# Forward Rate

Source: https://www.yieldcurve.pro/learn/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](https://www.yieldcurve.pro/forwards) 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.