The equity premium of interest in theoretical models is the extra return investors anticipate when purchasing risky stock instead of risk-free debt. Unfortunately, we do not observe this ex ante premium in the data; we only observe the returns that investors actually receive ex post, after they purchase the stock and hold it over some period of time during which random economic shocks affect prices. Over the past century U.S. stocks have returned roughly 6 percent more than risk-free debt, which is higher than warranted by standard economic theory; hence the "equity premium puzzle." In this paper we devise a method to simulate the distribution from which ex post equity premia are drawn, conditional on various assumptions about investors' ex ante equity premium. Comparing statistics that arise from our simulations with key financial characteristics of the U.S. economy, including dividend yields, Sharpe ratios, and interest rates, suggests a much narrower range of plausible equity premia than has been supported to date. Our results imply that the true ex ante equity premium likely lies very close to 4 percent.