Chapter 5
The Term
and Risk
Structure
of Interest
Rates
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Learning Objectives
• Envision and draw the yield curve and describe
the determinants of its slope
• Explain how risk is important in influencing
interest rates
• Comprehend the impact on interest rates of
income taxes
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5-2
The Term Structure of Rates and the
Yield Curve
• Term Structure—Relationship among Yields of
different maturities of the same type of security
• Yield Curve (Figure 5.1)
– Graphical relationship between yield and maturity
– Yield is measured on the vertical axis and term to
maturity is on the horizontal
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5-3
The Term Structure of Rates and the
Yield Curve (Cont.)
• Yield Curve (Figure 5.1) (Cont.)
– The basic question—does the curve slope upward,
downward, or horizontal (Figure 5.1)
– In the real world yields on all maturities tend to
move together while there are distinct, divergent
patterns between movements in short-term and longterm yields.
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5-4
FIGURE 5.1 Three alternative yield
curves.
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5-5
The Term Structure of Rates and the
Yield Curve (Cont.)
• Different Theories of the Shape of the Yield
Curve
– Supply and Demand
• Determined by relative supply/demand of different
maturities
• Deals with each maturity by itself and ignores the
interrelationships between different maturities of the
same security
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5-6
The Term Structure of Rates and the
Yield Curve (Cont.)
• Different Theories of the Shape of the Yield
Curve (Cont.)
– The Pure Expectations Approach
• Short-term and long-term securities are very good
substitutes for each other within investor’s portfolios who
collectively impact the market
• Therefore, there are not separate markets for short-term
and long-term securities, there is a single market
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5-7
The Term Structure of Rates and the
Yield Curve (Cont.)
• Different Theories of the Shape of the Yield Curve
(Cont.)
– The Pure Expectations Approach (Cont.)
• These investors are interested in the return over the period
and not the maturity date of the final payment
• Implies that expectation of future short-term rates
determines how long-term rates are related to short-term
rates
• Buying and selling pressure maintains the long-term rate
as an average of current short-term rate and the expected
future short-term rates
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5-8
The Term Structure of Rates and the
Yield Curve (Cont.)
• Different Theories of the Shape of the Yield
Curve (Cont.)
– The Pure Expectations Approach (Cont.)
• If expected future short-term rates are above current shortterm rates—yield curve will be upward sloping
• Alternatively, lower expected short-term rates will cause
the curve to be downward sloping
• The key to expectations theory is that short-term securities
and long-term securities are good substitutes for each
other
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5-9
The Term Structure of Rates and the
Yield Curve (Cont.)
• Different Theories of the Shape of the Yield
Curve (Cont.)
– The Liquidity Premium Modification
• Prices of long-term securities are more volatile
• Possibly suffer capital loss if owner needs to sell security
prior to maturity
• Prefer to hold short-term securities for liquidity
• Demand liquidity (risk) premium for exposure to price
uncertainty with long-term securities
• Suggests long-term rates will always be higher than shortterm
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5-10
The Term Structure of Rates and the
Yield Curve (Cont.)
• Different Theories of the Shape of the Yield
Curve (Cont.)
– The Preferred Habitat Approach
• Different investors actually have a preference for
different maturities—depends on their liquidity needs
• This suggests the supply/demand concept for different
maturities will establish the specific rates for each
maturity range
• Changes in supply/demand can cause the rates to get out
of line with expectations.
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5-11
The Term Structure of Rates and the
Yield Curve (Cont.)
• Different Theories of the Shape of the Yield
Curve (Cont.)
– The Preferred Habitat Approach (Cont.)
• However, Investors will drop preferred habitat if rates
get out of line with expectations and switch portfolio
holdings
• This portfolio adjustment will cause the rates to become
more in line with the expectations theory
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5-12
The Term Structure of Rates and the
Yield Curve (Cont.)
• Different Theories of the Shape of the
Yield Curve (Cont.)
