3-month & 6-month Regression using HAC Newey-West Test
6-month & 1-year Regression using HAC Newey-West Test
Dependent Variable: M3M3
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Dependent Variable: M6M6
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
M3M6SPREAD
MAVM3M6
-0.0417
0.2031
-0.2750
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0667
0.0487
0.3900
15.8197
-49.5574
3.7160
0.0276
0.0542
Std.
Error
0.0504
0.0843
0.3303
t-Statistic
Prob.
Variable
Coefficient
-0.8290
2.4076
-0.8324
0.4090
0.0178
0.4071
C
M6Y1SPREAD
MAVM6Y1
-0.1274
0.4600
-0.5539
-0.0293
0.3999
0.9824
1.0573
1.0128
2.2870
2.9993
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.2905
0.2768
0.3156
10.3597
-26.9087
21.2897
0.0000
0.000001
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
Std.
Error
0.0645
0.0809
0.4128
t-Statistic
Prob.
-1.9759
5.6834
-1.3419
0.0508
0.0000
0.1825
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.0306
0.3711
0.5590
0.6340
0.5894
2.0093
16.2304
172
1-year & 2-year Regression using HAC Newey-West Test
Dependent Variable: Y1Y1
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
Y1Y2SPREAD
MAVY1Y2
-0.0712
0.1538
-0.4604
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.1152
0.0982
0.2538
6.7000
-3.5931
6.7718
0.0017
0.0001
Std.
Error
0.0449
0.0408
0.2170
t-Statistic
Prob.
-1.5862
3.7678
-2.1213
0.1157
0.0003
0.0363
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.0290
0.2673
0.1232
0.1982
0.1536
1.8920
10.0183
1-year & 3-year Regression using HAC Newey-West Test
Dependent Variable: Y3Y3
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
Y1Y3SPREAD
MAVY1Y3
0.9662
-0.7738
-11.4883
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0847
0.0671
1.7785
328.9549
-211.9118
4.8111
0.0100
0.0000
Std.
Error
0.3902
0.3915
3.8109
t-Statistic
Prob.
2.4760
-1.9767
-3.0146
0.0149
0.0507
0.0032
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.1884
1.8413
4.0170
4.0920
4.0474
2.1035
11.6369
173
1-year & 10-year Regression using HAC Newey-West Test
1-year & 5-year Regression using HAC Newey-West Test
Dependent Variable: Y5Y5
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
Y1Y5SPREAD
MAVY1Y5
4.1984
-1.6902
-56.1917
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.2544
0.2400
3.1070
1003.9670
-271.6068
17.7404
0.0000
0.0000
Std.
Error
0.7776
0.3278
12.6329
t-Statistic
Prob.
5.3992
-5.1560
-4.4480
0.0000
0.0000
0.0000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.2979
3.5641
5.1328
5.2078
5.1632
2.0479
15.4870
Dependent Variable: Y10Y10
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
Y1Y10SPREAD
MAVY1Y10
4.2151
-1.3233
-36.3583
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0489
0.0306
6.0358
3788.8220
-342.6599
2.6734
0.0738
0.0101
Std.
Error
1.6119
0.4497
15.3429
t-Statistic
Prob.
2.6149
-2.9426
-2.3697
0.0103
0.0040
0.0196
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.5804
6.1304
6.4609
6.5359
6.4913
1.7492
4.8079
174
APPENDIX M:
TERM SPREAD REGRESSION MODEL WITH SQUARED EXCESS RETURNS BOND RISK PREMIUM RESULTS
USING HETEROSKEDASTICITY-AUTOCORRELATION CONSISTENT (HAC) NEWEY-WEST TEST
(TWO-PERIOD & N-PERIOD CASE)
3-month & 6-month Regression using HAC Newey-West Test
Dependent Variable: M3M3
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
M3M6SPREAD
M3M6EHR2
-0.0867
0.2062
-0.0017
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0573
0.0391
0.3920
15.9798
-50.0959
3.1580
0.0466
0.000074
Std.
Error
0.0236
0.0508
0.0056
t-Statistic
Prob.
-3.6693
4.0589
-0.3122
0.0004
0.0001
0.7555
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.0293
0.3999
0.9924
1.0674
1.0228
2.2824
10.4290
6-month & 1-year Regression using HAC Newey-West Test
Dependent Variable: M6M6
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
M6Y1SPREAD
M6Y1EHR2
-0.2025
0.5232
-0.1245
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.2804
0.2666
0.3178
10.5069
-27.6638
20.2626
0.0000
0.0000
Std.
Error
0.0276
0.0422
0.0784
t-Statistic
Prob.
-7.3413
12.3898
-1.5875
0.0000
0.0000
0.1154
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.0306
0.3711
0.5732
0.6481
0.6035
2.0704
99.7829
175
1-year & 2-year Regression using HAC Newey-West Test
1-year & 3-year Regression using HAC Newey-West Test
Dependent Variable: Y1Y1
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Dependent Variable: Y3Y3
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
Y1Y2SPREAD
Y1Y2EHR2
-0.1317
0.1422
-0.0031
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0676
0.0497
0.2606
7.0608
-6.3989
3.7690
0.0263
0.0038
Std.
Error
0.0400
0.0535
0.0410
t-Statistic
Prob.
Variable
Coefficient
-3.2910
2.6592
-0.0749
0.0014
0.0091
0.9404
C
Y1Y3SPREAD
Y1Y3EHR2
0.7877
-1.5599
0.4571
-0.0290
0.2673
0.1757
0.2506
0.2061
1.8480
5.8857
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.285
0.272
1.571
256.786
-198.661
20.778
0.0000
0.000014
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
Std.
Error
0.3143
0.4646
0.1064
t-Statistic
Prob.
2.5063
-3.3576
4.2973
0.0137
0.0011
0.0000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.1884
1.8413
3.7694
3.8443
3.7997
1.5929
12.4360
176
1-year & 10-year Regression using HAC Newey-West Test
1-year & 5-year Regression using HAC Newey-West Test
Dependent Variable: Y5Y5
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
Y1Y5SPREAD
Y1Y5EHR2
2.3924
-2.9771
0.6732
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.4153
0.4040
2.7514
787.3151
-258.6017
36.9314
0.0000
0.000032
Std.
Error
1.2289
0.8797
0.1438
t-Statistic
Prob.
1.9468
-3.3843
4.6820
0.0543
0.0010
0.0000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.2979
3.5641
4.8898
4.9647
4.9201
1.5118
11.4689
Dependent Variable: Y10Y10
Sample: 2006M01 2014M11
Included observations: 107
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
Y1Y10SPREAD
Y1Y10EHR2
5.9274
-5.1022
0.8780
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.2770
0.2631
5.2626
2880.3010
-327.9924
19.9188
0.0000
0.0013
Std.
Error
2.0052
1.3972
0.2809
t-Statistic
Prob.
2.9561
-3.6517
3.1256
0.0039
0.0004
0.0023
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.5804
6.1304
6.1868
6.2617
6.2172
1.5734
7.1234
177
APPENDIX N:
TERM SPREAD REGRESSION MODEL WITH GARCH-GENERATED STANDARD DEVIATION BOND RISK PREMIUM
RESULTS USING HETEROSKEDASTICITY-AUTOCORRELATION CONSISTENT (HAC) NEWEY-WEST TEST
(TWO-PERIOD & N-PERIOD CASE)
3-month & 6-month Regression using HAC Newey-West Test
Dependent Variable: M3M3
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
M3M6SPREAD
GARCHM3M6STDEV
-0.0008
0.2379
-0.1995
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0754
0.0575
0.3900
15.6659
-49.0740
4.2013
0.0176
0.0002
Std.
Error
0.0347
0.0612
0.0644
t-Statistic
-0.0222
3.8873
-3.0975
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
6-month & 1-year Regression using HAC Newey-West Test
Dependent Variable: M6M6
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Prob.
