Forward Rates: Implied Forward Rate Calculation

Bond A has five years to maturity and offers 3.86% yield, while Bond B has six years to maturity and offers a yield to maturity of 4.03%. The coupons are paid annually on both bonds. Which of the following is _closest_ to the implied forward yield 5_y_1_y_?

Correct! The implied forward rate is calculated from the following formula. $$\displaystyle (1+z_{A})^{A} \times (1+IFR_{A,B-A})^{B-A} = (1+z_{B})^{B}$$ Since the bonds are annual coupon bonds, $$A=5$$, $$B=6$$, $$z_{A}=0.0386$$, and $$z_{B}=0.0403$$. Therefore, the following is true. $$\displaystyle (1+0.0386)^5 \times (1+IFR_{5,1})^1 = (1+0.0403)^6$$ $$\displaystyle IFR_{5,1} = \frac{(1+0.0403)^6}{(1+0.0386)^5} - 1 \approx 0.049$$ Therefore, $$5y1y = 4.9 \%$$.

Incorrect. This answer choice would be accurate if the implied rate were for a semiannual period rather than the whole year.

Incorrect. One of the possible ways to obtain this answer choice is to divide the yield to maturity of the six-year bond by the yield to maturity of the five-year bond. This is not the correct method for computing implied forward rates.

2.4%

4.4%

4.9%