Mathematical Definition, Mapping, and Detection of (Anti)Fragility

Key Findings

The heuristic lends itself to immediate implementation, and uncovers hidden problems, and bank tail exposures (it explains risks related to company size, forecasting the forecasting biases). While simple to implement, it outperforms stress testing and other such methods such as Value-at-Risk.

Abstract

We provide a mathematical definition of fragility a semi-measure of dispersion and and antifragility as negative or positive sensitivity to volatility (a variant of negative or positive “vega”) and examine the link to nonlinear effects. We integrate model error (and biases) into the fragile or antifragile context. Unlike risk, which is linked to psychological notions such as subjective preferences (hence cannot apply to a coffee cup) we offer a measure that is universal and concerns any object that has a probability distribution (whether such distribution is known or, critically, unknown). We propose a detection of fragility, robustness, and antifragility using a single “fast-and-frugal”, model-free, probability free heuristic that also picks up exposure to model error.