Chapter 3: Q11-9B (page 360)
A nine-year bond has a yield of 10% and a duration of 7.194 years. If the bond’s yield changes by 50 basis points, what is the percentage change in the bond’s price?
3.27% decline.
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Philip Morris has issued bonds that pay annually with the following characteristics:
Coupon | Yield to Maturity | Maturity | Macaulay Duration |
8% | 8% | 15 Years | 15 Years |
a. Calculate modified duration using the information above.
b. Explain why the modified duration is a better measure than maturity when calculating the bond’s sensitivity to changes in interest rates.
c. Identify the direction of change in modified duration if:
i. The coupon of the bond was 4%, not 8%.
ii. The maturity of the bond was 7 years, not 15 years.
Question: Now suppose the bond in the previous question is selling for 102. What is the bond’s yield to maturity? What would the yield to maturity be at a price of 102 if the bond paid its coupons only once per year?
A 12.75-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has a convexity of 150.3 and a modified duration of 11.81 years. A 30-year maturity 6% coupon bond making annual coupon payments also selling at a yield to maturity of 8% has a nearly identical modified duration—11.79 years—but considerably higher convexity of 231.2.
a. Suppose the yield to maturity on both bonds increases to 9%. What will be the actual percentage of capital loss on each bond? What percentage of capital loss would be predicted by the duration-with-convexity rule?
b. Repeat part ( a ), but this time assume the yield to maturity decreases to 7%.
c. Compare the performance of the two bonds in the two scenarios, one involving an increase in rates, the other a decrease. Based on their comparative investment performance, explain the attraction of convexity.
d. In view of your answer to ( c ), do you think it would be possible for two bonds with equal duration, but different convexity, to be priced initially at the same yield to maturity if the yields on both bonds always increased or decreased by equal amounts, as in this example? Would anyone be willing to buy the bond with lower convexity under these circumstances?
Question: A 10-year bond of a firm in severe financial distress has a coupon rate of 14% and sells for $900. The firm is currently renegotiating the debt, and it appears that the lenders will allow the firm to reduce coupon payments on the bond to one-half the originally contracted amount. The firm can handle these lower payments. What are the stated and expected yields to maturity of the bonds? The bond makes its coupon payments annually.
Macaulay’s duration is less than the modified duration except for:
a . Zero-coupon bonds.
b. Premium bonds.
c. Bonds selling at par value.
d. None of the above.
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