Question

Suppose that a 1-year zero-coupon bond with face value $100 currently sells at $94.34, while a 2-year zero sells at $84.99. 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 12% 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) According to the expectations hypothesis, what are (i) the expected price of the coupon bond at the end of the first year and (ii) the expected holding-period return on the coupon bond over the first year?

 

Answer 1

a. Yield to maturity of the 2-yr zero-coupon bond = CAGR at which the current price will become 100 at the end of two years

ytm = [( 100/84.99)^(1/2) ] -1 = 8.47%

b. We use the ytm of 1-yr (6.00%) and 2-yr (8.47%) zero coupn bonds to calculate the price of the 2-yr coupon bond.

Price = present value of cash flow at year 1 end + present value of cash flow at year 2 end

= (12 / 1.06) + (12 + 100) /( 1.0847^2) = 106.5096

YTM = 8.33% using hit and trial method , i.e. keep the discount rate same for both years and then change it so as to get total present value of 106.5096

c.   Forward rate for second year = [ (1.0847^2) / 1.06 ] -1 =11.00%

d. (i) Expected price at year 1 end = present value of future cash flow = (12 +100) /  1.11 = 100.90

(ii) holding period return = [(100.90 - 106.5096 +12) /106.5096 ] -1 = 6.00%