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.

1 What is the yield to maturity of the 1 year bond?

2 What is the yield to maturity of the 2 years bond?

3 Assuming that the expectations hypothesis is valid, what is the expected short rate in the first year? 3

4 Assuming that the expectations hypothesis is valid, what is the expected short rate in the second year ?

5 Assuming the liquidity preference theory is valid and the liquidity premium in the second year is 0.01, what is the expected short rate in the second year?

6 Assuming that the expectations hypothesis is valid, what is the expected price of the 2 year bond at the beginning of the second year?

7 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.

Price of 1 year zero coupon bond = 943.40

face value = 1000

price = face value / ( 1 + S1)^1

where S1 is yield for 1 year

So

943.40 = 1000 / ( 1+S1)^1

so

S1 = 6%

2.

Price of 2 year zero coupon bond = 898.47

face value = 1000

price = face value / ( 1 + S2)^2

where S2 is yield for 2 year

So

898.47 = 1000 / ( 1+S2)^2

so

S2 = 5.5%

3.

Expected short rate for 1st year = S1 = 6%

4.

Expected short rate for 2nd year = 1f1

(1+S2)^2 = (1+S1)^1 * ( 1+1f1)

so

1f1 = 5.0024%

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