Estimating the Equity Premium

Existing empirical research investigating the size of the equity premium has largely consisted of a series of innovations around a common theme: producing a better estimate of the equity premium by using better data or a better estimation technique. The equity premium estimate that emerges from most of this work matches one moment of the data alone: the mean difference between an estimate of the return to holding equity and a risk-free rate. We instead match multiple moments of U.S. market data, exploiting the joint distribution of the dividend yield, return volatility, and realized excess returns, and find that the equity premium lies within 50 basis points of 3.5%, a range much narrower than was achieved in previous studies. Additionally, statistical tests based on the joint distribution of these moments reveal that only those models of the conditional equity premium that embed time variation, breaks, and/or trends are supported by the data. In order to develop the joint distribution of the dividend yield, return volatility, and excess returns, we need a model of price and return fundamentals. We document that even recently developed analytically tractable models that permit autocorrelated dividend growth rates and discount rates impose restrictions that are rejected by the data. We therefore turn to a wider range of models, requiring numerical solution methods and parameter estimation by the simulated method of moments. ∗Donaldson, [email protected], Sauder School of Business, University of British Columbia, 2053 Main Mall, Vancouver, BC V6T 1Z2, Canada; Kamstra, [email protected], Schulich School of Business, York University, 4700 Keele St., Toronto, ON M3J 1P3, Canada; and Kramer, [email protected], Rotman School of Management, University of Toronto, 105 St. George St., Toronto, ON M5S 3E6, Canada. We are grateful for the suggestions of Stephen Brown (the editor), Wayne Ferson, Mark Fisher, Ian Garrett, Joel Hasbrouck, Robert Hodrick (the referee), Raymond Kan, Patrick Kelly, Alan Kraus, Tom McCurdy, Federico Nardari, Cesare Robotti, Jacob Sagi, and Tan Wang; participants of the Western Finance Association Meetings, the Northern Finance Association Meetings, the Canadian Econometrics Study Group, the European Econometric Society Meetings, and the investment conference of the University of Colorado at Boulder’s Burridge Center for Securities Analysis and Valuation; and seminar participants at the Board of Governors of the Federal Reserve System, Emory University, the Federal Reserve Bank of Atlanta, Queen’s University, the U.S. Securities and Exchange Commission, and the University of British Columbia. We thank the Social Sciences and Humanities Research Council of Canada for financial support. Any remaining errors are our own. Previous versions of this paper were titled “Stare Down the Barrel and Center the Crosshairs: Targeting the Ex Ante Equity Premium” and “Estimating the Ex Ante Equity Premium.”