A 12.75-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has convexity of 150.3 and 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 nearly identical 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 capital loss on each bond? What percentage capital loss would be predicted by the duration-with-convexity rule?
Debenture Valuation
A debenture is a private and long-term debt instrument issued by financial, non-financial institutions, governments, or corporations. A debenture is classified as a type of bond, where the instrument carries a fixed rate of interest, commonly known as the ‘coupon rate.’ Debentures are documented in an indenture, clearly specifying the type of debenture, the rate and method of interest computation, and maturity date.
Note Valuation
It is the process to determine the value or worth of an asset, liability, debt of the company. It can be determined by many processes or techniques. Many factors can impact the valuation of an asset, liability, or the company, like:
A 12.75-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has convexity of 150.3 and 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 nearly identical 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 capital loss on each bond? What percentage 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 the 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?
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