Question

Currently the term structure is as follows: one-year bonds yield 6 percent, two-year bonds yield 7 percent, three-year bonds and greater maturity bonds all yield 8 percent. An investor with a one-year investment horizon is choosing between one-, two-, and three-year maturity bonds all paying annual coupons of 6 percent, once a year.

a. Which bonds should you buy if you strongly believe that at year-end the yield curve will be flat at 6 percent? Show your calculations.

b. Redo part (a) assuming at year-end the yield curve will be flat at 11 percent. Show your calculations.

c. What conclusion(s) can you make by comparing the results of parts (a) and (b) above?

Answer 1

Solution

Part A

Which bonds should you buy if you strongly believe that at year-end the yield curve will be flat at 6 per cent? Show your calculations.

Given

1. one-year bonds yield 6 per cent

2. Two-year bonds yield 7 per cent

3. Three-year bonds and greater maturity bonds all yield 8 per cent

The coupon rate for one year is 6 per cent

The expected return for one year bond = (1+.06)*(1+.06)-1

= (1.06)*(1.06)-1

= 1.1236-1

= 12.36%

Expected return for two year bond = (1+.07)*(1+.06)-1

=(1.07)*(1.06)-1

= 13.42%

Expected return for three year bond = (1+.08)*(1+.06)-1

=(1.08)*(1.06)-1

= 14.48%

Based on the above calculation of the expected rate of return for bonds with one year. two years and three-year maturity, we can see that the three-year maturity bond has the highest expected rate of return however this involves a higher risk of interest rate risks and inflation risks. Thus for an investor with lesser time horizon should invest in an option that it has the lowest risk of inflation and interest rates.

Part B

Redo part (a) assuming at year-end the yield curve will be flat at 11 percent.

Thus

Given

1. one-year bonds yield 6 per cent

2. Two-year bonds yield 7 per cent

3. Three-year bonds and greater maturity bonds all yield 8 per cent

The coupon rate for one year is 6 per cent

The expected return for one year bond = (1+.06)*(1+0.11)-1

= (1.06)*(1.11)-1

= 1.1766-1

= 17.66%

Expected return for two year bond = (1+.07)*(1+0.11)-1

=(1.07)*(1.11)-1

= 1.1877-1

= 18.77%

Expected return for three year bond = (1+.08)*(1+0.11)-1

=(1.08)*(1.11)-1

= 1.1988-1

= 19.88%

PART C

By comparing the expected rate of return result of the two different scenarios with the different yield curve of 6 per cent and 11 per cent flat.
Based on this we can see that yield curve have a major impact on how the expected rate of return turns out to be.

Yield curve reflects the different interest rates for different bonds in a year and this is the average of interest one would get in the worst-case scenario. Whereas the coupon rate declared is what should be expected from the bond in most favourable condition.