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? (Do not round intermediate calculations. Round your answers to 3 decimal places. Omit the "%" sign in your response.)

What is the forward rate for the second year? (Do not round intermediate calculations and rounded to whole number. Omit the "%" sign in your response.)

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? (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "$" & "%" signs in your response.)

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

What is the yield to maturity of the 2-year zero? The 2-year coupon bond? (Do not round intermediate calculations. Round your answers to 3 decimal places. Omit the "%" sign in your response.)

Explanation / Answer

a:

Zero-coupon bond:

1-year rate = 100/90.44 – 1 = 0.105705 = 10.571%

2-year rate = (100/81.59)^(1/2) – 1 = 0.107086 = 10.709%

Coupon bond:

PV = 9/(1 + r1) + 109/(1 + r2)^2

r1 = 10.571%. r2 = 10.709%

PV = $97.07

PV = 9/(1 + y) + 109/(1 + y)^2

y = 0.107042 = 10.704%

Yield on 2-year coupon bond = 10.704%

b:

1.105705*(1 + r) = 1.107086^2

r = 1.107086^2/1.105705 – 1 = 0.108469

1-year forward rate after 1 year = 10.847% or 11%

c:

PV at (t = 1) = 109/1.108469 = 98.33

Price after one year = $98.33

HPR = (98.33 + 9)/97.07 – 1 = 0.105697 = 10.57%

d:

If there is any liquidity risk, you need to add liquidity risk premium; hence expected return would be higher.

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