A Model of Returns and Trading in Futures Markets

This paper develops an equilibrium model of a competitive futures market in which investors trade to hedge positions and to speculate on their private information. Equilibrium return and trading patterns are examined. ~1! In markets where the information asymmetry among investors is small, the return volatility of a futures contract decreases with time-to-maturity ~i.e., the Samuelson effect holds!. ~2! However, in markets where the information asymmetry among investors is large, the Samuelson effect need not hold. ~3! Additionally, the model generates rich time-tomaturity patterns in open interest and spot price volatility that are consistent with empirical findings. AN ISSUE CENTRAL TO THE ANALYSIS of futures markets is the relationship between speculation and futures price volatility. A long line of models ~see, e.g., Grossman ~1977!, Bray ~1981!! have tried to understand the effects of speculation on futures price volatility. This line of research is economically relevant as speculative trades appear to be an important determinant of volatility in futures markets. For instance, Roll ~1984! finds that public information accounts for only a fraction of the movement in orange juice futures prices, which suggests that investors bring their own private information into the market through their trades. Unfortunately, existing models of speculation in futures are essentially static ones and cannot speak to a number of interesting aspects of returns and trading in futures markets. An example is the relationship between the price volatility and the timeto-maturity of a futures contract. The analysis of this issue is an important one and has a long history. Assuming the existence of a representative investor and an exogenous spot price process, Samuelson ~1965! shows that when there is a mean-reverting component in the spot price process and no * Graduate School of Business, Stanford University. I am deeply indebted to Jiang Wang for his advice, encouragement, and insights. I am also very thankful to Jeremy Stein for his many comments. I also thank Hank Bessembinder, Darrell Duffie, Glenn Ellison, P. Pf leiderer, Ken Singleton, René Stulz ~the editor!, two anonymous referees, and A. Subrahmanyam for helpful comments. I have also received many helpful comments from seminar participants at Baruch College, Carnegie Mellon, CBOT Seminar Series, Columbia, Harvard Business School, London Business School, MIT, Northwestern, New York University, Queen’s-Cornell Conference, the University of British Columbia, the University of California at Berkeley, the University of Chicago, the University of Michigan, Stanford, Wharton, and WFA 1997. I acknowledge financial support from the World Economy Laboratory at MIT. THE JOURNAL OF FINANCE • VOL. LV, NO. 2 • APRIL 2000