THE RISK AND TERM STRUCTURE OF INTEREST RATES
• Risk Structure of Interest Rates
•Default risk
•Liquidity
•Income Tax Consideration
•
Term Structure of Interest Rates
•Pure Expectation Theory
•Market Segmentation Theory
•Liquidity Premium Theory
Risk and Term Structure of Interest Rates -- Fin 331
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Risk Structure of Long Bonds in the US
Risk and Term Structure of Interest Rates -- Fin 331
2
Puzzling Phenomenon
1. Riskfree bonds have a lower return than risky
bonds
2. High risk bonds have a higher return than low
risk bonds
3. Municipal bonds have a lower return than US
Government long term bonds
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3
Increasing Default Risk on Corporate Bonds
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Bond Ratings
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Decrease in Liquidity of
Corporate Bonds
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Why bonds have different liquidity
• US Treasury bonds are the most liquid because
they are widely traded
• Corporate bond are less liquid because fewer
bonds are traded and it’s costly to sell bonds in an
emergency
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Tax Advantages of Municipal
Bonds
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Term Structure Facts to Be
Explained
1. Interest rates for different maturities move together
2. Yield curves tend to have steep upward slope when short
rates are low and downward slope when short rates are
high
3. Yield curve is typically upward sloping
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Interest rate
maturities
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Three Theories of Term Structure
1. Pure Expectations Theory
2. Market Segmentation Theory
3. Liquidity Premium Theory
A. Pure Expectations Theory explains 1 and 2, but not 3.
B. Market Segmentation Theory explains 3, but not 1 and 2
C. Solution: Combine features of both Pure Expectations
Theory and Market Segmentation Theory to get Liquidity
Premium Theory and explain all facts
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Interest Rates on Different Maturity Bonds
Move Together
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Yield Curves
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Pure Expectations Theory
Key Assumption:
Bonds of different maturities are perfect
substitutes
Implication:
RETe on bonds of different maturities are
equal
Investment strategies for two-period horizon
1. Buy $1 of one-year bond and when matures buy another
one-year bond
2. Buy $1 of two-year bond and hold it
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Pure Expectations Theory
it  i
i 2t 
2
e
t 1
See definitions on page 131
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More generally for n-period bond:
i t  i 1  i  2  ...  i  n 1
i nt 
n
In words: Interest rate on long bond = average of
short rates expected to occur over life of long
bond
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More generally for n-period bond:
Numerical example:
One-year interest rate over the next five years 5%, 6%,
7%, 8% and 9%,
Interest rate on two-year bond:
Interest rate for five-year bond:
Interest rate for one to five year bonds:
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Another example (on future short-term
rate):
The interest rates for 1-year through 5-year bonds
are 5%, 6%, 7%, 8% and 9%,
Expected interest rate of a 1-year bond in year 2:
Expected interest rate of a 1-year bond in years 3,
4, and 5
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Pure Expectations Theory and Term
Structure Facts
Explains why yield curve has different slopes:
1. When short rates expected to rise in future, average of future
short rates = int is above today's short rate: therefore yield
curve is upward sloping
2. When short rates expected to stay same in future, average of
future short rates same as today's, and yield curve is flat
3. Only when short rates expected to fall will yield curve be
downward sloping
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Pure Expectations Theory and
Term Structure Facts
Pure Expectations Theory explains Fact 1 that short and long
rates move together
1. Short rate rises are persistent
2. If it  today, iet+1, iet+2 etc.   average of future rates  
int 
3.Therefore: it   int , i.e., short and long rates move
together
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Pure Expectations Theory and Term
Structure Facts
Explains Fact 2 that yield curves tend to have steep slope when
short rates are low and downward slope when short rates are
high
1. When short rates are low, they are expected to rise to normal
level, and long rate = average of future short rates will be well
above today's short rate: yield curve will have steep upward
slope
2. When short rates are high, they will be expected to fall in future,
and long rate will be below current short rate: yield curve will
have downward slope
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Pure Expectations Theory and
Term Structure Facts
Doesn't explain Fact 3 that yield curve usually has upward
slope
Short rates as likely to fall in future as rise, so average of
expected future short rates will not usually be higher than
current short rate: therefore, yield curve will not usually
slope upward
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Market Segmentation Theory
Key Assumption:
Bonds of different maturities are
not substitutes at all
Implication:
Markets are completely segmented:
interest rate at each maturity
determined separately
Explains Fact 3 that yield curve is usually upward sloping
People typically prefer short holding periods and thus have
higher demand for short-term bonds, which have higher prices
and lower interest rates than long bonds
Does not explain Fact 1 or Fact 2 because assumes long and short
rates determined independently
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Liquidity Premium Theory
Key Assumption:
Bonds of different maturities are
substitutes, but are not perfect
substitutes
Implication:
Modifies Pure Expectations Theory
with features of Market
Segmentation Theory
Investors prefer short rather than long bonds  must be paid
positive liquidity premium, lnt, to hold long term bonds
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Liquidity Premium Theory
Results in following modification of Pure
Expectations Theory
i nt  l nt 
it  i
e
t 1
i
e
t 2
 ...  i
e
t  n 1
n
Risk and Term Structure of Interest Rates -- Fin 331
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Relationship Between the Liquidity Premium and
Pure Expectations Theory
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Liquidity Premium Theory:
Explains all 3 Facts
Explains Fact 3 of usual upward sloped yield curve by
liquidity premium for long-term bonds
Explains Fact 1 and Fact 2 using same explanations as
pure expectations theory because it has average of
future short rates as determinant of long rate
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Numerical Example:
1. One-year interest rate over the next five years:5%, 6%, 7%,
8% and 9%
2. Investors' preferences for holding short-term bonds so
liquidity premium for one to five-year bonds: 0%, 0.25%,
0.5%, 0.75% and 1.0%.
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Numerical Example:
Interest rate on the two-year bond:
Interest rate on the five-year bond:
Interest rates on one to five-year bonds:
Comparing with those for the pure expectations theory,
liquidity premium theory produces yield curves more
steeply upward sloped
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Calculate future short term rate
1. Interest rates for one- to five-year bonds are:5%, 6%, 7%,
8% and 9%
2. Investors' preferences for holding short-term bonds so
liquidity premium for one to five-year bonds: 0%, 0.25%,
0.5%, 0.75% and 1.0%.
3. Calculate 1-year short-term rate over the next five years.
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Market Predictions of Future
Short Rates
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Forward Rate
The expected future short-term rate is also
known as forward rate, as opposed to the
current short-term rate, known as the spot
rate.
Two ways to compute forward rates:
(1) Using the formula covered in the class
(2) Formula in the text book (page 123-126,
not required)
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