On the Long Run Volatility of Stocks

Abstract

In this paper we investigate whether or not the conventional wisdom that the volatility per period of stocks is lower over longer horizons. Taking the perspective of an investor, we evaluate the predictive variance of k-period returns for different models and prior specifications. We adopt the state space modeling framework of Pastor and Stambaugh [2012] as we feel it is the best alternative for capturing all important expected returns dynamics and accounting for the associated uncertainties. Part of the development includes an extension of the modeling framework to incorporate time-varying volatilities and covariances in a constrained prior information set up. We conclude, that in the U.S. market, there are plausible prior specifications such that stocks are indeed less volatile in the long run. Our results are supported by model assessment exercises that provide evidence to our assumptions. To understand the generality of the results, we extend our analysis to a number of international equity indices.