On the Return Distributions of a Basket of Cryptocurrencies and Subsequent Implications

Abstract: This paper evaluates and assesses the risk associated with capital allocation in cryptocurrencies (CCs). In this regard, we take a basket of 27 CCs and the CC index EWCI$^-$ into account. After considering a series of statistical tests we find the stable distribution (SDI) to be the most appropriate to model the body of CCs returns. However, as we find the SDI to possess less favorable properties in the tail area for high quantiles, the generalized Pareto distribution is adapted for a more precise risk assessment. We use a combination of both distributions to calculate the Value at Risk and the Conditional Value at Risk, indicating two subgroups of CCs with differing risk characteristics.