Question

The yield curve for default-free zero-coupon bonds is currently as follows: Maturity (years) 1 2 3 Maturity (years) YTM 1 2 3 9.7% Required: a. What are the implied one-year forward rates? (Do not round intermediate calculations. Round your answers to 2 decimal places.) 10.7 11.7 YTM 9.7% 10.7% 11.7% Forward rate 11.71 % 12.71 %

Answer 1

The student's question on calculating implied one-year forward rates can be answered by comparing the compounded return of investing in longer-term zero-coupon bonds to a series of shorter-term bonds, and isolating the forward rate for the period in question.

Step-by-step explanation:

The question involves calculating the implied one-year forward rates given the yield curve for default-free zero-coupon bonds. Forward rates are interest rates implied by current zero-coupon bond yields for periods in the future. The calculation is based on the relationship that the return on an investment in a long-term bond should be equivalent to a series of investments in shorter-term bonds, rolled over to match the maturity of the longer-term bond.

To calculate the forward rates, we take the following steps:

1. Calculate the total compounded return of investing in longer-term bonds.
2. Compute the total compounded return of investing in consecutive shorter-term bonds up to that same point.
3. Isolate the forward rate for the remaining period.

For example, an investor can lock in a return today for two successive one-year investments (the first year at 9.7% YTM and the second year at an unknown forward rate) equivalent to a two-year investment at 10.7% YTM. Solving this equation gives us the one-year forward rate starting one year from now.

This approach can be applied repeatedly to find the implied forward rates for subsequent periods, given the multi-year YTMs.