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A Markov-switching COGARCH approach to cryptocurrency portfolio selection and optimization


Blockchain is a new technology slowly integrating our economy with cryptocurrencies such as Bitcoin and many more applications. Bitcoin and other versions of it (known as Altcoins) are traded everyday at various cryptocurrency exchanges and have drawn the interest of many investors. These new types of assets are characterized by wild swings in prices, and this can lead to large swings in profit and losses. To respond to these dynamics, cryptoinvestors need adequate tools to guide them through their choice of portfolio selection and optimization. Bitcoin returns have shown some form of regime change, suggesting that regime-switching models could more adequately capture the volatility dynamics. This paper presents a two-state Markov-switching COGARCH-R-vine (MSCOGARCH) model for cryptocurrency portfolio selection and compares the performance to the single-regime COGARCH-R-vine (COGARCH). The findings here are in line with the literature where MSCOGARCH outperforms the single-regime COGARCH with regard to the expected shortfall risk. The COGARCH specifications here capture the structural breaks and heavy tailness within each state of the Markov switching in order to achieve a minimal risk and a maximum return. The flexibility of R-vine copula allows adequate bivariate copula selection for each pair of cryptocurrencies to achieve suitable dependence structure through pair-copula construction architecture.

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    At the time of this writing, there are 2103 tradable cryptocurrencies according to Coinmarketcap (

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The authors are grateful to anonymous reviewers for their valuable comments and suggestions, which led to significant improvement in the presentation and quality of this paper. The first author acknowledges financial support from AAMP programme of the University of Johannesburg.

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Correspondence to Jules Clement Mba.

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See Tables 3, 4, 5, 6, 7, 8 and Figs. 4, 5.

Table 3 Regime 1 portfolio
Table 4 Weights Regime 1
Table 5 MSCOGARCH Regime 2 (ES and mean)
Table 6 MSCOGARCH Regime2 weights
Table 7 COGARCH single-regime (ES and mean)
Table 8 COGARCH single-regime weights
Fig. 4

Historical prices and returns

Fig. 5

Historical prices and returns

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Mba, J.C., Mwambi, S. A Markov-switching COGARCH approach to cryptocurrency portfolio selection and optimization. Financ Mark Portf Manag (2020).

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  • Long range dependence
  • Lévy processes
  • Differential evolution
  • R-vine copula
  • Portfolio optimization

JEL Classification

  • C02
  • G11
  • G17