Predicting Long-Term Stock Return Volatility: Implications for Accounting and Valuation of Equity Derivatives

This study examines empirically the prediction of long-term stock return volatility. We find: (1) when using historical volatility to predict five-year monthly volatility, returns should be measured either weekly or monthly, and the historical period should be approximately five years; (2) when constructing a forecast based solely on historical volatilities of comparable firms, comparable firms should be selected on the basis of industry and firm size; and (3) a shrinkage forecast formed by adjusting a historical forecast toward a comparable-firms forecast is more accurate than either a historical or a comparable-firms forecast. Our results suggest that errors in pricing employee stock options due to errors in predicting long-term volatility would rarely have a material effect on net income.