Suppose that a 1-year zero-coupon bond with face value $100 currently sells at $

Question

Suppose that a 1-year zero-coupon bond with face value $100 currently sells at $90.44, while a 2-year zero sells at $81.59. 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 9% per year

What is the yield to maturity of the 2-year zero? The 2-year coupon bond

What is the forward rate for the second year

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?

What is the yield to maturity of the 2-year zero? The 2-year coupon bond

What is the forward rate for the second year

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?

Explanation / Answer

a. YTM of two year zero bond ; PV = FV/(1+r)^n where PV =81.59, FV =100 and n =2

81.59 = 100/(1+r)^2

(1+r)^2 = 100/81.59

1+r = (100/81.59)^(1/2)

r = 0.1071 = 10.71%

Yield to maturity of the two year zero = 10.71%

2 -year maturity bond: The YTM of the couopon bond also should be equal to 10.71% since investors should make the same return

(b) The forward rate for the seocnd year: The rate in year 1 = 9%

According expectation theory: (1+rate yr 1) *(1+ rate yr 2) =( 1 + total)^2 = (1+0.09) *(1+y2) = (1+0.1071)^2

On solving, y2 = 0.1245

The forward rate for second year = 12.45%

c. (1) Price at the end of the first year = Face Value = $100

(2) Expected holding period return = 9% (Coupon rate)

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