Variable
Coefficient
0.9823
0.0002
0.0025
C
M6Y1SPREAD
GARCHM6Y1STDEV
0.0043
0.5168
-0.4384
-0.0300
0.4017
0.9825
1.0579
1.0131
2.3343
9.0255
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.2981
0.2845
0.3151
10.2283
-26.4785
21.8745
0.0000
0.0000
Std.
Error
0.0499
0.0333
0.0817
t-Statistic
0.0856
15.5088
-5.3685
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
Prob.
0.9320
0.0000
0.0000
-0.0322
0.3725
0.5562
0.6316
0.5868
1.9219
138.7064
178
1-year & 2-year Regression using HAC Newey-West Test
Dependent Variable: Y1Y1
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
1-year & 3-year Regression using HAC Newey-West Test
Dependent Variable: Y3Y3
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
Y1Y2SPREAD
GARCHY1Y2STDEV
0.0591
0.2841
-0.3423
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.1226
0.1055
0.2535
6.6176
-3.4007
7.1930
0.0012
0.0003
Std.
Error
0.0734
0.0671
0.1075
t-Statistic
0.8056
4.2320
-3.1827
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
Prob.
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
0.4224
0.0001
0.0019
C
Y1Y3SPREAD
GARCHY1Y3STDEV
-0.0306
0.2680
0.1208
0.1961
0.1513
1.8127
8.9658
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
Coefficient
5.4473
3.9151
-7.9452
0.3327
0.3198
1.5219
238.5816
-193.4049
25.6809
0.0000
0.0000
Std.
Error
1.2059
0.6303
1.3958
t-Statistic
4.5172
6.2110
-5.6921
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
Prob.
0.0000
0.0000
0.0000
-0.2011
1.8453
3.7058
3.7811
3.7363
2.3023
19.4891
179
1-year & 5-year Regression using HAC Newey-West Test
Dependent Variable: Y5Y5
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
1-year & 10-year Regression using HAC Newey-West Test
Dependent Variable: Y10Y10
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
C
Y1Y5SPREAD
GARCHY1Y5STDEV
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
Coefficient
3.7559
-0.3679
-1.7671
0.1025
0.0851
3.4238
1207.4230
-279.3461
5.8845
0.0038
0.0623
Std.
Error
1.9422
1.0385
0.8872
t-Statistic
1.9338
-0.3543
-1.9918
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
Prob.
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
0.0559
0.7238
0.0490
C
Y1Y10SPREAD
GARCHY1Y10STDEV
-0.2880
3.5796
5.3273
5.4027
5.3578
2.1815
2.8524
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
Coefficient
44.4836
31.3826
-45.9519
0.4048
0.3932
4.7943
2367.4740
-315.0329
35.0211
0.0000
0.0000
Std.
Error
6.3699
4.6441
6.6448
t-Statistic
6.9834
6.7575
-6.9155
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
Prob.
0.0000
0.0000
0.0000
-0.5570
6.1547
6.0006
6.0760
6.0312
1.3536
24.4197
180
APPENDIX O:
TERM SPREAD REGRESSION MODEL WITH GARCH-GENERATED VARIANCE BOND RISK PREMIUM RESULTS USING
HETEROSKEDASTICITY-AUTOCORRELATION CONSISTENT (HAC) NEWEY-WEST TEST
(TWO-PERIOD & N-PERIOD CASE)
3-month & 6-month Regression using HAC Newey-West Test
6-month & 1-year Regression using HAC Newey-West Test
Dependent Variable: M3M3
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Dependent Variable: M6M6
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
M3M6SPREAD
GARCHM3M6VAR
-0.0557
0.2369
-0.1336
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.0823
0.0645
0.3885
15.5490
-48.6768
4.6203
0.0120
0.0001
Std.
Error
0.0266
0.0531
0.0359
t-Statistic
Prob.
Variable
Coefficient
-2.0901
4.4623
-3.7243
0.0391
0.0000
0.0003
C
M6Y1SPREAD
GARCHM6Y1VAR
-0.1331
0.4957
-0.2906
-0.0300
0.4017
0.9750
1.0504
1.0056
2.3646
10.8332
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.2937
0.2800
0.3161
10.2932
-26.8139
21.4116
0.0000
0.0000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
Std.
Error
0.0338
0.0329
0.0524
t-Statistic
Prob.
-3.9365
15.0828
-5.5472
0.0002
0.0000
0.0000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.0322
0.3725
0.5625
0.6379
0.5931
1.9243
154.4022
181
1-year & 2-year Regression using HAC Newey-West Test
1-year & 3-year Regression using HAC Newey-West Test
Dependent Variable: Y1Y1
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Dependent Variable: M3M3
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
Y1Y2SPREAD
GARCHY1Y2VAR
-0.1081
0.2691
-0.1444
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.1095
0.0922
0.2554
6.7162
-4.1851
6.3306
0.0026
0.0010
Std.
Error
0.0391
0.0706
0.0533
t-Statistic
Prob.
Variable
Coefficient
-2.7616
3.8109
-2.7079
0.0068
0.0002
0.0079
C
Y1Y3SPREAD
GARCHY1Y3VAR
-0.0018
2.6882
-1.8489
-0.0306
0.2680
0.1356
0.2109
0.1661
1.7860
7.4174
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.3132
0.2999
1.5440
245.5611
-194.9331
23.4872
0.0000
0.000043
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
Std.
Error
0.3212
0.5962
0.4006
t-Statistic
Prob.
-0.0057
4.5085
-4.6155
0.9954
0.0000
0.0000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.2011
1.8453
3.7346
3.8100
3.7651
2.1166
11.1118
182
1-year & 5-year Regression using HAC Newey-West Test
1-year & 10-year Regression using HAC Newey-West Test
Dependent Variable: Y5Y5
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Dependent Variable: Y10Y10
Sample (adjusted): 2006M01 2014M10
Included observations: 106 after adjustments
HAC standard errors & covariance (Prewhitening with lags = 3 from AIC
maxlags = 4, Bartlett kernel, Integer Newey-West automatic bandwidth =
9.0000, NW automatic lag length = 4)
Variable
Coefficient
C
Y1Y5SPREAD
GARCHY1Y5VAR
2.0226
0.0376
-0.6062
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.1203
0.1032
3.3898
1183.5760
-278.2889
7.0407
0.0014
0.0935
Std.
Error
1.5472
0.6829
0.2775
t-Statistic
Prob.
Variable
Coefficient
1.3073
0.0551
-2.1849
0.1940
0.9562
0.0312
C
Y1Y10SPREAD
GARCHY1Y10VAR
-4.6250
8.6186
-2.2642
-0.2880
3.5796
5.3073
5.3827
5.3379
2.1753
2.4252
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
0.1178
0.1007
5.8365
3508.6710
-335.8838
6.8801
0.0016
0.0003
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
Std.
Error
3.3847
2.9963
0.6543
t-Statistic
Prob.
