Management Chapter 16 Several characteristics of duration make

Solutions for Chapter 16: Questions and Problems

CHAPTER 16

BOND PORTFOLIO MANAGEMENT STRATEGIES

Answers to Questions

1. High-yield bonds have been described as having characteristics of common stocks, such

as higher yields and more risks. The higher yield on high-yield bonds (just like common

2. Investment horizon a year later = 3

Duration of portfolio a year later = 3.2

3. Several characteristics of duration make it impossible to set a duration equal to the initial

time horizon of a portfolio and ignore it thereafter. First, because duration declines more

slowly than term-to-maturity, even if one assumes no changes in interest rates, the

portfolio manager must periodically rebalance the portfolio. Second, if there is a change

Solutions for Chapter 16: Questions and Problems

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CHAPTER 16

Answers to Problems

1. (i) The manager purchased a longer maturity, lower coupon bond; by purchasing a longer

duration bond the manager must expect market interest rates to fall.

(ii) The manager will benefit if the shape of the yield curve either stays flat or becomes

2.

2(a). $200 million × (1.06)2 = $224.72 million (assuming semiannual coupon payments in the

bond portfolio).

3(a). Computation of Duration (assuming 10% market yield)

(1) (2) (3) (4) (5) (6)

Year Cash Flow PV@10% PVof Flow PV as % of Price (1) × (5)

3(b). Computation of Duration (assuming 10% market yield)

(1) (2) (3) (4) (5) (6)

Year Cash Flow PV@10% PVof Flow PV as % of Price (1) × (5)

1 120 .9091 109.09 .1026 .1026

Solutions for Chapter 16: Questions and Problems

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3(c). The duration of the portfolio should always be equal to the remaining time horizon and

4(a). Computation of Duration (assuming 8% market yield)

(1) (2) (3) (4) (5) (6)

Year Cash Flow PV@8% PVof Flow PV as % of Price (1) × (5)

1 100 .9259 92.59 .0868 .0868

4(b). Computation of Duration (assuming 12% market yield)

(1) (2) (3) (4) (5) (6)

Year Cash Flow PV@12% PV of Flow PV as % of Price (1) × (5)

1 100 .8929 89.29 .0951 .0951

4(c). A portfolio of bonds is immunized from interest rate risk if the duration of the portfolio is

always equal to the desired investment horizon. In this example, although nothing

5. Assuming semi-annual coupons. Current and year-later prices can easily be found using a

financial calculator:

CURRENT CANDIDATE

BOND BOND

Dollar Investment 839.54 961.16

Coupon 90.00 110.00

Solutions for Chapter 16: Questions and Problems

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6. Assuming semi-annual coupons. Current and year-later prices can easily be found using a

financial calculator:

CURRENT CANDIDATE

BOND BOND

Dollar Investment 868.21 849.09

Coupon 90.00 90.00

7.

7(a) The portfolio’s modified duration will be a weighted average of those of the component

bonds. Since there are 5 equally-weighted bonds, the weight of each is 0.20:

portfolio duration = 0.20(2.727+6.404+3.704+4.868+10.909) = 5.722 years

7(b) The liability’s duration (6.50 years) is less than the portfolio’s duration. This means the

endowment is subject to net reinvestment rate. Cash is coming into the portfolio (via