Using MAD instead of standard deviation in the formula for correlation would result in the possibility of random values being "correlated" by values that exceed

Using MAD instead of standard deviation in the formula for correlation would result in the possibility of random values being "correlated" by values that exceed 1 in magnitude (the proof for a correlation coefficient being bounded by 1 relies on the Cauchy-Schwarz inequality, which could no longer be appealed to). This doesn't detract from Taleb's points at all, but it does show a mathematically "nice" property that results in the usage of standard deviations. [1] https://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality#Probability_theory https://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequal...