The Futures-Forward Convexity Bias

A forward contract settles once, at expiry: you either owe or are owed the full gain or loss in one lump sum. A futures contract on the exact same underlying settles daily — gains and losses are paid and received every day through marking-to-market. If interest rates and the underlying move together, this daily cash flow timing matters: a trader who's long futures on something positively correlated with rates tends to receive cash on days rates are high (so it can be reinvested at a good rate) and pay cash on days rates are low (so borrowing to cover it is cheap). That's a small, built-in advantage over the equivalent forward, and in a competitive market it gets priced away — the futures price sits fractionally below the forward price when the correlation is positive, and above it when the correlation is negative.

For most short-dated equity or FX futures the effect is a rounding error and desks treat futures and forwards as interchangeable. It becomes material for long-dated contracts and especially for interest-rate futures themselves, like Eurodollar futures, where the underlying is an interest rate — the correlation between the underlying and the discounting rate is essentially 1, and Eurodollar futures prices are known to run consistently below the corresponding forward rate. Traders correct for this with a convexity adjustment, added to the futures-implied rate to recover a usable forward rate for curve building.