Acceptable Risk: Finding that Space between Prudence and Folly
Chitro MAJUMDAR
Board Member at RsRL; Founder at AI Ethics & Bias Validation*; Sr. Advisor on Tail Risk Hedging & Risk Quantification et al...
This article is still under review for a promising journal. The opinion column of this topic is also upcoming for a mainstream media. However I must add two quick remarks hereby. The introduction of the set of acceptable elements (cones when coherent, convex in general) was the basic idea when introducing the monetary utility functions or in the early days (1993) called risk measures. Acceptable positions were then introduced to derive the quantitative capital requirements instead of using VaR. The convexity of the acceptable positions permitted to use capital allocation techniques over the different business lines. VaR (augmented with covariance techniques) leads to strange effects. The reason is lack of convexity.
In a more dimensional gaussian distribution (in math terms in a gaussian vector space) correlation equal to zero (in maths terms orthogonality) means stochastic independence. Translated this means that when you couple two probability laws with a gaussian copula, you introduce stochastic independence where it might not exist. In more dimensions (say bigger than 2) pairwise orthogonality in a gaussian space means stochastic independence. When you use gaussian copulae this could mean that you replace
- in a first step some correlation coefficient being zero is replaced by the much stronger stochastic independence
- in a second step pairwise independence is replaced by the stronger independence of the whole system
No wonder that the use of gaussian copulae gave a false feeling of safety and led to a "financial surprise”.
FYI: The fact that correlation equal to zero does not imply independence was an error that was made before and created a false hedge. (no details available but it happened in a big bank).
To be continued...