Stock Price Volatility, Learning, and the Equity Premium
- Author(s): Brennan, Michael;
- Xia, Yihong
- et al.
The determination of stock prices and equilibrium expected rates of return in a general equilibrium setting is still imperfectly understood. In particular, as Grossman and Shiller (1981) and others have argued, stock returns appear to be too volatile given the smooth process for dividends and consumption growth. Mehra and Prescott (1985) claim that this smoothness in consumption and dividend growth gives rise to an “equity premium paradox” since it makes it impossible to explain the equity risk premium with a risk aversion parameter of less than an implausible 35. This paper reconciles the apparent smoothness of aggregate dividends and the volatility of observed stock prices by developing a model of stock prices in a dynamic general equilibrium setting in which learning is important. Dividends, which are one component of the aggregate consumption endowment, are assumed to follow a stochastic process with a mean-reverting drift that is not directly observable by the representative agent but must be estimated from the realized growth rates of dividends and aggregate consumption. The stock price-dividend ratio is shown to depend on the current estimate of the dividend growth rate as well as on the level of uncertainty about the true growth rate. This non-observability of the growth rate of dividends introduces an element of learning into the stock valuation process which is shown to increase the volatility of the stock price and therefore reduce the level of risk aversion required to explain the equity premium. The model is calibrated to the observed joint dividend and consumption process for the US, and is shown to yield an interest rate and stock price process that conform closely to the stylized facts for US capital markets.