Are Stocks Really Less Volatile in the Long Run?

Conventional wisdom views stocks as less volatile over long horizons than over short horizons due to mean reversion induced by return predictability. In contrast, we find 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. We decompose return variance into five components, which include mean reversion and various uncertainties faced by the investor. Although mean reversion makes a strong negative contribution to long-horizon variance, it is more than offset by the other components. Using a predictive system, we estimate annualized 30-year variance to be nearly 1.5 times the 1-year variance.

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