Question

The price of a zero-coupon bond with maturity 1 year is $943.40. The price of a zero-coupon bond with maturity 2 years is $898.47. For this problem, express all yields as net (not gross) rates. Assume the face values of the bonds are $1000.

Assuming that the expectations hypothesis is valid, what is the expected price of the 2 year bond at the beginning of the second year? Expected sort term rate being .05 or 5% in the second year.

What is the rate of return that you expect to earn if you buy the 2 year bond at the beginning of the first year and sell it at the beginning of the second year?

Answer 1

1. Yield of 1 Year Bond = Face Value = Current Price * (1 + r)^n

1000 = 943.40 * (1 + r)^1

1 + r = 1.06

Yield = 6%

2. Yield of 2 Year Bond = Face Value = Current Price * (1 + r)^n

1000 = 898.47 * (1 + r)^2

1 + r = 1.113^(1/2)

1 + r = 1.055

Yield = 5.50%

3. Expected Price of 2 year bond at the beginning of second year = Current Price * (1 + r)^n

898.47 * (1 + 0.06)^1

$952.38

4. Rate of Return = Price at second year - Price at First Year / Price at first year

Rate of Return = 952.38 - 898.47 / 898.47

Rate of Return = 6.00%