Volatility's Double Agent: When Mean Absolute Deviation Masquerades as Standard Deviation

Ever felt like you've been speaking two different languages when discussing volatility with colleagues? You might not be alone. A recent study by Daniel Goldstein and Nassim Nicholas Taleb uncovered a fascinating quirk in how finance professionals perceive market variability.

The Great Volatility Mix-Up

In the world of finance, volatility is typically measured using standard deviation. But what if we're actually discussing mean absolute deviation (MAD) without realizing it? This seems to be a common mistake among financial professionals and students alike, as evidenced by Goldstein and Taleb's survey of 87 respondents.

Why does this matter? Well, in a Gaussian world, MAD is about 0.8 times the standard deviation. So if you're thinking in terms of MAD when you should be considering standard deviation, your estimate of volatility could be off by as much as 25%. In markets with 'fat tails,' this discrepancy can balloon up to 90%.

Volatility Drag: A Hidden Portfolio Hazard

Let's translate these findings into portfolio implications. Consider the VIX (CBOE Volatility Index), our market's fear gauge. If you're mistaking MAD for standard deviation, you might be underestimating the true volatility of your holdings in EEM (iShares MSCI EM ETF) or C (Caterpillar Inc.). This could lead to unexpected portfolio drawdowns during periods of heightened market uncertainty.

Opportunities? On the flip side, being aware of this bias could help you identify undervalued opportunities. For instance, you might spot attractive pricing in TIP (iShares TIPS Bond ETF) or IEF (iShares 7-10 Year Treasury Bond ETF) when their implied volatilities are artificially low due to this MAD-versus-standard-deviation confusion.

A Tale of Two Volatilities: Mean Absolute Deviation and Standard Deviation

To avoid falling into the volatility trap, always double-check which measure you're working with. Here's a simple way to remember it:

- Standard deviation (SD): Measures the average distance from the mean; useful for symmetric distributions. - Mean absolute deviation (MAD): Measures the average distance from the median; robust against outliers.

Actionable Insight: Clarify Your Volatility Metrics

Before you next assess your portfolio's risk exposure or consider options strategies, pause and ensure you're using the correct volatility metric. Make it a habit to clarify whether you're discussing standard deviation or mean absolute deviation. After all, understanding the distinction could be the key to making more informed trading decisions.