FNCE 4070: FINANCIAL MARKETS
AND INSTITUTIONS
Lecture 6: Forecasting With the Term
Structure of Interest Rates
Forecasting Business Cycle
Turning Points (A Recession)
Forecasting Future Interest
Rates (Estimating Forward Rates)
Forecasting Inflation with
Treasury Inflation Protected
Securities (TIPS)
Where is This Financial Center?
Downward Sweeping or Inverted Yield
Curve And Economic Activity
Inverted Yield Curve
Discussion



Inverted Yield Curve: An interest
rate environment in which longterm debt instruments have
a lower yield than short-term
debt instruments of the same
credit quality.
This type of yield curve is the
rarest of the three main curve
types and is considered by
some to be a predictor of an
economic recession (i.e.,
business cycle turning point).
Why: An inverted yield curve
signals a future fall in interest
rates which is consistent with a
recession.
Interest Rates and Business Cycles:
1969 – 1983
Interest Rates Spreads and Business
Cycles: 1969 – 1983 (Monthly Data)
Interest Rates and Business Cycles:
1987 – 2011
Interest Rate Spreads and Business
Cycles: 1987 – 2011 (Daily Data)
Probability of a Recession Using
Yield Curves (Fed of New York)
Monthly Yield Curve Analysis




Refer to the Fed of Cleveland web site for a
monthly analysis of the yield curve.
http://www.clevelandfed.org/research/data/yie
ld_curve/index.cfm?DCS.nav=Local
Link to early 2007 to see what this site was
saying about the probably of a recession in
the United States.
Recall the recession officially began in Dec
2007
Forecasting Interest Rates with The
Expectations Theory

Recall that the Expectations Theory assumes that
the current long term spot interest rate is
comprised of:
 (1) Current (spot) short term interest rate
(which can designate as iss) and
 (2) Expected, future (forward) short-term
interest rates (which we can designate as ie).
isst  iet 1  iet 2  ...  ien
ils n 
n
Forecasting Interest Rates

If we assume the long term spot rate (ils) is an
average of short term rates (iss and ie),
ils n

iss t  iet 1  iet  2  ...  ien

n
Then it is possible to derive the “expected”
forward rate (ie), on a one-period bond for some
future time period (n-t) through the following
formula:
ien t 
1  ils n n
1  iss t 
1
Forecasting With The Expectations
Model: Example #1

Assume the following:



Current 1 year spot (iss1) = 4.75% (0.0457)
Current 2 year spot (ils2) = 5.50% (0.055)
Use the formula on the previous slide to calculate
the implied forward rate, or the 1year rate, 1 year
from now:
n
2

1  ils n 

1  0.055
ie

 1 ie 
 1  0.06255  6.26%
n t


1  iss t 
n t
1  0.0475
Or using an approximation formula: (ils x 2) – iss
(5.5 x 2) – 4.75 = 11.0 – 4.75 = 6.25%
Yield Curve For Example #1
Yield Curve
interest rate
6.0%
oie (6.26%)
5.5
oils2 (5.50%)
5.0
o iss1 (4.75%)
1y
2y
Term to Maturity
The Forward Rate
 The calculated forward
rate of 6.26% is the
market’s expected 1 year
interest rate one year
from now.
 This rate of 6.26%
becomes our forecasted
interest rate using the
pure expectations model.
Forecasting With The Expectations
Model: Example #2

Assume the following:



Current 1 year spot (iss1) = 7.0% (0.07)
Current 2 year spot (ils2) = 5.0% (0.05)
Use the formula on the previous slide to calculate
the implied forward rate, or the 1year rate, 1 year
from now:
2
n

1  ils n 

1  0.05
ien t 
 1 ien t 
 1  0.0304  3.04%
1  iss t 
1  0.07
Or as an approximation: (ils x 2) – iss
(5.0 x 2) – 7.0 = 10.0 – 7.0 = 3.00%
Yield Curve For Example #2
Yield Curve
interest rate
7.0% oiss1 (7.0%)
5.0
oils2 (5.0%)
3.0
oie (3.04%)
1y
2y
Term to Maturity
The Forward Rate
 The calculated forward
rate of 3.04% is the
market’s expected 1 year
interest rate one year
from now.
 This rate of 3.04%
becomes our forecasted
interest rate using the
pure expectations model.
Using Current Yield Curve Data to
Forecast Interest Rates
Bloomberg Data: U.S.
Treasuries, April 3, 2012
Expectations Model
What is the yield curve data
telling us about the markets
expectation regarding future
interest rates:
Going up or going down?
Now calculate some forward
rates?
(1) 3 month rate, 3 months
from now?
(2) 1 year rate, 1 year from
now?
Answer to Previous Examples
3 month rate, 3 months
from now:
 PE Model: 0.21004%
ien t 
ie n t 


