Forward Rate Agreement

FRAs are quoted with a two-number convention: a 3x6 contract begins three months from today and covers the three-month period ending six months from today. The first number is the time to expiration, the second the time to the end of the underlying deposit period, and the difference between them is the tenor of the reference rate.

Settlement occurs at expiration, not at the end of the interest period. The gross difference equals the notional multiplied by the spread between the realised reference rate and the contract rate, scaled by the day count fraction for the underlying period. Because that difference economically accrues at the end of the period, it is discounted back to the settlement date at the realised reference rate for the same tenor. The long position, the fixed-rate payer, receives the payment when the reference rate fixes above the contract rate and pays when it fixes below.

The contract rate is not a forecast. It is the forward rate implied by the current term structure: the rate that makes investing for the longer horizon equivalent to investing for the shorter horizon and rolling into the forward period. Because that no-arbitrage rate is set at inception, the FRA has zero value to both parties when it is written, and no premium changes hands.

After inception, value emerges as the curve moves. The mark-to-market value to the long is the present value of the difference between the currently implied forward rate for the remaining period and the original contract rate, applied to the notional and the day count fraction, discounted from the end of the underlying period back to the valuation date using current spot rates. A curve shift upward creates positive value for the fixed-rate payer; a downward shift creates a liability.

FRAs are bilateral OTC instruments, documented under master agreements and increasingly subject to collateral posting, which means counterparty exposure is managed rather than eliminated. Their exchange-traded analogue is the short-term interest rate future, which is standardised, daily margined and linearly settled, producing the convexity difference that separates futures rates from true forward rates.

The reference benchmark now tends to be a term risk-free rate or a surviving IBOR such as EURIBOR rather than LIBOR. The spread between FRA rates and overnight index swap rates has long served as a market gauge of bank funding stress, widening sharply in credit crises. Corporate treasurers, banks managing gap positions between assets and liabilities, and asset managers hedging reinvestment risk are the natural users.

Three tasks recur. First, translate the a x b notation into an expiration date and an underlying rate tenor, then identify which spot rates in a given term structure bracket that forward period. Second, derive the contract rate as the implied forward rate by compounding the shorter spot rate forward and solving for the residual. Third, compute a settlement amount: apply the rate differential to the notional over the day count fraction, then discount one period at the realised rate.

Candidates should also be able to state the direction of exposure without hesitation, map the FRA payoff onto the underlying borrowing or lending exposure it hedges, and explain why the hedge is imperfect when the loan's reset dates, day count basis or credit spread differ from the contract's terms.