Investment Management
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 yield-to-maturity is 9.4%, the bond prices are, respectively, 1 25 1000 1.036 1000 1.047 827.62
1
25
579.01
Price of bond A decreases by 8.95%, while price of bond B drops by 22.45%. The longer term bond is more sensitive to a given change in the discount rate. This will always be the case. Mathematically, there are more terms in the equation for the longer-term bond that are influenced by the discount rate. Practically speaking, your money is tied up longer with a longer term bond and so you will experience greater capital losses and gains when interest rates change. 2. A bond with a coupon rate of 4.7% is priced to yield 6.30%. Coupon is paid is semi-annually; the par value is $1,000. The bond has 5 years remaining until maturity. Assuming that market rates stay the same over the next five years, calculate the value of the bond at the beginning of
each year and the amount of change in the bond’s value from year to year. Describe the behavior of the bond’s value over time. At t = 0, at issue the price will be 1 1 1.0315 0.0315 1 1.0315 0.0315 1 1.0315 0.0315 1 1.0315 0.0315 1 1.0315 0.0315 23.5 1000 1.0315 932.28
At the end of year 1, the price becomes 1 23.5 1000 1.0315 1000 1.0315 1000 1.0315 1000 1.0315 944.20
1
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 yield-to-maturity is 9.4%, the bond prices are, respectively, 1 25 1000 1.036 1000 1.047 827.62
1
25
579.01
Price of bond A decreases by 8.95%, while price of bond B drops by 22.45%. The longer term bond is more sensitive to a given change in the discount rate. This will always be the case. Mathematically, there are more terms in the equation for the longer-term bond that are influenced by the discount rate. Practically speaking, your money is tied up longer with a longer term bond and so you will experience greater capital losses and gains when interest rates change. 2. A bond with a coupon rate of 4.7% is priced to yield 6.30%. Coupon is paid is semi-annually; the par value is $1,000. The bond has 5 years remaining until maturity. Assuming that market rates stay the same over the next five years, calculate the value of the bond at the beginning of
each year and the amount of change in the bond’s value from year to year. Describe the behavior of the bond’s value over time. At t = 0, at issue the price will be 1 1 1.0315 0.0315 1 1.0315 0.0315 1 1.0315 0.0315 1 1.0315 0.0315 1 1.0315 0.0315 23.5 1000 1.0315 932.28
At the end of year 1, the price becomes 1 23.5 1000 1.0315 1000 1.0315 1000 1.0315 1000 1.0315 944.20
1