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# Investing vs. Gambling: Understanding Risk-Adjusted Performance

### (Originally published by Forbes on June 1, 2022)

The most important term that every investor—from institutional to retail—must understand as a prerequisite to making sound investments or allocation decisions is “risk-adjusted performance,” yet effectively no one does.

People rely on the same visceral cues that drive social interactions to make investment decisions. At the institutional level, these individual drivers are replaced with equally ineffective bureaucracy and heuristics, which often lead to the opposite of the desired effect. If you ask most financial professionals to define risk, you’ll get an unclear answer. You'll get a pretentious rambling of incomplete ideas attempting to describe variables that may contribute to risk, but they can’t tell you what risk actually is.

On the flip side, even the most naive grandmothers tend to understand that a casino’s business model is predicated on the odds of the games and, in many instances, take a more rigorous approach to protecting their money. Only one variable distinguishes investing from gambling: The probability of losing on a gamble always exceeds the probability of gain; in investing, the probability of a gain is expected to exceed the probability of a loss.

When I’m asked to define risk, this is the answer:

*“Risk is not a story; it’s not a relationship; it’s not a feeling; and risk is not an asset class. Risk is a number: It’s the probability of loss weighted by the expected degree of that loss.”*

To assess the quality of any investment, you have to compare its expected return to its corresponding risk: its risk-adjusted performance. This is not an opinion. This is a matter of objective fact. I’ll leave the epistemological discussion for another time and place, but I will begin to discuss the mathematics here:

For a basic introduction to the concept of risk-adjusted performance, take a look at the example of a coin toss that I used in this video. The point is that regardless of your feelings about the variables associated with any bet and by extension any investment, math (when applied properly) is the only clear, objective and accurate standard of evaluation.

To accurately measure investment risk and prevent falling for the Ludic Fallacy, all four statistical moments must be taken into account—mean (i.e., expected return), variance (i.e., beta), skewness and kurtosis—across a minimum of one complete market cycle (i.e., January 2007 to present).

There are many risk-adjusted performance metrics, each describing a different facet of risk, with some better than others:

• Alpha and beta tell you much more about the opportunity cost associated with an asset or portfolio than about its actual risk characteristics.

• The Omega Ratio (“Ω”) elegantly captures all four statistical moments of risk.

• Maximum Drawdown (“MDD”) tells you just that: how much you should expect to potentially lose.

• Maximum Drawdown Duration tells you how long to expect it will take to recover from your maximum losses.

• The Summers Measure (“SΩ”) captures all four statistical moments while providing a user-friendly output as a percentage relative to the market.

I should note that, by definition, the risk associated with black swan events cannot be captured quantitatively, but they can’t be captured anecdotally either. So, if you make investment decisions based upon accurate measurement of risk-adjusted performance, you’re still going to win on a relative basis.

While there are many other risk-adjusted performance measures worth considering, accurately measured expected return, maximum drawdown, maximum drawdown duration, omega ratio and Modigliani measure viewed collectively paint a comprehensive and accurate picture of the quality of any asset or portfolio and allow any investment—regardless of asset class—to be compared in definitive apples-to-apples terms.

Everything else is just noise.