Brealy Chapter 23

2963 Words Oct 17th, 2012 12 Pages
Answers to Practice Questions

1. Downward sloping. This is because high coupon bonds provide a greater proportion of their cash flows in the early years. In essence, a high coupon bond is a ‘shorter’ bond than a low coupon bond of the same maturity.

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 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 C1 . . . C5 C6 Price
6% bond 12% 60 . . . 60 1,060 $753.32
10% bond 8% 100 . . . 100 1,100 $1,092.46 From the
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5%, five-year note: 3. 10%, five-year note: d. First, we calculate the yield for each of the two bonds. For the 5% bond, this means solving for r in the following equation: r = 0.05964 = 5.964% For the 10% bond: r = 0.05937 = 5.937% The yield depends upon both the coupon payment and the spot rate at the time of the coupon payment. The 10% bond has a slightly greater proportion of its total payments coming earlier, when interest rates are low, than does the 5% bond. Thus, the yield of the 10% bond is slightly lower.

e. The yield to maturity on a five-year zero coupon bond is the five-year spot rate, here 6.00%.

f. First, we find the price of the five-year annuity, assuming that the annual payment is $1:

Now we find the yield to maturity for this annuity:

r = 0.05745 = 5.745%

g. The yield on the five-year Treasury note lies between the yield on a five-year zero-coupon bond and the yield on a 5-year annuity because the cash flows of the Treasury bond lie between the cash flows of these other two financial instruments. That is, the annuity has fixed, equal payments, the zero-coupon bond has one payment at the end, and the bond’s payments are a combination of these.

7. A 6-year spot rate of 4.8 percent implies a negative forward rate: (1.0486/1.065) – 1 = –0.010 = –1.0%
To make money, you could borrow $1,000 for 6 years at 4.8 percent and lend $990 for 5 years at 6 percent. The

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