-1.3664
2.8764
-3.4605
0.1748
0.0049
0.0008
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
Wald F-statistic
-0.5570
6.1547
6.3940
6.4694
6.4246
1.5944
8.7980
183
APPENDIX P:
MACROECONOMIC VARIABLES FOR THE PANEL REGRESSION
Economic
Activity
Prices
PesoDollar
Rate
Excess
Liqudity
OFW
Remittances
Monetary
Stance
US Prices
Federal
Funds
Rate
Government
Budget Deficit
(% of GDP)
Government
debt (% of
GDP)
Stock
Market
Activity
Gross
International
Reserves
Lagged
BRP
Bond
Spread
Period
gmersales
ginf
gforex
gm2
gofwrem
grrp
guscpi
gfedrate
gdeficit
gdebt
gpsei
ggir
brplag
spread
2006M01
1.0395
0.0700
0.0000
7.6805
0.0000
0.000
0.0399
0.0000
-2.2709
0.0276
29.5713
2.7132
0.5260
2006M02
4.5775
0.1300
-0.0152
9.0204
-0.0554
0.000
0.0360
0.0466
0.6159
-0.2732
-0.0105
23.9039
2.8443
0.5970
2006M03
6.8537
0.0700
-0.0115
8.7325
0.1920
0.000
0.0336
0.0223
0.0901
-0.1398
0.0344
24.9294
3.0302
0.6030
2006M04
1.1194
0.0300
0.0027
9.5214
-0.1293
0.000
0.0355
0.0436
-1.6484
-3.8478
0.0340
24.7251
0.7813
3.3030
2006M05
-0.2235
0.0500
0.0149
12.5003
0.2705
0.000
0.0417
0.0313
-0.6706
-0.0258
0.0113
21.2306
0.8321
0.4410
2006M06
-2.0497
0.0300
0.0197
14.0286
-0.0326
0.000
0.0432
0.0101
1.1774
-0.8488
-0.0511
19.1859
0.8913
0.4370
2006M07
1.8194
0.0600
-0.0143
13.9473
-0.0511
0.000
0.0415
0.0501
-2.3443
-4.9986
0.0973
20.4050
0.5778
-1.7450
2006M08
-3.6870
0.0300
-0.0198
12.8876
0.0415
0.000
0.0382
0.0019
-1.8427
-1.4262
-0.0329
20.0463
0.5581
0.5510
2006M09
0.9131
0.0100
-0.0187
14.9499
-0.0709
0.000
0.0206
0.0000
-2.1322
-3.0667
0.1057
16.4545
0.5698
0.4660
2006M10
-3.3099
0.0200
-0.0079
15.5334
0.1694
0.000
0.0131
0.0000
-0.6400
-2.0703
0.0594
23.2717
0.5712
0.5580
2006M11
3.7728
0.0200
-0.0032
18.7113
-0.0352
0.000
0.0197
0.0000
-0.6458
-1.9072
0.0295
25.4208
0.5280
0.5130
2006M12
3.6440
-0.0200
-0.0076
22.9065
0.1534
0.000
0.0254
-0.0019
2.1276
-2.1388
0.0696
24.1823
0.5699
0.0070
2007M01
5.0277
-0.0100
-0.0112
22.2418
-0.1668
0.000
0.0208
0.0019
3.1779
-0.1638
0.0861
16.1387
0.6117
0.0000
2007M02
1.0593
0.0000
-0.0109
22.1364
-0.0126
0.000
0.0242
0.0019
-1.3739
-1.5881
-0.0530
19.8242
0.5877
0.6280
2007M03
5.1134
0.0200
0.0028
27.1078
0.2020
0.000
0.0278
0.0000
-4.0032
-0.1100
0.0444
19.5641
0.6243
0.3880
2007M04
2.4956
0.0500
-0.0143
28.4363
-0.0868
0.000
0.0257
-0.0019
-1.3583
-4.7798
0.0210
20.3195
0.6496
0.2840
2007M05
5.8240
0.0400
-0.0211
20.8602
0.0383
0.000
0.0269
0.0000
-1.1462
-0.9133
0.0624
22.1928
0.6208
0.8390
2007M06
5.4208
0.0300
-0.0140
20.4141
-0.0981
0.000
0.0269
0.0000
-1.4476
-4.0214
0.0536
24.8987
0.6094
-0.4670
2007M07
6.7056
0.0700
-0.0116
19.4278
-0.0172
-0.120
0.0236
0.0019
1.0396
6.5068
-0.0436
31.7047
0.6571
0.1240
2007M08
9.2975
0.0200
0.0098
14.1462
0.1007
-0.091
0.0197
-0.0456
7.7129
-0.6619
-0.0388
41.5235
0.6697
0.6940
2007M09
1.9490
0.0400
0.0013
12.0153
-0.0556
0.000
0.0276
-0.0159
-2.0449
-0.8902
0.0617
43.1096
0.5320
0.9780
2007M10
10.9215
0.0500
-0.0380
12.3970
0.2181
-0.033
0.0354
-0.0364
-0.8982
-5.1043
0.0521
45.6687
0.4937
0.7510
2007M11
0.9642
0.0800
-0.0262
9.9879
-0.1451
-0.034
0.0431
-0.0567
-37.5986
-3.2153
-0.0480
44.4605
0.4677
0.7330
2007M12
0.1423
0.1000
-0.0341
10.6946
0.1769
-0.036
0.0408
-0.0557
-1.4630
0.7551
0.0120
46.9563
0.4144
0.8220
184
2008M01
4.3288
0.1200
-0.0193
7.4956
-0.0952
-0.030
0.0428
-0.0708
-0.4436
-2.7549
-0.0982
46.9115
0.3982
0.6150
2008M02
6.0272
0.0700
-0.0065
7.0889
-0.0043
-0.046
0.0403
-0.2437
0.3633
-1.5061
-0.0416
47.8590
0.3769
0.8190
2008M03
-3.6509
0.1300
0.0143
1.8732
0.1344
0.000
0.0398
-0.1242
-0.0196
-0.4675
-0.0464
48.3690
0.2978
0.8240
2008M04
6.3780
0.2800
0.0137
0.4736
-0.0123
0.000
0.0394
-0.1264
-2.3831
-0.5689
-0.0787
44.9029
0.2990
0.7540
2008M05
-0.0821
0.1600
0.0259
3.2830
0.0139
0.000
0.0418
-0.1316
-0.7273
1.7777
0.0282
41.5396
0.1375
1.0850
2008M06
-1.0096
0.2400
0.0321
4.5635
0.0147
0.042
0.0502
0.0101
-0.8905
3.0353
-0.1300
39.1516
0.1543
-0.2190
2008M07
-1.2731
0.1400
0.0153
3.9005
-0.0579
0.054
0.0560
0.0050
-21.0636
-1.0176
0.0476
31.6998
0.1623
0.4420
2008M08
0.4772
0.0400
-0.0018
9.7952
-0.0254
0.053
0.0537
-0.0050
-1.1091
-0.0270
0.0431
20.5267
0.1749
-0.0330
2008M09
5.2344
-0.0100
0.0405
13.4449
0.0007
0.038
0.0494
-0.0950
-13.8509
-15.9064
-0.0441
18.7537
0.1179
0.5960
2008M10
3.2163
-0.0100
0.0285
13.3032
0.0764
0.000
0.0366
-0.4641
-0.5858
1.0839
-0.2407
10.6268
0.1025
-0.2780
2008M11
7.0480
-0.0500
0.0242
15.4718
-0.0860
0.000
0.0107
-0.5979
-0.5156
-0.7070
0.0105
12.5581
0.1000
0.2210
2008M12
1.4758
-0.0900
-0.0222
15.4318
0.0735
-0.023
0.0009
-0.5897
-0.6677
-1.8405
-0.0501
11.2582
0.1129
0.0510
2009M01
-9.8985
0.0300
-0.0184
15.8887
-0.1010
-0.067
0.0003
-0.0625
25.3899
4.4362
-0.0255
12.7507
0.0413
0.3760
2009M02
-2.6767
0.0800
0.0080
14.3199
0.0431
-0.086
0.0024
0.4667
-0.2381
-2.0707
0.0258
7.2663
0.0515
0.2290
