What is the use of mean absolute deviation in finance? Is there a perfect senario where we use MAD over variance and standard deviation? All of them are calculation of the variability from central tendancy (which is a measure of risk). But I don’t understand why Standard deviation is used more frequently.

Because of two of the fundamental organizing principles of the Universe (really) a) The Pythagorean theorem: Those variance decompositions that are always part of regression analysis, ANOVA, and so on are really just restatements of the Pythagorean theorem in more general spaces. Does “sum of SQUARES error” + “sum of SQUARES regression” = 'Sum of SQUARES total" look a lot like a^2 + b^2 = c^2? Do we seek out things to covet? Make an effort to answer… b) The normal distribution: Diffusion without order takes on the shape of the normal distribution. The normal distribution is characterized by its variance much more naturally than it’s MAD. I think you should almost never use the MAD in finance because it downweights outliers relative to the variance which is a standard estimator if you believe you just have normal errors. Almost all tails in finance are fatter than normal not thinner.