A Map and Simple Heuristic to Detect Fragility, Antifragility, and Model Error

Abstract

The main results are 1) definition of fragility, antifragility and model error (and biases) from missed nonlinearities and 2) detection of these using a single “fast-and-frugal”, model-free, probability free heuristic. We provide an expression of fragility and antifragility as negative or positive sensitivity to convexity effects, i.e., dispersion and volatility (a variant of negative or positive “vega”) beyond Jensen’s Inequality, across domains, and show similarities to model errors coming from missing hidden convexities -model errors treated as left or right skewed random variables. Broadening and formalizing the methods of Dynamic Hedging, Taleb (1997), we present the effect of nonlinear transformation (convex, concave, mixed) of a random variable with applications ranging from exposure to error, tail events, the fragility of porcelain cups, deficits and large firms and the antifragility of trial-and-error and evolution. The heuristic lends itself to immediate implementation, and uncovers hidden risks related to company size, forecasting problems, and bank tail exposures (it explains the forecasting biases). While simple, it vastly outperforms stress testing and other such methods such as Value-at-Risk.