2009M03
7.7598
0.0400
0.0184
14.9854
0.1147
-0.044
-0.0038
-0.1818
0.8156
-0.6959
0.0609
6.6002
0.0522
0.2210
2009M04
-1.4223
0.0300
-0.0050
13.0841
-0.0202
-0.033
-0.0074
-0.1667
-1.1502
-0.8053
0.0590
8.1437
0.0638
0.1690
2009M05
-0.7566
-0.0300
-0.0144
14.7796
0.0280
-0.030
-0.0128
0.2000
-2.4403
-9.0062
0.1359
9.2630
0.0705
0.2330
2009M06
3.0553
0.0000
0.0080
12.0225
0.0112
-0.051
-0.0143
0.1667
1.6570
0.1639
0.0204
7.5649
0.0806
0.1970
2009M07
3.6348
-0.0200
0.0050
12.5069
-0.0031
-0.029
-0.0210
-0.2381
0.1449
0.2962
0.1478
8.8574
0.0671
0.2480
2009M08
5.0092
0.0200
0.0003
12.7350
-0.0836
-0.030
-0.0148
0.0000
-0.3653
-3.7973
0.0307
12.9271
0.0810
0.1400
2009M09
5.5046
0.0700
-0.0004
10.8915
0.0569
0.000
-0.0129
-0.0625
0.2516
-0.7103
-0.0289
15.8906
0.0915
0.2460
2009M10
5.0000
0.1200
-0.0268
11.7984
0.0583
0.000
-0.0018
-0.2000
0.0375
-0.7804
0.0384
20.0878
0.1063
0.1180
2009M11
5.5000
0.1000
0.0038
11.5776
-0.0471
0.000
0.0184
0.0000
-0.7743
1.2157
0.0469
19.9287
0.1182
0.1860
2009M12
6.0000
0.0900
-0.0130
7.6200
0.0745
0.000
0.0272
0.0000
3.0374
-6.6198
0.0025
17.8207
0.1092
0.4950
2010M01
32.4400
0.0200
-0.0084
8.1000
-0.1244
0.000
0.0263
-0.0833
0.4274
-0.8650
-0.0326
16.1625
0.1169
0.2470
2010M02
14.6600
0.0600
0.0061
9.9000
0.0294
0.000
0.0214
0.1818
-0.1060
-9.3612
0.0307
17.5719
0.1050
0.4380
2010M03
7.0100
0.0400
-0.0123
9.8300
0.0993
0.063
0.0231
0.2308
0.9244
-0.7111
0.0388
16.7983
0.1189
0.1240
2010M04
10.8000
0.0400
-0.0243
12.0200
-0.0214
0.000
0.0224
0.2500
-1.0407
0.3906
0.0406
19.4007
0.1360
0.1280
2010M05
14.9000
-0.0300
0.0217
10.2600
0.0386
0.000
0.0202
0.0000
-12.7457
-0.4427
-0.0053
20.4607
0.1548
0.1040
2010M06
15.4000
-0.0200
0.0154
9.6300
0.0283
0.000
0.0105
-0.1000
0.1341
0.6538
0.0305
23.3350
0.1690
0.1820
185
2010M07
5.5000
0.0000
0.0004
9.5500
-0.0042
0.000
0.0124
0.0000
-0.0557
2.0232
0.0161
22.1057
0.1804
0.2750
2010M08
5.5000
0.0400
-0.0030
7.9900
-0.0704
0.000
0.0115
0.0556
-1.0403
-1.1376
0.0406
20.2771
0.1986
0.1830
2010M09
6.9000
0.0200
-0.0405
7.5000
0.0650
0.000
0.0114
0.0000
-25.0211
-0.2864
0.1497
26.3947
0.2160
0.2060
2010M10
10.5000
0.0200
-0.0194
10.1900
0.0457
0.000
0.0117
0.0000
-0.6682
-2.3830
0.0411
32.3812
0.2291
0.2100
2010M11
7.5000
0.1100
0.0032
7.0000
-0.0364
0.000
0.0114
0.0000
-1.0458
-0.3989
-0.0738
37.1269
0.1296
0.3060
2010M12
8.0000
0.0700
-0.0007
10.6000
0.0505
0.000
0.0150
-0.0526
-93.6084
-11.0271
0.0626
40.9796
0.1240
0.3200
2011M01
7.0000
0.0400
0.0119
9.6000
-0.1282
0.000
0.0163
-0.0556
-1.2125
-0.6509
-0.0761
39.3686
0.1347
0.2700
2011M02
8.0000
0.1100
-0.0086
9.7000
0.0162
-0.059
0.0211
-0.0588
-2.6009
-2.0187
-0.0296
39.6068
0.1369
0.0180
2011M03
-3.7000
0.0100
-0.0041
10.6000
0.0770
0.000
0.0268
-0.1250
-0.1563
-0.2301
0.0766
44.7019
0.0970
0.4120
2011M04
-1.6000
0.0600
-0.0064
7.5000
-0.0004
0.063
0.0316
-0.2857
-2.4482
0.1520
0.0652
45.8953
0.1039
0.1730
2011M05
-2.5000
0.0300
-0.0025
8.6000
0.0448
0.059
0.0357
-0.1000
-1.3656
-0.3911
-0.0173
44.3783
0.1177
0.2750
2011M06
-2.2000
0.0400
0.0181
11.9000
0.0291
0.000
0.0356
0.0000
-0.1989
-0.6601
0.0110
41.6630
0.1358
0.1870
2011M07
1.3000
0.0300
-0.0251
8.8000
-0.0127
0.000
0.0363
-0.2222
2.4432
-3.9940
0.0495
46.5543
0.1476
0.1300
2011M08
3.4000
0.0100
-0.0091
10.0000
-0.0264
0.000
0.0377
0.4286
-1.3482
-0.5778
-0.0344
52.1679
0.1044
0.2050
2011M09
0.8000
0.0700
0.0144
7.6000
0.0393
0.000
0.0387
-0.2000
-3.0066
-10.0809
-0.0802
39.8476
0.1122
0.0410
2011M10
5.5000
0.0400
0.0086
6.9000
0.0239
0.000
0.0353
-0.1250
0.1490
-0.9551
0.0835
32.6804
0.0909
-0.7060
2011M11
4.8000
0.0300
0.0021
7.2000
0.0034
0.000
0.0339
0.1429
0.0351
4.3352
-0.0283
25.8243
0.0941
0.3300
2011M12
5.5000
0.0100
0.0069
6.3000
0.0092
0.000
0.0296
-0.1250
3.6130
-3.9177
0.0382
20.7290
0.0506
-0.6550
2012M01
8.6000
0.0200
-0.0039
7.2000
-0.1348
-0.056
0.0293
0.1429
-0.8549
-1.0967
0.0710
21.7451
0.0635
0.1610
2012M02
8.0000
0.0000
-0.0220
7.2100
0.0195
0.000
0.0287
0.2500
-1.6683
22.9730
0.0460
20.5369
0.0782
0.1610
2012M03
13.3000
0.0300
0.0047
5.8000
0.0695
-0.059
0.0265
0.3000
-3.6862
-0.9881
0.0429
15.3756
0.0697
0.4210
2012M04
8.3000
0.0600
-0.0037
9.0000
0.0020
0.000
0.0230
0.0769
-2.0839
1.0842
0.0186
11.7522
0.0844
0.0130
2012M05
11.8000
0.0200
0.0035
7.8000
0.0426
0.000
0.0170
0.1429
-1.6401
2.1236
-0.0214
10.4984
0.1003
0.0120
2012M06
8.3000
0.0600
-0.0016
7.0900
0.0210
0.000
0.0166
0.0000
-0.4140
2.1031
0.0305
10.3389
0.1148
0.1210
2012M07
11.0000
0.0500
-0.0203
8.6000
-0.0013
0.000
0.0140
0.0000
2.3725
-0.6756
0.0117
10.9553
0.1302
0.0820
2012M08
-0.1000
0.0800
0.0033
7.1000
-0.0067
-0.063
0.0170
-0.1875
-1.0643
3.2316
-0.0210
6.3038
0.1300
0.2510
2012M09
2.3000
0.0200
-0.0071
8.4000
0.0231
0.000
0.0199
0.0769
-14.0139
2.4680
0.0288
9.1184
0.1162
0.2870
2012M10
7.8000
0.0000
-0.0072
9.4000
0.0487
-0.067
0.0216
0.1429
