Optimisation of Cryptocurrency Trading Using the Fractal Market Hypothesis with Symbolic Regression

Abstract

Cryptocurrencies like Bitcoin can be considered commodities under the Commodity Exchange Act (CEA) and the Commodity Futures Trading Commission (CFTC) has jurisdiction over cryptocurrencies considered to be commodities, particularly in the context of futures trading. This paper presents a method for long and short term trend prediction of certain cryptocurrencies which is predicated on an application of the Fractal Market Hypothesis. This is an area of market theory where the self-affine properties of a fractal stochastic field are used to model a financial time series. After an introduction to the underlying theory and mathematical modelling, a fundamental analysis of Bitcoin and Ethereum to U.S. Dollar exchange markets is conducted. This analysis is based on a consideration that a changes in polarity of the 'Beta-to-Volatility' and the 'Lyapunov-to-Volatility' ratios to indicate an impending change to the Bitcoin/Ethereum price trend signal. This is used to recommend a long, a short or a hold trading position for which algorithms are provided (coded in Matlab) and 'back-tested'. An optimisation of these algorithms is conducted, leading to a strategy for implementing an ideal range of the key parameters for 'driving' the algorithms developed. This is based on maximising the accuracy and profitability to assure a high level of confidence. The application of the trading strategy developed through this approach is demonstrated to provide useful information to aid cryptocurrency investments and quantify the likelihood that the market will become bull or bear dominant. Under stable conditions, Machine Learning (using the 'TuringBot') is shown to provide useful estimates of future price values and/or fluctuations over small event horizons in time. This minimises any \lq trading delay' caused by filtering the data and increases returns by providing optimal trade positions within a \lq micro-trend' that is too fast for detection otherwise. In certain cases, this increase can reach ~10%. The results presented confirm that Bitcoin and Ethereum exchanges are self-affine (fractal) stochastic fields with L\'evy distributions, displaying a Hurst Exponent of ~ 0.32, a Fractal Dimension of ~ 1.68 and Levy Index of ~1.22. They also confirm that the Fractal Market Hypothesis and its indices provide a suitable market model, that generates returns on investments that outperform all Buy and Hold strategies based on more standard market indices.