Crypto-assets portfolio selection and optimization: a COGARCH-Rvine approach

Jules Clement Mba; Sutene Mwambetania Mwambi

doi:10.1515/snde-2020-0072

Abstract

Blockchain is a new technology slowly integrating our economy with crytocurrencies such as Bitcoin and many more applications. Bitcoin and other version of it (known as Altcoins) are traded everyday at various cryptocurrency exchanges and have drawn the interest of many investors. These new type of assets are characterised by wild swings in prices and this can lead to great profit as well as large losses. To respond to these dynamics, crypto investors need adequate tools to guide them through their choice of optimal portfolio selection. This paper presents a portfolio selection based on COGARCH and regular vine copula which are able to capture features such as abrupt jumps in prices, heavy-tailed distribution and dependence structure respectively, with the optimal portfolio achieved through the stochastic heuristic algorithm differential evolution known for its global search solution ability. This method shows great performance as compared with other available models and can achieve up to 50% of total returns in some periods of optimization.

Keywords: COGARCH; differential evolution; Levy process; portfolio optimization; regular vine copula

JEL: C02; G11; G17

Corresponding author: Jules Clement Mba, University of Johannesburg, Faculty of Science, Mathematics and Applied Mathematics, Cnr Kingsway Rd and University Rd, Johannesburg, Gauteng 2006, South Africa, E-mail: jmba@uj.ac.za

Author contribution: The contribution of each author is as follows: Conceptualization, Jules Mba and Sutene Mwambi; methodology, Jules Mba and Sutene Mwambi.; software, Jules Mba and Sutene Mwambi; validation, Jules Mba and Sutene Mwambi; formal analysis, Jules Mba and Sutene Mwambi; investigation, Jules Mba, and Sutene Mwambi; resources, Jules Mba and Sutene Mwambi; data curation, Jules Mba and Sutene Mwambi.; writing—original draft preparation, Jules Mba; writing—review and editing, Jules Mba and Sutene Mwambi; visualization, Jules Mba, Sutene Mwambi; supervision, Jules Mba.; project administration, Jules Mba, Sutene Mwambi; funding acquisition, Not Applicable. All authors have read and agreed to the published version of the manuscript.
Research funding: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

Ardia, D., K. Boudt, P. Carl, K. Mullen, and B. G. Peterson. 2011. “Differential Evolution with Deoptim: An Application to Non-Convex Portfolio Optimization.” The R Journal 3 (1): 27–34. https://doi.org/10.32614/rj-2011-005.Search in Google Scholar

Barndorff-Nielsen, O. E., and V. Perez-Abreu. 1999. “Stationary and Self-Similar Processes Driven by Lévy Processes.” Stochastic Processes and their Applications 84 (2): 357–69. https://doi.org/10.1016/s0304-4149(99)00061-7.Search in Google Scholar

Bedford, T., and R. M. Cooke. 2001. “Probability Density Decomposition for Conditionally Dependent Random Variables Modeled by Vines.” Annals of Mathematics and Artificial Intelligence 32 (1–4): 245–68. https://doi.org/10.1023/a:1016725902970.10.1023/A:1016725902970Search in Google Scholar

Bedford, T., and R. M. Cooke. 2002. “Vines: A New Graphical Model for Dependent Random Variables.” Annals of Statistics 30: 1031–68. https://doi.org/10.1214/aos/1031689016.Search in Google Scholar

Bollerslev, T. 1986. “Generalized Autoregressive Conditional Heteroskedasticity.” Journal of Econometrics 31 (3): 307–27. https://doi.org/10.1016/0304-4076(86)90063-1.Search in Google Scholar

Boudt, K., P. Carl, and B. Peterson. 2012. “Portfolioanalytics: Portfolio Analysis, Including Numeric Methods for Optimization of Portfolios.” In R Package Version 0.8 2. https://github.com/braverock/PortfolioAnalytics.Search in Google Scholar

Brunnermeier, M. K. 2008. “Deciphering the 2007–08 Liduidity and Credit Crunch.” The Journal of Economic Perspectives 23: 77–100. https://doi.org/10.3386/w14612.Search in Google Scholar

Cherubini, U., E. Luciano, and W. Vecchiato. 2004. Copula Methods in Finance. Chichester, England: John Wiley & Sons.10.1002/9781118673331Search in Google Scholar

Duong, D., and T. L. D. Huynh. 2020. “Tail Dependence in Emerging Asean-6 Equity Markets: Empirical Evidence from Quantitative Approaches.” Financial Innovation 6 (1): 1–26. https://doi.org/10.1186/s40854-019-0168-7.Search in Google Scholar