1  ils n n
1  iss t 
1
1  0.00142
1  0.0007 
1
= 0.21004%
Approximation: 0.21%
= (0.14 x 2) – 0.07
= 0.21%
1 year rate, 1 year from
now:
 PE Model: 0.54028%
ien t 
ie n t 




1  ils n n
1  iss t 
1
1  0.0037 2  1
1  0.0020 
= 0.54028%
Approximation: 0.5400
= (0.37 x 2) – 0.20
= 0.54%
Treasury Inflation-Protected
Securities

Treasury Inflation-Protected Securities, or TIPS, are
securities whose principal (par value) is tied to the
Consumer Price Index (CPI) .




First issued in the U.S. in January 1997 (U.K. first issued in
1981).
The par amount (principal value) increases with
inflation and decreases with deflation.
TIPs have a fixed coupon rate and they pay interest
against the adjusted par value every six months.
When the security matures, the U.S. Treasury pays
the original ($1,000) or adjusted principal, whichever
is greater.
TIPs Example: Work Through
Example and Fill in Years 4 and 5
Year Par Value
Beginning
of Year
(Par =
$1,000
when
issued)
CPI
Adjustment
Change to Par Value
for Year (Based on
CPI for
Year)
New Par
Value:
End of
Year
1
$1,000
+2.2%
+$22.00
$1,022.00 3.5%
$35.77
2
$1,022
+0.0%
+$00.00
$1,022.00 3.5%
$35.77
3
$1,022
-1.0%
-$10.22
$1,011.78
$35.41
4
+1.5%
5
-0.5%
Coupon
Rate
(Fixed
3.5% at
Offering)
3.5%
Interest
Paid
(Against
New Par
Value)
Answers to Previous Slide (Years 4
and 5)
Year Par Value
Beginning
of Year
(Par =
$1,000
when
issued)
CPI
Adjustment
Change to Par Value
for Year (Based on
CPI for
Year)
New Par
Value:
End of
Year
Coupon
Rate
(Fixed
3.5% at
Offering)
Interest
Paid
(Against
New Par
Value)
1
$1,000
+2.2%
+$22.00
$1,022.00 3.5%
$35.77
2
$1,022
+0.0%
+$00.00
$1,022.00 3.5%
$35.77
3
$1,022
-1.0%
-$10.22
$1,011.78
3.5%
$35.41
4
$1,011.78
+1.5%
+$15.18
$1,026.96 3.5%
$35.94
5
$1,026.96
-0.5%
-$5.14
$1,021.82 3.5%
$35.76
Estimating Future Rates of Inflation

Using the TIPS market to determine the
“breakeven” inflation rate.

Assumptions:



Conventional Treasury rate (yield to maturity) includes both
real rate and inflation premium.
TIPS rate (yield to maturity) is simply the real rate.
Breakeven inflation rate = Yield to maturity on
conventional Treasuries – Yield to maturity on
TIPS.


Difference (i.e., Breakeven rate) is the market’s annual
inflation expectation over the maturity period.
Important: Use similar maturities when calculating
Breakeven rate.
10-Year Break Even Inflation Rate (10
Year Conventionals -TIPs 10)
5-Year Break Even Inflation Rate (5
Year Conventionals -TIPs 5 year yield)
TIPs Breakeven 5-Year Forecast (i.e.,
average annual expected 5 year rate)
with Actual CPI
What Determines Inflationary
Expectations?

Inflation targeting by a central bank:


Levin (2004) found that inflationary expectations
(measured by private-sector inflation forecasts) were
not found to be sensitive to actual inflation in inflation
targeting countries; but that in non-inflation targeting
countries inflationary expectations were highly
correlated to lagged inflation.
Commodity Prices

IMF (2012) study found that commodity prices have a
significant impact on inflationary expectations
U.S. Treasury Yield Curve Site for
Observing Breakeven Rate of Inflation

Link to the U.S.
Treasury site below
for the nominal and
TIPS yield curve.

http://www.treasury.gov/resourc
e-center/data-chartcenter/interestrates/Pages/Historic-Yield-DataVisualization.aspx
Set the date for January 2, 2009
and observe the breakeven rate.



