Analysing Extreme Risk in the South African Financial Index (J580) using the Generalised Extreme Value Distribution
Abstract
The aim of this study is to model the probabilistic behaviour of unusually large financial losses (extreme-risk)and gains of the South African Financial Index (J580). Risk is defined as uncertainty in return in this paper. This study makes use of Extreme Value Theory (EVT) for the period years: 1995-2018 to build models that are used to estimate extreme losses and gains. The quarterly block maxima/minima of monthly returns are tted to the Generalised Extreme Value Distribution (GEVD). Return levels (maximum loss/gain) based on the parameters from the GEVD are estimated. A comparative analysis with the Generalised Pareto Distribution (GPD) is carried out. The study reveals that EVT provides an efficient method of forecasting potentially high risks in advance. The conclusion is that analysing extreme risk in the South African Financial Index helps investors understand its riskness better and manage to reduce the risk exposure in this portfolio.References
T. Rahman, Z. Hossain, and M. Habibullah, Stock Market Crash in Bangladesh: The Moneymaking Psychology of Domestic Investors, American Journal of Theoretical and Applied Business, vol. 3, no. 3, pp. 43, 2017, doi: 10.11648/j.ajtab.20170303.12.
S. Aboura, When the U.S. Stock Market Becomes Extreme?, Risks, vol. 2, no. 2, pp. 211225, 2014, doi:10.3390/risks2020211.
G. Magnou, An application of extreme value theory for measuring financial risk in the Uruguayan Pension Fund COMPENDIUM, vol. 4, no. 7, pp. 119, 2017.
P. Yiou, et al. Nonlinear Processes in Geophysics Weather regime dependence of extreme value statistics for summer temperature and precipitation, Nonlinear Processes in Geophysics, vol. 15, pp. 365378, 2008.
C. Sigauke, M.R. Makhwiting, and M. Lesaoana, Modelling conditional heteroskedasticity in JSE stock returns using the Generalised Pareto Distribution, African Review of Economics and Finance, vol. 6, no. 1, pp. 4155, 2014.
H.M. Markowitz, Portfolio Selection, The Journal of Finance, vol. 7, no. 1, pp. 7791, 1952, doi:10.2307/2975974. JSTOR 2975974.
M. Gilli, and E. Kllezi, E. An application of extreme value theory for measuring financial risk, Computational Economics, vol. 27, no. 23, pp. 207228, 2006, doi: 10.1007/s10614-006-9025-7.
D.E. Allen, A.K. Singh, and R.J. Powell, Extreme Market Risk - An Extreme Value Theory Approach, Edith Cowan University Publication, 2011.
M.R. Makhwiting, C. Sigauke, and M. Lesaoana, Modelling tail behaviour of returns using the generalised extreme value distribution, Economics, Management, and Financial Markets, vol. 9, no. 1, 2014.
A. Heymans, and L. Santana, How efficient is the Johannesburg Stock Exchange really?, South African Journal of Economic and Management Sciences, vol. 21, no. 1, 2018, a1968. https://doi. org/10.4102/sajems. v21i1.1968.
B.Y.A. Ferreira, and L. De Haan, On the block maxima method in extreme value theory: PWM estimators, Annals of Statistics, vol. 43, no. 1, pp. 276298, 2015, doi: 10.1214/14-AOS1280.
H. Hasan, N.F.A. Radi, and S. Kassim, Modeling the distribution of extreme share return in Malaysia using Generalized Extreme Value (GEV) distribution, AIP Conference Proceedings, 1450(May 2012), pp. 8289, 2012, doi: 10.1063/1.4724121.
N. Boudrissa, H. Cheraitia, and L. Halimi, Modelling maximum daily yearly rainfall in northern Algeria using generalized extreme value distributions from 1936 to 2009, Meteorological Applications, vol. 24, no. 1, pp. 114119, 2017, doi:10.1002/met.1610.
G. Lazoglou, and C. Anagnostopoulou, An Overview of Statistical Methods for Studying the Extreme Rainfalls in Mediterranean, Proceedings, Vol. 1, no. 5, pp. 681, 2017, doi: 10.3390/ecas2017-04132.
S. Coles, An Introduction to Statistical Modeling of Extreme Values. 3rd edn. Bristol: Springer, 2001.
A.F. Jenkinson, (1955) The Frequency Distribution of the Annual Maximum (or Minimum) of Meteorological Elements, Quarterly Journal of the Royal Meteorological Society, vol. 81, no. 348, pp. 158171, 1955.
B. Balkema, and L. deHaan, Residual lifetime at great age, Annals of Probability, Vol. 2, pp. 792-804, 1974.
J. Pickands, Statistical inference using extreme order statistics, Annals of Statistics, vol. 3, pp. 119-131, 1975.
R. Engle, Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica, vol. 50, no. 4, pp. 9871007, 1982.
P. Hawkins, South Africas financial sector ten years on: performance since democracy Development Southern Africa, vol. 21, no. 1, pp. 179204, 2004.
B. Butterworth, and S. Malherbe, For the Department of Trade and Industry, July 1999.
A. Mwamba, and T. Mhlanga, Extreme conditional value at risk: a coherent scenario for risk management, University of Johannesburg,2013.
D.C. Wentzel, and E. Mare, Extreme value theory An application to the South African equity market, Investment Analysts Journal, vol. 33, no. 66, pp. 73-77, 2007.
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