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. MEAN REVERSION IN STOCK index basis changes has been amply documented. MacKinlay and Ramaswamy (1988) find significant negative first-order autocorrelation in normalized intraday basis changes of the S&P 500 index futures traded on the Chicago Mercantile Exchange (CME). Yadav and Pope (1990) find similar behavior using Financial Times Stock Exchange (FTSE) 100 index futures data from the London International Financial FuturesExchange (LIFFE), as does Lim (1990) using Nikkei 225 index futures from the Singapore International Monetary Exchange (SIMEX). The trading activity of stock index arbitragers has been presumed to be driving this elastic realignment of stock index and index futures prices. When the basis widens beyond its theoretical level, arbitragers simultaneously sell index futures and buy the index portfolio, pulling the difference between the futures and index 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. 480The Journal of Finance prices back to normal levels. When the basis narrows, opposite trading actions and price reactions occur.We shall propose here an alternative explanation for the observed negative autocorrelation in basis changes, to wit, that it is mainly a statistical illusion, arising because many stocks in the index portfolio trade infrequently. Even if arbitrage in the formal sense never occurred, reported basis changes would appear to be negatively autocorrelated as lagging stocks eventually trade and get their prices updated.Basis reversions of this kind, unrelated to arbitrage, have long been recognized when they occur at the openings on days with a heavy imbalance in overnight orders, like Monday, October 19, 1987. The futures market opened that day down seven percent, an enormous one day drop by past standards. The reported index did not fall immediately, however, because it is based on the last transaction price of each component stock, and some large capitalization stocks in the index, including IBM, did not trade at the regular opening. The index was thus reporting mainly the long-since obsolete prices of Friday's close, not the prices actually achievable at Monday's opening. As each stock in turn opened ...

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The hedging problem is examined where futures prices obey the cost-ofcarry model. The resultant hedging model explicitly incorporates maturity effects in the futures basis. Formulas for the optimal static and dynamic hedges are derived. Although these formulas are developed for the case of direct hedging, the framework used is sufficiently flexible so that these formulas can be applied to many cross-hedging situations. The performance of the model is compared with that of several other models for two hedging scenarios: one involving a financial asset and the other involving a commodity. In both cases, significant maturity effects were found in the first and second moments of the futures basis. Our hedging formulas outperformed other hedging strategies on an ex-ante basis.

The correlation structure of asset returns is a crucial parameter in risk management as well as in theoretical finance. In practice, however, the true correlation structure between the returns of assets can easily become obscured by time variation in the observed correlation structure and in the liquidity of the assets. We employed a timestamped high-frequency data set of exchange rates, namely, the US$-deutsche mark and the US$-yen exchange rates, to calibrate the observed time variation in the correlation structure between theirThe authors would like to thank an anonymous referee and the editor, Robert Webb, for their suggestions and recommendations. returns. We also documented time variation in the liquidity structure of these rates. We then attempted to link the observed correlations with the liquidity via an application of an illiquid trading model first developed by Scholes and Williams (1976). We show that the observed correlation structure is strongly biased by the liquidity and that it is possible to effect at least a partial rectification of the otherwise downward-biased observed correlation. The rectified sample correlation is, therefore, more appropriate for input into models used for forecasting, option pricing, and other risk management applications.