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.

Merton H. Miller, Jayaram Muthuswamy, Robert E. Whaley, Mean Reversion of Standard & Poor's 500 Index Basis Changes: Arbitrage-Induced or Statistical Illusion?, The Journal of Finance, Vol. 49, No. 2 (Jun., 1994), pp. 479-513

The need to understand and measure the determinants of market maker bid/ask spreads is crucial in evaluating the merits of competing market structures and the fairness of market maker rents. This study develops a simple, parsimonious model for the market maker's spread that accounts for the effects of price discreteness induced by minimum tick size, order-processing costs, inventory-holding costs, adverse selection, and competition. The inventory-holding and adverse selection cost components of spread are modeled as an option with a stochastic time to expiration. This inventory-holding premium embedded in the spread represents compensation for the price risk borne by the market maker while the security is held in inventory. The premium is partitioned in such a way that the inventory-holding and adverse selection cost components, as well as the probability of an informed trade, are identified. The model is tested empirically using Nasdaq stocks in three distinct minimum tick size regimes and is shown to perform well both in an absolute sense and relative to competing specifications.

This study analyzes the effects of changes in S&P 500 index composition from January 1986 through June 1994, a period during which Standard and Poor's began its practice of preannouncing changes five days beforehand. The new announcement practice has given rise to the “S&P game” and has altered the way stock prices react. We find that prices increase abnormally from the close on the announcement day to the close on the effective day. The overall increase is greater than under the old announcement policy although part of the increase reverses after the stock is included in the index.

Using transaction data on the S&P 100 index options, we study the effect of valuation simplifications that are commonplace in previous research on the timeseries properties of implied market volatility. Using an American‐style algorithm that accounts for the discrete nature of the dividends on the S&P 100 index, we find that spurious negative serial correlation in implied volatility changes is induced by nonsimultaneously observing the option price and the index level. Negative serial correlation is also induced by a bid/ask price effect if a single option is used to estimate implied volatility. In addition, we find that these same effects induce spurious (and unreasonable) negative cross‐correlations between the changes in call and put implied volatility.

Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) hypothesize that asset return volatility is a deterministic function of asset price and time, and develop a deterministic volatility function (DVF) option valuation model that has the potential of fitting the observed cross section of option prices exactly. Using S&P 500 options from June 1988 through December 1993, we examine the predictive and hedging performance of the DVF option valuation model and find it is no better than an ad hoc procedure that merely smooths Black–Scholes (1973) implied volatilities across exercise prices and times to expiration.