*By Jason Voss, CFA and C. Thomas Howard*

One modern portfolio theory (MPT) pillar that is unquestionably broken is the use of volatility, specifically standard deviation, as a measure of risk. This initial error in MPT’s development is a major contributor to active investment management underperformance.

Volatility Is Not Risk

The concept of volatility as risk rests on a critical assumption that is overlooked by most of the industry: Only in finance is risk defined as volatility, or the bumpiness of the ride.

Various dictionary definitions of risk converge on something like the “chance of loss.”

- Noun:
*exposure to the chance of injury or loss; a hazard or dangerous chance.* - Insurance:
*the degree of probability of such loss.* - Verb:
*to expose to the chance of injury or loss; hazard.*

Not a single definition includes volatility as a part of its explanation. Dictionary definitions and popular understandings of risk might differ from a business definition, yet a popular business dictionary describes over a dozen different forms of risk, ranging from exchange rate risk to unsystematic risk, all of which focus on the chance of permanent loss.

The insurance business relies on an understanding of risk, and an insurance licensing tutorial says that “Risk means the same thing in insurance that it does in everyday language. Risk is the chance or uncertainty of loss.”

Only finance defines risk as short-term volatility. Why? In the 1950s, academics recognized that hundreds of years of statistics research thinking could be borrowed to analyze the performance of investment portfolios — if some of the definitions could be bent to their aims. Once standard deviation was transformed into “risk,” the work of analyzing portfolios could begin and theories could be developed.

The Origins of This Misconception

Harry Markowitz states, “V (variance) is the average squared deviation of Y from its expected value. V is a commonly used measure of dispersion,” in his seminal 1952 *Journal of Finance* paper “Portfolio Selection.” Then he continues:

“We next consider the rule that the investor does (or should) consider expected return a desirable thing *and* variance of return an undesirable thing. . . . We illustrate geometrically relations between beliefs and choice of portfolio according to the ‘expected returns — variance of returns’ rule.”

Whoa, hold on a second! Investors *do* want variance of return, and to the upside. Not only that, how did a blithe proposition regarding a statistical calculation turn into a rule in less than a paragraph? As Markowitz then states, again blithely, “[This rule] assumes that there is a portfolio which gives both maximum expected return and minimum variance, and it commends this portfolio to the investor.”

This sentence creates a major problem for how investment managers are currently evaluated. When investment product distributors prefer “maximum return versus minimum variance,” then closet indexing is not far behind.

Markowitz is borrowing on hundreds of years of statistical theory to make an important point: Diversification can lead to better outcomes in investing. But to make the leap to volatility and its close cousin, beta, as risk measures, as much of the industry has done, is an egregious mistake.

Volatility Is Emotions

Nobel laureate Robert Shiller showed that stock prices fluctuate much more than the underlying dividends, the source of value, in his seminal paper. The implication is that stock price changes are largely driven by something other than changing fundamentals. Volatility is the result of investors’ collective emotional decisions. Shiller’s contention has withstood the test of time. Numerous studies have attempted and failed to dislodge it.

So not only does volatility capture both undesirable down price movements along with desirable up movements, it is mostly driven by the collective emotions of investors and has little to do with fundamental risks. Since emotions are transitory and much of the resulting effect can be diversified away over time, volatility fails as a risk measure.

Finally, some maintain that since investors enter and exit funds based on strong short-term upsurges and short-term drawdowns, volatility *represents* business risk for the fund. But why should fund business risk be intertwined with investment risk? There need to be separate measures since the risk faced by investors and funds is distinctly different.

*Possible Risk Measures*

So if volatility as risk is flawed, how do we measure investment risk? The metric should focus on the chance of permanent loss — investment value dropping to zero, for example — or the opportunity cost of underperforming a benchmark.

*Qualitative Risk Measures*

One approach that we used at the Davis Appreciation and Income Fund is to carefully consider the fundamental risks facing a business. The varieties of risk could include economic, environmental, political, regulatory, public opinion, geographic, technology, competition, management, organizational, overhead, pricing power, equipment, raw materials, product distribution, access to capital, and capital structure, to name a few.

If the business is affected by one or more of these risks, that will likely influence the firm’s ability to make good on its promises regardless of where you claim a cash flow in its capital structure (debt, preferred, convertible, equity, option, etc.). One drawback of such evaluation techniques: The subjective nature of these risks cannot be summarized in a single measure. But the truth is investment risk *is* complex and multifaceted, so no single number could suffice, much less an emotionally driven statistical measure like standard deviation.

*Returns Relative to Opportunity Set*

Pioneering work by Ron Surz called Portfolio Opportunity Distributions (POD) takes an entirely different approach. This performance- and risk-evaluation technique examines the strategy laid out by the investment manager in the prospectus and explores all possible portfolios the manager may have held within these constraints. It then compares actual manager performance to these opportunity sets.

This approach unshackles managers from being compared to an index. Instead, they are measured against their opportunity set. Significantly, the metric also takes care of the “free pass” problem, when benchmarks are the basis for comparison.

Tom Howard’s firm AthenaInvest has developed a similar approach that evaluates fund performance relative to that of a strategy peer group.

This technique can also be applied to asset allocation and other portfolio decisions. For example, investing $10,000 in the S&P 500 at the end of 1950 would have generated $9 million by the end of 2016, while an investment in T-Bonds would have generated less than $500,000. The $8.5 million “left on the table” is the true risk, not the increased volatility of stocks over this period. The chance of a real loss should be the risk measure used in making such decisions, not the bumpiness of the ride. Viewed in this light, bonds are far riskier than stocks for building long-horizon wealth.

No Simple Solution

As Tom has told his investment classes for years: Academics have little meaningful insight into measuring risk. This hasn’t exactly endeared him to department colleagues or to some of his students. In essence, he was saying that the research on measuring risk conducted at hundreds of academic institutions over the decades has largely been fruitless.

No discipline likes to admit such monumental failure. But this is where we are in finance today.

Forty years ago, measuring investment risk was largely the purview of sell-side and buy-side analysts. Today, we have come full circle: Once again analysts are the go-to source for assessing risk. It may be frustrating that their analysis cannot be summed up in a single number. But we tried a model that did just that and it failed.

Measuring investment risk is a messy process and is not amenable to a simple solution.