Fractal Press

I’ve written before on the topic of stability and robustness to sudden shocks. In mathematical terms, any attempt to squeeze the second moment (volatility) of the distribution will push mass into the tails and drastically increase the fourth moment (kurtosis)

You can see above that the probability distributions with fatter tails have “thinner” bodies. While sampling these distributions, measures such as variance, standard deviation, and volatility will appear lower than for the ones from thin-tailed distributions (note how “thick” the thin-tailed distributions are), giving the appearance of lower risk and volatility.

Since probabilities need to sum up to unity, there is no way to get around this constraint. Squeezing the second moment will increase the fourth.

This is a tradeoff that needs to be considered carefully. At the moment decisions only take into account the second moment and we’ve put in place processes that tend to minimize the second moment without heed to what is happening to larger moments.