The GARCH-EVT-Copula Approach to Investigating Dependence and Quantifying Risk in a Portfolio of Bitcoin and the South African Rand

Thabani Ndlovu () and Delson Chikobvu
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Thabani Ndlovu: Department of Mathematical Statistics and Actuarial Science, University of the Free State, Bloemfontein 9300, South Africa
Delson Chikobvu: Department of Mathematical Statistics and Actuarial Science, University of the Free State, Bloemfontein 9300, South Africa

JRFM, 2024, vol. 17, issue 11, 1-16

Abstract: This study uses a hybrid model of the exponential generalised auto-regressive conditional heteroscedasticity (eGARCH)-extreme value theory (EVT)-Gumbel copula model to investigate the dependence structure between Bitcoin and the South African Rand, and quantify the portfolio risk of an equally weighted portfolio. The Gumbel copula, an extreme value copula, is preferred due to its versatile ability to capture various tail dependence structures. To model marginals, firstly, the eGARCH(1, 1) model is fitted to the growth rate data. Secondly, a mixture model featuring the generalised Pareto distribution (GPD) and the Gaussian kernel is fitted to the standardised residuals from an eGARCH(1, 1) model. The GPD is fitted to the tails while the Gaussian kernel is used in the central parts of the data set. The Gumbel copula parameter is estimated to be α = 1.007 , implying that the two currencies are independent. At 90%, 95%, and 99% levels of confidence, the portfolio’s diversification effects (DE) quantities using value at risk (VaR) and expected shortfall (ES) show that there is evidence of a reduction in losses (diversification benefits) in the portfolio compared to the risk of the simple sum of single assets. These results can be used by fund managers, risk practitioners, and investors to decide on diversification strategies that reduce their risk exposure.

Keywords: Gaussian kernel; generalised Pareto distribution; Gumbel copula; tail dependence; diversification effects; value at risk; expected shortfall (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2024
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