Validation of index and benchmark assignment: adequacy of capturing tail risk

Lukasz Prorokowski

Abstract

This paper provides practical recommendations for the validation of risk models under the Targeted Review of Internal Models (TRIM). The European Central Bank has recently launched the first phase of the TRIM, which investigates the ability of banks’ internal risk models to adequately capture tail risk in underlying portfolio items. Against this background, using empirical examples, this paper reviews statistical tools for validating the assumption that a given risk proxy (in this case, an equity index/fund benchmark) adequately represents tail risk in the returns of an individual asset (in this case, equity/fund). Our paper reviews the following validation tools for comparing the return distributions of the proxy and the underlying assets: the Kappa coefficient, the paired t-test and the two-sample Kolmogorov–Smirnov test. In doing so, this paper shows the shortcomings of using certain statistical tools to assess the ability to capture tail risk. The motivation of this paper is to advise on specific aspects of the validation practice that have grown in importance under the TRIM framework but remain under-researched, with no academic studies explicitly advising on the validation of the risk proxy assignment.