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

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.