Abstract
Recent years have seen a growing interest among investors in the new technology of blockchain and cryptocurrencies and some early investors in this new type of digital assets have made significant gains. The heuristic algorithm, differential evolution, has been advocated as a powerful tool in portfolio optimization. We propose in this study two new approaches derived from the traditional differential evolution (DE) method: the GARCH-differential evolution (GARCH-DE) and the GARCH-differential evolution t-copula (GARCH-DE-t-copula). We then contrast these two models with DE (benchmark) in single and multi-period optimizations on a portfolio consisting of five cryptoassets under the coherent risk measure CVaR constraint. Our analysis shows that the GARCH-DE-t-copula outperforms the DE and GARCH-DE approaches in both single- and multi-period frameworks. For these notoriously volatile assets, the GARCH-DE-t-copula has shown risk-control ability, hereby confirming the ability of t-copula to capture the dependence structure in the fat tail.
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Notes
Pearson’s correlation coefficients provide the degree of linear relationship between two variables.
Kendall is a nonparametric test that measures the strength of dependence between two variables. It is given by: \(\tau =\frac{n_c-n_d}{\frac{1}{2}n(n-1)}\), where \(n_c\) is the number of concordant (ordered in the same way) pairs and \(n_d\) is the number of discordant (ordered differently) pairs.
Although there are no absolute standards, many analysts view coefficients, in absolute values, of less than 0.25 as describing weak relationships, coefficients between 0.25 and 0.50 as moderate relationships, and those greater than 0.50 as strong relationships.
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We would like to thank the anonymous referee for the valuable comments to improve the quality of this paper.
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Mba, J.C., Pindza, E. & Koumba, U. A differential evolution copula-based approach for a multi-period cryptocurrency portfolio optimization. Financ Mark Portf Manag 32, 399–418 (2018). https://doi.org/10.1007/s11408-018-0320-9
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DOI: https://doi.org/10.1007/s11408-018-0320-9