How does price (in)efficiency influence cryptocurrency portfolios performance? The role of multifractality

AbstractThis paper proposes a new investment strategy in the cryptocurrency market based on a two-step procedure. The first step is the computation of the asset's levels of efficiency in an universe of cryptocurrencies. Price returns efficiency degrees are measured by their corresponding levels of multifractality, obtained by the multifractal detrended fluctuation analysis method. The higher the multifractality, the higher the inefficiency in terms of the weak form of market efficiency. Cryptocurrencies are then ranked in terms of efficiency. The second step is the construction of portfolios under the Markowitz framework composed of the most/least efficient digital coins. Minimum variance, maximum Sharpe ratio, equally weighted and (in)efficient-based portfolios were considered. The former strategy is also proposed, where the weights are computed proportionally to the assets levels of (in)efficiency. The main findings are: cryptocurrency price returns are multifractal and their levels of (in)efficiency change over time; returns exhibit left-sided asymmetry, which implies that subsets of large fluctuations contribute substantially to the multifractal spectrum; in bull markets portfolios with the least efficiency assets provided a better risk–return relation; in periods of high volatility and high price depreciation (bear market) a better performance is associated with the portfolios composed by the more efficient cryptocurrencies.Keywords: Portfolio allocationCryptocurrencyMarket efficiencyMF-DFAMultifractalityJEL Classifications: G14G11 Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 Markiel and Fama (Citation1970) and Titan (Citation2015) are surveys regarding the empirical analysis of the weak form of market efficiency.2 The Hurst exponent, referred to as the ‘index of dependence’ or ‘index of long-range dependence’, is used as a measure of long-term memory of time series. Originally developed in hydrology and commonly studied in fractal geometry, it relates to the autocorrelations of the time series, and the rate at which these decrease as the lag between pairs of values increases (Hurst Citation1951).3 Traditional nonlinear variance ratio tests or autocorrelation functions are not able to identify multifractal structures. Fractal properties are associated to time series that present heavy tails and long memory. As these features are commonly observed in financial asset price returns (stylized facts), the use of MF-DFA appears as a suitable technique to evaluate random walk properties in such series, as stated by the econophysics literature (Arshad et al. Citation2016, Ali et al. Citation2018, Tiwari et al. Citation2019).4 The works of Mensi et al. (Citation2018), Sukpitak and Hengpunya (Citation2016), Dewandaru et al. (Citation2015), Tiwari et al. (Citation2019), Shahzad et al. (Citation2017), Zhu and Zhang (Citation2018) and Rizvi and Arshad (Citation2017) are examples of using MF-DFA to evaluate the weak form of market efficiency in financial markets, mostly stock markets.5 Ozkan (Citation2021), Diniz-Maganini et al. (Citation2021), Mnif et al. (Citation2020), Naeem et al. (Citation2021), Naeem et al. (Citation2021), Mensi et al. (Citation2020), Choi (Citation2021) and Mensi et al. (Citation2021) also found evidence on the impacts of the COVID-19 pandemic on the level of efficiency in different markets.6 As suggested by Rizvi and Arshad (Citation2014), the scaling range assumed the values of smin=10 and smax=(T/4), where T is the series' number of observations.7 More sophisticated methods for covariance matrix estimation may be used, such as EWMA and multivariate GARCH-family models. However, testing different methodologies for covariances in portfolio selection is beyond the main objective of this work.8 Rebalancing schemes can be considered, however, the identification of the time of rebalancing, as well as the consideration of transaction costs, are complex tasks, being considered as future work due to length limitations.9 Data were collected at https://finance.yahoo.com/.10 All experiments in this work were performed using R software.11 The Hurst exponents, H(q), from q=−4 to q=4 are not presented here due to length limitations but are available upon request.12 It is important to highlight that the year of 2021 is associated with a bear market and this behavior might be associated with the decrease of the level of efficiency of the corresponding cryptocurrencies. However, the analysis of the temporal dynamics of multifractality if out of the scope of this paper.Additional informationFundingThis work was supported by the Brazilian National Council for Scientific and Technological Development (CNPq) under Grant 304456/2020-9; and the Ripple Impact Fund, a donor advised fund of the Silicon Valley Community Foundation, under Grant 2018-196450(5855), as part of the University Blockchain Research Initiative, UBRI.