Estimating the Ex Ante Equity Premium

We find that the true ex ante equity premium very likely lies within 50 basis points of 3.5%. This estimate is similar to values obtained in some recent studies but is considerably more precise. In addition to narrowing the range of plausible ex ante equity premia, we also find that equity premium models that allow for time-variation, breaks, and/or trends are the models that best match the experience of US markets and are the only models not rejected by our specification tests. This suggests that time-variation, breaks, and/or trends are critical features of the equity premium process. Our approach involves simulating the distribution from which interest rates, dividend growth rates, and equity premia are drawn and determining the prices and returns consistent with these distributions. We achieve the narrower range of ex ante equity premium values and the narrower set of plausible models by comparing statistics that arise from our simulations with key financial characteristics of the US economy, including the mean dividend yield, return volatility, and mean return. Our findings are achieved in part with the imposition of more structure than is typically exploited in the literature. In order to mitigate the potential for misspecification with this additional structure, we consider a broad collection of models that variously do or do not incorporate features such as an adjustment in dividend growth rates to account for recently increased share repurchase activity, sampling uncertainty in generating model parameters, and cross-correlation between interest rates, dividend growth rates, and equity premia. Estimating the Ex Ante Equity Premium Financial economic theory is often concerned with the premium that investors demand ex ante, when they first decide whether to purchase risky stocks instead of risk-free debt. In contrast, empirical tests of the equity premium often focus on the return investors received ex post. It is well known that estimates of the ex ante equity premium based on ex post data can be very imprecise; such estimates have very wide margins of error, as wide as 1000 basis points in typical studies and 320 basis points in some recent studies. This fact makes it challenging to employ the equity premium estimates for common practical purposes, including evaluating the equity premium puzzle, performing valuation, and conducting capital budgeting. The imprecision of traditional equity premium estimates also makes it difficult to determine if the equity premium has changed over time. Our goals, therefore, are to develop a more precise estimate of the ex ante equity premium and to determine what kind of equity premium model can be supported by the experience of US markets. We accomplish these goals by employing simulation techniques that identify a range of models of the equity premium and the values of the ex ante equity premium that are consistent with values of several key financial statistics that are observed in US market data, including dividend growth rates, interest rates, Sharpe ratios, price-dividend ratios, volatilities, and of course the ex post equity premium. Our results suggest that the mean ex ante equity premium lies within 50 basis points of 3.5%. These results stand even when we allow for investors’ uncertainty about the true state of the world. The tightened bounds are achieved in part with the imposition of more structure than has been commonly employed in the equity premium literature. In order to mitigate the potential for misspecification with this additional structure, we consider a broad collection of models that variously do or do not incorporate features such as a conditionally time-varying equity premium, a downward trend in the equity premium, a structural break in the equity premium, an adjustment in dividend growth rates to account for increased share repurchase activity in the last 25 years, sampling uncertainty in generating model parameters, a range of time series models, and crosscorrelation between interest rates, dividend growth rates, and equity premia. We also find that The equity premium literature is large, continuously growing, and much too vast to fully cite here. For recent work, see Bansal and Yaron (2004), Graham and Harvey (2005), and Jain (2005). For excellent surveys see Kocherlakota (1996), Siegel and Thaler (1997), Mehra and Prescott (2003), and Mehra (2003).