Say why forward and futures prices may not be equal
The idea
Futures and forward prices on the same underlying would be identical if interest rates were constant or known in advance. The difference comes from daily marking to market. A futures gain is received in cash each day and can be reinvested, and a loss must be financed; a forward's gain or loss arrives only at expiry. When the underlying's price is positively correlated with interest rates, futures gains tend to arrive when rates are high and can be reinvested profitably, while losses arrive when rates are low and are cheap to finance, so a long futures position is more attractive and the futures price exceeds the forward price. When the correlation is negative, as for bond futures, the futures price is lower. With zero correlation the prices are effectively equal. In practice the differences are small, and at Level I the forward pricing model is usually applied to futures, though credit risk and liquidity also differ between the two.
A practice question
What is the main reason a futures price can differ from the forward price on the same underlying?
- Futures have no underlying assetWhy not: Futures and forwards both reference an underlying; that is not the difference.
- Futures are marked to market daily — correct
- Forwards cannot be settled in cashWhy not: Many forwards are cash-settled; settlement form does not drive the gap.
Daily settlement creates interim cash flows that are reinvested or financed at uncertain rates, which a forward avoids by settling once at expiry.
A harder one
If an underlying asset's price is positively correlated with interest rates, how does the futures price compare with the forward price?
- The futures price is higher — correct
- The futures price is lowerWhy not: Holds for negative correlation, where gains arrive when rates are low.
- The two prices are equalWhy not: Equality requires zero correlation or constant rates.
Futures gains then tend to come when rates are high, so they are reinvested at attractive rates, and losses come when financing is cheap. That favours the long futures, raising its price.
The hardest tier
For a futures contract on a government bond, whose price falls when interest rates rise, the futures price is most likely:
- slightly above the forward priceWhy not: Would follow from positive correlation; bond prices move opposite to rates.
- exactly equal to the forward priceWhy not: Equality needs zero correlation, but bond prices are strongly rate-sensitive.
- slightly below the forward price — correct
Bond prices are negatively correlated with rates. A long futures holder gains when rates are low, reinvesting at low rates, and loses when rates are high, financing at high rates, so the contract is less attractive and priced lower.
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