Long Run Stock Volatility: A Reinvestigation

The conventional wisdom that stocks are relatively safe when held over long horizons has been challenged recently. Pastor and Stambaugh (2012) emphasize the importance of accounting for multiple sources of uncertainty in evaluating the volatility of stock return. They show that, after accounting for the uncertainty in future expected returns, current expected return, unexpected return and estimation risk, stocks are substantially more volatile in long horizons from the perspective of a Bayesian investor. Their analysis, however, ignores the basic consistency constraint in asset return, namely that unexpected return is equal to the present value of innovations in future dividend growth, net of the present value of innovations in future returns. In this paper, we show that once this restriction is imposed, the evidence for a larger volatility in long horizons is significantly weakened. We find that, for an investor conducting inference with the post-war quarterly data or historical annual data, conditional variance per period is mildly decreasing in horizon