Traditional financial theory has relied heavily on standard deviation or variance (the square of standard deviation) to quantify historic risk. Markowitz mean-variance optimization and the Sharpe ratio are two such examples under the umbrella of modern portfolio theory that reference variance or standard deviation as a proxy for risk in their formulation. However, there are some concerns with using these risk metrics that should be considered.

Over the past several years there has been a shift in thinking with regards to investment risk. Influential managers Howard Marks [1] and James Montier [2] both share the perspective that true risk isn’t a statistical measure, but simply the permanent loss of capital. Additionally, Nassim Taleb, in his now famous work The Black Swan discussed the disconnect between traditional statistical measures (such as standard deviation) and the occurrence of extreme events

If the world of finance were Gaussian, an episode such as the crash (more than twenty standard deviations) would take place every several billion lifetimes of the universe [3]

History has taught us that crashes occur much more frequently than every several billion lifetimes. While the “fat-tails” phenomenon has been discussed many times before there are still more issues that arise when using standard deviation to quantify risk. Consider the returns of Fidelity’s Magellan Fund under Peter Lynch. From May of 1977 through May of 1990 every full year return was positive. Compare this performance to the S&P 500 which had two slightly negative years. Magellan had a standard deviation of 21.1% and the S&P 500 came in at 16.0%. Was Magellan truly riskier?

In other words does an asset that jumps around a lot but produces very consistent positive returns represent a risky asset? In this circumstance it probably depends on your temperament. It’s very possible that the volatile nature of an asset could certainly cause angst and investors to flee to something more stable. That’s a valid position to take, and from that perspective standard deviation is certainly a legitimate measure of risk.

What standard deviation really quantifies is the dispersion or spread of the data being analyzed. Theoretically as the dispersion gets wider and wider the probability associated with large movements should increase. But nowhere does it say that those large movements need be positive or negative in outcome. Furthermore the extreme movements at the tails may outliers (few and far between), and therefore not accurately represented through a measure such as standard deviation.

Negative outcomes, or the potential for loss are the true underlying foundation of risk. As humans we actually place more weight on negative outcomes than positive outcomes as Daniel Kahneman and Amos Tversky famously demonstrated. We’re actually quite risk averse

When directly compared or weighted against each other, losses loom larger than gains. This asymmetry between the power of positive and negative expectations or experiences has an evolutionary history. Organisms that treat threats as more urgent than opportunities have a better chance to survive and reproduce. [4]

Let’s take another look at the performance of Magellan and the S&P 500. This time with maximum drawdown–the worst negative outcome–as a proxy for risk

Fidelity Magellan Fund and S&P 500 Performance (May 1977 – May 1990)
	FMAGX	S&P 500
Annualized Return	29.1%	15.5%
Annualized Std Dev	21.1%	16.0%
Maximum Drawdown	-33.1%	-29.6%

Note that the maximum drawdown experienced by Magellan and the S&P 500 were -33.1% and -29.6% respectively–roughly similar in magnitude. So while Magellan was clearly more volatile, the potential for loss between the two was actually quite similar (it’s worth noting that both experienced their worst drawdown during November 1987, shortly after the Black Monday Crash).

Using maximum drawdown as the metric one could conclude, at least historically, that both assets exhibited similar risk. It follows that if Magellan were indeed riskier it would have had a much larger downside than the S&P 500. At the very least this situation should demand some thought about whether volatility provides the appropriate information to judge risk. Just because something is volatile–that it has experienced a wide range of outcomes–doesn’t necessarily mean that it is risky.

This train of thought can actually get more interesting. Consider an asset that has a standard deviation similar to that of the S&P 500 (or other developed markets for that matter), but with substantially greater drawdown. This isn’t a hypothetical exercise. Below are the standard deviations and maximum drawdowns for several global markets

		Std Dev	Max Drawdown
United States	Jan 1970 – Sep 2016	15.3%	-50.9%
Europe	Jan 1970 – Sep 2016	17.5%	-59.0%
Pacific	Jan 1970 – Sep 2016	19.8%	-52.2%
Emerging Markets	Jan 1988 – Sep 2016	23.1%	-61.4%
Frontier Markets	Jun 2002 – Sep 2016	18.8%	-66.1%
Precious Metal Equity	Jan 1970 – Sep 2016	38.1%	-77.4%

The standard deviations of emerging and frontier markets should jump out–only 23.1% and 18.8% respectively. Substantially lower than I would have expected, but look at those drawdowns! Thinking that frontier markets had roughly the same risk as the US and Europe, by measure of standard deviation, was deceptive at the very least and disasterous at the very worst.

There is a valid claim that both emerging and frontier markets don’t have as much data as their developed market counterparts. This is essentially a claim on the law of large numbers. As more data becomes available standard deviations should begin to fall in line with the drawdowns that these markets have experienced (maybe). Unfortunately investors today don’t have 10, 20 or 30 years to wait around for additional data to make a judgement regarding risk. Here’s what those drawdowns looked like back in the 2007 through 2009 period

That’s a pretty ugly picture, and not something that could be identified by looking at standard deviations. This isn’t to say that volatility (standard deviation) is insignificant. In fact volatility provides a wonderful metric for measuring the dispersion of returns, and plays a role in the rebalancing bonus earned in a regularly rebalanced portfolio of uncorrelated assets. But expecting standard deviation to capture and communicate worst case scenarios, or the potential for loss, may well be a risky endeavor on its own.

As a former colleague once told me: If you want to understand the true nature of something examine it under extreme events. Well said

References
1. Marks, Howard. The Most Important Thing Illuminated. Columbia University Press. New York, NY. 2013.
2. Montier, James. The Seven Immutable Laws of Investing. GMO White Paper. March 2011. https://ftalphaville-cdn.ft.com/wp-content/uploads/2011/03/JM_SevenImmutableLaws_312.pdf.
3. Taleb, Nassim. The Black Swan. Random House. New York, NY. 2007. p.276.
4. Kahneman, Daniel. Thinking, Fast and Slow. Farrar, Straus and Giroux. New York, NY. 2011. p.282.

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What I’m Reading
Lazy Work, Good Work (Morgan Housel)
The Emerging Markets Hat Trick (Rob Arnott and Brandon Kunz)
The Danger in Valuation-Based Market Timing (Sam Lee)
A Dynamic Approach to Factor Allocation (EconomPic)
20 Rules of Personal Finance (Ben Carlson)
Soros, Fallibility, Reflexivity, and the Importance of Adapting (Tadas Viskanta)
Efficiency, Rationality, and Arbitrage (William Bernstein)