Skewness and kurtosis also go to infinity. Taleb pushes (I think?) "mean deviation" as a volatility measure, which converges for some, but not all, distributions. Not sure if anyone uses it. I am not aware of anyone doing academic research in the area either.In fact, the tools people use to measure risk have evolved over time: drawdown, ATR, volatility, skewness/kurtosis, VaR, and so on. Interestingly, based on my recent heartfelt tests, even ancient and silly risk metrics have okay judgment. I can distinguish high risk stocks from low risk stocks using extremely shitty indicators. The main problem is that common indicators tend to be consciously manipulated, which leads to the emergence of newer indicators that reduce their manipulation.The above statement has been repeated in this thread many times, which doesn't make it any less false. Fat tails imply that, as a data set increases in size, the standard deviation approaches infinity. Standard deviation for fat-tailed data sets is a random number generator.In financial and investment jargon risk means specifically variability of return measured as the standard deviation of periodic returns over a time.
If you are married to standard deviation, then you are left having to explain why the distribution of deviations is not normally distributed. For gluttons of punishment who want to see the logic.
Statistics: Posted by bh1 — Sat Aug 10, 2024 12:00 pm — Replies 66 — Views 3881
