Cryptocurrency: Not far from equilibrium

The rapid growth and expanding applications of cryptocurrencies are the main factors that have led them to be considered potential assets to investment portfolios. However, the fierce ups-and-downs that Bitcoins have experienced recently, coupled with the extreme volatility in the Bitcoin prices, have cast doubts on the eligibility of cryptocurrencies to be classified as assets. To investigate the characteristics of cryptocurrencies, this study compares Bitcoin, one of the most popular cryptocurrencies, with other major investment assets. Our analysis focuses on the efficient market hypothesis measured by the Hurst exponent, together with long-term market equilibrium measured by Shannon entropy. The findings suggest that although the Bitcoin market is less efficient than other markets, it is not significantly different from the other markets in terms of its long-term market equilibrium. To elucidate these properties, we probe the Fokker–Planck and Schrödinger equations and derive a probability density function, considering the speed of mean reversion and dispersion.