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

We propose a new asset pricing model that generalizes the mean-variance framework by including probability weighting, specifically the overweighting of rare, high-impact events. Our model-the $ \Pi $-CAPM-generates several new predictions: (i) skewness has a positive price effect, amplified by volatility; (ii) the price effect of volatility is negative for left-skewed assets but positive for right-skewed assets; and (iii) option-implied variance premiums for stocks have a U-shaped relation to skewness, amplified by volatility. We find strong empirical support for these predictions. Finally, we show that the $ \Pi $-CAPM predicts an exaggerated co-movement of assets and can explain the correlation premium.