Working Paper Series no. 841: Strategic Trading, Welfare and Prices with Futures Contracts

Forward and futures contracts are pervasive in security, currency and commodity markets. These derivative contracts allow traders to buy or sell an underlying asset at a future date at a pre-agreed price: when the future asset price is not predictable, this hedges traders against adverse price movements for future transactions. Swaps are portfolios of futures of different maturities.

Futures are often used by agents who cannot trade today: for instance, a wheat producer wishes to hedge against uncertainty regarding the price at which it will sell its crop before sowing, an international company wishes to hedge against exchange rate risk regarding future income or expenses, etc. Were it possible, agents could as well buy or sell their asset immediately, and they would be perfectly hedged without resorting to futures.

But there are important cases, notably major sovereign bond markets, where futures are traded while agents plausibly can trade the asset immediately. For instance, in safe government bond markets (US, Germany, France, …), it is possible to trade with relatively limited constraints: it is possible to borrow funds to purchase a bond by putting it as collateral for the lender; many maturities are available to investors having such a preference without having to wait for issuance; and spot markets can absorb very large quantities. Yet futures are massively traded: in the US, there have always been between 1.5 and 2 trillion dollars of Treasury futures outstanding over the last three years. One partial explanation is that some investors exploit the spread between futures price and spot prices: but this does not explain why futures are traded in the first place.

Therefore, if it is easy to buy or sell a sovereign bond immediately, why should investors use futures contracts? Is their introduction desirable?

This paper provides a theoretical explanation for this, and finds in particular that 1) futures contracts decreases traders’ overall profitability, and 2) futures and their underlying asset trade at different prices, although no investor is precluded to trade in either market.

A first result is that a market incompleteness, i.e. a situation where traders would like to trade derivatives, is created by imperfect competition. When traders are imperfectly competitive, i.e. when they care about the impact of their trades on equilibrium prices, they choose to slice the quantities they want to buy or sell into smaller pieces to be executed successively. This behavior is widely observed in practice. By delaying trade in this way, traders also expose themselves to the risk that the price moves when they trade later: buyers would then fear that the price moves up, and sellers that the price moves down. If futures were introduced, buyers of the underlying asset may be willing to buy futures to sellers of the underlying asset: this rationalizes the use of futures in markets like for safe sovereign bonds.

But when futures are introduced, they are not traded in order to share risk. Traders instead trade futures in a direction opposite to their hedging needs: this is because they also want to influence the futures’ payoff, which is the difference between the spot price at futures’ maturity, and the futures price at which the contract was set. To do so, they modify their trading strategy in the underlying asset in order to influence the spot price at futures’ maturity.

Since futures are not used for risk sharing, they may not smooth traders’ revenue and therefore adversely impact their risk-adjusted profitability: I show this formally. However, this does not necessarily call for further regulation by financial market authorities. In fact, traders in this model are assumed to be large, and all are adversely affected, so that they may devise rules by themselves, e.g. within the framework of the futures exchange.

Finally, I show that the futures contract can trade below or above the underlying asset, without assuming storage cost or non-zero interest rates. This is surprising, because an investor could then purchase the cheapest asset (underlying or futures contract) and simultaneously sell the most expensive, locking in a risk-free profit while making both prices converge. Such failures of the law of one price are almost always justified by the fact that some traders are constrained not to trade in one market or the other, and limited capacity by those who can trade in both markets to exploit the difference. For instance, in Keynes’ theory of normal backwardation, speculators buy futures to commodity producers and cannot trade in the spot market. But some contemporary commodity traders explicitly refer to simultaneous trade in the spot and futures market as a source of profit. While trading constraints may certainly explain part of observed spreads, imperfect competition in markets with large traders may well be another valid explanation, as this model suggests.