Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors

• DOI: 10.17016/feds.2016.065
• Publication Date: 2016-08-12T16:42:24Z
• Authors: Dobrislav Dobrev; Travis D. Nesmith; Dong Hwan Oh
• Keywords: Quantile; Tail risk

We provide an accurate closed-form expression for the expected shortfall of linear portfolios with elliptically distributed risk factors. Our results aim to correct inaccuracies that originate in Kamdem (2005) and are present also recent comprehensive survey by Nadarajah, Zhang, Chan (2014) on estimation methods shortfall. In particular, we show correction popular multivariate Student t setting eliminates understatement a factor varying from at least 4 more than 100 across different tail quantiles degrees freedom. As such, resulting economic impact financial management applications could be significant. More generally, our findings point extra scrutiny required when deploying new practice.