Investment Theory and Risk Management, + Website

Forward Rates

Forward rates are interest rates for money to be borrowed between any two dates in the future, but determined today. For example, I don't know what the one-year spot rate will be next year. I do know, however, what the one-year spot rate is today. I also know the two-year spot rate today. So, I could do one of two things:

1. I could lend $1 today for a period of two years at the two-year spot rate, earning .

2. I could lend $1 today for one year, earning and then roll this amount over at the spot rate that materializes one year from now (whatever that is).

The one-year spot rate, one year hence, is unobserved. Let's denote this forward rate by f. Then it must be true that the following relation holds:

The rate f is referred to as the one-year forward rate. The presence of s₁ and s₂ imply a forward rate in this case. It is:

For example, if and , then f = 6.6 percent . That is,

which means that the one year forward implied by s₁ and s₂ must equal 6.6 percent for us to ...