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.
Yield to maturity
Coupons per year
To calculate the bond’s duration in excel, we can use the formulae given in the screenshot.
Usually, with a decrease in payment frequency, the duration increases, as in the above case. However, in this specific case, the reduction is noted because of the timing of the settlement. This implies that in place of maturity of $70 on 15 Nov.2021, there are two maturities of $35, first on 15th May 2021 and the other on 15th Nov. 2021. Since the weighted average of the maturity would be shorter than the other ones, the decrease is noted.
Rank the interest rate sensitivity of the following pairs of bonds.
a. Bond A is an 8% coupon, 20-year maturity bond selling at par value.
Bond B is an 8% coupon, 20-year maturity bond selling below par value.
b. Bond A is a 20-year, non-callable coupon bond with a coupon rate of 8%, selling at par.
Bond B is a 20-year, callable bond with a coupon rate of 9%, also selling at par.
Question: Consider the following $1,000 par value zero-coupon bonds:
Years until maturity
Yield to maturity
According to the expectations hypothesis, what is the market’s expectation of the one year interest rate three years from now?
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?
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