The term structure for zero-coupon bonds is currently: Maturity (Years) YTM (%)

ID: 2740073 • Letter: T

Question

The term structure for zero-coupon bonds is currently:

Maturity (Years)

YTM (%)

4.9%

5.9

6.9

Next year at this time, you expect it to be:

Maturity (Years)

YTM (%)

5.9%

6.9

7.9

What do you expect the rate of return to be over the coming year on a 3-year zero-coupon bond?

Under the expectations theory, what yields to maturity does the market expect to observe on 1- and 2-year zeros at the end of the year?

Is the market's expectation of the return on the 3-year bond greater or less than yours?

The term structure for zero-coupon bonds is currently:

Current year yield on a 3-year bond = 6.9%

Current price of 3-year bond with face value $100 = $100/1.0693 = $81.86

After one year, this 3-year bond shall be a 2-year bond having 2 years to maturity. Next year yield on a 2-year bond is 6.9%.

Price of 3-year bond next year = $100/1.0692 = $87.51

Total return over the coming year = $87.51-$81.86 = $5.65

Expected rate of return over coming year = $5.65/$81.86 = 0.069 = 6.9%

Forward rate for 2-year and 3-year bond on the basis of current year yield are as below:

Forward rate for 2-year bond = (1.0592/1.049)-1 = 0.0691 = 6.91%

Forward rate for 3-year bond = (1.0693/1.0592)-1 = 0.0893 = 8.93%

Using the forward rates calculated above, the forecasted next year are as below:

Forecasted yield for 1-year bond = 6.91%

Forecasted yield for 2-year bond = (1.0691*1.0893)1/2 – 1 = 0.0792 = 7.92%

The market forecasted return is higher than the our forecast.

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