|
|
 |
| |
|
|
|
Fitting Statistical Parent Distributions to Quantify Financial Risk in the South African Financial Index (J580): an Extended Analysis |
|
|
|
PP: 369-382 |
|
|
|
doi:10.18576/jsap/140304
|
|
|
|
Author(s) |
|
|
|
Sandile C. Shongwe,
Lesego E. Malumane,
Nasreen A. Paulse,
George Mazondo,
Lulo Sifumba,
|
|
|
|
Abstract |
|
|
| Statistical distribution fitting and risk estimation are an important exercise in financial data analysis because the fitted distribution properties tend to provide more theoretically established information about the data. Consequently, in this paper, we correct and extend the analysis of the South African Financial Index, also known as J580 (which is an important index, with a significant market capitalization and it is listed in the Johannesburg Stock Exchange). A paper published in this journal, fitted four distributions (gamma, Weibull, exponential and Burr) to the J580 returns using two goodness-of-fit tests (Akaike information criterion (AIC) and Bayesian information criterion (BIC)) and two risk measures (value-at-risk and expected shortfall). This latter paper had incorrect descriptives and the analysis is of little depth; thus, in this paper, we conduct a more thorough analysis by extending this work by using six goodness-of-fit (AIC, BIC, Kolmogorov-Smirnov, Anderson-Darling, Cramer von Mises, negative log-likelihood) and the same two risk measures to instead nineteen statistical distributions (i.e. we re-evaluate the four distributions in full and conduct model fitting of fifteen additional ones). To strike a balance between goodness-of-fit and risk measures performance, a ranking method is implemented, and it is observed that the Burr distribution (also identified as the best distribution by the paper published in this journal) is consistently competitive in modelling losses (especially with an excellent goodness-of-fit and partially good with risk measures). The other strong competitors that can be implemented instead of the Burr are the generalized Pareto and transformed beta distributions. However, the exponential distribution which was identified by the paper published in this journal is not even in the top 5 of best distributions under gains; instead, the most ideal distributions are the transformed gamma, transformed beta and Weibull (in that order). From the findings as well as since the kurtosis and skewness of the losses are much greater than that of the gains, it is advisable to hold a short position in the long run; however, in the short run, investors need to closely monitor the candlestick trends so that they can make rational decisions based on the underlying patterns observed.
|
|
|
|
|
|
|
|
