Chapter Four Risk and
Term Structure of
Interest Rate
ⅠRisk Structure of Interest
Rate
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Discussion: What do you find from the
following table?
table 1 Interest rate of U.S.
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1.Default risk
2.Liquidity
3.Income tax considerations
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default risk: the risk of unable to make
interest payments or pay off the face vale
when the bond mature.
Risk premium= interest rate on default risk
bonds﹣interest rate on default risk free
bonds
Please calculate the risk premium of Moody’s
Baa corporation bonds.
4.91-2.77=2.04
The Risk Structure of Interest
Rate
Default risk liquidity
Interest rate positive
negative
Tax exempt
low
ⅡTerm Structure of Interest
Rates
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Introduction: Yield Curve
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A plot of the yields on bonds with differing
terms to maturity but the same risk, liquidity,
and tax considerations is called a yield
curve.
It describes the term structure of interest
rates for particular types of bonds.
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The shape of yield curve
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
Ascending Yield
Curve
This is the common
shape in developed
countries. It shows that
yield rises for longer
maturities.
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Descending Yield
Curve This shape
shows that short term
interest rates are higher
than long term rates.
This shape is often
seen when the market
expects interest rates to
fall.

Flat Yield Curve Short
term rates are the same
as long term rates.
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Humped Yield Curve
Shape often seen when
the market expects that
interest rates will first
rise (fall) during a
period and fall (rise)
during another.
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Please draft the yield curve of government
security of U.S. ,what can you find from the
curves.
7
6
5
4
3
2
1
0
i of
AUG
2012
i of
AUG
1999
30
20
10
7
5
3
2
1
5
0.
25
0.
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1.interest rates on bonds of different
maturities move together over time.
2.the yield curves of U.S. government
security are upward slope.
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How to explain the different shape of yield
curve?
1.Expectation Theory
2. Segmented market theory
3.liqudity premium theory
1.Expectation Theory
(1)The key assumption
buyers of bonds do not prefer bonds of one
maturity over another, so they will not hold any
quantity of a bond if its expected return is less
than that of another bond with a different maturity.
(2) basic proposition: The interest rate on a long-term bond will
equal an average of short-term interest rates that people expect
to occur over the life of the long-term bond.
i
i i
i

t
nt
e
e
t 1
t 2
     it n
e
n

int=n-period interest rate

i
t
e
today’s interest rate on a one-period bond
 interest rate on a one year bond expected for next period

i

This equation means that n period interest rate equals the
average of the one period interest rate to occur over the n period
life of the bond.
t 1
(3)Analyze
A.When short term interest rates are low, people
generally expected them to rise to some normal
level in the future, and the average future
expected short term interest rate is high relative to
current short term interest rate. Therefore long
term interest rate will be above current short term
rates, the yield curve would be an upward slope.
B.If short term interest rate are high, people
usually expected them to come back down, long
term interest rate would drop below short term
interest rates because the average of expected
future short term would be below the current short
rates and the yield curve would slope down ward
and become inverted.

C.Short term interest rates have had a characteristic
that if they increase today, they will tend to be higher
in the future. Hence a rise in short term rates will
raise people’s expectations of future short term rates.
Because long term interest rates are the average of
expected future short term interest rates, a rise in
short term interest rates will also raise long term
interest rates, causing short term and long term
rates to move together.
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(4)Summary of Expectation Theory
A. The interest rate on long term bonds will
equal an average of short term interest rate
that people expected to occur over the life of
the long term bond.
B. The difference of interest rate on bonds of
different maturities is attributing that short
term interest rates are expected to have
different values at future dates.
2. Segmented market theory
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(1)Assumption
bonds of different maturities are not
substitutes at all.
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(2)Key point:
Sees markets for different –maturity bonds as
completely separate and segmented. The
interest rate for each bonds with different
maturity is determined by the supply and
demand for that bond with no effects from
expected returns on other bonds with other
maturity.
3. Liquidity premium theory
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(1)Introduction
most widely accepted theory of term structure
of interest rates, it combines the features of
both the expectations theory and segmented
market theory by asserting that a long term
interest rate will be the sum of a liquidity
(term) premium and average of short term
interest rates that are expected to occur over
the life of bonds
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(2)Abstract
Interest rate on a long term bond will equal
an average of short term interest rates
expected to occur over the life of the long
term bonds plus a liquidity premium (also
refer to as a term premium)
(3)Assumption

bonds of different maturity are substitutes,
which mean that the expected return on one
bonds dose influence the expected return on
bond of a different maturity. But it allows
investors to prefer one maturity over another.
In other words, bond of different maturity are
assume to substitutes but not perfect
substitute.
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（4）Analyze
in  iat  pnt


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n is period , t at time t
iat average short term interest rates.
pntliquidity premium
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When short term interest rates rise, then
long term interest rate will also rise with it,
therefore interest rates on bonds of different
maturity move together.

When short term interest rates are low,
investor expect them will rise to some normal
level, therefore, the average of future
expected short term interest rates will be high
relative to current short term interest rates,
with additional positive interest rate premium,
long term interest rates will higher than short
term interest rates, therefore ,yield curve will
be upward slope.

If short term interest rates are high , and
investor expect short rates will come back
down, the average expected short term
interest rates would below short current short
term interest rates, therefore long term rates
will drop fairly below short term interest rates
and overwhelm positive liquidity premiums,
the yield curve will be invert to downward
slope.
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The theory also helps us predict the movement of
short-term interest rates in the future. A steeply
upward slope of yield curve means that future short
term rates are expected to rise, a mildly upward
slope curve indicates that short term interest rates
are expected to stay on the same, a flat slope
means that short term rates are expected to fall
moderately, and an invert curve means that short
term rates are expected to fall sharply.
Summary

Bonds with same maturity will have different
interest rates because of three factors: default risk,
liquidity, and tax consideration. The greater
default risk the higher the interest rates, the
greater the bond’s liquidity, the lower the interest
rate, and bonds with tax exempt have lower
interest rate.

Interest rates of different maturity are different
which can be explained by three term structure
theory. the expectation theory views the interest
rate on long term bonds equal an average of short
term interest rate that people expected to occur
over the life of the long term bond. The difference
of interest rate on bonds of different maturities is
attributing that short term interest rates are
expected to have different values at future dates.

Segmented market theory states that The interest
rate for each bonds with different maturity is
determined by the supply and demand for that
bond with no effects from expected returns on
other bonds with other maturity.

Liquidity premium theory combines the features of
both the expectations theory and segmented
market theory by asserting that a long term
interest rate will be the sum of a liquidity(term)
premium and average of short term interest rates
that are expected to occur over the life of bonds.
questions
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1.please use the theory you learned to
explain why different bonds with same
maturity have different interest rate?
2.please use the theory you learned to
explain why the same bond with different
maturity have different interest rate?
3.please sketch the expectation theory.
4.please sketch the segmented market theory.
5.please sketch the Liquidity premium theory .
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6.key words:
default risk
Default free bonds
Expectations theory
liquidity premium theory
Risk premium
Segmented market theory
Yield curve