Long-Run Stock Return Distributions: Empirical Inference and Uncertainty

Abstract

We analyze empirical estimation of the distribution of total payoffs for stock investments over very long horizons, such as 30 years. Formal results for recently proposed bootstrap estimators are derived and alternative parametric methods are proposed. All estimators should be viewed as inconsistent for longer investment horizons. Valid confidence bands are derived and should be the focus when performing inference. Empirically, confidence bands around long-run distributions are very wide and point estimates must be interpreted with great caution. Consequently, it is difficult to distinguish long-run aggregate return distributions across countries; long-run U.S. returns are not significantly different from global returns.