Does the Market Understand Time Variation in the Equity Premium?

We test whether the "representative agent" has intertemporally consistent expectations about time variation in the equity premium. First, we use option prices to estimate the expected future log equity premium (the forward rate) and compare this estimate to the log equity premium estimated in the future (the future spot rate). Forward rates are strong predictors of future spot rates, explaining 20% of the variation at the 6-month horizon. Second, using less stringent conditions than required to estimate forward and spot rates separately, we estimate and examine equity premium forecast errors. We can reject rational expectations for many specifications of the stochastic discount factor. The forecast errors can be explained by a model in which an increase in expected stock returns (spot rates) causes investors to overestimate expected stock returns in the future (forward rates). Alternatively, the forecast errors can be rationalized by a stochastic discount factor that features a highly volatile and counter-cyclical price of discount-rate risk