The equity premium puzzle, first documented by Mehra and Prescott, refers to the empirical fact that stocks have greatly outperformed bonds over the last century. As Mehra and Prescott point out, it appears difficult to explain the magnitude of the equity premium within the usual economics paradigm because the level of risk aversion necessary to justify such a large premium is implausibly large. We offer a new explanation based on Kahneman and Tversky's 'prospect theory'. The explanation has two components. First, investors are assumed to be 'loss averse' meaning they are distinctly more sensitive to losses than to gains. Second, investors are assumed to evaluate their portfolios frequently, even if they have long-term investment goals such as saving for retirement or managing a pension plan. We dub this combination 'myopic loss aversion'. Using simulations we find that the size of the equity premium is consistent with the previously estimated parameters of prospect theory if investors evaluate their portfolios annually. That is, investors appear to choose portfolios as if they were operating with a time horizon of about one year. The same approach is then used to study the size effect. Preliminary results suggest that myopic loss aversion may also have some explanatory power for this anomaly.