Finance

We characterize the joint dynamics of expected returns, stochastic volatility, and prices. In particular, with a given dividend process, one of the processes of the expected return, the stock volatility, or the price-dividend ratio fully determines the other two. For example, the stock volatility determines the expected return and the price-dividend ratio. By parameterizing one, or more, of expected returns, volatility, or prices, common empirical specifications place strong, and sometimes inconsistent, restrictions on the dynamics of the other variables. Our results are useful for understanding the risk-return trade-off, as well as characterizing the predictability of stock returns.