Extremes of extremes: risk assessment for very small samples with an exemplary application for cryptocurrency returns

Christoph J. Börner, Ingo Hoffmann, Jonas Krettek, Lars M. Kürzinger and Tim Schmitz

Abstract

Regulatory authorities require some institutional investors to carry out a worst-case risk assessment and a worst-case risk forecast. In many cases, the amount of (ex post) available data is limited, and long-term time ranges must be covered ex ante in the risk report. Both of these factors make a risk assessment appear impossible at first glance. We present a method of conducting a risk assessment for very small samples (and, in the extreme case, for a single data point) based on the statistical distribution of the extreme value. The proposed risk assessment method is demonstrated using cryptocurrency returns as an example.