A proposal for optimal VaR and CVaR parameters estimation

Traditional strategies of managing financial portfolios are based on the assumption of normally distributed losses, i.e., the likelihood of observing extreme adverse events is negligible and close to zero. Indeed, many financial data reject the Gaussian model and exhibits fat-tailed distributions. In this paper we analyze and compare the relative performances of VaR and CVaR estimators with respect to daily stock market returns of four different emerging markets indexes, i.e., MSCI Emerging Markets, Latin America, Middle East Europe and Africa index and South Africa. All indices exhibit slightly negative skewed distributions and are characterized by a significant positive excess of kurtosis. This implies heavy tails in the distribution of risky returns, which are thus more likely of being affected by extreme values. In order to discriminate among time-series datasets we conducted two different level of analyses: 1) identify the timing of regional markets crashes along with the related market crisis periods 2) measure the strength of co-movements among time-series across different timescales. With reference to the first objective, we followed the methodology applied in [1]. What emerges is that all markets have been affected by the same crisis but their effects, in terms of price decline and duration, appear to be less severe for the MSCI South Africa. Moreover, it would seem that the MXZA index is positively lagged with respect to the other markets. In order to give evidence to the above consideration we have run a Wavelet Multiple (Cross) Correlation analysis [2]. By means of the Extreme Value Theory (EVT), we backtest the risk measures over several classes of density distributions and well-known modeling approaches such as the Exponential Weighted Moving Average (EWMA) and the Historical Simulation Method (HSM). Results give evidence of how the efficacy of the applied risk measures as well as of the selected model strictly depends on the cumbersome parameters’ settings [3]. In this view, we propose two metaheuristic (C)VaR based algorithms for optimally estimating and fitting within an EVT framework the two-sided tail distribution of returns. References [1]. Sandeep A. Patel and Asani Sarkar. Crises in developed and emerging stock markets. Financial Analysts Journal, 54(6):50–61, 1998. [2]. J. Fern ́andez-Macho. Wavelet multiple correlation and cross-correlation: A multiscale analysis of eurozone stock markets. Physica A: Statistical Mechanics and its Applications, 391(4):1097–1104, 2012. [3]. J. Andria. A computational proposal for a robust estimation of the pareto tail index: An application to emerging markets. Applied Soft Computing, 114:108048, 2022.