University of Missouri Southwind Finance Conference Discussion of “Does Option Trading Have a Pervasive Impact on Underlying Stock Prices?” Xuemin (Sterling) Yan University of Missouri Southwind Finance Conference University of Kansas April 4, 2008

Interesting Paper A typical option pricing paper Technical Relevant for options only This paper Intuitive arguments and plausible hypothesis Impact on stock market Issue of stock volatility is important

Game Plan Summary of hypothesis Economic significance of results Statistical and methodological issues Alternative interpretations Alternative tests Minor suggestions Conclusion

Hypothesis In rational models, volatility is driven by the arrival of new information, and the process by which this information is incorporated into prices. Hedge rebalancing is clearly not information-based. Non-information trading does not affect stock prices in frictionless markets. Arbitragers In less than perfectly liquid markets and in the presence of limited arbitrage, hedge rebalancing might affect stock prices through price impact. Specifically, stock prices may temporarily move in the direction of trading.

Hypothesis To remain delta neutral, delta hedgers with negative gamma (when they write options) will buy the underlying stock after price increase and sell the underlying stock after price decrease. stock prices will rise (fall) more than they would otherwise if solely based on information. Because this price movement is not information-based, it will tend to reverse in subsequent periods. Negative gamma  Higher volatility Positive gamma  lower volatility Negative correlation between gamma and volatility

Economic Significance How much trading does the rebalancing of delta-hedgers potentially generate? Average non-Normalized net gamma is approximately 10,000 (Table 1) Assuming all market makers remain delta neutral, this implies approximately 1 million shares of trading when the stock price moves by 1 dollar Economically significant!

Economic Significance (Table 2) Standard deviation of net gamma is 6.772, therefore, impact on volatility for a one-standard deviation change in net gamma is 36.8 bps, or 11.8% of average daily absolute return. However, the independent variable is not net gamma. Rather, difference in net gamma. The difference in net gamma is much less variable because the two terms are highly positively correlated.

Economic Significance Even if the independent variable is net Gamma, one should be cautious about using the standard deviation for calibration if net Gamma is highly persistent. A better approach is to use the average daily change in net Gamma Finally, for the fraction of volatility explained by hedge re-balancing, could alternatively use change in R-squared Economic significance may have been overstated

Statistical/Methodological Issues The paper uses absolute return as a proxy for volatility and then run a time-series regression for each stock Alternative methodologies Two-step regressions GARCH models More importantly, volatility is highly persistent I believe net Gamma is persistent Potential spurious results use first difference?

Alternative Interpretations Investors have private information about volatility Buy option if volatility is to increase Sell option if volatility is to decrease I am not as concerned about this reverse causality issue. At best, a small subset of public investors have private information about volatility. I am more concerned about a related possibility Investors buy options when volatility is high If persistence in volatility not adequately controlled Hedger’s net Gamma negatively related to volatility

Alternative Tests Delta hedgers with negative gamma will buy after price increase and sell after price decrease. Therefore, stock prices rise (or fall) more than they should. Since the price movement is not driven by information, it subsequently reverses. Why not directly examine return autocorrelations? In the case of negative net gamma Positive autocorrelation in the short-run Negative autocorrelation in the long-run Horizon depends on frequency of rebalancing E.g., intra-daily and daily Not subject to the endogeneity concerns

Minor Suggestions Table 1 Report autocorrelations Report gamma? Interpretations of values Table 2 Report the number of coefficients statistically significant

Conclusion Important issue Plausible hypothesis Economic significance Statistical issues Endogeneity Alternative tests Interesting paper