A quick look at bond quotes will tell you that GMAC has many different issues of bonds oustanding. Suppose the four of them have identical coupon rates of 7.25% but mature on four different dates. One matures in 2 years, one in 5 years, one in 10 years, and the last in 20 years. Assume that they all made coupon payments yesterday.
a. If the yield curve were flat and all four bonds had the same yield to maturity of 9%, what would be the fair price of each bond today?
b. Suppose that during the first hour of operation of the capital markets today, the term structure shifts and the yield to maturity of all these bonds changes to 10%. What is the fair price of each bond now?
c. Suppose that in the second hour of trading, the yield to maturity of all these bonds changes once more to 8%. Now what is the fair price of each bond?
d. Based on the price changes in response to the changes in yield to maturity, how is the interest-rate risk a function of the bond's maturity? That is, is interest-rate risk the same for all four bonds, or does it depend on the bond's maturity?
The solution computes fair value of bond with different maturity but identical coupon rates and finds out the interest rate risk.