Abstract
The paper deals with the analysis of the empirical distribution of returns of selected market indices of developed and developing markets in relation to applications in the field of financial risks. The probability distribution of returns plays a key role for both the theoretical and practical part of financial theory. The assumption of a normal distribution of returns, which is crucial for several financial theories, is rejected in line with our analysis of the daily returns of 30 markets. From the perspective of financial risk assessment, the choice of an appropriate distribution is key to the accuracy of the achieved results. In this paper, we examine the possibility of applying alternative distributions, in order to better capture the observed leptokurtic behavior of the empirical distribution of daily returns as compared to the assumption of normality. We perform the analysis on the daily returns of stock market indices in order to examine the possible differences between the empirical distribution of developed and emerging markets. We investigate the suitability and relative performance of these alternative distributions: the generalized skewed t distribution (sgt), the generalized lambda distribution (gld), the exponential power distribution (GED), the Hansen's skewed t distribution and the Laplace distribution. The best relative performance of fit for market index returns providing the sgt_2 and gld distributions, with gld appearing to be a more prominent adept than with the perspective of relative stability of quality of fit and also quality of risk estimation.
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Acknowledgements
This work was supported by the Grant Agency of Slovak Republic – VEGA grant no. 1/0339/20 “ Hidden Markov Model Utilization in Financial Modeling ”.
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Appendix
Appendix
See Figs. 6, 7, 8, 9, 10, 11, 12, and 13.
Comparison of differences between AIC values of selected model and AIC of best model for individual two-year subperiods and developed markets. The interpretation of the graphs is as follows. For TA125.TA and subperiod 90_91 the model with the lowest AIC value is gld, for Laplace, sgt_1, sgt_2 and GED it is true that ∆AIC is less than 10, (on the graph highlighted by a black dotted line) which means we cannot unambiguously exclude the given models as unsuitable alternatives. The normal distribution provides a comparatively poorer quality of adaptation than other alternatives
Comparison of differences between AIC values of selected model and AIC of best model for individual two-year subperiods and emerging markets
Comparison of differences between BIC values of selected model and BIC of best model for individual two-year subperiods and developed markets
Comparison of differences between BIC values of selected model and BIC of best model for individual two-year subperiods and emerging markets
Comparison of differences between AIC values of selected model and AIC of best model for individual five-year subperiods and developed markets
Comparison of differences between AIC values of selected model and AIC of best model for individual five-year subperiods and emerging markets
Comparison of differences between BIC values of selected model and BIC of best model for individual five-year subperiods and developed markets
Comparison of differences between BIC values of selected model and BIC of best model for individual five-year subperiods and emerging markets
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Pekár, J., Pčolár, M. Empirical distribution of daily stock returns of selected developing and emerging markets with application to financial risk management. Cent Eur J Oper Res 30, 699–731 (2022). https://doi.org/10.1007/s10100-021-00771-4
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DOI: https://doi.org/10.1007/s10100-021-00771-4