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 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.
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 shortterm rates are expected to rise (fall).
A flat yield curve
implies that the market expects shortterm rates to remain constant.
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6.
The yield curve slopes upward because shortterm rates are lower than longterm
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 nearterm.
7.
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%
8.
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.)
Beginning
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%
9.
If expectations theory holds, then the forward rate equals the short rate, and the one
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 Three '11
 3213
 Interest Rates, Interest, Interest Rate, Liquidity, Yield Curve, Forward rate

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