Following up (sort of) on my comments on The Black Swan . . .

Dan Goldstein and Nassim Taleb’s paper write: “Finance professionals, who are regularly exposed to notions of volatility, seem to confuse mean absolute deviation with standard deviation, causing an underestimation of 25% with theoretical Gaussian variables. In some fat tailed markets the underestimation can be up to 90%. The mental substitution of the two measures is consequential for decision making and the perception of market variability.”

This interests me, partly because I’ve recently been thinking about summarizing variation by the mean absolute difference between two randomly sampled units (in mathematical notation, E(|x_i-x_j})), because that seems like the clearest thing to visualize. Fred Mosteller liked the interquartile range but that’s a little too complicated for me, also I like to do some actual averaging, not just medians which miss some important information. I agree with Goldstein and Taleb that there’s not necessarily any good reason for using sd (except for mathematical convenience in the Gaussian model).