On the Long-Run Volatility of Stocks

In this article, we investigate whether or not the volatility per period of stocks is lower over longer horizons. Taking the perspective of an investor, we evaluate the predictive variance of <i>k</i>-period returns under different model and prior specifications. We adopt the state-space framework of Pástor and Stambaugh to model the dynamics of expected returns and evaluate the effects of prior elicitation in the resulting volatility estimates. Part of the developments includes an extension that incorporates time-varying volatilities and covariances in a constrained prior information set-up. Our conclusion for the U.S. market, under plausible prior specifications, is that stocks are less volatile in the long run. Model assessment exercises demonstrate the models and priors supporting our main conclusions are in accordance with the data. To assess the generality of the results, we extend our analysis to a number of international equity indices. Supplementary materials for this article are available online.

本文旨在探究股票的单期波动率是否在更长投资周期中更低。本文从投资者视角出发，在不同模型与先验设定下，对k期收益的预测方差进行评估。本文采用帕斯特与斯坦博（Pástor and Stambaugh）提出的状态空间框架，对预期收益的动态变化进行建模，并评估先验信息设定对最终波动率估计结果的影响。本研究的一项拓展工作，是在约束型先验信息框架下纳入时变波动率与协方差项。在合理的先验设定下，针对美国市场的研究结论为：股票在长期中的波动率更低。模型评估实验表明，支撑本文核心结论的模型与先验设定与实际数据相符。为验证研究结论的普适性，本文将分析拓展至多只国际股票指数。本文的补充材料可在线获取。