The cryptocurrencies risk measure based on the Laplace distribution

Abstract

Current research has led to a rejection of the hypothesis of a normal distribution of financial assets returns. Under these conditions, portfolio variance cannot serve as a good risk measure. In this paper analyzed the daily returns of the most common cryptocurrencies: Bitcoin, Ethereum, XRP, USDT, Bitcoin Cash, Litecoin. It is shown that the asset returns are not normally distributed, but with good precision follow the Cauchy distribution and Laplace distribution. The analytical expressions for risk measure were obtained using the distribution function and the VaR technique. However, the risk assessment of the return obtained on the basis of the Cauchy distribution is twice as high as the risk assessment obtained on the basis of the Laplace distribution. Therefore, the question arises: what distribution law to use to measurement the cryptocurrency risk? The paper shows that the Laplace distribution is the most adequate basis for measuring of cryptocurrencies risk.