Interest Rate Derivativesintermediate

FRA vs Futures

FRAs and short-term interest rate futures both lock in a future rate, but they differ on five dimensions, venue (OTC vs exchange), standardisation (custom vs fixed lot and expiry), settlement (start of period, discounted, vs daily mark-to-market), counterparty risk (bilateral, usually collateralised vs central clearing) and the convexity adjustment that makes futures-implied rates slightly higher than forward rates for long maturities (Hull, 2022, §6.4).

Why it matters

Think of FRAs as bespoke tailoring and futures as off-the-rack. A treasurer who needs to hedge A$7.3 million for exactly 62 days starting in 47 days gets a precise fit from an FRA. The same hedge in 90-day bank bill futures requires rounding to A$7 million in 7 contracts and to the next quarterly expiry, leaving residual basis risk. The trade-off is liquidity and credit, futures are anonymous and centrally cleared, FRAs are bilateral and need ISDA documentation.

Formulas

Convexity adjustment (Ho-Lee)

R_{\text{fwd}} \approx R_{\text{fut}} - \tfrac{1}{2}\sigma^2 T_1 T_2

Hull's simple approximation.

\sigma

is the short-rate volatility,

T_1

is the start of the rate period,

T_2

is the end. The forward rate is lower than the futures rate (Hull, 2022, §6.3).

Worked examples

Scenario

A treasurer needs to hedge a A$7.3 million borrowing for exactly 62 days, starting in 47 days.

Solution

An OTC FRA can match the notional, start date and tenor exactly. Trading ASX bank bill futures instead requires using 7 contracts (A$7m) at the nearest quarterly expiry, leaving notional, timing and tenor mismatches. The futures hedge is cheaper to execute but carries basis risk.

Scenario

A 5-year SOFR futures contract implies a rate of 4.20%. Annualised short-rate volatility is 1.0%.

Solution

Using Hull's approximation with $T_1 = 5$ , $T_2 = 5.25$ , $\sigma = 0.01$ , the convexity adjustment is $\tfrac{1}{2}(0.01)^2(5)(5.25) \approx 0.000131$ , about 1.3 basis points. The corresponding forward rate is about 4.187%. The gap grows with the square of horizon and is far larger at 10 years.

Common mistakes

✗FRAs and futures give identical hedges. Daily mark-to-market on futures introduces a convexity bias. Hedgers who are long futures earn margin variation when rates rise (and reinvest at higher rates), which makes the futures-implied rate slightly higher than the equivalent forward rate.
✗Futures always win on liquidity. True for standard tenors and expiry dates, but a custom notional or non-quarterly date can be matched only by an FRA. The right tool depends on the cash-flow profile.

Revision bullets

•FRA, OTC, custom, settled at start
•Futures, exchange, standardised, daily MTM
•FRA, counterparty risk, usually collateralised
•Futures, clearinghouse absorbs credit risk
•Convexity adjustment, futures rate > forward rate
•Adjustment grows with $\sigma^2 T_1 T_2$

Quick check

A key advantage of FRAs over short-term interest rate futures is

The convexity adjustment between futures-implied rates and FRA forward rates

Connected topics

IR Futures FRA

In learning paths

Fixed Income & Rates Path

Sources

Hull (2022), §6.3-6.4
Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022. ISBN 978-0-13-693997-9.
Compares FRAs and short-term rate futures, derives the Ho-Lee convexity adjustment, and explains why the futures rate exceeds the forward rate.
Hull Technical Note 1
Hull, John C. "Technical Note No. 1, Convexity Adjustments to Eurodollar Futures." University of Toronto, accessed 2026.
Author's own technical note giving the derivation and worked example of the convexity adjustment between futures and forward rates.
BIS, OTC Interest Rate Derivatives
Bank for International Settlements. "OTC derivatives statistics, semi-annual survey." BIS Statistical Release, 2025.
Provides the relative size of OTC FRA and exchange-traded short rate futures markets, useful for context on which instrument dominates which hedging niche.

How to cite this page

Dr. Phil's Quant Lab. (2026). FRA vs Futures. Derivatives Atlas. https://phucnguyenvan.com/concept/fra-vs-futures

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