Standard Deviation: In Defense of an Often-Dismissed Investing Metric

A Reader’s Objection

In response to my article, Is the Stock Market Too Concentrated?, which relied upon standard-deviation calculations to assess investment risk, a reader wrote: “My problem [with your argument] is simple. I suppose I am merely echoing what I have heard some fund managers say: a large (small) standard deviation of performance does not equate to risk (or lack thereof). You have undoubtedly heard this 10 times as often as I have.”

Probably 100 times. There are three primary versions of this argument.

Issue Number One: Measuring Skill

The first account addresses skill. Fund managers concede that for everyday investors, standard deviation is a sound barometer of risk. However, because fund managers are professionals, goes the claim, their portfolios diverge from the norm. They benefit fully from bull markets, while also protecting against downturns. Heads, the funds win; tails, they do not entirely lose.

Were that to occur, the standard-deviation calculation would be unfair, because it would penalize fund managers for excelling at their jobs. If a fund gains 7% when the stock market rises by 5%, those extra 2 percentage points of return increase the fund’s risk score. Where is the justice in that?

On the surface, the logic is compelling. For years, I asked that very question. In Morningstar’s early days, its Morningstar Rating for funds—the “star rating”—incorporated that logic. When assessing risk, the star rating considered only months during which the fund had failed to match the return on cash. Faithfully, I informed audiences of that method’s advantage. They invariably nodded in agreement.

We were wrong. As it turns out, while such gifted portfolio managers exist in theory, they rarely do in practice. Over any relatively long period, very few funds outperform during bull markets while also resisting downturns. And those that do achieve both feats almost never repeat the accomplishment.

Here, let me show you. I screened for all actively run large-blend US stock funds with 20-year track records, sorting each decade of their returns into risk quartiles. With that exercise, I employed two risk measures: 1) “downside capture,” which assesses fund performances during months when the index loses money, and 2) standard deviation.

According to the skill argument, those statistics should flash different signals for the most adept portfolio managers, with the downside capture ratio showing meaningfully lower risk than the standard deviation calculation. However, that event rarely occurred. During the first 10-year period, only four of the study’s 168 funds exhibited that pattern. Over the second period, only three funds did, none of which had appeared on the first decade’s list.

In short, when addressing the loss potential of everyday investments, one risk measure performs much like another. Given that fact, standard deviation is the preferable choice, because it is a conventional and widely known calculation, rather than one invented solely for investment analysis. When possible, researchers should use a common language.

Issue Number Two: Hidden Risks

The second complaint about the standard-deviation calculation is that it overlooks hidden risks. This is certainly true; there are many real-life examples. One, notoriously, was the hedge fund Long-Term Capital Management, which parlayed the prestige of its Nobel Prize-winning management team and early strong returns into a $5 billion asset base. The fund then imploded, wiping out its shareholders.

While institutions suffered LTCM’s blow, retail investors were the losers with short-term multimarket income funds. In the early ‘90s, such funds bought bonds from high-yielding European currencies—this was before the euro had launched—while shorting those from low-yielding currencies. As with LTCM, their results initially impressed, but then reversed. Within five years, multimarket funds were extinct.

A third case is the most infamous: Bernie Madoff’s funds. That catastrophe differed from others because the problem was fraud rather than concealed investment risks. But the principle was the same. As with LTCM and multimarket funds, the standard deviations for Madoff’s funds bore no evidence of future troubles. The funds worked for their investors, until they did not work.

While this is a valid indictment of standard deviation, it once again is also a valid indictment of standard deviation’s competitors. The truth is, the performance-based statistics that fill so many consultants’ reports and glaze so many eyes cannot identify latent dangers. Doing so requires fundamental research. Such discoveries come from insight, not number crunching.

Issue Number Three: Time Horizon

The third quarrel with standard deviation, which I think was the motivation of the reader who wrote to me, involves time horizon. In the very short term, securities with high standard deviations might well lose. If you buy a stock market index fund on Monday and sell it on Friday, there’s a good chance you will lose money. But over longer horizons, the odds for risky but potentially lucrative investments sharply improve. In fact, over the past century, US stocks have posted nominal gains through every rolling 20-year period.

This tendency has led most investment researchers to conclude that although risk statistics show that cash is the safest investment, bonds the next safest, and stocks the most dangerous, the opposite holds for investors who are seeking to preserve—or, better yet, improve—their purchasing power. By that standard, stocks have been the safest of the three investments, with cash and bonds falling well behind.

As I pointed out in Do Equities Improve with Age?, Nobel laureate Paul Samuelson has disputed such claims, with a mathematically sound but intuitively unappealing rebuttal. I will not repeat his argument here, as it is addressed in that article, but the point remains: Although the standard-deviation calculation is often regarded as immaterial for long-term investors, even in that instance, the statistic does retain some value.

My Conclusion

It’s fashionable to dismiss the usefulness of standard-deviation calculations. Portfolio managers contend that the figure misrepresents their accomplishments, investment disasters confound expectations, and researchers who emphasize long-term results, rather than shorter-term performance, shrug off such computations as being irrelevant. But if used correctly, as one instrument among many, standard deviation is a valuable tool. No rival statistic does its job better.