Forward Rate

Study guide: Exam FM-2

A forward rate f_{t_1, t_2} is the interest rate agreed upon today for an investment (or loan) beginning at a future time t_1 and maturing at time t_2. Forward rates are implied by the Yield Curve via Spot Rates:

(1+s_{t_2})^{t_2} = (1+s_{t_1})^{t_1} \cdot (1+f_{t_1, t_2})^{t_2-t_1}

f_{t, t+1} = \frac{(1+s_{t+1})^{t+1}}{(1+s_t)^t} - 1

• The second formula gives the one-period forward rate from time t to t+1
• Forward rates are used to price interest rate derivatives and to construct Yield Curves from market data

Computing a Forward Rate The 1-year spot rate is 4\% and the 2-year spot rate is 5\%. Find the 1-year forward rate for year 2.

Answer (1.05)^2 = (1.04)(1+f_{1,2}) \implies 1+f_{1,2} = \frac{(1.05)^2}{1.04} = \frac{1.1025}{1.04} = 1.0601 f_{1,2} = 6.01\%