a.What is the duration of a five-year bond with a 6.5 percent semiannual coupon

Question

a.What is the duration of a five-year bond with a 6.5 percent semiannual coupon if the yield to maturity (ytm) is 7.125%? What is the duration of a 20-year zero coupon bond with a yield to maturity of 7.625% You expect a sudden, but widely unanticipated, increase in the market rates of interest due to a change in position by the Federal Reserve. Would you rather be holding in your asset portfolio the bond from a. above (BOND A) or the zero from b. above (BOND B)? Which bond would you prefer, and why?

Explanation / Answer

Solution: As per CHEGG policy asnwered One full question. Assuming that face value and maturity value of bond is $1000 Assuming coupon rate and YTM given is half yearly. Interest half year = 1000 * 6.5% * 6/12 = 32.5 YTM half year = 7.125% /2 = 3.5625% YEAR CFAT PVF @ 3.5625% PV PV * YEAR a b c d= b*c e= d*a 0.5 32.5 0.9656 31.3820 15.6910 1 32.5 0.9324 30.3025 30.3025 1.5 32.5 0.9003 29.2601 43.8901 2 32.5 0.8693 28.2536 56.5071 2.5 32.5 0.8394 27.2817 68.2041 3 32.5 0.8106 26.3432 79.0295 3.5 32.5 0.7827 25.4370 89.0295 4 32.5 0.7558 24.5620 98.2479 4.5 32.5 0.7298 23.7170 106.7267 5 1032.5 0.7047 727.5533 3637.7664 Total 974.09 4225.39 B-0 SUM So Macaulay duration is Mac. Duration = SUM/ B-0 = 4225.39 / 974.09 = 4.338 years approx

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