UNIVERSITY OF TEXAS AT DALLAS SCHOOL OF MANAGEMENT FIN6310: INVESTMENT MANAGEMENT SOLUTIONS TO PROBLEM SET #1 PROF. ARZU OZOGUZ SPRING 2013

1. Calculate the value of the following two bonds. Assume that coupon payments are made semi-annually and that par value is $1,000 for both bonds. Coupon rate Time to maturity Yield-to-maturity Bond A 5% 5 yrs 7.2% Bond B 5% 25 yrs 7.2%

Recalculate the bonds’ values if the yield to maturity changes to 9.4%. Which bond is more sensitive to the changes in the yield? Will this always be the case? When the yield-to-maturity is 7.2%, the bond prices are, respectively, 1 1 1.036 0.036 1 1.036 0.036 1 1.047 0.047 1 1.047 0.047 25 1000 1.036 1000 1.036 908.98

1

25

746.58

When the …show more content…

811.62. Since this bond

Similarly, if you purchase a three-year zero coupon bond today, the forecasted price a year later is 1000 1.130136 Today, this bond’s price is simply expected holding period return is 78.295 71.178 1 78.295
.

71.178. Therefore, the

10%

6. Consider the following three bonds. You are investigating how the bonds would react to changes in interest rates. Bond A Face value Years to maturity Coupon rate Yield-to-maturity $1,000 3 5.5% 4.80% Zero-coupon bond $1,000 2.85 0 4.80% Bond B $1,000 3 8.75% 4.80%

Assume that coupons are paid once a year. a. Find the duration of each bond. Bond A Time 1 2 3 Price ZCB Time 2.85 Price Bond B Time 1 2 3 Price Cash Flow 87.5 87.5 1087.5 Present value 83.49 79.67 944.81 1107.97 Weight 0.075 0.072 0.853 Cash Flow 1000 Present value 874.92 874.92 Weight 1.000 Cash Flow 55 55 1055 Present value 52.48 50.08 916.58 1019.13 Weight 0.051 0.049 0.899

Hence, the durations are:

0.051 0.075

1 1

0.049 0.072

2 2

0.899 0.853

3 3

2.85 2.78

2.85

b. Calculate the modified duration of each bond. The modified durations are
∗ ∗

2.85 2.72 1.048 2.78 2.65 1.048

c. Calculate the estimated percentage change in price of each bond due to a 0.50% change in yield to maturity. The percentage change in the price of each bond due to a change in the