To assess potential return, investors rely on historical averages. Variations from those averages are called risk. But the greater risk may lie in their assumptions—namely that history repeats itself.

That’s because investors often rely on a normal distribution of returns, commonly called the bell curve. Here’s how it works. Assume a portfolio has a mean return of 10%, with a risk of 19%. That’s approximately how the S&P 500 has performed from 1926 until now.

In a normal distribution, two thirds of the time an investor will receive 10%, plus or minus 19%. Thus, an annual return could vary between -9% and +29%. That may be a reasonable risk assumption. But as investors have learned this past decade, the range of annual returns has varied more widely—5% of the time, the portfolio will return between -28% and +48%. Why?

First, risk is defined by standard deviation, a measure of variance. It is the engine behind mean-variance optimization — first proposed by Harry Markowitz in his doctoral dissertation in the 1950s and now part of the foundation of modern portfolio theory.

Most investors are satisfied with returns that fall within one standard deviation of the historical result. For years, institutions have modelled the possibility of loss as the range of outcomes that could occur 95% of the time—two standard deviations—or 19 out of every 20 days, in a process known as Value at Risk.

Inaccurate assumptions

What makes this problematic, says Morningstar research, is extreme stock returns occur much more frequently—in fact, 10 times more frequently than expected if returns followed the path of a bell curve.

Thomas Idzorek, chief investment officer and director of research at Ibbotson Associates, has written, “Asset-class return distributions are not normally distributed, but the typical Markowitz MVO framework that has dominated the asset-allocation process for more than 50 years relies on only the first two moments of the return distribution.”

He also found investors are “particularly concerned about downside risk, which is a function of skewness and kurtosis”.

Normal not always the norm