Forward rate

The forward rate is the future yield on a bond. It is calculated using the yield curve. For example, the yield on a three-month Treasury bill six months from now is a forward rate.

To extract the forward rate, we need the zero-coupon yield curve.

We are trying to find the future interest rate ${\displaystyle r_{1,2}}$ for time period ${\displaystyle (t_{1},t_{2})}$, ${\displaystyle t_{1}}$ and ${\displaystyle t_{2}}$ expressed in years, given the rate ${\displaystyle r_{1}}$ for time period ${\displaystyle (0,t_{1})}$ and rate ${\displaystyle r_{2}}$ for time period ${\displaystyle (0,t_{2})}$. To do this, we use the property that the proceeds from investing at rate ${\displaystyle r_{1}}$ for time period ${\displaystyle (0,t_{1})}$ and then reinvesting those proceeds at rate ${\displaystyle r_{1,2}}$ for time period ${\displaystyle (t_{1},t_{2})}$ is equal to the proceeds from investing at rate ${\displaystyle r_{2}}$ for time period ${\displaystyle (0,t_{2})}$.

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