An Analysis of the Idiosyncratic Risk Puzzle

Understanding the relation between idiosyncratic risk and returns has been a highly debated subject among researchers in the past. Ang et al. (2006, 2009), among others, find evidence in support of the Idiosyncratic Risk Puzzle which postulates that idiosyncratic risk is negatively correlated with equity returns. This paper provides evidence supporting the negative relation between idiosyncratic risk and returns found in Ang et al. (2009) using the CAPM and three factor Fama French model within a similar Fama-MacBeth framework. However, when we sort the idiosyncratic risk values into quantiles, we do not observe a monotonous relation over the spectrum of idiosyncratic risk values. More specifically, we find a large spike in returns for the smallest 20% quantile in terms of size and for the lowest 20% in terms of idiosyncratic risk values on both an equally-weighted and value-weighted basis for the double-sort portfolio. And so, while we find evidence to support the findings of Ang et al. (2009) that there is a negative relation between idiosyncratic risk and returns, we believe that Fama-MacBeth regressions do not serve as a comprehensive analysis of the relation between idiosyncratic risk and returns. Ultimately, we find evidence that the negative relation identified by Ang et al. (2009) might simply be limited to a select few small-sized companies with low idiosyncratic risk values and relatively high returns. In addition, we have shown that similar conclusions are drawn when performing this exercise using a PCA approach, rarely applied to idiosyncratic risk in previous literature.