The Idiosyncratic Risk-Return Relation: A Quantile Regression Approach Based on the Prospect Theory

Given some debate on the empirical idiosyncratic risk-return relation in the literature, we reexamine the relation using a quantile regression approach based on the prospect theory developed by Kahneman and Tversky [1979]. The quantile regression approach allows the coefficient on the independent variable (idiosyncratic risk) to vary across the distribution of the dependent variable (return). Our sample consists of stocks traded on the NYSE, AMEX, and NASDAQ during 1980–2010: 80,324 firm-year observations and 8,123 firms in total. The quantile regression results show that idiosyncratic risk is positively (negatively) related to returns at the high (low) quantiles of returns. The findings are consistent with the prospect theory that investors have a tendency to be less (more) willing to gamble with profits (losses). The results also demonstrate that the least-squares and least-sum optimization methods commonly used in prior research do not capture the relations between idiosyncratic risk and returns at the tail parts of the distribution of returns. Therefore, our empirical results provide new insights into the idiosyncratic risk-return relation in the literature.