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THE EFFECT OF TRADING FUTURES ON SHORT SALE CONSTRAINTS

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  • We would like to thank Professor Walter Schachermayer for providing the main ideas that led to Example 6.9. We would also like to thank the anonymous referees for their careful reviews of the manuscript. P. Protter is supported in part by NSF grant DMS-0906995.

Abstract

It is commonly believed that the trading of futures on a commodity enables the market to overcome short selling constraints on the spot commodity itself. This belief is embedded in the notion that trading strategies involving futures contracts enable traders to replicate the payoffs as if they were short the spot commodity. The purpose of this paper is to investigate this common belief in a general arbitrage-free semimartingale financial model with trading in futures and a short selling prohibition on the spot commodity. We show via various examples that, in general, this common belief is incorrect. Furthermore, we provide a set of sufficient conditions, albeit very restrictive, under which the common belief is true.

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