Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Major Topics:
– Introduction
– Yield Curve Patterns
– Term Structure Theories
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Economics of Capital Markets
Introduction
Introduction
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Introduction
Introduction
„
Behavior of interest rates to explain
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Introduction
Introduction (Continued)
(Continued)
The structure of rates for a particular type of
security where the only difference among
them is maturity is called the term structure
„ A plot of the rates vs. maturity is called the
yield curve
„
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Notes
Economics of Capital Markets
Yield
Yield Curve
Curve Patterns
Patterns
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Yield
Yield Curve
Curve Patterns
Patterns
„
Three general patterns to yield curves
Problem: accounting for pattern
„ Typical pattern found in Wall Street
Journal in Credit Market column
„
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Notes
Economics of Capital Markets
Term
Term Structure
Structure Theories
Theories
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Term
Term Structure
Structure Theories
Theories
„
Four theories dominate literature
–
–
–
–
„
Expectations Hypothesis
Liquidity Preference Theory
Segmented Markets Theory
Preferred Habitat Theory
Each theory will be examined in turn
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Expectations
Expectations Hypothesis
Hypothesis
„
Founded on concept that a rational
economic agent is indifferent between equal
returns from one investment possibility and
the next best alternative
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Expectations
Expectations Hypothesis
Hypothesis (Continued)
(Continued)
„
Basic assumption
– Buyers of bonds do not prefer one maturity to
another
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Expectations
Expectations Hypothesis
Hypothesis (Continued)
(Continued)
„
Theory development
–
–
Investment problem: invest for two years
Two investment strategies
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Expectations
Expectations Hypothesis
Hypothesis (Continued)
(Continued)
„
Notation
i01 = Nominal interest rate in period 0 for 1
year
i11e = Nominal interest rate expected in period
1 for 1 year
i02 = Nominal interest rate in period 0 for 2
years
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Expectations
Expectations Hypothesis
Hypothesis (Continued)
(Continued)
„
Strategy 1
„
Strategy 2
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Expectations
Expectations Hypothesis
Hypothesis (Continued)
(Continued)
„
Conjecture
„
Focus is on interest rates, not dollar returns
– What are the rate relationships?
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Expectations
Expectations Hypothesis
Hypothesis (Continued)
(Continued)
„
We require that
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Expectations
Expectations Hypothesis
Hypothesis (Continued)
(Continued)
„
Conclusion
– More generally, for an n-period security
i 0n =
e
+ i e21 + ... + i en −1,1
i 01 + i11
n
where
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i ej1 is the forward rate
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Expectations
Expectations Hypothesis
Hypothesis (Continued)
(Continued)
„
Conclusions
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Expectations
Expectations Hypothesis
Hypothesis (Continued)
(Continued)
„
Properties of short-term rates
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Expectations
Expectations Hypothesis
Hypothesis (Continued)
(Continued)
„
Properties of short-term rates (Continued)
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Expectations
Expectations Hypothesis
Hypothesis (Continued)
(Continued)
„
Policy implication
– Short-term and long-term rates are perfect
substitutes in portfolios
– FED cannot influence yield curve by buying
one maturity and selling another - can only
influence expectations
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Expectations
Expectations Hypothesis
Hypothesis (Continued)
(Continued)
„
Problem with hypothesis
– Implies any shape to yield curve
– Yield curve almost always slopes upward
implying that short-term rates are expected to
rise
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Liquidity
Liquidity Preference
Preference Theory
Theory
„
Recall that wealth can be held in form of money
balances or bonds
–W=M+B
» M is perfectly liquid and riskless
» B is highly illiquid and risky
– Investors trade off liquid for illiquid assets
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Liquidity
Liquidity Preference
Preference Theory
Theory (Continued)
(Continued)
„
Focus on B
– B is a series of risky, illiquid assets
– Not only do investors tradeoff between M and
