The equity premium is the extra return investors anticipate when purchasing risky stock instead of riskfree debt. Unfortunately, we cannot observe this ex ante premium; we only observe returns investors receive ex post, after purchasing and holding stock over some period during which random shocks impact prices. US stocks have historically returned 6% more than debt (more than warranted by standard economic theory); hence the "equity premium puzzle". We devise a method to simulate the distribution of ex post equity premia, conditional on various ex ante equity premium values. We calibrate our approach to US data to find that with a 2% ex ante premium, the economy could reasonably have produced a 6% ex post equity premium. Thus the 6% historical premium observed in US data may be due to fortunate market outcomes rather than a true asset pricing puzzle.