1. 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

2. 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

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

4. 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.

5. 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

6. 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!

7. 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.

8. 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

9. 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?

10. 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

11. 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

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

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