What was this date telling you about
the market’s expectation regarding
inflation?
Recall: The breakeven inflation rate
is the difference between the two
yield curves.
U.S. Treasury Yield Curve Site for
Observing Breakeven Rate of Inflation

Again, link to the U.S. Treasury site below for
the nominal and TIPS yield curve.

http://www.treasury.gov/resource-center/data-chart-center/interestrates/Pages/Historic-Yield-Data-Visualization.aspx
What is the most recent data telling you about the market’s
expectation regarding inflation?
Note: The 5-year, 7-year and 10-year TIPS yield curve data point is
incorrect (however, the actual data is correct).





According to the Treasury Department, the graphing function “is flawed.”
From this site, one can also download the actual data (link to text
version of Treasury Yield Curve).
Can you explain the current TIPs yield to maturity?
Bloomberg Sites for TIPs and
Breakeven Rates
Current TIPs Yields
 http://www.bloomberg.co
m/
 April 11, 2012
Breakeven Rates (10-Year)
http://www.bloomberg.com/
quote/USGGBE10:IND
Appendix 1
Why Do Markets Care about Yield Curves?
The following is from Bonds on Line and
summarizes why yield curves are important.
http://www.bondsonline.com/Corporate_Bond_Yield_Inde
x.php#why
Using Yield Curves



“The shape of the yield curve is closely followed by bond investors. It provides
information about the yields of short term compared to long term fixed-income
investments. Investors analyze and interpret the yield curve shape to give some
insights on the future direction of rates and the economy.
A yield curve normally has an upward sloping shape. That is, in a normal yield
curve, shorter-term yields are lower than longer-term yields, with yields
generally increasing as years to maturity increase. The yields are higher on
securities with longer maturities because these securities are more vulnerable to
price changes caused by changes in interest rates over time. Investors in
longer-term securities are typically rewarded with a higher yield for taking the
risk that interest rates could rise and cause the prices of their securities to fall.
Investors pay attention to both the current shape of the yield curve, whether it is
steep or flat, and yield curve movements. That is, investors will look at whether
the entire curve is shifting up or down in a parallel fashion which suggests that
rates across the maturity spectrum are changing by the same magnitude or,
alternatively, the shape or slope of the curve is becoming flatter or steeper. For
example, when Federal Reserve monetary policy is more accommodative and
reduces short term rates, the yield curve generally steepens, and flattens when
monetary policy tightens the Fed raises short term rates.
Using Yield Curves


When the yield curve is steep, that is when the difference between
short-term and long-term yields is large, the market often expects
interest rates to rise, though there are a number of variables, including
the rate of economic growth and inflationary expectations, that go into
interest rate analysis and forecasting; the risk at the long end of the
maturity range is therefore greater, and so is the return or yield. When
the yield curve is relatively flat, the difference between short-term yields
and long-term yields is not that great. When this happens, the market
is not rewarding investors for taking the risk of a longer maturity,
possibly because the market believes interest rates will decline, causing
bond prices to rise and yields to fall. Investors holding securities with
longer maturities tend to benefit more from a declining interest rate
trend.
There have been brief and unusual periods of time when the there has
been what is known as an “inverted” yield curve shape, where, at
certain points along the maturity spectrum, short-term yields have been
higher than long-term yields. Inversely sloped yield curves are not
sustainable – either short term yields will eventually fall or long term
yields rise. An inverted yield curve is considered an omen of recession
as well as lower interest rates.”
Appendix 2
Ben Bernanke and the 2006 Yield Curve.
Shortly after Bernanke became Chair of the Fed (Feb 1, 2006) he
spoke before the Economic Club of New York. The presentation to
that group was given on March 20, 2006. The yield curve which
had been upward sweeping in 2004 (and thus normal) began to
flatten in 2005 through 2006 and was approaching almost flat by the
time Bernanke spoke. The following is a direct quote from
Bernanke’s presentation regarding the flattening yield curve in 2006.
Ben Bernanke Discusses the 2006
Yield Curve

“Although macroeconomic forecasting is fraught with hazards, I would
not interpret the currently very flat yield curve as indicating a significant
economic slowdown to come, for several reasons. First, in previous
episodes when an inverted yield curve was followed by recession, the
level of interest rates was quite high, consistent with considerable
financial restraint. This time, both short- and long-term interest rates--in
nominal and real terms--are relatively low by historical standards.
Second, as I have already discussed, to the extent that the flattening or
inversion of the yield curve is the result of a smaller [liquidity] term
premium, the implications for future economic activity are positive rather
than negative. Finally, the yield curve is only one of the financial
indicators that researchers have found useful in predicting swings in
economic activity. Other indicators that have had empirical success in
the past, including corporate risk spreads, would seem to be consistent
with continuing solid economic growth. In that regard, the fact that
actual and implied volatilities of most financial prices remain subdued
suggests that market participants do not harbor significant reservations
about the economic outlook.”