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Mean Reversion of Standard & Poor's 500 Index Basis Changes: Arbitrage-induced or Statistical Illusion?





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    • Miller is from the Graduate School of Business, University of Chicago. Muthuswamy is from the National University of Singapore. Whaley is from the Fuqua School of Business, Duke University. This research is supported by the Futures and Options Research Center at Duke University. We are grateful for valuable comments and suggestions by Craig Ansley, Messod D. Beneish, Fischer Black, John Cochrane, Wayne Ferson, David Hsieh, Stephen Kaplan, Laura Kodres, Paul Kupiec, Fred Lindahl, Rob Neal, David Siegmund, Tom Smith, René Stulz, and two anonymous referees, as well as seminar participants at the Commodity Futures Trading Commission (CFTC), Clemson University, Duke University, Erasmus University, Johns Hopkins University, Laval University, London Business School, University of Chicago, University of Karlsruhe, University of Michigan, University of North Carolina, University of Pennsylvania, University of Science and Technology at Hong Kong, University of Toronto, University of Virginia, and the 1992 Western Finance Association meetings in San Francisco, California. We are also grateful to Carl Bell and Robert Nau for technical support and to Jim Shapiro at the NYSE for providing the index arbitrage trading volume data.


Mean reversion in stock index basis changes has been presumed to be driven by the trading activity of stock index arbitragers. We propose here instead that the observed negative autocorrelation in basis changes is mainly a statistical illusion, arising because many stocks in the index portfolio trade infrequently. Even without formal arbitrage, reported basis changes would appear negatively autocorrelated as lagging stocks eventually trade and get updated. The implications of this study go beyond index arbitrage, however. Our analysis suggests that spurious elements may creep in whenever the price-change or return series of two securities or portfolios of securities are differenced.

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