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.
JEL classification: G12, C13, C15, C22
Keywords: equity risk premium, equity premium puzzle, Monte Carlo simulation
The authors have benefited from the suggestions of Wayne Ferson, Mark Fisher, Raymond Kan, Patrick Kelly, Alan Kraus, Federico Nardari, Cesare Robotti, Tan Wang, participants at the 2002 meetings of the Western Finance Association and the Northern Finance Association, and seminar participants at Emory University, the Federal Reserve Bank of Atlanta, Queen’s University, and the University of British Columbia. They are also grateful to the Social Sciences and Humanities Research Council of Canada for financial support. The views expressed here are the authors’ and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors’ responsibility.
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