Chapter 3: Q11-4B (page 360)
A bond currently sells for \(1,050, which gives it a yield to maturity of 6%. Suppose that if the yield increases by 25 basis points, the price of the bond falls to \)1,025. What is the duration of this bond?
10.09 years.
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Rank the following bonds in order of descending duration.
Bond | Coupon | Time to Maturity | Yield to maturity |
A | 15% | 20 | 10% |
B | 15 | 15 | `10 |
C | 0 | 20 | 10 |
D | 8 | 20 | 10 |
E | 15 | 15 | 15 |
Find the convexity of a seven-year maturity, 6% coupon bond selling at a yield to maturity of 8%. The bond pays its coupons annually.
( Hint: You can use the spreadsheet from this chapter’s Excel Application on Convexity, setting cash flows after year 7 equal to zero. The spreadsheet is available at www.mhhe.com/bkm; link to Chapter 11 material.)
Question: Is the coupon rate of the bond in the previous problem more or less than 9%?
A bond has a current yield of 9% and a yield to maturity of 10%. Is the bond selling above or below par value? Explain.
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?
What is the bond duration in the previous problem if coupons are paid annually? Please explain why the duration changes in the direction it does.
Find the bond's duration with a settlement date of May 27, 2012, and a maturity date of November 15, 2021. The bond's coupon rate is 7%, and the bond pays coupons semi-annually.
The bond is selling at a yield to maturity of 8%. You can use Spreadsheet 11.2, available at www.mhhe.com/bkm; link to Chapter 11 material.
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