Chapter 15  The Term Structure of Interest Rates
151
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 less 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 shortterm 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 longterm yields to exceed shortterm yields is an expectation of
higher shortterm 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, longterm yields may
exceed shortterm yields
despite
expectations of falling short rates.
4.
Maturity
Price
YTM
Forward Rate
1
$943.40
6.00%
2
$898.47
5.50%
(1.055
2
/1.06) – 1 = 5.0%
3
$847.62
5.67%
(1.0567
3
/1.055
2
) – 1 = 6.0%
4
$792.16
6.00%
(1.06
4
/1.0567
3
) – 1 = 7.0%
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View Full DocumentChapter 15  The Term Structure of Interest Rates
152
5.
The expected price path of the 4year 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.)
Beginnin
g of Year
Expected Price
Expected Rate of Return
1
$792.16
($839.69/$792.16) – 1 = 6.00%
2
69
.
839
$
07
.
1
06
.
1
05
.
1
000
,
1
$
=
×
×
($881.68/$839.69) – 1 = 5.00%
3
68
.
881
$
07
.
1
06
.
1
000
,
1
$
=
×
($934.58/$881.68) – 1 = 6.00%
4
58
.
934
$
07
.
1
000
,
1
$
=
($1,000.00/$934.58) – 1 = 7.00%
6.
a.
A 3year zero coupon bond with face value $100 will sell today at a yield of 6%
and a price of:
$100/1.06
3
=$83.96
Next year, the bond will have a twoyear maturity, and therefore a yield of 6%
(from next year’s forecasted yield curve). The price will be $89.00, resulting in a
holding period return of 6%.
b.
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 Spring '09
 WUXueping
 Interest, Interest Rate

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