Chance or Chaos? Fractal Geometry Aimed to Inspect the Nature of Bitcoin

Abstract

The aim of this paper is to analyse Bitcoin in order to shed some light on its nature and behaviour. We select 9 cryptocurrencies that account for almost 75% of total market capitalisation and compare their evolution with that of a wide variety of traditional assets: commodities with spot and future contracts, treasury bonds, stock indices, and growth and value stocks. Fractal geometry will be applied to carry out a careful statistical analysis of the performance of Bitcoin returns. As a main conclusion, we have detected a high degree of persistence in its prices, which decreases the efficiency but increases its predictability. Moreover, we observe that the underlying technology influences price dynamics, with fully decentralised cryptocurrencies being the only ones to exhibit self-similarity features at any time scale.

Keywords

• Bitcoin
• cryptocurrencies
• fractal geometry
• hurst exponent
• long-term memory
• efficient market