Statistical Analysis of Bitcoin in a Multivariate Framework

Abstract

This work elaborates on the statistical study of the first cryptocurrency made: Bitcoin. It presents a brief introduction to the basic concepts behind the functioning of the entity, as well as some studies regarding technical, ethical, and legal aspects. Regarding the Economic and Financial themes, the issue to approach relates with the implementation into markets. The introduction of new assets into the basket available for investors may cause certain risks if it is now fully understood and inadequate assumptions are used to assess the exposure or asset allocation. To address this topic, this document is divided in 5 chapters regarding the analysis of certain properties through financial models. First, the stylized facts on the diversity of cryptocurrencies is studied through descriptive statistic and qualitative techniques. Second, a bubble detection algorithm is deployed over the Bitcoin series detecting 11 episodes. It is then analyzed the reasons behind such events. The results indicate the existence of three stages in the series: the oldest related with government intervention, second a speculative bubble and third a stabilization period related with the evolution of the market. Third, with these results a Value at Risk and Expected Shortfall methodology with the Normal Inverse Gaussian (NIG) distribution is presented as an argument to use this specification for further developments. Fourth, determined the capability of NIG to fit data (even above the general distribution) a multivariate rolling window estimation is used in trivariate baskets of financial assets. With the parameters adjusted to the statistical properties, the asset allocation problem is set to find the optimal weights that reduce risk. The results show the transition of Bitcoin from being a speculative asset with almost zero weight, to develop a hedging capability in the commodity portfolio.