Nobody Knows Much

Generally speaking, our sample sizes for historical investment performance are small and hard to interpret. 200 years of U.S. stock market data seems like a lot at first glance, but it’s less informative than you might think. For instance, your own investment horizon might span 60 or more years. That’s a sizable chunk of the existing data set.

It’s also common to limit historical sampling to U.S. markets. Stock returns over the past 40 years look much different in Japan, for instance. Is it naive to focus on a single country’s performance history in forward-looking analysis? What risk factors might be overlooked in doing so?

It’s also difficult to compare returns across historical periods. How did investment performance in Period A impact investment performance in Period B? What specific factors contributed to the performance of Period A, and how different are those factors in Period B? If returns aren’t independent from one period to the next, does this change how we should interpret models that rely on historical sampling to simulate future portfolio performance?

Lubos Pastor (University of Chicago) and Robert Stambaugh (University of Pennsylvania) published a paper in 2011 challenging the conventional wisdom that stocks are less volatile over the long-run. Core to their findings is the fact that uncertainty plays an increasingly important role as the investment timeline grows.

“Mean reversion reduces long-horizon variance considerably, but it is more than offset by other effects. As a result, long-horizon variance substantially exceeds short-horizon variance on a per-year basis. A major contributor to higher long-horizon variance is uncertainty about future expected returns, a component of variance that is inherent to return predictability, especially when expected return is persistent. Estimation risk is another important component of predictive variance that is higher at longer horizons. Uncertainty about current expected return, arising from predictor imperfection, also adds considerably to long-horizon variance. Accounting for predictor imperfection is key in reaching the conclusion that stocks are substantially more volatile in the long run. Overall, our results show that long-horizon stock investors face more volatility than short-horizon investors, in contrast to previous research.”

Pastor, Lubos and Stambaugh, Robert F., Are Stocks Really Less Volatile in the Long Run? (December 2011).

Nobel Laureate Eugene Fama (University of Chicago) and his partner Kenneth French (Dartmouth College) co-authored research in 2017 on historical long-term stock returns, reinforcing key conclusions reached by Pastor and Stambaugh.

"Like Pastor and Stambaugh (2012), we find that uncertainty about the expected monthly return can have a large impact on uncertainty about long-horizon payoffs. Noise in the estimate of a monthly or annual expected return is dwarfed by uncertainty about the unexpected return, but imprecision in the estimate of the expected return has a big impact on the dispersion of possible payoffs from a 20-year investment. Investment implications are obvious: investors can improve assessments of distributions of distant payoffs by including uncertainty about expected returns in simulations."

Fama, Eugene F. and French, Kenneth R., Long Horizon Returns (November 2017).

In short: even (or especially) in the long run, market performance is highly uncertain. History can only tell us so much, and even then, we’re not always good at teasing out the right takeaways. We must stay humble in our assumptions and dubious of our own intuition.