-0.6448
-0.8810
0.0147
7.8011
0.1015
0.3480
2012M11
4.4000
0.0100
-0.0080
10.6100
-0.0048
0.000
0.0176
0.0000
-0.0162
1.4569
0.0398
10.1398
0.1158
0.1880
2012M12
8.0000
0.0300
-0.0027
7.8000
0.0293
0.000
0.0160
0.0000
9.0867
-1.2845
0.0305
11.3262
0.1334
0.0350
186
2013M01
3.9000
0.0300
-0.0068
10.8000
-0.1397
0.000
0.0165
-0.1250
-0.8313
-3.5036
0.0740
10.2331
0.1376
0.2750
2013M02
1.3000
0.0300
-0.0015
10.6000
0.0008
0.000
0.0150
0.0714
-0.3984
-0.3012
0.0767
8.5858
0.1486
0.2360
2013M03
-1.5000
0.0200
0.0010
10.6000
0.0402
0.000
0.0150
-0.0667
1.9958
0.6694
0.0187
10.2747
0.1686
0.0000
2013M04
9.2000
0.0000
0.0106
10.4000
0.0287
0.000
0.0110
0.0714
-2.0456
-0.6024
0.0326
8.7217
0.1890
0.0710
2013M05
5.4000
0.0500
0.0039
10.4000
0.0329
0.000
0.0110
-0.2667
-1.3577
1.4796
-0.0069
7.7351
0.1896
0.1000
2013M06
6.4000
0.0400
0.0390
21.1000
0.0297
0.000
0.0120
-0.1818
-0.3580
-0.5063
-0.0793
6.7331
0.2111
0.0250
2013M07
4.6000
0.0300
0.0126
28.0000
0.0058
0.000
0.0150
0.0000
5.2977
5.9426
0.0269
4.2796
0.2201
0.0520
2013M08
7.6000
0.0300
0.0094
29.1900
-0.0041
0.000
0.0150
-0.1111
-1.4115
-0.8556
-0.0849
2.6796
0.2280
-0.2020
2013M09
5.9000
0.0800
-0.0007
31.6000
0.0077
0.000
0.0120
0.0000
-1.8500
1.2315
0.0192
1.8026
0.2456
0.1000
2013M10
0.7000
0.0200
-0.0148
33.0000
0.0668
0.000
0.0090
0.1250
-0.3964
-0.4587
0.0636
2.2755
0.2179
0.4200
2013M11
2.7000
0.0700
0.0087
36.6000
0.0006
0.000
0.0100
-0.1111
-1.0890
-1.4703
-0.0572
-0.4304
0.2418
0.0890
2013M12
0.9000
0.0800
0.0125
33.8000
0.0456
0.000
0.0120
0.1250
-53.5983
1.1590
-0.0514
-0.7686
0.2665
0.1240
2014M01
1.8000
0.0700
0.0188
39.5000
-0.1723
0.000
0.0160
-0.2222
-0.4300
-1.7478
0.0257
-6.9378
0.2779
0.1000
2014M02
1.0000
0.0100
-0.0007
38.1000
-0.0024
0.000
0.0110
0.0000
-0.7160
-0.1610
0.0635
-3.6876
0.1994
0.7470
2014M03
1.4000
0.0200
-0.0023
36.0000
0.0490
0.000
0.0150
0.1429
3.1352
-0.9350
0.0006
-5.1286
0.1844
0.4810
2014M04
1.3000
0.0200
-0.0034
33.6000
0.0158
0.000
0.0200
0.1250
-3.0119
6.6384
0.0434
-4.0487
0.1885
-0.1790
2014M05
1.7000
0.0900
-0.0161
27.5000
0.0347
0.000
0.0210
0.0000
-0.8543
1.8144
-0.0090
-2.1043
0.1420
0.6600
2014M06
6.8000
0.0200
-0.0023
24.2000
0.0349
0.000
0.0210
0.1111
-6.3035
0.0383
0.0296
-0.6426
0.0595
0.7190
2014M07
11.9000
0.0700
-0.0080
18.7000
0.0068
0.000
0.0200
-0.1000
-0.9718
-0.4853
0.0030
-3.0394
0.0739
0.1400
2014M08
13.7000
0.0300
0.0069
18.8000
-0.0051
0.071
0.0170
0.0000
-17.9496
-0.8357
0.0271
-2.4351
0.0767
0.2880
2014M09
4.7000
0.0200
0.0070
16.0000
0.0258
0.067
0.0170
0.0000
-1.1740
4.1820
0.0329
-4.7306
0.0777
0.3630
2014M10
5.3000
0.0300
0.0164
15.2000
0.0557
0.000
0.0170
0.0000
-0.5133
-2.2709
-0.0093
-5.0214
2.7132
0.2370
187
APPENDIX Q:
RESULTS OF THE FIXED EFFECTS PANEL REGRESSION FOR THE WHOLE SAMPLE CASE
(ALL VARIABLES & SELECTED VARIABLES)
Whole Sample Macro-BRP Fixed Effects Panel Regression
(All Variables)
Dependent Variable: BRP
Sample (adjusted): 2006M02 2014M10
Periods included: 105
Cross-sections included: 6
Total panel (balanced) observations: 630
Std.
Variable
Coefficient
t-Statistic
Error
C
0.3513
0.0559
6.2801
BRPLAG
0.7662
0.0247
31.0612
MERSALES
-0.0055
0.0024
-2.3344
INF
-0.0675
0.2716
-0.2484
GFOREX
0.9399
0.8709
1.0791
M2
-0.0028
0.0016
-1.7688
GOFWREM
-0.0363
0.1573
-0.2307
FRRP
0.0847
0.0826
1.0256
USCPI
-0.2129
0.9665
-0.2203
GFEDRATE
-0.0478
0.0801
-0.5972
GDEFICIT
-0.0020
0.0010
-1.9384
DEBT
0.0042
0.0065
0.6398
GPSEI
0.3305
0.2555
1.2935
Effects Specification
Cross-section fixed (dummy variables)
R-squared
0.1095
Mean dependent var
Adjusted R-squared
0.0922
S.D. dependent var
S.E. of regression
0.2554
Akaike info criterion
Sum squared resid
6.7162
Schwarz criterion
Log likelihood
-4.1851
Hannan-Quinn criter.
F-statistic
6.3306
Durbin-Watson stat
Prob(F-statistic)
0.0026
Wald F-statistic
Prob(Wald F-statistic)
0.0010
Prob.
0.0000
0.0000
0.0199
0.8039
0.2809
0.0774
0.8176
0.3055
0.8257
0.5506
0.0530
0.5226
0.1963
-0.0306
0.2680
0.1356
0.2109
0.1661
1.7860
7.4174
Whole Sample Macro-BRP Fixed Effects Panel Regression
(Selected Variables)
Dependent Variable: BRP
Sample (adjusted): 2006M02 2014M10
Periods included: 105
Cross-sections included: 6
Total panel (balanced) observations: 630
Std.
Variable
Coefficient
t-Statistic
Error
C
0.3669
0.0435
8.4423
BRPLAG
0.7655
0.0238
32.1238
MERSALES
-0.0067
0.0024
-2.8274
GFOREX(-1)
1.7091
0.7947
2.1505
M2
-0.0028
0.0014
-1.9458
GFEDRATE(-1)
0.2083
0.0792
2.6305
Effects Specification
Cross-section fixed (dummy variables)
R-squared
0.9208
Mean dependent var
Adjusted R-squared
0.9195
S.D. dependent var
S.E. of regression
0.2970
Akaike info criterion
Sum squared resid
54.6098
Schwarz criterion
Log likelihood
-123.5966
Hannan-Quinn criter.
F-statistic
719.8925
Durbin-Watson stat
Prob(F-statistic)
0.0000
Wald F-statistic
Prob(Wald F-statistic)
0.9208
Prob.
