CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
PROBLEM SETS.
1. In general, the forward rate can be viewed as the sum of the market’s expectation of
the future short rate plus a potential risk (or liquidity) premium. According to the
expectations theory of the term structure of interest rates, the liquidity premium is
zero so that the forward rate is equal to the market’s expectation of the future short
rate. Therefore, the market’s expectation of future short rates (i.e., forward rates)
can be derived from the yield curve, and there is no risk premium for longer
maturities.
The liquidity preference theory, on the other hand, specifies that the liquidity
premium is positive so that the forward rate is greater than the market’s expectation
of the future short rate. This could result in an upward sloping term structure even if
the market does not anticipate an increase in interest rates. The liquidity preference
theory is based on the assumption that the financial markets are dominated by short-
term investors who demand a premium in order to be induced to invest in long
maturity securities.
2. True. Under the expectations hypothesis, there are no risk premia built into bond
prices. The only reason for long-term yields to exceed short-term yields is an
expectation of higher short-term rates in the future.
3. Uncertain. Expectations of lower inflation will usually lead to lower nominal
interest rates. Nevertheless, if the liquidity premium is sufficiently great, long-term
yields may exceed short-term yields despite expectations of falling short rates.
4. The liquidity theory holds that investors demand a premium to compensate them for
interest rate exposure and the premium increases with maturity. Add this premium
to a flat curve and the result is an upward sloping yield curve.
5. The pure expectations theory, also referred to as the unbiased expectations theory,
purports that forward rates are solely a function of expected future spot rates. Under
the pure expectations theory, a yield curve that is upward (downward) sloping,
means that short-term rates are expected to rise (fall). A flat yield curve implies that
the market expects short-term rates to remain constant.
15-1
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McGraw-Hill Education.
, CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
6. The yield curve slopes upward because short-term rates are lower than long-term
rates. Since market rates are determined by supply and demand, it follows that
investors (demand side) expect rates to be higher in the future than in the near-term.
7. Maturity Price a. YTM b. Forward Rate
1 $943.40 6.00%
2 $898.47 5.50% (1.0552/1.06) – 1 = 5.0%
3 $847.62 5.67% (1.05673/1.0552) – 1 = 6.0%
4 $792.16 6.00% (1.064/1.05673) – 1 = 7.0%
8. The expected price path of the 4-year zero coupon bond is shown below. (Note that
we discount the face value by the appropriate sequence of forward rates implied by
this year’s yield curve.)
Beginning
of Year a. Expected Price b. Expected Rate of Return
1 $792.16 ($839.69/$792.16) – 1 = 6.00%
$1,000
2 = $839.69 ($881.68/$839.69) – 1 = 5.00%
1.05 1.06 1.07
$1,000
3 = $881.68 ($934.58/$881.68) – 1 = 6.00%
1.06 1.07
$1,000
4 = $934.58 ($1,000.00/$934.58) – 1 = 7.00%
1.07
9. First calculate the short rates
E (r1 ) = 5.00%
1.062
E (r2 ) = = 7.01%
1.05
1.0653
E (r3 ) = = 7.51%
1.05 1.0701
1.07 4
E (r4 ) = = 8.51%
1.05 1.07011.0751
In one year, the market’s expectation of the yield curve is:
Bond Years to Maturity YTM(%)
B 1 7.01%
C 2 7.26%
15-2
Copyright © 2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
PROBLEM SETS.
1. In general, the forward rate can be viewed as the sum of the market’s expectation of
the future short rate plus a potential risk (or liquidity) premium. According to the
expectations theory of the term structure of interest rates, the liquidity premium is
zero so that the forward rate is equal to the market’s expectation of the future short
rate. Therefore, the market’s expectation of future short rates (i.e., forward rates)
can be derived from the yield curve, and there is no risk premium for longer
maturities.
The liquidity preference theory, on the other hand, specifies that the liquidity
premium is positive so that the forward rate is greater than the market’s expectation
of the future short rate. This could result in an upward sloping term structure even if
the market does not anticipate an increase in interest rates. The liquidity preference
theory is based on the assumption that the financial markets are dominated by short-
term investors who demand a premium in order to be induced to invest in long
maturity securities.
2. True. Under the expectations hypothesis, there are no risk premia built into bond
prices. The only reason for long-term yields to exceed short-term yields is an
expectation of higher short-term rates in the future.
3. Uncertain. Expectations of lower inflation will usually lead to lower nominal
interest rates. Nevertheless, if the liquidity premium is sufficiently great, long-term
yields may exceed short-term yields despite expectations of falling short rates.
4. The liquidity theory holds that investors demand a premium to compensate them for
interest rate exposure and the premium increases with maturity. Add this premium
to a flat curve and the result is an upward sloping yield curve.
5. The pure expectations theory, also referred to as the unbiased expectations theory,
purports that forward rates are solely a function of expected future spot rates. Under
the pure expectations theory, a yield curve that is upward (downward) sloping,
means that short-term rates are expected to rise (fall). A flat yield curve implies that
the market expects short-term rates to remain constant.
15-1
Copyright © 2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
, CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
6. The yield curve slopes upward because short-term rates are lower than long-term
rates. Since market rates are determined by supply and demand, it follows that
investors (demand side) expect rates to be higher in the future than in the near-term.
7. Maturity Price a. YTM b. Forward Rate
1 $943.40 6.00%
2 $898.47 5.50% (1.0552/1.06) – 1 = 5.0%
3 $847.62 5.67% (1.05673/1.0552) – 1 = 6.0%
4 $792.16 6.00% (1.064/1.05673) – 1 = 7.0%
8. The expected price path of the 4-year zero coupon bond is shown below. (Note that
we discount the face value by the appropriate sequence of forward rates implied by
this year’s yield curve.)
Beginning
of Year a. Expected Price b. Expected Rate of Return
1 $792.16 ($839.69/$792.16) – 1 = 6.00%
$1,000
2 = $839.69 ($881.68/$839.69) – 1 = 5.00%
1.05 1.06 1.07
$1,000
3 = $881.68 ($934.58/$881.68) – 1 = 6.00%
1.06 1.07
$1,000
4 = $934.58 ($1,000.00/$934.58) – 1 = 7.00%
1.07
9. First calculate the short rates
E (r1 ) = 5.00%
1.062
E (r2 ) = = 7.01%
1.05
1.0653
E (r3 ) = = 7.51%
1.05 1.0701
1.07 4
E (r4 ) = = 8.51%
1.05 1.07011.0751
In one year, the market’s expectation of the yield curve is:
Bond Years to Maturity YTM(%)
B 1 7.01%
C 2 7.26%
15-2
Copyright © 2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