Embrechts, P., F. Lindskog, and A. McNeil. 2003. “Modelling Dependence with Copulas and Applications to Risk Management.” In Handbook of Heavy Tailed Distributions in Finance, edited by S. Rachev. Amsterdam: Elsevier.10.1016/B978-044450896-6.50010-8Search in Google Scholar

Florackis, C., A. Kontonikas, and A. Kostakis. 2014. “Stock Market Liquidity and Macro-Liquidity Shocks: Evidence from the 2007–2009 Financial Crisis.” Journal of International Money and Finance 44: 97–117. https://doi.org/10.1016/j.jimonfin.2014.02.002.Search in Google Scholar

Gârleanu, N., and L. H. Pedersen. 2013. “Dynamic Trading with Predictable Returns and Transaction Costs.” The Journal of Finance 68 (6): 2309–40. https://doi.org/10.1111/jofi.12080.Search in Google Scholar

Holland, J. 1975. Adaptation in Natural and Artificial Systerrns. Ann Arbor, MI: University of Michigan Press.Search in Google Scholar

Huynh, T. L. D., T. Burggraf, and M. Wang. 2020a. “Gold, Platinum, and Expected Bitcoin Returns.” Journal of Multinational Financial Management 56: 100628. https://doi.org/10.1016/j.mulfin.2020.100628.Search in Google Scholar

Huynh, T. L. D., E. Hille, and M. A. Nasir. 2020b. “Diversification in the Age of the 4th Industrial Revolution: the Role of Artificial Intelligence, Green Bonds and Cryptocurrencies.” Technological Forecasting and Social Change 159: 120188. https://doi.org/10.1016/j.techfore.2020.120188.Search in Google Scholar

Huynh, T. L. D., M. A. Nasir, S. P. Nguyen, and D. Duong. 2020c. “An Assessment of Contagion Risks in the Banking System Using Non-parametric and Copula Approaches.” Economic Analysis and Policy 65: 105–16. https://doi.org/10.1016/j.eap.2019.11.007.Search in Google Scholar

Huynh, T. L. D., M. A. Nasir, X. V. Vo, and T. T. Nguyen. 2020d. “‘Small Things Matter Most’: The Spillover Effects in the Cryptocurrency Market and Gold as a Silver Bullet.” The North American Journal of Economics and Finance 54: 101277. https://doi.org/10.1016/j.najef.2020.101277.Search in Google Scholar

Huynh, T. L. D., S. P. Nguyen, and D. Duong. 2018. “Contagion Risk Measured by Return Among Cryptocurrencies.” In International Econometric Conference of Vietnam, 987–98. Springer.10.1007/978-3-319-73150-6_71Search in Google Scholar

Joe, H. 1994. “Multivariate Extreme-Value Distributions with Applications to Environmental Data.” Canadian Journal of Statistics 22 (1): 47–64. https://doi.org/10.2307/3315822.Search in Google Scholar

Klüppelberg, C., A. Lindner, and R. Maller. 2004. “A Continuous-Time Garch Process Driven by a Lévy Process: Stationarity and Second-Order Behaviour.” Journal of Applied Probability 41: 601–22. https://doi.org/10.1239/jap/1091543413.Search in Google Scholar

Krink, T., S. Mittnik, and S. Paterlini. 2009. “Differential Evolution and Combinatorial Search for Constrained Index-Tracking.” Annals of Operations Research 172 (1): 153. https://doi.org/10.1007/s10479-009-0552-1.Search in Google Scholar

Krink, T., and S. Paterlini. 2011. “Multiobjective Optimization Using Differential Evolution for Real-World Portfolio Optimization.” Computational Management Science 8 (1–2): 157–79. https://doi.org/10.1007/s10287-009-0107-6.Search in Google Scholar

Kurowicka, D., and R. M. Cooke. 2006. Uncertainty Analysis with High Dimensional Dependence Modelling. Chichester, England: John Wiley & Sons.10.1002/0470863072Search in Google Scholar

Low, R. K. Y., J. Alcock, R. Faff, and T. Brailsford. 2013. “Canonical Vine Copulas in the Context of Modern Portfolio Management: Are They Worth it?.” Journal of Banking & Finance 37 (8): 3085–99. https://doi.org/10.1016/j.jbankfin.2013.02.036.Search in Google Scholar

