Stock Volatility and the Levels of the Basis and Open Interest in Futures Contracts

Abstract

This article tests a theoretical model of the basis and open interest of stock index futures. The model is based on the differences between stock and futures in terms of investors' ability to customize stock portfolios and liquidity. Empirical evidence confirms the model's prediction that increased volatility decreases the basis and increases open interest. School of Economics, and the University ofRhode Island for helpful comments, Paine-Webber for some of the data, and James Berens and Feng Zhang for research assistance. 281 282 The Journal of Finance attractiveness of portfolio tailoring and market liquidity to an investor, CV may be positive or negative. When making asset allocation adjustments, stocks can be traded selectively. Because of this, the CV associated with these trades can have a significant influence on the choice between trading stocks or futures, as well as on which stocks to trade. Diversified investors are likely to have an inventory of stock positions with differential and nonzero CVs. Suppose they choose to reduce their exposure in equities. By selling futures instead of stocks, they can keep the CV of their inventory intact as they reduce their equity exposure. Should the spread between the futures and cash prices be sufficient to justify stock trades, investors will maximize the CV of their remaining portfolio by selling the shares with the smallest CVs first. Therefore, as equity exposure is reduced, the marginal CV of portfolios increases.1 The marginal CV of portfolios should be reflected in the relative prices of stocks and index futures (up to arbitrage bound constraints). As the underlying volatility changes, risk-averse investors respond by adjusting their portfolios, affecting relative prices. In particular, as volatility increases, investors holding equity positions respond by selling stocks and futures. The CV of the marginal stocks in their portfolios increases; this is reflected in a higher equilibrium price of stocks relative to futures. New investors, entering the market to help bear the increased risk, purchase both stocks and futures; this increases the number of futures contracts outstanding (open interest). Both a formal model and empirical evidence in support of these hypotheses are presented in this article.Section I reviews the relevant literature. Section II presents the theoretical model and its predictions. Section III presents the empirical results, while Section IV concludes.

Stock Market Crashes, Precursors and Replicas

“…• Fig.2 : Time evolution of the implied variance in log-scale of the S&P 500 index after the crash, taken from [11]. The + represent an exponential decrease with • Fig.3 : Time evolution of the S&P 500 index over a time window of a few weeks after the October 19 crash.…”

“…The standard procedure is then to see what the market forces decide for the option price and then determine the implied volatility by inversion of the Black and Scholes formula for option pricing [10,9]. Fig.2 presents the time evolution of the implied variance of the S&P 500 index after the crash, taken from [11]. As expected, the variance decreases dramatically after the crash, while exhibiting characterizing log-periodic oscillations.…”

Order imbalance and the pricing of index futures

“…Chan, Chung, and Johnson (1993) do show that increases in market volatility reduce the arbitrage spread. Chen, Cuny, and Haugen (1995) report that market conditions affect the customization value of stocks relative to futures that determine the index-futures basis. An increase in market volatility reduces the customization value of stock, which lowers the basis.…”

The Impact of Volatility and Net Buying Pressure on the Trading Demand of Speculators and Hedgers

“…We expect to find that the trading demand for speculative activities will have a negative correlation with volatility, consistent with the findings of Peck (1981). Conversely, we expect to find that the trading demand for hedging purposes will have a positive correlation with volatility, essentially because of the demand amongst investors for hedging their spot positions when there is greater volatility in the market (Chen, Cuny and Haugen, 1995).…”