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

TL;DR

This paper analyzes the return distributions of a basket of 27 cryptocurrencies and an index, finding stable distributions suitable for modeling returns but using generalized Pareto for tail risk, to improve risk assessment.

Contribution

It introduces a combined approach using stable and generalized Pareto distributions for more accurate risk measurement of cryptocurrency returns.

Findings

Stable distribution best models the body of returns.

Generalized Pareto improves tail risk estimation.

Identifies two subgroups of cryptocurrencies with different risk profiles.

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.