Are Stocks Really Less Volatile in the Long Run?




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    • Pástor is at the University of Chicago Booth School of Business, NBER, and CEPR. Stambaugh is at the Wharton School of the University of Pennsylvania and NBER. We are grateful for comments from John Campbell, Peter Christoffersen, Darrell Duffie, Gene Fama, Wayne Ferson, Michael Halling, Cam Harvey, Anthony Lynch, Matt Richardson, Jeremy Siegel, Georgios Skoulakis, Pietro Veronesi, Luis Viceira, Rob Vishny, an Associate Editor, two anonymous referees, workshop participants at the following universities: Amsterdam, Berkeley, Chicago, Columbia, Comenius, Cornell, Erasmus, George Mason, Louisiana State, Princeton, Stanford, Tilburg, UCLA, USC, Warwick, Washington, Pennsylvania, WU Wien, and Yale, and participants in the following conferences: 2010 AFA, 2009 WFA, 2009 EFA, 2009 NBER Summer Institute, 2009 Gerzensee, 2010 Chicago Booth Management Conference, 2010 Q Group, CFA Institute of Chicago, and the 2009 Symposium on Quantitative Methods in Finance at the University of Texas at Austin. We also gratefully acknowledge research support from the Q Group, and we thank Hyun Paul Lee for helpful research assistance.


According to conventional wisdom, annualized volatility of stock returns is lower over long horizons than over short horizons, due to mean reversion induced by return predictability. In contrast, we find that stocks are substantially more volatile over long horizons from an investor's perspective. This perspective recognizes that parameters are uncertain, even with two centuries of data, and that observable predictors imperfectly deliver the conditional expected return. Mean reversion contributes strongly to reducing long-horizon variance but is more than offset by various uncertainties faced by the investor. The same uncertainties reduce desired stock allocations of long-horizon investors contemplating target-date funds.