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Estimation of Financial Risk using the Archimedean Gumbel Copula with Log-Normal Distributed Marginals |
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PP: 543-560 |
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doi:10.18576/jsap/140605
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Author(s) |
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Owen Jakata,
Delson Chikobvu,
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Abstract |
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| This study uses the Archimedean Gumbel copula to model the dependence between the South African Industrial Index (J520) and South African Financial Index (J580) growth rates. This study aims to estimate extreme portfolio risk and account for diversification benefits of investing in a portfolio consisting of the growth rates from the two assets. This study uses growth rates, which contain only positive values, in contrast to financial returns used in other studies. Growth rates align with the requirements of copula models, which accept input values only within the (0, 1) interval, whereas financial returns can be either negative or positive. The Log-Normal distribution is used as the marginal distribution of each of the two growth rates, instead of the Normal distribution, to characterise better the heavy tails, a typical stylised fact prevalent in financial returns and growth rates. The scatterplots and AIC/BIC indicate that the dependence for the financial growth rates is best captured using the Archimedean Gumbel copula. The Archimedean Gumbel copula is used to capture extreme risk in the data sets. Monte Carlo simulation is used to quantify the risk of the portfolio. The results show minimal diversification benefits when investing in the two assets. The observation of minimal diversification benefits can suggest that the South African economy may be more stable, with limited contagion between the Industrial and Financial sectors. This information has important implications for both local and international investors regarding their strategies for investment, diversification, contagion management, and hedging decisions. |
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