Can Rare Events Explain the Equity Premium Puzzle?

Probably not. First, allowing the probabilities attached to the states of the economy to differ from their sample frequencies, the Consumption-CAPM is still rejected by the data and requires a very high level of Relative Risk Aversion (RRA) in order to rationalize the stock market risk premium. This result holds for a variety of data sources and samples -- including ones starting as far back as 1890. Second, we elicit the likelihood of observing an Equity Premium Puzzle (EPP) if the data were generated by the rare events probability distribution needed to rationalize the puzzle with a low level of RRA. We find that the historically observed EPP would be very unlikely to arise. Third, we find that the rare events explanation of the EPP significantly worsens the ability of the Consumption-CAPM to explain the cross-section of asset returns. This is due to the fact that, by assigning higher probabilities to bad -- economy wide -- states in which consumption growth is low and all the assets in the cross-section tend to yield low returns, the rare events hypothesis reduces the cross-sectional dispersion of consumption risk relative to the cross-sectional variation of average returns.