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%
8.
a.
Under the expectations theory, the expected spot rate equals the forward
rate, which is equal to:
(1.06
5
/1.059
4
)  1 = 0.064 = 6.4 percent
b.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 '10
 .
 Spot rate

Click to edit the document details