A quantile regression analysis of the cross section of stock market returns

Traditional methods of testing the Capital Asset Pricing Model (CAPM) do so at the mean of the conditional distribution. Instead, we test whether the conditional CAPM holds at other points of the distribution by utilizing the technique of quantile regression (Koenker and Bassett 1978, Buchinsky 1998). This method allows us to model the performance of firms or portfolios that underperform or overperform in the sense that the conditional mean under- or overpredicts the return of the portfolio; we interpret firms that fall in the lower (upper) quantiles as having received bad (good) news during the sample period. Quantile regression also helps to alleviate some of the statistical problems which plague the conditional CAPM literature, such as errors-in-variables, omitted variables bias, sensitivity to outliers and non-normal error distributions. We find, among other results, that in the context of a conditional CAPM, beta is significant in both tails of the distribution of returns - negative for firms that underperform and positive for firms that overperform - but is insignificant around the median.