What is the convexity bias in Eurodollar (now SOFR) futures and how big is it?

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AcadiFi · Accepted Answer

Eurodollar (and now SOFR) futures settle linearly in price with respect to rate changes: a 1bp rate move equals $25 per contract regardless of level. Forwards, in contrast, are non-linear because the discount factor is a convex function of rates. Futures holders are marked to market daily: when rates rise they receive cash immediately (reinvest at high rate); when rates fall they pay out (borrow at low rate). This correlation between cash flows and reinvestment rates benefits the short and disadvantages the long, so futures rates trade above forward rates.

The convexity adjustment is approximately (1/2) * sigma^2 * T1 * T2, where T1 is time to futures expiry and T2 is time to end of the rate period, and sigma is the short-rate volatility. For a 5-year-forward 3-month contract with sigma = 1.2%, adjustment is 0.5 * (0.012)^2 * 5 * 5.25 = 18.9bps. Riverton Swaps uses this to bootstrap zero curves from deep futures strips. Ignoring convexity in long-dated Eurodollar pack pricing creates 20-40bp errors beyond 5 years, compounding into material portfolio mispricing.

What is the convexity bias in Eurodollar (now SOFR) futures and how big is it?

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