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Stocks are more volatile over long horizons than over short horizons from an investor's perspective. This perspective recognizes that observable predictors imperfectly deliver true expected return and that parameters are uncertain, even with two centuries of data. Stocks are often considered less volatile over long horizons due to mean reversion induced by predictability. However, mean reversion's negative contribution to long-horizon variance is more than offset by uncertainty about future expected return, combined with effects of predictor imperfection and parameter uncertainty. Using a predictive system to capture these effects, the authors find 30-year variance is 21 to 75 percent higher per year than 1-year variance.
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