Comparison of Estimators of Equity Return Standard Deviation Using Pitman Closeness Criterion and Control Charting Applications

Measurement of dispersion and variation have been studied and evaluated in many applications. Volatility in the field of finance is an important measure as it directly impacts allocation, risk management, and valuation. Pitman Closeness criterion is used to compare estimators of standard deviation from equity returns in a control charting application. Three estimators are evaluated over the 30 DJIA component stocks in an effort to determine if one method of estimation has better performance within an application of control charting for identifying outliers. The study uses three sample sizes to also determine if the better estimator is sample size dependent.