Forward Rate

A forward rate is the interest rate implied by the current yield curve for a future period. It is derived from the no-arbitrage condition: investing for two years at the 2-year spot rate must produce the same return as investing for one year at the 1-year spot rate and then reinvesting for one year at the 1-year rate, one year forward.

Mathematically, the 1-year rate, 1-year forward (denoted 1y1y) satisfies:

(1 + r_2)^2 = (1 + r_1)(1 + f_{1,1})

where r_1 and r_2 are the 1-year and 2-year spot rates, and f_{1,1} is the forward rate.

Forward rates serve multiple purposes:

• Market expectations: Forward rates reflect the market's pricing of where rates will be, though they include a term premium component and do not purely represent expectations
• Relative value: Comparing forward rates to economists' rate forecasts reveals whether the market is pricing in more or less easing/tightening than expected
• Hedging: Forward rate agreements (FRAs) and interest rate swaps are priced using forward curves

The forwards tool on this site computes and visualizes the implied forward curve for any horizon, allowing users to see what the current par curve implies about future rate levels. A steep forward curve suggests the market prices higher future rates (or positive term premium), while a declining forward curve suggests expectations of lower rates.