A study done by Daniel E. Goldstein, We Don't Quite Know What We are Talking About When We Talk About Volatility, show that humans beings, even financial professionals, habitually underestimate standard deviation when given absolute (mean) deviations, on an average of about 25%. CXO Advisory elaborates that:

• Only 3 of 87 respondents provide the correct value for the standard deviation.
• The ratio of too-low answers to too-high answers is 6.5:1, with the typical response 25% below the actual standard deviation.
• Real-life asset returns generally do not have normal distributions, and extrapolating the reasoning used by most respondents to some "fat tailed" asset returns would result in underestimation of the standard deviation by 90%. Confusion regarding measures of market variability is therefore consequential for decision making.

This is obviously detrimental to decision making, and is partially the reason that people simply aren't rational when it comes to even a coarse estimate of volatility -> risk. But the 3rd point brings up an important issue with this view - perhaps for the stock market at least, standard deviations are simply unsuitable for describing distributions with significant (positive) kurtosis?

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