0.0000
0.0000
0.0048
0.0319
0.0521
0.0087
0.9208
0.9195
0.2970
54.6098
-123.596
719.8925
0.0000
188
APPENDIX R:
RESULTS OF THE FIXED EFFECTS PANEL REGRESSION FOR THE PERIODICAL CASE (2006-2010 & 2011-2014)
(ALL VARIABLES & SELECTED VARIABLES)
2006 to 2010: Macro-BRP Fixed Effects Panel Regression
(All Variables)
Dependent Variable: BRP
Sample (adjusted): 2006M02 2010M12
Periods included: 59
Cross-sections included: 6
Total panel (balanced) observations: 354
Std.
Variable
Coefficient
t-Statistic
Error
C
0.2967
0.0882
3.3621
BRPLAG
0.7330
0.0358
20.4646
MERSALES
-0.0014
0.0031
-0.4350
INF
0.2617
0.4014
0.6520
GFOREX
1.4017
1.1372
1.2326
M2
0.0027
0.0042
0.6459
GOFWREM
-0.0123
0.1916
-0.0641
FRRP
0.0475
0.1129
0.4207
USCPI
-1.1662
1.2535
-0.9303
GFEDRATE
0.1242
0.1219
1.0190
GDEFICIT
-0.0033
0.0013
-2.4652
DEBT
0.0008
0.0100
0.0825
GPSEI
-0.1273
0.3609
-0.3527
Effects Specification
Cross-section fixed (dummy variables)
R-squared
0.8917
Mean dependent var
Adjusted R-squared
0.8862
S.D. dependent var
S.E. of regression
0.3332
Akaike info criterion
Sum squared resid
37.3021
Schwarz criterion
Log likelihood
-104.0106
Hannan-Quinn criter.
F-statistic
162.6834
Durbin-Watson stat
Prob(F-statistic)
0.0000
Prob.
0.0009
0.0000
0.6638
0.5148
0.2186
0.5188
0.9489
0.6742
0.3529
0.3089
0.0142
0.9343
0.7246
2006 to 2010: Macro-BRP Fixed Effects Panel Regression
(Selected Variables)
Dependent Variable: BRP
Sample (adjusted): 2006M02 2010M12
Periods included: 59
Cross-sections included: 6
Total panel (balanced) observations: 354
Std.
Variable
Coefficient
t-Statistic
Error
C
0.3492
0.0455
7.6795
BRPLAG
0.7153
0.0343
20.8608
GFOREX(-1)
3.4374
1.0937
3.1429
GFEDRATE
0.2527
0.1164
2.1716
Effects Specification
Cross-section fixed (dummy variables)
R-squared
0.8918
Mean dependent var
Adjusted R-squared
0.8893
S.D. dependent var
S.E. of regression
0.3286
Akaike info criterion
Sum squared resid
37.2415
Schwarz criterion
Log likelihood
-103.7227
Hannan-Quinn criter.
F-statistic
355.6102
Durbin-Watson stat
Prob(F-statistic)
0.0000
Prob.
0.0000
0.0000
0.0018
0.0306
1.1842
0.9877
0.6369
0.7352
0.6760
2.1962
1.1842
0.9877
0.6893
0.8861
0.7676
2.2106
189
2011 to 2014: Macro-BRP Fixed Effects Panel Regression
(All Variables)
Dependent Variable: BRP
Sample: 2011M01 2014M10
Periods included: 46
Cross-sections included: 6
Total panel (balanced) observations: 276
Std.
Variable
Coefficient
t-Statistic
Error
C
0.5369
0.1023
5.2495
BRPLAG
0.7122
0.0393
18.1324
MERSALES
-0.0142
0.0045
-3.1685
INF
-0.6943
0.7940
-0.8744
GFOREX
-0.7116
1.4703
-0.4840
M2
-0.0050
0.0020
-2.5015
GOFWREM
-0.0866
0.3771
-0.2297
FRRP
0.2149
0.1531
1.4034
USCPI
0.2312
2.2587
0.1024
GFEDRATE
-0.2745
0.1496
-1.8347
GDEFICIT
-0.0014
0.0019
-0.7666
DEBT
0.0094
0.0103
0.9111
GPSEI
0.6400
0.3970
1.6122
Effects Specification
Cross-section fixed (dummy variables)
R-squared
0.9591
Mean dependent var
Adjusted R-squared
0.9564
S.D. dependent var
S.E. of regression
0.2324
Akaike info criterion
Sum squared resid
13.9369
Schwarz criterion
Log likelihood
20.4217
Hannan-Quinn criter.
F-statistic
355.5020
Durbin-Watson stat
Prob(F-statistic)
0.0000
Prob.
0.0000
0.0000
0.0017
0.3827
0.6288
0.0130
0.8185
0.1617
0.9185
0.0677
0.4440
0.3631
0.1081
1.3633
1.1126
-0.0175
0.2186
0.0772
1.6714
2011 to 2014: Macro-BRP Fixed Effects Panel Regression
(Selected Variables)
Dependent Variable: BRP
Sample (adjusted): 2011M02 2014M10
Periods included: 45
Cross-sections included: 6
Total panel (balanced) observations: 270
Std.
Variable
Coefficient
t-Statistic
Error
C
0.4946
0.0747
6.6236
BRPLAG
0.7342
0.0380
19.3465
MERSALES
-0.0179
0.0036
-4.9700
M2
-0.0048
0.0015
-3.2185
FRRP
0.3223
0.1320
2.4408
GFEDRATE(-1)
0.3163
0.0997
3.1742
DEBT(-1)
0.0133
0.0074
1.7992
GPSEI
0.9865
0.3319
2.9722
Effects Specification
Cross-section fixed (dummy variables)
R-squared
0.9597
Mean dependent var
Adjusted R-squared
0.9579
S.D. dependent var
S.E. of regression
0.2282
Akaike info criterion
Sum squared resid
13.3842
Schwarz criterion
Log likelihood
22.4733
Hannan-Quinn criter.
F-statistic
510.4842
Durbin-Watson stat
Prob(F-statistic)
0.0000
Prob.
0.0000
0.0000
0.0000
0.0015
0.0153
0.0017
0.0732
0.0032
1.3630
1.1116
-0.0702
0.1031
-0.0006
1.6277
190
APPENDIX S:
RESULTS OF THE FIXED EFFECTS PANEL REGRESSION FOR THE SHORT RATE BRP AND LONG RATE BRP
(2006-2014) (ALL VARIABLES & SELECTED VARIABLES)
2006 to 2014: Macro-BRP Fixed Effects Panel Regression for the Short
Rate (All Variables)
Dependent Variable: BRP
Sample (adjusted): 2006M02 2014M10
Periods included: 105
Cross-sections included: 3
Total panel (balanced) observations: 315
Std.
Variable
Coefficient
t-Statistic
Prob.
Error
C
0.1003
0.0523
1.9194
0.0559
BRPLAG
0.7639
0.0329
23.2436
0.0000
MERSALES
-0.0039
0.0028
-1.3956
0.1639
INF
-0.0876
0.3144
-0.2787
0.7807
GFOREX
-0.1344
1.0145
-0.1325
0.8947
M2
-0.0002
0.0018
-0.0843
0.9329
GOFWREM
0.0108
0.1829
0.0589
0.9531
FRRP
0.0279
0.0960
0.2904
0.7717
USCPI
1.3544
1.1725
1.1552
0.2489
GFEDRATE
-0.0461
0.0931
-0.4953
0.6207
GDEFICIT
-0.0005
0.0012
-0.3894
0.6973
DEBT
-0.0042
0.0076
-0.5497
0.5829
GPSEI
0.0067
0.2977
0.0226
0.9820
Effects Specification
Cross-section fixed (dummy variables)
R-squared
0.7684
Mean dependent var
0.4930
Adjusted R-squared
0.7576
S.D. dependent var
0.4991
S.E. of regression
0.2457
Akaike info criterion
0.0774
Sum squared resid
18.1175
Schwarz criterion
0.2561
Log likelihood
2.8066
Hannan-Quinn criter.
