Expected Shortfall Estimation

Abstract: This thesis evaluates the performance of Expected Shortfall estimation with normal, student-t and skewed distributions. It is stylized fact that student-t distribution generally outperforms normal distribution. What is particularly peculiar is whether there is marginal gain of increased distributional complexity with combining two half normal (skewed) distributions, developed by de Roon and Karehnke (2016), in comparison with t-distribution. In the cited paper authors suggest that recent research has identified skewness as one of the most prominent features of risk. For my research I utilized daily total returns (TR) on four composite indexes: Standard & Poor 500 (S&P 500), Russell 2000, Morgan Stanley Capital International (MSCI) and Goldman Sachs Commodity Index (GSCI). The sample period used for the empirical analysis runs from January 2002 to the end of December 2018. Nonetheless, MSCI is only available starting from 2007. Once distributions are estimated, I implement back-testing methodology to evaluate which outputs pass the traffic light test developed by Costanzino and Curran (2018). From the results presented in this paper, I conclude that generally skewed and t-distributions outperform the normal distribution in fitting financial returns and forecasting Expected Shortfall. However, the winner model remains student-t distribution with fat tails.