We show that investors price short-term stock market outcomes very different from outcomes that occur further into the future. To this end, we introduce the expected forward pricing kernel and decompose long-term pricing kernels into short-term and expected forward pricing kernels. Using index options, we find that kernels with maturities of up to 12 months are U-shaped and show that this results from the shape of the 1-month pricing kernel. Once we remove the impact of the 1-month kernel, the expected forward kernels are in line with standard long-run risk models in terms of their shape, level, and time-series variation.

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 $ Π $-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 $ Π $-CAPM predicts an exaggerated co-movement of assets and can explain the correlation premium.