B, but also between different Bs
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Liquidity
Liquidity Preference
Preference Theory
Theory (Continued)
(Continued)
„
Basic concept
– Planning or investment horizon
» Expected amount of time you will be invested in the
market
» Example: plan to close on a house in 6 months
„
Investor chooses a B matching or close to
matching the planning horizon
– Focus on risk over planning horizon
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Liquidity
Liquidity Preference
Preference Theory
Theory (Continued)
(Continued)
„
Two kinds of risk
Reinvestment risk
Price risk
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Liquidity
Liquidity Preference
Preference Theory
Theory (Continued)
(Continued)
„
Two kinds of risk (Continued)
Summary
Change in
Rates
Risks
Reinvestment
Price
Rise
Fall
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Liquidity
Liquidity Preference
Preference Theory
Theory (Continued)
(Continued)
Gains and losses example for bonds
Bond prices and yields
Yield
6.00%
7.00%
8.00%
9.00%
9.50%
10.00%
Price (5 Yrs)
$112.7953
$108.3166
$104.0554
$100.0000
$98.0459
$96.1391
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Liquidity
Liquidity Preference
Preference Theory
Theory (Continued)
(Continued)
Price-Yield Curve
105
100
Price ($)
110
Slightly Non-Linear
Pattern
6
7
8
Yield (%)
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9
10
Plot
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Liquidity
Liquidity Preference
Preference Theory
Theory (Continued)
(Continued)
„
Differences in price response
– Current yield = 7.00%
Falls to 6.00% => Price rises to $112.7953 From $108.3166
Rises to 8.00% => Price falls to $104.0554
» Percentage point change in yield is the same:
+/- 1% pt.
» But note differences in price changes
% price increase: 4.135%
%price decrease: -3.934%
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Liquidity
Liquidity Preference
Preference Theory
Theory (Continued)
(Continued)
„
Symmetry of gains/losses
– Gains/losses not symmetric
» The gain from a rate decrease is larger in
percentage terms than the loss from a rate increase
of the same amount
„
Conclusion
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Liquidity
Liquidity Preference
Preference Theory
Theory (Continued)
(Continued)
„
Additional fact about bonds
– For given percentage change in yields, the
percentage change in bond prices will be
greater the longer the bond’s maturity
Prices
Yield
6.00%
7.00%
8.00%
5 Year
$112.7953
$108.3166
$104.0554
20 Year
4.135% $134.6722
-3.934% $121.3551
$109.8964
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10.974%
-9.442%
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Liquidity
Liquidity Preference
Preference Theory
Theory (Continued)
(Continued)
„
For previous case of a 6 month investment
– Could avoid all risk by buying 1 6-month bond
– If cannot buy 1 6-month bond
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Liquidity
Liquidity Preference
Preference Theory
Theory (Continued)
(Continued)
„
Risk vs. planning horizon
Risk
Increasing
Price
Risk
Increasing
Reinvestment
Risk
Maturity
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3 Months
6 Months
Planning Horizon
12 Months
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Liquidity
Liquidity Preference
Preference Theory
Theory (Continued)
(Continued)
„
Liquidity Preference Theory assumes
market dominated by investors with short
horizons
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Liquidity
Liquidity Preference
Preference Theory
Theory (Continued)
(Continued)
„
We know from CAPM that the market
interest rate is sum of two components
– Risk free rate
– Risk premium
Market
Interest
Rate
Source of Rate
{
Risk Premium
Liquidity
Preference
Theory Gives
This Part
Risk Free Rate
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Liquidity
Liquidity Preference
Preference Theory
Theory (Continued)
(Continued)
„
Yield curve implication
– Longer term bonds have more overall risk so
higher expected returns are demanded
regardless of expectations of short-term rate
movements
– Therefore, even if rates are expected to remain
constant, long-term rates will still be higher
» Contrary to expectations hypothesis
„
Yield curve combination of both theories
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Preferred
Preferred Habitat
Habitat Theory
Theory
„
Liquidity Preference has strong assumption
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Preferred
Preferred Habitat
Habitat Theory
Theory (Continued)
(Continued)
„
Long-term institutional investors
„
Preferred Habitat Theory sometimes called
institutional demand theory
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Preferred
Preferred Habitat
Habitat Theory
Theory (Continued)
(Continued)
Different planning horizons
Risk
In
ual
divid
Inve
stor
ercial
Comm
Bank
Insuran
.
