CHAPTER 24
Valuing Debt
Answers to Practice Questions
1.
Some reasons Fisher’s theory might not be true are:
a.
Taxes are levied on nominal interest.
Therefore, if expected inflation is
high, part of the tax is actually on the real principal.
b.
Inflation may be associated with the level of real economic activity, which,
in turn, may affect real interest rates.
c.
It ignores uncertainty about inflation.
2.
If expected real interest rates are negative, then individuals will be tempted to
save by buying and storing real goods.
This forces the prices of goods up and
the prices of securities down until real rates are no longer negative.
However, goods are costly to store and expensive to resell if you do not want
them.
Some goods are impossible to store, e.g., haircuts and appendectomies.
Prices of these goods may be expected to rise faster than the interest rate.
Note
also that it is difficult for a country on its own to maintain a very low real rate
without imposing exchange controls on its citizens.
3.
The key here is to find a combination of these two bonds (i.e., a portfolio of
bonds) that has a cash flow only at t = 6.
Then, knowing the price of the portfolio
and the cash flow at t = 6, we can calculate the 6-year spot rate.
We begin by specifying the cash flows of each bond and using these and their
yields to calculate their current prices:
Investment
Yield
C
1
. . .
C
5
C
6
Price
6% bond
12%
60
. . .
60
1,060
$753.32
10% bond
8%
100
. . .
100
1,100
$1,092.46
From the cash flows in years one through five, it is clear that the required
portfolio consists of one 6% bond minus 60% of one 10% bond, i.e., we should
buy the equivalent of one 6% bond and sell the equivalent of 60% of one 10%
bond.
This portfolio costs:
$753.32 – (0.6
×
$1,092.46) = $97.84
The cash flow for this portfolio is equal to zero for years one through five and, for
year 6, is equal to:
$1,060 – (0.6
×
1,100) = $400
Thus:
$97.84
×
(1 + r
6
)
6
= 400
r
6
= 0.265 = 26.5%
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