Luu Duc Huynh, T. 2019. “Spillover Risks on Cryptocurrency Markets: A Look from Var-Svar Granger Causality and Student’st Copulas.” Journal of Risk and Financial Management 12 (2): 52. https://doi.org/10.3390/jrfm12020052.Search in Google Scholar

Maringer, D., and O. Oyewumi. 2007. “Index Tracking with Constrained Portfolios.” Intelligent Systems in Accounting Finance and Management: International Journal 15 (1–2): 57–71. https://doi.org/10.1002/isaf.285.Search in Google Scholar

Markowitz, H. 1959. Portfolio Selection. New York: John Wiley.Search in Google Scholar

Markowitz, H. M. 1952. “Portfolio Selection.” The Journal of Finance 7 (1): 77–91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x.Search in Google Scholar

Markowitz, H. M., and A. Perold. 1981. “Portfolio Analysis with Factors and Scenarios.” The Journal of Finance 36 (4): 871–7. https://doi.org/10.1111/j.1540-6261.1981.tb04889.x.Search in Google Scholar

Mba, J. C., E. Pindza, and U. Koumba. 2018. “A Differential Evolution Copula-Based Approach for a Multi-Period Cryptocurrency Portfolio Optimization.” Financial Markets and Portfolio Management 32 (4): 399–418. https://doi.org/10.1007/s11408-018-0320-9.Search in Google Scholar

Merton, R. C. 1972. “An Analytic Derivation of the Efficient Portfolio Frontier.” Journal of Financial and Quantitative Analysis 7: 1851–72. https://doi.org/10.2307/2329621.Search in Google Scholar

Moshirian, F. 2011. “The Global Financial Crisis and the Evolution of Markets, Institutions and Regulation.” Journal of Banking and Finance 35 (3): 502–11. https://doi.org/10.1016/j.jbankfin.2010.08.010.Search in Google Scholar

Nguyen, S. P., and T. L. D. Huynh. 2019. “Portfolio Optimization from a Copulas-Gjrgarch-Evt-Cvar Model: Empirical Evidence from Asean Stock Indexes.” Quantitative Finance and Economics 3 (3): 562.10.3934/QFE.2019.3.562Search in Google Scholar

Nystrup, P., H. Madsen, and E. Lindström. 2018. “Dynamic Portfolio Optimization across Hidden Market Regimes.” Quantitative Finance 18 (1): 83–95. https://doi.org/10.1080/14697688.2017.1342857.Search in Google Scholar

Rachev, S. T., C. Menn, and F. J. Fabozzi. 2005. Fat-tailed and Skewed Asset Return Distributions: Implications for Risk Management, Portfolio Selection, and Option Pricing, Vol. 139. Hoboken, New Jersey: John Wiley & Sons.Search in Google Scholar

Simo-Kengne, B. D., K. A. Ababio, J. Mba, and U. Koumba. 2018. “Behavioral Portfolio Selection and Optimization: an Application to International Stocks.” Financial Markets and Portfolio Management 32 (3): 311–28. https://doi.org/10.1007/s11408-018-0313-8.Search in Google Scholar

Sklar, M. 1959, “Fonctions de Repartition an Dimensions et Leurs Marges,” Publications de l’Institut Statistique de l’Université de Paris 8: 229–31.Search in Google Scholar

Storn, R., and K. Price. 1997. “Differential Evolution–A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces.” Journal of Global Optimization 11 (4): 341–59. https://doi.org/10.1023/a:1008202821328.10.1023/A:1008202821328Search in Google Scholar

Thampanya, N., M. A. Nasir, and T. L. D. Huynh. 2020. “Asymmetric Correlation and Hedging Effectiveness of Gold & Cryptocurrencies: From Pre-industrial to the 4th Industrial Revolution.” Technological Forecasting and Social Change 159: 120195. https://doi.org/10.1016/j.techfore.2020.120195.Search in Google Scholar

Wajdi, M., B. Nadya, and G. Ines. 2020. “Asymmetric Effect and Dynamic Relationships over the Cryptocurrencies Market,” Computers and Security 96: 101860. https://doi.org/10.1016/j.cose.2020.101860.Search in Google Scholar

Yollin, G. 2009. “R Tools for Portfolio Optimization,” In Presentation at R/Finance Conference, Vol. 2009.Search in Google Scholar

Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/snde-2020-0072)

Received: 2020-06-29

Revised: 2021-02-18

Accepted: 2021-03-08

Published Online: 2021-03-26

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Supplementary Material Details

Crypto-assets portfolio selection and optimization: a COGARCH-Rvine approach

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