Π-CAPM: The classical CAPM with probability weighting and skewed assets

We propose a new asset pricing model which generalizes the mean-variance framework by including probability weighting, specifically the overweighting of rare, high-impact events. Our model—the Π-CAPM—allows for disentangling volatility and skewness effects and predicts that idiosyncratic risk is priced. We show that the price impact of volatility is skewness-dependent, negative for left-skewed assets but potentially positive for right-skewed assets. Further, probability weighting translates into an exaggerated co-movement of assets and can explain the empirical correlation premium. Finally, we empirically verify that option-implied variance premiums for individual stocks have a U-shaped relation to the stock’s skewness, as predicted by the Π-CAPM.