| Summary: | The probability density distribution of stock returns is crucial in financial modelling and the estimation of financial risk measures. Numerous papers have been devoted to finding the best-fit distributional specifications of stock returns but no consensus has been reached in answering the question of whether there is a unique distributional family that fits all markets and market conditions. Similarly, numerous papers have been devoted to modelling tail risk but no consensus has been reached with regard to which methods provide the most accurate and reliable estimates. This research brings these two strands of the literature together by investigating how distributional specifications differ between the bull and bear markets, and between the developed and the emerging stock exchanges. It also contributes to our understanding of how the knowledge of distributional specifications informs the discussion on the best method of the VaR and ES estimation. In its empirical part, this research investigates the probability density distributions of daily equity returns for 19 developed stock exchanges and 19 emerging stock exchanges. It considers the period of 01 January 2000 to 31 December 2016 and then separately for the bull and bear sub-periods. The results show that there are considerable differences in the probability density distributions for the developed and the emerging stock exchanges. Moreover, the probability density distributions of stock market returns change as the markets switch between the bull and the bear market regimes. These changes in the probability density distribution specifications impact on the values of VaR and ES. This research sheds light on the shortcomings of commonly used VaR and ES estimation methods such as Historical Simulation and Extreme Value Theory.
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