0.1488
F-statistic
71.0837
Durbin-Watson stat
2.0791
Prob(F-statistic)
0.0000
2006 to 2014: Macro-BRP Fixed Effects Panel Regression for the Short
Rate (Selected Variables)
Dependent Variable: BRP
Sample (adjusted): 2006M02 2014M10
Periods included: 105
Cross-sections included: 3
Total panel (balanced) observations: 315
Std.
Variable
Coefficient
t-Statistic
Prob.
Error
C
0.0931
0.0205
4.5411
0.0000
BRPLAG
0.7873
0.0300
26.2604
0.0000
Effects Specification
Cross-section fixed (dummy variables)
R-squared
0.7645
Mean dependent var
0.4930
Adjusted R-squared
0.7622
S.D. dependent var
0.4991
S.E. of regression
0.2434
Akaike info criterion
0.0243
Sum squared resid
18.4234
Schwarz criterion
0.0720
Log likelihood
0.1690
Hannan-Quinn criter.
0.0434
F-statistic
336.4543
Durbin-Watson stat
2.1000
Prob(F-statistic)
0.0000
191
2006 to 2014: Macro-BRP Fixed Effects Panel Regression for the Long
Rate (All Variables)
Dependent Variable: BRP
Sample (adjusted): 2006M02 2014M10
Periods included: 105
Cross-sections included: 3
Total panel (balanced) observations: 315
Std.
Variable
Coefficient
t-Statistic
Prob.
Error
C
0.6831
0.1208
5.6537
0.0000
BRPLAG
0.7339
0.0393
18.6874
0.0000
MERSALES
-0.0072
0.0038
-1.8921
0.0594
INF
-0.1185
0.4445
-0.2666
0.7899
GFOREX
2.0057
1.4105
1.4220
0.1561
M2
-0.0060
0.0026
-2.2821
0.0232
GOFWREM
-0.1064
0.2560
-0.4155
0.6781
FRRP
0.1593
0.1352
1.1783
0.2396
USCPI
-1.8374
1.5602
-1.1776
0.2399
GFEDRATE
-0.0365
0.1305
-0.2800
0.7797
GDEFICIT
-0.0033
0.0017
-2.0199
0.0443
DEBT
0.0131
0.0106
1.2316
0.2191
GPSEI
0.6879
0.4141
1.6612
0.0977
Effects Specification
Cross-section fixed (dummy variables)
R-squared
0.8529
Mean dependent var
2.0323
Adjusted R-squared
0.8460
S.D. dependent var
0.8712
S.E. of regression
0.3418
Akaike info criterion
0.7375
Sum squared resid
35.0570
Schwarz criterion
0.9162
Log likelihood
-101.1589
Hannan-Quinn criter.
0.8089
F-statistic
124.2553
Durbin-Watson stat
2.0345
Prob(F-statistic)
0.0000
2006 to 2014: Macro-BRP Fixed Effects Panel Regression for the Long
Rate (Selected Variables)
Dependent Variable: BRP
Sample (adjusted): 2006M02 2014M10
Periods included: 105
Cross-sections included: 3
Total panel (balanced) observations: 315
Std.
Variable
Coefficient
t-Statistic
Prob.
Error
C
0.6157
0.0939
6.5551
0.0000
BRPLAG
0.7457
0.0374
19.9372
0.0000
MERSALES
-0.0086
0.0038
-2.2561
0.0248
GFOREX
2.5622
1.3518
1.8954
0.0590
M2
-0.0051
0.0024
-2.1350
0.0336
GFEDRATE(-1)
0.2446
0.1275
1.9183
0.0560
GDEFICIT
-0.0032
0.0016
-1.9789
0.0487
GPSEI
0.7952
0.3723
2.1362
0.0335
Effects Specification
Cross-section fixed (dummy variables)
R-squared
0.8524
Mean dependent var
2.0323
Adjusted R-squared
0.8481
S.D. dependent var
0.8712
S.E. of regression
0.3396
Akaike info criterion
0.7090
Sum squared resid
35.1691
Schwarz criterion
0.8281
Log likelihood
-101.6619
Hannan-Quinn criter.
0.7566
F-statistic
195.7728
Durbin-Watson stat
2.0113
Prob(F-statistic)
0.0000
192
APPENDIX T:
RESULTS OF THE FIXED EFFECTS PANEL REGRESSION FOR THE SHORT RATE BRP
WITH PERIODICAL TESTS (ALL VARIABLES & SELECTED VARIABLES)
2006 to 2010: Macro-BRP Fixed Effects Panel Regression for the Short
Rate (All Variables)
Dependent Variable: BRP
Sample (adjusted): 2006M02 2010M12
Periods included: 59
Cross-sections included: 3
Total panel (balanced) observations: 177
Std.
Variable
Coefficient
t-Statistic
Prob.
Error
C
0.0699
0.0963
0.7257
0.4691
BRPLAG
0.7168
0.0481
14.8983
0.0000
MERSALES
-0.0027
0.0040
-0.6778
0.4989
INF
-0.0917
0.5053
-0.1816
0.8562
GFOREX
-0.1171
1.4355
-0.0816
0.9351
M2
0.0030
0.0053
0.5703
0.5693
GOFWREM
0.0648
0.2417
0.2680
0.7890
FRRP
0.0108
0.1426
0.0760
0.9395
USCPI
1.9101
1.6929
1.1283
0.2609
GFEDRATE
0.0806
0.1531
0.5266
0.5992
GDEFICIT
-0.0008
0.0017
-0.4615
0.6451
DEBT
-0.0095
0.0126
-0.7534
0.4523
GPSEI
-0.2966
0.4574
-0.6485
0.5176
Effects Specification
Cross-section fixed (dummy variables)
R-squared
0.6860
Mean dependent var
0.5001
Adjusted R-squared
0.6588
S.D. dependent var
0.5089
S.E. of regression
0.2973
Akaike info criterion
0.4926
Sum squared resid
14.3154
Schwarz criterion
0.7617
Log likelihood
-28.5908
Hannan-Quinn criter.
0.6017
F-statistic
25.2783
Durbin-Watson stat
2.1802
Prob(F-statistic)
0.0000
2006 to 2010: Macro-BRP Fixed Effects Panel Regression for the Short
Rate (Selected Variables)
Dependent Variable: BRP
Sample (adjusted): 2006M02 2010M12
Periods included: 59
Cross-sections included: 3
Total panel (balanced) observations: 177
Std.
Variable
Coefficient
t-Statistic
Prob.
Error
C
0.0733
0.0370
1.9791
0.0494
BRPLAG
0.7268
0.0441
16.4937
0.0000
USCPI
2.0847
1.2460
1.6732
0.0961
Effects Specification
Cross-section fixed (dummy variables)
R-squared
0.6814
Mean dependent var
0.5001
Adjusted R-squared
0.6740
S.D. dependent var
0.5089
S.E. of regression
0.2906
Akaike info criterion
0.3941
Sum squared resid
14.5257
Schwarz criterion
0.4839
Log likelihood
-29.8816
Hannan-Quinn criter.
0.4305
F-statistic
91.9528
Durbin-Watson stat
2.1914
Prob(F-statistic)
0.0000
193
2011 to 2014: Macro-BRP Fixed Effects Panel Regression for the Short
Rate (All Variables)
Dependent Variable: BRP
Sample: 2011M01 2014M10
Periods included: 46
Cross-sections included: 3
Total panel (balanced) observations: 138
Std.
Variable
Coefficient
t-Statistic
Prob.
