A Statistical analysis of the log returns of cryptocurrencies

Abstract

There has been an increase in interest and demand for cryptocurrencies and thus understanding their statistical properties is important for it implies their risk. Understanding the risk involved in investing in the cryptocurrencies allows one to evaluate the same risk against their own risk tolerance and thus determine whether it is worthwhile to venture into cryptocurrencies and if so, the optimal weight of the investment in the portfolio. This study seeks to find the statistical distribution from a family of fat tailed distributions that best explains the log returns of cryptocurrencies. lt was conducted in Nairobi between May 2021 and February 2022. The data used was obtained from Yahoo Finance. The results suggested that the Generalized Hyperbolic Distribution gives the best fit for the large cryptocurrencies ranked by market capitalization.