ce Cos
Planning Horizon
1 Year
10 Years
20 Years
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Preferred
Preferred Habitat
Habitat Theory
Theory (Continued)
(Continued)
„
“Preferred Habitat” name due to each type
of investor having preferred - zero risk investment maturity
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Preferred
Preferred Habitat
Habitat Theory
Theory (Continued)
(Continued)
„
Preferred Habitat does not preclude
possibility that most funds come from
investors with short horizons
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Preferred
Preferred Habitat
Habitat Theory
Theory (Continued)
(Continued)
„
Preferred Habitat recognizes both types of
risk
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Preferred
Preferred Habitat
Habitat Theory
Theory (Continued)
(Continued)
„
Assume Expectations Hypothesis is still
correct
– Add Preferred Habitat on top of equation
i 0n =
e
i 01 + i11
+ i e21 + ... + i en −1,1
n
+ k 0n
where
k 0n > 0 is the risk premium
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Preferred
Preferred Habitat
Habitat Theory
Theory (Continued)
(Continued)
„
Preferred Habitat is consistent with two
empirical facts
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Preferred
Preferred Habitat
Habitat Theory
Theory (Continued)
(Continued)
„
Can account for downward sloping yield
curve
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Preferred
Preferred Habitat
Habitat Theory
Theory (Continued)
(Continued)
„
Additional empirical fact about yield curves
– Tend to have especially steep upward slope
when short-term rates are low and a downward
slope when short-term rates are high
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Segmentation
Segmentation Theory
Theory
„
Under Preferred Habitat, investors move
from preferred maturity only if
compensated by risk premium
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Segmentation
Segmentation Theory
Theory (Continued)
(Continued)
„
Assume infinite risk aversion
– Investors then do not move from preferred
habitat
» Invest in securities matching preferred horizons
– Market is perfectly segmented
» Extreme version of Preferred Habitat
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Segmentation
Segmentation Theory
Theory (Continued)
(Continued)
„
Implication
– Long-term and short-term rates determined in
separate markets
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Review
Review Questions
Questions
„
„
„
„
„
„
„
„
State some empirical facts about interest rates.
What is a yield curve?
What is the term structure of the interest rate?
What are the major theories of the term structure?
What is a planning horizon?
What risk is implied by the Liquidity Preference Theory?
What is a major assumption of the Liquidity Preference
Theory?
What is a Preferred Habitat?
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Key
Key Terms
Terms and
and Concepts
Concepts
Planning Horizon
„ Preferred Habitat
„ Term Structure
„ Yield Curve
„
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Suggested
Suggested Readings
Readings
„
„
„
Fabozzi, F.J. and Modigliani, F. 1992. Capital
Markets: Institutions and Instruments. Englewood
Cliffs, NJ: Prentice Hall.
Livingston, M. 1993. Money and Capital
Markets, 2nd. ed. NY: New York Institute of
Finance.
Malkiel. B.G. 1987. “Term Structure of Interest
Rates.” in The New Palgrave.
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Appendix
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Autocorrelated
Autocorrelated Structures
Structures
„
For Any Time Series, Zt
Z t = φ Z t -1 + u t
u t = N(0, σ 2u )
φ < 1 to ensure a finite variance
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Notes
Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Extended
Extended Bond
Bond Yield-Price
Yield-Price Relationship
Relationship
$180
$160
5 Yr Price
Price
$140
20 Yr. Price
$120
$100
$80
$60
$40
4.00
6.25
8.50
10.75
13.00
Yield (%)
15.25
17.50
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Economics of Capital Markets
Term
Term Structure
Structure of
of Interest
Interest Rates
Rates
Riskless
s io
n
Risky
Real
Nominal
Value Dimension
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ity
tu r
Short-term
Di
me
n
Long-term
Ma
Risk Dimension
Introduction
Introduction
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