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?

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

Following is the formula for computation of yield on the bonds:

Yield on bonds=[Interest+(Face Value-Current Price)/Years to Maturity]/(Face Value+Current Price)/2

1.

Interest=$0

Face Value=$1,000

Current Price=$943.40

Years to Maturity=1

Following is the computation of yield on bonds for the 1 year coupon bond:

Yield on bonds=[$0+($1,000-$943.40)/1]/($1,000+$943.40)/2

=($0+$56.6/$971.7)

=0.0582 or 5.82%

2.

Interest=$0

Face Value=$1,000

Current Price=$898.47

Years to Maturity=2

Following is the computation of yield on bonds for the 1 year coupon bond:

Yield on bonds=[$0+($1,000-$898.47)/2]/($1,000+$898.47)/2

=($0+$50.765/$949.235)

=0.0535 or 5.35%

3.

In the given case, it has been required to determine the expected short rate in the first year following the expectations theory of interest rates.

The expectation hypothesis endeavors to anticipate what interest rate will be later on dependent on current long term financing interest rate. The hypothesis recommends that a financial specialist procures a similar measure of enthusiasm by putting resources into a one-year bond every so often another year bond after the principal bond matures, when contrasted with obtaining a two-year bond in the present.

As per the above theory, the short term rate in the future will be based on the long term rate which will be considered of long term maturity for the given short term rate. In given case, such short term rate will be more than 5.35% (Long term interest rate) as such theory suggests that short term rate is based on long term rate.

4.

In the given case, it has been required to determine the expected short rate in the second year following the expectations theory of interest rates.

As per the above theory, the short term rate in the future will be based on the long term rate which will be considered of long term maturity for the given short term rate. In given case, such short term rate will be computed as multiplication of expected short term rate and current short term rate for the given period.