An analysis of the extreme returns distribution: The case of the Istanbul Stock Exchange

The assumption of normality of asset returns is widely used in financial modelling, financial regulation on risks and capital and Value-at-Risk (VaR) modelling. As observed during times of stock market crashes or financial stress, extreme returns cannot be adequately modelled using the Gaussian distribution. In this study, we use the Extreme Value Theory (EVT) to model the extreme return behaviour of the Istanbul Stock Exchange (ISE), Turkey. Three different distributions are used, namely Gumbel, Fréchet and Weibull, for modelling extreme returns over different investment horizons. The goodness-of-fit for these distributions is verified by the Anderson-Darling goodness-of-fit test. VaR is computed with the proposed distributions and backtesting results indicate that the EVT provides superior risk management in all the sub-intervals considered compared to the VaR estimation under the assumption of a normal distribution.