Quantile Regression : Estimating Moments of the Stock Return Distribution

This paper offers a simple yet effective way of estimating the moments of a stock's return distribution. The methodology is based on quantile regression, which is able to effectively summarize a stock's return moments by using a rich set of information about different parts of the stock's return distribution. Using recursively estimated monthly panel data quantile regressions, the proposed methodology first estimates the conditional quantiles of the stock return distribution as a linear function of exogenous variables that are found to be important in return predictability literature. Next, combining the estimates from quantile regressions with the values of the predictor variables measured at the end of the estimation window, the methodology generates forward-looking estimates of stocks' return quantiles at different return horizons ranging from 1 day to 2 years. Potential application areas of the proposed methodology are discussed and an example in variance forecasting is offered