Error
C
0.2543
0.0810
3.1380
0.0021
BRPLAG
0.8228
0.0478
17.2209
0.0000
MERSALES
-0.0117
0.0042
-2.7900
0.0061
INF
0.7913
0.7390
1.0707
0.2864
GFOREX
-0.4658
1.3743
-0.3389
0.7352
M2
-0.0045
0.0018
-2.5325
0.0126
GOFWREM
-0.5204
0.3440
-1.5128
0.1329
FRRP
0.2094
0.1430
1.4643
0.1457
USCPI
-4.3508
2.0878
-2.0839
0.0392
GFEDRATE
0.0146
0.1392
0.1052
0.9164
GDEFICIT
-0.0008
0.0017
-0.4493
0.6540
DEBT
0.0147
0.0096
1.5343
0.1275
GPSEI
0.4597
0.3696
1.2438
0.2159
Effects Specification
Cross-section fixed (dummy variables)
R-squared
0.9118
Mean dependent var
0.4840
Adjusted R-squared
0.9018
S.D. dependent var
0.4879
S.E. of regression
0.1529
Akaike info criterion
-0.8159
Sum squared resid
2.8750
Schwarz criterion
-0.4978
Log likelihood
71.2998
Hannan-Quinn criter.
-0.6866
F-statistic
90.8658
Durbin-Watson stat
1.6996
Prob(F-statistic)
0.0000
2011 to 2014: Macro-BRP Fixed Effects Panel Regression for the Short
Rate (Selected Variables)
Dependent Variable: BRP
Sample: 2011M01 2014M10
Periods included: 46
Cross-sections included: 3
Total panel (balanced) observations: 138
Std.
Prob.
Variable
Coefficient
t-Statistic
Error
C
0.1149
0.0346
3.3165
0.0012
BRPLAG
0.8305
0.0471
17.6367
0.0000
MERSALES
-0.0077
0.0033
-2.3200
0.0219
Effects Specification
Cross-section fixed (dummy variables)
R-squared
0.9010
Mean dependent var
0.4840
Adjusted R-squared
0.8980
S.D. dependent var
0.4879
S.E. of regression
0.1558
Akaike info criterion
-0.8446
Sum squared resid
3.2293
Schwarz criterion
-0.7386
Log likelihood
63.2802
Hannan-Quinn criter.
-0.8015
F-statistic
302.5043
Durbin-Watson stat
1.5664
Prob(F-statistic)
0.0000
194
APPENDIX U:
RESULTS OF THE FIXED EFFECTS PANEL REGRESSION FOR THE LONG RATE BRP
WITH PERIODICAL TESTS (ALL VARIABLES & SELECTED VARIABLES)
2006 to 2010: Macro-BRP Fixed Effects Panel Regression for the Long
Rate (All Variables)
Dependent Variable: BRP
Sample (adjusted): 2006M02 2010M12
Periods included: 59
Cross-sections included: 3
Total panel (balanced) observations: 177
Std.
Variable
Coefficient
t-Statistic
Prob.
Error
C
0.7011
0.1799
3.8977
0.0001
BRPLAG
0.6563
0.0612
10.7184
0.0000
MERSALES
0.0007
0.0048
0.1414
0.8877
INF
0.4722
0.6180
0.7640
0.4460
GFOREX
2.7058
1.7405
1.5546
0.1220
M2
0.0011
0.0065
0.1735
0.8625
GOFWREM
-0.0957
0.2931
-0.3265
0.7445
FRRP
0.1211
0.1754
0.6903
0.4910
USCPI
-4.4339
1.9324
-2.2945
0.0230
GFEDRATE
0.2130
0.1887
1.1289
0.2606
GDEFICIT
-0.0053
0.0020
-2.6198
0.0096
DEBT
0.0133
0.0154
0.8673
0.3870
GPSEI
0.1168
0.5510
0.2119
0.8325
Effects Specification
Cross-section fixed (dummy variables)
R-squared
0.8419
Mean dependent var
1.8682
Adjusted R-squared
0.8282
S.D. dependent var
0.8696
S.E. of regression
0.3604
Akaike info criterion
0.8777
Sum squared resid
21.0412
Schwarz criterion
1.1469
Log likelihood
-62.6766
Hannan-Quinn criter.
0.9869
F-statistic
61.6213
Durbin-Watson stat
2.1827
Prob(F-statistic)
0.0000
2006 to 2010: Macro-BRP Fixed Effects Panel Regression for the Long
Rate (Selected Variables)
Dependent Variable: BRP
Sample (adjusted): 2006M02 2010M12
Periods included: 59
Cross-sections included: 3
Total panel (unbalanced) observations: 176
Std.
Variable
Coefficient
t-Statistic
Prob.
Error
C
0.5983
0.1037
5.7705
0.0000
BRPLAG
0.6963
0.0536
12.9854
0.0000
GFOREX(-1)
4.1547
1.5461
2.6871
0.0079
GDEFICIT(-1)
0.0079
0.0035
2.2464
0.0260
Effects Specification
Cross-section fixed (dummy variables)
R-squared
0.8357
Mean dependent var
1.8681
Adjusted R-squared
0.8309
S.D. dependent var
0.8721
S.E. of regression
0.3586
Akaike info criterion
0.8205
Sum squared resid
21.8655
Schwarz criterion
0.9286
Log likelihood
-66.2027
Hannan-Quinn criter.
0.8643
F-statistic
172.9518
Durbin-Watson stat
2.0614
Prob(F-statistic)
0.0000
195
2011 to 2014: Macro-BRP Fixed Effects Panel Regression for the Long
Rate (All Variables)
Dependent Variable: BRP
Sample: 2011M01 2014M10
Periods included: 46
Cross-sections included: 3
Total panel (balanced) observations: 138
Std.
Variable
Coefficient
t-Statistic
Prob.
Error
C
1.1013
0.2209
4.9867
0.0000
BRPLAG
0.5751
0.0675
8.5210
0.0000
MERSALES
-0.0191
0.0078
-2.4635
0.0151
INF
-2.0512
1.3521
-1.5170
0.1318
GFOREX
-1.1838
2.5000
-0.4735
0.6367
M2
-0.0088
0.0037
-2.3804
0.0188
GOFWREM
-0.0739
0.6706
-0.1103
0.9124
FRRP
0.2042
0.2604
0.7840
0.4345
USCPI
6.2300
3.9012
1.5969
0.1128
GFEDRATE
-0.5062
0.2557
-1.9799
0.0500
GDEFICIT
-0.0027
0.0032
-0.8439
0.4004
DEBT
0.0084
0.0177
0.4726
0.6373
GPSEI
0.9249
0.6767
1.3667
0.1742
Effects Specification
Cross-section fixed (dummy variables)
R-squared
0.8980
Mean dependent var
2.2427
Adjusted R-squared
0.8864
S.D. dependent var
0.8300
S.E. of regression
0.2798
Akaike info criterion
0.3928
Sum squared resid
9.6291
Schwarz criterion
0.7110
Log likelihood
-12.1034
Hannan-Quinn criter.
0.5221
F-statistic
77.3216
Durbin-Watson stat
1.5393
Prob(F-statistic)
0.0000
2011 to 2014: Macro-BRP Fixed Effects Panel Regression for the Long
Rate (Selected Variables)
Dependent Variable: BRP
Sample (adjusted): 2011M02 2014M10
Periods included: 45
Cross-sections included: 3
Total panel (balanced) observations: 135
Std.
t-Statistic
Error
C
1.0463
0.1811
5.7780
BRPLAG
0.6446
0.0599
10.7552
MERSALES
-0.0295
0.0060
-4.8733
M2
-0.0101
0.0029
-3.5202
FRRP
0.5874
0.2176
2.7003
GFEDRATE(-1)
0.5783
0.1651
3.5022
DEBT
0.0273
0.0138
1.9781
GPSEI
1.4846
0.5524
2.6872
Effects Specification
Cross-section fixed (dummy variables)
R-squared
0.9028
Mean dependent var
Adjusted R-squared
0.8958
S.D. dependent var
S.E. of regression
0.2676
Akaike info criterion
Sum squared resid
8.9504
Schwarz criterion
Log likelihood
-8.3899
Hannan-Quinn criter.
F-statistic
128.9905
Durbin-Watson stat
Prob(F-statistic)
0.0000
Variable
Coefficient
Prob.
0.0000
0.0000
0.0000
0.0006
0.0079
0.0006
0.0501
0.0082
2.2405
0.8289
0.2724
0.4876
0.3599
1.5609
196
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