Question

one-, two-, and three-year maturity, default-free, zero-coupon bonds have yields to maturity of 7%, 8%, and 9%, respectively. what is the implied 1-year forward rate 1 year from today?

Answer 1

The implied 1-year forward rate 1 year from today can be calculated using the concept of the yield curve. The yield curve compares the yields to maturity of bonds with different maturities. By comparing the yields of two- and three-year bonds, we can calculate the implied forward rate. In this case, the implied 1-year forward rate 1 year from today is 11.36%.

Step-by-step explanation:

To calculate the implied 1-year forward rate 1 year from today, we can use the concept of the yield curve. The yield curve is a graphical representation of the yields to maturity of bonds with different maturities. In this case, we have one-, two-, and three-year maturity bonds with yields to maturity of 7%, 8%, and 9%, respectively.

By comparing the yields to maturity of bonds with different maturities, we can calculate the implied forward rates. To calculate the implied 1-year forward rate 1 year from today, we need to compare the yield on the two-year bond with the yield on the three-year bond:

1. First, we calculate the total return on the two-year bond: 1 + 0.08 = 1.08
2. Then, we calculate the total return on the three-year bond: (1 + 0.09) * (1 + forward rate)
3. Since the one-year forward rate is not known, we can use the formula: Forward rate = (1 + total return on three-year bond)/(1 + total return on two-year bond) - 1
4. Substituting the values, we get: Forward rate = (1 + 0.09)/(1 + 0.08) - 1 = 0.1136 or 11.36%

Therefore, the implied 1-year forward rate 1 year from today is 11.36%.