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Modelling Portfolio Risk and Diversification Effects of a Portfolio Using the Exponential Distribution – Bivariate Archimedean Gumbel Copula Model

Year: 2023       Vol.: 72       No.: 1      

Authors: Owen Jakata and Delson Chikobvu


This study uses the Archimedean Gumbel copula model to construct the dependence structure and joint probability distributions using the Exponential Distribution as the marginal distribution to asset returns. The main objective of this study is to estimate the diversification effects of investing in a portfolio consisting of two financial assets, viz: the South African Industrial and Financial Indices. The Exponential Distribution is used as the marginal distribution of the returns, instead of the Normal distribution, to better characterise the financial returns of the two assets. The scatterplots indicate that the dependence in gains, as well as the losses are better captured using the Archimedean Gumbel copula. Monte Carlo simulation of an equally weighted portfolio of the two financial assets is used to model and quantify the risk of the resultant portfolio. The results confirm 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. It is less risky to invest in diversified portfolios that includes assets from the two different industries/stock markets. Due to dependence and contagion between Global stock markets, the findings of this study are useful information for the local and international investors seeking a portfolio which include developing countries’ stock market Indices containing, say the South African financial assets. This study provides investors with a framework to quantify diversification effects, which allows for the avoidance of extreme risks, whilst benefiting from extreme gains.

Keywords: Expected Shortfall. Monte Carlo simulation, Value-at-Risk

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