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Analyzing the South African Industrial Index Data using Numerous Standard Statistical Distributions |
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PP: 27-44 |
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doi:10.18576/jsap/140103
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Author(s) |
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Sandile C. Shongwe,
Zander Greyling,
Thandiwe Zwane,
Sihle Gcanga,
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Abstract |
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| Model fitting and risk estimation are an important everyday aspect of a successful financial institution.
Consequently, in this paper, we discuss risk quantification of the South African Industrial Index (also known as J520) using 22 standard light- and heavy-tailed statistical distributions. Given the importance of the J520 index (since it has the highest market capitalization in the Johannesburg Stock Exchange), investors may have a very keen interest in fully understanding the loss and gain returns characteristics and underlying statistical distribution’s properties, including tail properties. Thus, an in-depth goodness-of-fit evaluation is conducted by assessing six different tests (i.e. Kolmogorov-Smirnov, Anderson- Darling, Cramer von Mises, negative log-likelihood, Akaike information criterion, Bayesian information criterion) as well as two risk measures (i.e., value-at-risk and tail value-at-risk) are computed and interpreted within the context of J520 index. It is observed that the best distribution to fit to loss returns are the inverse Burr or transformed beta while for the gain returns it is either transformed gamma, inverse Burr or generalized beta distributions. The latter distributions strike a better balance with respect to excellent goodness-of-fit and risk measures that are very close to the corresponding ones for the empirical distribution. Given our findings, it may not be advisable for investors to hold very long positions in the J520 index since loss returns have much higher leptokurtic and heavy-tailed as compared to the lighter-tailed gain returns. Therefore, the growth shares observed over the long term indicate that a more prudent strategy would be to consider shorting the index. By doing so, investors could better align their strategies with the highly likely potential for substantial
drawdowns inherent in this market. |
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