Question

The term structure for zero-coupon bonds is currently: Maturity (Years) YTM (%) 6.0% 7.0 8.0 Next year at this time, you expect it to be: Maturity (Years) YTM (%) 7.0% 8.0 9.0 Nm a. What do you expect the rate of return to be over the coming year on a 3-year zero-coupon bond? (Round your answer to 1 decimal place.) Rate of return % b-1. 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? (Round your answers to 2 decimal places.) Maturity YTM

b-2. Is the market's expectation of the return on the 3-year bond greater or less than yours?

• Greater

• Less

Answer 1

a)
Current year yield on a 3-year bond = 8%

Face value = $100

Current price of 3-year bond = $100 / 1.08^3 = $79.38

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 8%.

Price of 3-year bond next year = $100/1.08^2 = $85.73

Expected rate of return over coming year = ($85.73 - $79.38) / $79.38
= $6.35 / $79.38
= 8%

Expected rate of return over coming year = 8.0%

b)
Forward rate for 2-year bond = (1.07^2 / 1.06) - 1 = 8.01%

Forward rate for 3-year bond = (1.08^3 / 1.07^2) - 1 = 10.03%

Forecasted yield for 1-year bond = 8.01%

Forecasted yield for 2-year bond = (1.0801 * 1.1003)^(1/2) - 1 = 9.01%

c)
The market forecasted return is higher than the our forecast.