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

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.