Convexity Bias

What Is Convexity Bias?

Convexity bias is a structural pricing difference between interest rate futures (such as SOFR futures or the now-defunct Eurodollar futures) and equivalent forward rate agreements (FRAs) or OIS swaps. The bias arises because futures are daily mark-to-market instruments: gains are received and losses are paid immediately in cash, whereas an FRA or OIS forward settles at a single future date. This asymmetry in cash flow timing creates a systematic advantage for the party who is short interest rate futures when rates rise — their margin gains arrive early and can be reinvested at higher rates. To eliminate this arbitrage, futures must trade at a slightly higher implied rate than the equivalent forward, meaning futures overprice rates relative to the true forward curve. The adjustment, known as the convexity correction, grows with the square of time to maturity and the level of interest rate volatility, making it most significant for contracts more than two years out.

Why It Matters for Traders

For rates traders and macro strategists building yield curves, ignoring convexity bias leads to a systematically upward-shifted curve at the long end. When stripping a forward curve from SOFR futures to price swaps or structure hedges, the convexity adjustment must be explicitly subtracted. Failure to do so can cause mispricing of 5y and 10y swap rates by several basis points — material in high-notional institutional trades. Relative value desks running Eurodollar (now SOFR) vs. OIS swap positions exploit periods when the market misprices this adjustment, particularly after volatility regime changes. The bias is also central to the basis trade between listed futures and OTC derivatives.

How to Read and Interpret It

The convexity correction is typically estimated using a Hull-White or Vasicek interest rate model. A rough approximation is:

Correction ≈ ½ × σ² × T₁ × T₂

where σ is the short-rate volatility, T₁ is the futures expiry date, and T₂ is the end of the contract's accrual period. At 10-year maturities with 100bps of short-rate volatility, corrections can reach 30–50 basis points. When implied volatility (e.g., from swaptions) rises sharply, the theoretically correct adjustment increases — if market prices haven't updated, a relative value opportunity exists. Watch the spread between SOFR futures-implied rates and OIS forward rates as a real-time gauge.

Historical Context

The convexity bias became a widely discussed academic and practitioner issue in the early 1990s as the Eurodollar futures market grew to be the largest futures market in the world by open interest. Research by Galen Burghardt and Bill Hoskins (1994–1995) quantified corrections of 15–25 basis points for 5-year deferred contracts under the interest rate volatility environment of that era. During the 2022 Fed tightening cycle, with SOFR volatility surging and the SOFR futures strip extending, convexity adjustments on 3-year deferred SOFR contracts widened noticeably, complicating curve construction for swap desks transitioning from Eurodollar to SOFR infrastructure.

Limitations and Caveats

Convexity bias calculations are model-dependent — different assumptions about the short-rate process (mean reversion speed, volatility structure) yield materially different corrections. In practice, dealers use proprietary models that differ enough to create inter-dealer disagreement of a few basis points. Additionally, the correction assumes continuous margin reinvestment at the risk-free rate, which breaks down under funding stress or in negative rate environments where reinvestment assumptions collapse. The adjustment is also less relevant for very short-dated contracts (under 6 months) where the time effect is negligible.

What to Watch

• SOFR swaption implied volatility: Rising vol widens the theoretically correct adjustment, creating potential mispricings in the strip.
• SOFR futures vs. OIS swap spread at the 2y–5y tenor: Persistent wedges signal convexity mispricing or funding dislocations.
• Fed hiking/cutting cycle inflection points: Regime changes in rate volatility cause rapid repricing of convexity adjustments across the strip.
• Open interest concentration in deferred SOFR contracts: Heavy positioning in the 8–12 quarter contracts amplifies convexity-related basis risk.