Why forward and futures prices differ

When are forward and futures prices equal?

A forward and a futures contract on the same asset and date pay the same total gain or loss, but the cash arrives at different times. Futures cash arrives daily; forward cash arrives at expiry. That timing matters only if the interest rate on the daily cash changes in a way that is linked to the futures price.

The prices are therefore equal in two cases: interest rates are constant, or the futures price is uncorrelated with interest rates. The gap appears when the correlation of futures prices with interest rates is not zero.

How does correlation create a price gap?

Consider a long with positive correlation. When the futures price rises, rates also tend to be high, so the gains paid into the margin account can be invested at those high rates. When the price falls, rates tend to be low, so the losses are financed cheaply. This reinvestment of daily gains works in the long’s favor, so the long prefers the futures contract and is willing to pay more for it. The futures price is higher than the forward price.

With negative correlation the logic reverses: gains arrive when rates are low and losses when rates are high. The long prefers the forward, and the forward price is higher.

Same underlying and expirythe price gap depends on interest rates

• Prices equal Memorize no gap
  • Interest rates constant reinvestment rate never changes
  • Futures price uncorrelated with rates gains and losses meet rates at random
• Futures price higher Memorize positive correlation with rates
  • Gains arrive when rates are high, reinvested well
  • Losses arrive when rates are low, financed cheaply
• Forward price higher Memorize negative correlation with rates
  • Gains arrive when rates are low, reinvested poorly
  • Losses arrive when rates are high, financed dearly

The rule of thumb: the contract that is more attractive to the buyer has the higher price. The gap grows with the volatility of interest rates and with longer maturities, but for the short maturities of most futures it is small.

Exam tip Follow the daily cash: gains that arrive when rates are high favor futures.

What is convexity bias in interest rate contracts?

Rate futures pay a fixed amount per basis point (the basis point value, or BPV), so their payoff is linear in the rate. A forward rate agreement (FRA) settles at the start of the period, with the net payment discounted at the new reference rate. Because the discount rate moves with the rate, the FRA’s payoff is slightly curved. That difference is convexity bias . It comes from the FRA’s discounting, not from the futures contract.

$$Settlement = \frac{\Delta bp \times BPV}{1 + MRR \times \text{Period}}$$

Slide the correlation from negative to positive and watch the price gap change sign. On the second tab the futures payoff is a straight line while the FRA curves slightly away from it.

Forward and futures price differenceusually small for short maturities

• Correlation with interest rates Memorize sets the sign of the gap
• Rate volatility and maturity Use it bigger moves and longer periods widen it
• Convexity bias in rate contracts Memorize FRA is discounted (curved); futures are linear
• Central clearing of OTC contracts Memorize futures-like margin narrows it

How does central clearing narrow the gap?

In central clearing, over-the-counter (OTC) dealers post margin or eligible collateral to a central counterparty, and they usually require the same from their clients. This margin for OTC derivatives gives forwards daily cash flows similar to futures. The gap in cash flow pattern, and so in price, becomes smaller. central clearing does not remove the need for liquidity: users of either contract must hold cash or eligible collateral ready for margin calls.

Go deeper Why bond and rate futures often show negative correlation with rates

A bond price falls when rates rise, so a bond future is negatively correlated with rates. By the rule above its forward price is slightly higher than its futures price. The effect is small but it is the usual direction for fixed-income underlyings.

Go deeper Stress and closeout

In a stress period a futures position is closed out if a margin call is missed, and the loss is crystallized. An OTC forward with flexible credit terms can stay open. Central clearing reduces this contrast, but the dealer’s own margin terms still apply to the client.