Question

Suppose that a 1-year zero-coupon bond with face value $100 currently sells at $89.75, while a 2-year zero sells at $79.88. You are considering the purchase of a 2-year-maturity bond making annual coupon payments. The face value of the bond is $100, and the coupon rate is 10% per year.
a. What is the yield to maturity of the 2-year zero

b. What is the yield to maturity of the 2-year coupon bond?


c. What is the forward rate for the second year?


d. If the expectations hypothesis is accepted, what are (1) the expected price of the coupon bond at the end of the first year and (2) the expected holding-period return on the coupon bond over the first year?

e. Will the expected rate of return be higher or lower if you accept the liquidity preference hypothesis?

Higher

Lower

Answer 1

Answer:

Check the explanation

Explanation:

Let’s assume that a one/1-year zero-coupon bond with facial value of $100 sells for $89.75 as at present, while a 2year zero sells at a figure of $79.88. You are contemplating the purchase of a 2year maturity bond making yearly coupon payments. The facial value of the bond is $100, and the coupon rate is 10% per year.

a. the yield to maturity of the 2-year zero, y2 = (100 / 79.88)1/2 - 1 = 11.89%

b. the yield to maturity of the 1-year zero, y1 = (100 / 89.75) - 1 = 11.42%

Price of a 2 year coupon bond, P0 = 10 / (1 + y1) + 110 / (1 + y2)2 = 10 / (1 + 11.42%) + 110 / (1 + 11.89%)2 = 96.843

Hence, YTM of the 2 year coupon bond = Rate (Period, PMT, PV, FV) = RATE (2,10, -96.843, 100) = 11.86%

c. The forward rate for the second year, F12 = (1 + y2)2 / (1 + y1) - 1 = (1 + 11.89%)2 / (1 + 11.42%) - 1 = 12.36%

d. If the expectations hypothesis is accepted:

(1) the expected price of the coupon bond at the end of the first year, P1 = 110 / (1 + F12) = 110 / (1 + 12.36%) = 97.90

and (2) the expected holding-period return on the coupon bond over the first year = (P1 + Coupon - P0) / P0 = (97.90 + 10 - 96.843) / 96.843 = 11.42%

e. the correct answer to question E is the second option showing: Lower