We derive a formula for the expected return on a stock in terms of the risk‐neutral variance of the market and the stock's excess risk‐neutral variance relative to that of the average stock. These quantities can be computed from index and stock option prices; the formula has no free parameters. The theory performs well empirically both in and out of sample. Our results suggest that there is considerably more variation in expected returns, over time and across stocks, than has previously been acknowledged.

We study the effect of subjective mortality beliefs on life‐cycle behavior. With new survey evidence, we document that survival is underestimated (overestimated) by the young (old). We calibrate a canonical life‐cycle model to elicited beliefs. Relative to calibrations using actuarial probabilities, the young undersave by 26%, and retirees draw down their assets 27% slower, while the model's fit to consumption data improves by 88%. Cross‐sectional regressions support the model's predictions: Distorted mortality beliefs correlate with savings behavior while controlling for risk preferences, cognitive, and socioeconomic factors. Overweighting the likelihood of rare events contributes to mortality belief distortions.

Using a large sample of institutional investors’ investments in private equity funds raised between 1991 and 2011, we estimate the extent to which investors’ skill affects their returns. Bootstrap analyses show that the variance of actual performance is higher than would be expected by chance, suggesting that some investors consistently outperform. Extending the Bayesian approach of Korteweg and Sorensen, we estimate that a one‐standard‐deviation increase in skill leads to an increase in annual returns of between one and two percentage points. These results are stronger in the earlier part of the sample period and for venture funds.