A Fitting Return to Fitting Returns: Cryptocurrency Distributions Revisited

33 Pages Posted: 18 May 2021

See all articles by Savva Shanaev

Savva Shanaev

Northumbria University

Binam Ghimire

University of Northumbria at Newcastle

Date Written: April 16, 2021

Abstract

This study fits 22 theoretical distribution functions, four of them originally derived, onto 772 cryptocurrency daily returns with goodness-of-fit evaluated using Cramer-von Mises, Anderson-Darling, Kuiper, Kolmogorov-Smirnov, and Chi-squared tests, as well as a harmonic mean p-value synthetic criterion. Most cryptocurrency return distributions can be sufficiently approximated with a Johnson SU function or an asymmetric power function. Johnson SU, asymmetric Student, and asymmetric Laplace distributions have better fit for larger cryptocurrencies, while error, generalised Cauchy, and Hampel (a Gaussian-Cauchy mixture) distributions are more characteristic of smaller cryptocurrencies, with larger coins demonstrating better overall fit. Less than 8% of sample coins and less than 4% of the top quartile by size do not fit into any of the investigated distributions, three largest “misbehaving” cryptocurrencies being Litecoin, Dogecoin, and Decred. Bitcoin and Ethereum are best modelled with error and asymmetric power law distributions, respectively, with asymmetric power law distributions stable through time. More than 30% of sample cryptocurrencies, and 26% from the top quartile, have infinite theoretical variance, severely limiting the diversification potential with such cryptoassets. Three most prominent infinite-variance coins are Bitcoin SV, Tezos, and ZCash. This study has substantial implications for risk management, portfolio management, and cryptocurrency derivative pricing.

Keywords: cryptocurrency, return distribution, skewness, kurtosis, goodness-of-fit

JEL Classification: C4, C22, C46, C49

Suggested Citation

Shanaev, Savva and Ghimire, Binam, A Fitting Return to Fitting Returns: Cryptocurrency Distributions Revisited (April 16, 2021). Available at SSRN: https://ssrn.com/abstract=3847351 or http://dx.doi.org/10.2139/ssrn.3847351

Savva Shanaev (Contact Author)

Northumbria University ( email )

Pandon Building
208, City Campus East-1
Newcastle-Upon-Tyne, Newcastle NE1 8ST
United Kingdom

Binam Ghimire

University of Northumbria at Newcastle ( email )

Pandon Building
208, City Campus East-1
Newcastle-Upon-Tyne, Newcastle NE1 8ST
United Kingdom

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