Estimation of Diversification Effects/Benefits Using the Generalised Pareto Distribution - Extreme Value Gumbel Copula Model

Authors

O. Jakata, Department of Mathematical Statistics and Actuarial Sciences, Faculty of Natural and Agricultural Sciences, University of the Free State, 205 Nelson Mandela Dr, Park West, Bloemfontein, 9301, South AfricaFollow
D. Chikobvu, Department of Mathematical Statistics and Actuarial Sciences, Faculty of Natural and Agricultural Sciences, University of the Free State, 205 Nelson Mandela Dr, Park West, Bloemfontein, 9301, South AfricaFollow

Author Country (or Countries)

South Africa

Abstract

The objective of this paper is to estimate the diversification effects/benefits of an investment in a portfolio consisting of the South African Industrial (J520) and the Financial (J580) Indices using the Generalised Pareto Distributions (GPDs) with an extreme value Gumbel copula. The GPD is used as the marginal distribution to both assets to better characterise the extreme risk of returns in both Indices tails. The extreme value Gumbel copula captures the dependence structure (co-movement) of the financial assets in the portfolio. The Akaike information criterion (AIC) and Bayesian information criterion (BIC) goodness of fit tests and the scatterplots indicate that the upper tail of the gains (the larger gains) risk and the losses tail (the larger losses) are best captured using the extreme value Gumbel copula. Monte Carlo simulation of an equally weighted portfolio of the two Indices is used to estimate the portfolio risk. The univariate marginal risks and the portfolio risks are used to calculate the diversification effects/benefits. The results show that there are benefits in diversification since the riskiness of the portfolio is less than the sum of the risk of the two financial assets. This implies that VaR, although not additive theoretically, is sub-additive in this practical situation. This property of sub-additivity represents the benefits of diversification for a portfolio. The implication is that investors investing in individual risky assets can benefit from constructing such a portfolio to reduce extreme risk. Due to high dependence and contagion between developed markets/Global markets, this is useful information for local and international investors seeking a portfolio which includes developing countries market Indices, such as South African assets, which are less correlated with other Global markets, thereby reducing the risk of contagion.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/jsap/12S111

Recommended Citation

Jakata, O. and Chikobvu, D. (2023) "Estimation of Diversification Effects/Benefits Using the Generalised Pareto Distribution - Extreme Value Gumbel Copula Model," Journal of Statistics Applications & Probability: Vol. 12: Iss. 4, Article 11.
DOI: http://dx.doi.org/10.18576/jsap/12S111
Available at: https://digitalcommons.aaru.edu.jo/jsap/vol12/iss4/11