spot and forward rates

The yield curve hides two different but related kinds of rate. A spot rate is the interest rate you can lock in today for money invested from now until some future date — for example, the rate for a single lump invested today and repaid in five years. A forward rate is the rate, agreed today, for borrowing or lending over a future period that has not started yet — for instance, the one-year rate that will apply from year four to year five, fixed now. Both come straight out of the term structure.

Spot rates are the natural rates for discounting: a payment due in t years is worth its amount divided by (1 plus the t-year spot rate) to the power t. Forward rates are implied by, and consistent with, the spot rates, because there must be no free lunch. Investing for five years must give the same result as investing for four years and then rolling over for the fifth at the agreed forward rate; this no-arbitrage condition lets you compute any forward rate from two spot rates. If the five-year spot is higher than the four-year spot, the implied one-year forward from year four to five is higher still.

Spot and forward rates are the precise tools that replace the convenient fiction of a single flat rate. Actuaries use spot rates to value liabilities cash-flow by cash-flow, and forward rates to project reinvestment, price interest-rate guarantees, and value derivatives. A common confusion: a forward rate is not a forecast of what rates will actually be — it is the rate the market sets today so that no riskless profit is possible. Whether realised rates match forwards is a separate, empirical question.