Markets

Are Stocks Less Volatile in the Long Run?

By Larry Swedroe

Updated on: June 6, 2011 / 11:52 AM EDT / MoneyWatch

The conventional wisdom about stocks is that the annualized volatility of stock returns is lower over long horizons. Historically, this has been true, because there has been mean reversion of stock returns, at least in the United States. Professor Jeremy Siegel's popular book, Stocks for the Long Run, contributed to this idea. Siegel, using two centuries of U.S. equity returns, found that the standard deviation of returns realized over investment horizons of several decades are substantially lower than short-horizon variances on a per-year basis. However, this isn't the most relevant question. The question is: "Is this backward-looking approach the right way to determine whether stocks are risky for the long term?"

Professors Lubos Pastor and Robert Stambaugh took a different approach. In contrast to Siegel, they found that stocks are substantially more volatile over long horizons from an investor's perspective -- the only perspective that matters. This is because, despite two centuries of data, the parameters are uncertain, and that observable predictors of stock returns (such as dividend yield) imperfectly deliver the conditional expected return. The uncertainties include:

Uncertainty about the future distribution of returns
Uncertainty about future expected returns
Uncertainty about the current expected returns
Estimation risk (investors face incomplete information)

Of these, the most important is uncertainty about future expected returns -- a subject often neglected in discussions of how return predictability affects long-horizon return variance.

They found that while mean reversion contributes to reducing long-horizon variance, it's more than offset by the many uncertainties faced by the investor -- especially uncertainty about the expected return. Despite more than two centuries of data, investors don't know for certain the values of the parameters that generate expected returns. The observable predictors we have to forecast returns are highly uncertain. This uncertainty about the expected return contributes to the investor's overall uncertainty about what the upcoming realized returns will be. And the longer the horizon, the more important the role of uncertainty becomes. For example, they found that the 25-year predictive variance is 92 percent larger than the one-year variance, and the 50-year predictive variance is nearly three times the one-year variance.

Pastor and Stambaugh used predictive systems and up to 206 years of data to compute long-horizon variance of real stock returns from the perspective of an investor who recognizes that parameters are uncertain and predictors are imperfect. They concluded that while mean reversion reduces long-horizon variance, the effect is swamped by other effects. They concluded that long-run variance is substantially higher than short-horizon variance because predictors are imperfect. Thus, stocks are less appealing to long-horizon investors than conventional wisdom suggests.

Their findings have important implications for investors, including those choosing target-date funds.

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