Solutions – Tutorial Week 9
Chapter 23
2.
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 6year 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
= 0.2645 = 26.45%
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 '10
 .
 Spot rate

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