– Real-World Observations
• When interest rates are high relative to past rates,
investors expect them to decline and the price of
bonds to rise in the future resulting in big capital
gains
• Investors would then favor long-term securities,
which drives up price and lowers yield—downward
sloping yield curve (Figure 5.2)
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5-13
FIGURE 5.2 Yields on U.S.
government securities.
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5-14
The Term Structure of Rates and the
Yield Curve (Cont.)
• Different Theories of the Shape of the Yield
Curve (Cont.)
– Real-World Observations (cont.)
• Opposite if interest rates are low relative to past—results
in an upward sloping curve
• Historically, over the business cycle short-term rates
fluctuate more than longer-term rates (Figure 5.3)
• Yield curves tend to be upward sloping more often,
suggesting the liquidity premium is the dominant theory
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5-15
FIGURE 5.3 Three different
Treasury rates.
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5-16
The Term Structure of Rates and the
Yield Curve (Cont.)
• Different Theories of the Shape of the Yield
Curve (Cont.)
– Summary of term structure theory
• Expectations theory forms the foundation of the slope of
the curve
• Liquidity premium theory makes a long-term permanent
modification that suggests an upward sloping curve
• Over short periods, relative supplies of securities have an
impact on yields, altering the shape of the curve
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5-17
The Term Structure of Rates and the
Yield Curve (Cont.)
• Different Theories of the Shape of the Yield
Curve (Cont.)
– An Aside on Marketability
• Recently issued government bonds (current coupon—“on
the run”) are more marketable as compared to older
issues (“off the run”)
• Because these newly issued bonds are highly marketable,
they carry somewhat lower yields to maturity as compared
to older issues
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5-18
Risk and Tax Structure of Rates
• Default Risk
– Other than US Federal government securities, bonds carry a
risk of default
– Risk on municipal bonds used to be considered very low
– However, experience of New York City (1975), Cleveland
(1978) and Orange Country, California (1995) suggest these
bonds are becoming riskier
– Corporate bonds generally have a higher default risk than
municipal bonds
– Investors will expect higher return to compensate for
increased default risk
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5-19
Risk and Tax Structure of Rates
(Cont.)
• Default Risk (Cont.)
– Standard and Poor’s and Moody’s Investors Service rate the
default risk on bonds which serve as a guide to investors
– The introduction of risk in the yield curve will cause the
curve to shift since another variable other than “maturity” has
changed
– The higher the perceived risk, the greater the upward shift of
the curve for that particular security (Figure 5.4)
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5-20
FIGURE 5.4 Riskier securities carry
higher yields.
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5-21
Risk and Tax Structure of Rates
(Cont.)
• Tax Structure
– Investors are concerned about the after tax return
on bonds
– Although municipal bonds are riskier than federal
government bonds, tax exempt status of municipal
bonds will generally result in a lower yield
(downward shift of the curve) (Figure 5.4)
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5-22
TABLE 5.1 A Guide to Bond
Ratings
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Appendix
BOND PRICE
VOLATILITY:
DURATION
VERSUS
MATURITY
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APPENDIX—BOND PRICE
VOLATILITY: DURATION VERSUS
MATURITY
• Problem with relationship between bond price
volatility and maturity stems from the way
maturity is defined
– Maturity is typically the date of final repayment of principal
– This ignores the fact that the bond makes coupon payments
before principal is repaid
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5-25
APPENDIX—BOND PRICE
VOLATILITY: DURATION VERSUS
MATURITY (cont.)
• More comprehensive measure of maturity is
duration
– Duration is defined as a weighted average of the time periods
when a bond’s payments are made
– Takes into account the timing of coupon and principal payments
– A bond with longer duration has greater price volatility than a bond
with short duration
– The higher the yield to maturity, the lower the duration of a bond
– Lower coupon payments mean longer duration
– Duration always equals maturity for zero-coupon bond (and is less
than maturity for bonds with coupons
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5-26
TABLE 5A.1 Duration of Bonds
with Different Maturities
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