Question

5. SupPose you buy a five-year zero-coupon Treasury bond for $800 per $1,000 face value. Answer the following questions: (a) What is the yield to maturity (annual compounding) on the bond? (b) Assume the yield to maturity on comparable zeros increases to 7% immediately after purchasing the bond and remains there. Calculate your annual return (holding period yield) if you sell the bond after one year. (c) Assume yields to maturity on comparable bonds remain at7%, calculate your annual return if you sell the bond after two years. (d) Suppose after 3 years, the yield to maturity on similar zeros declines to 3%, Calculate the a,mual return if you sell the bond at that time. (e) If yield remains at 3%, calculate your annual return after four years. (f) After five years. (g) What explains the relationship between annual returns calculated in (b) through (f) and the yield to maturity in (a)?

Answer 1

ANSWER:

a) YTM = (1000 / 800)^(1/5) - 1 = 4.56%

b) After one year, Bond Price,

P1 = FV / (1 + YTM)^n

= 1000 / 1.07^4 = $762.9

Annual Return = 762.9 / 800 - 1 = - 4.64%

c) After two years, P2 = 1000 / 1.07^3 = $816.3

Annual Return = (816.3 / 800)^(1/2) - 1 = 1.01%

d) After three years, P3 = 1000 / 1.03^2 = $942.6

Annual Return = (942.6 / 800)^(1/3) - 1 = 5.62%

e) After four years, P4 = 1000 / 1.03 = $970.9

Annual Return = (970.9 / 1000)^(1/4) - 1 = 4.96%

f) After five years, P5 = 1000, your annual return = YTM = 4.56%