Chapter 11
Managing Bond Portfolios

1. Duration can be thought of as a weighted average of the ‘maturities’ of the cash flows paid to holders of the perpetuity, where the weight for each cash flow is equal to the present value of that cash flow divided by the total present value of all cash flows. For cash flows in the distant future, present value approaches zero (i.e., the weight becomes very small) so that these distant cash flows have little impact, and eventually, virtually no impact on the weighted average.

2. A low coupon, long maturity bond will have the highest duration and will, therefore, produce the largest price change when interest rates change.

3. An intermarket spread swap should work. The trade would be to long the corporate bonds and short the treasuries. A relative gain will be realized when the rate spreads return to normal.

4. Change in Price = – (Modified Duration Change in YTM) Price
= -Macaulay's Duration1+ YTM Change in YTM Price

Given the current bond price is $1,050, yield to maturity is 6%, and the increase in YTM and new price, we can calculate D:
$1,025 – $1,050 = – Macaulay's Duration1+ 0.06 0.0025 $1,050 D = 10.0952

5. d. None of the above.

6. The increase will be larger than the decrease in price.

7. While it is true that short-term rates are more volatile than long-term rates, the longer duration of the longer-term bonds makes their rates of return more volatile. The higher duration magnifies the sensitivity to interest-rate savings. Thus, it can be true that rates of short-term bonds are more volatile, but the prices of long-term bonds are more volatile.

8. When YTM = 6%, the duration is 2.8334.

(1) | (2) | (3) | (4) | (5) | Time until Payment (Years) | Payment | Payment Discounted at 6% | Weight | Column (1)×Column (4) | 1 | 60 | 56.60 | 0.0566 |