Stare Down the Barrel and Center the Crosshairs: Targeting the Ex Ante Equity Premium

Abstract

Abstract: The 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 premia are drawn, conditional on various assumptions about investors' ex ante 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 premia than has been supported to date. Our results imply that the true ex ante premium likely lies very close to 4 percent. JEL classification: G12, C13, C15, C22 Key words: risk premium, premium puzzle, Monte Carlo simulation ********** Over the past century the average annual return to investing in the US stock market has been roughly 6% higher than the return to investing in risk-free US T-bills. Mehra and Prescott [1985] argue that consumption within the US has not been sufficiently volatile to warrant such a large premium on risky stocks relative to riskless bonds; hence the well known equity premium puzzle. (1) The premium at issue in economic theory is the premium investors anticipate ex ante, at the moment they first make the decision to purchase stocks instead of risk-free debt. Conversely, the premium we observe in market data is the return investors actually received ex post, after they have held the stock for some time and nature has buffeted the economy with its random shocks. To examine the premium puzzle, we devise a method to simulate the distribution from which ex post premia are drawn, conditional on various values for investors' ex ante premium. We calibrate our approach to SP conversely, we develop a method for determining the probability of observing a 6% premium ex post even if the ex ante premium is as low as, say, 2%. …