One shape fits all? A comprehensive examination of cryptocurrency return distributions

ABSTRACT

We perform the most comprehensive test of cryptocurrency return distributions to date. We fit 58 hypothetical distributions to 15 major cryptocurrencies to establish which of these best describes cryptocurrency returns. The answer is: ‘It depends.’ A sharp-peaked Cauchy distribution is the most likely distribution for the majority of return series. Specific distributions are definitively identified for only a handful of cryptocurrencies. The best fitting distributions are peaked and thick-tailed, with some possessing variable shape parameters. Our findings have implications for financial modelling and its applications, such as risk measurement and risk management.

KEYWORDS:

• Cryptocurrencies
• return distributions
• bitcoin
• skewness
• kurtosis

JEL CLASSIFICATION:

• C4
• C22
• C49

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplementary material

Supplemental data for this article can be accessed here

Notes

¹ For a more detailed description of the best fitting distributions, see Table A3 in the Online Appendix.

² Full results of distribution fitting and rankings are available upon request.