Volatility and Risk – Median Shortfall or Value at Risk

The value-at-risk (VaR) is a widely used risk measure by financial institutions and regulators even though it fails to capture risk at the tail end. The purpose of this research is to contribute to the ongoing discourse on risk management by assessing the median shortfall (MS) as an alternative risk measure by comparing it with the VaR. We investigate the performance of VaR forecasts considering the following models: historical simulation (HS) and Glosten-Jagannathan-Runkle-generalized autoregressive conditional heteroscedasticity (GJR-GARCH). For MS forecasts, we consider only the HS. The comparison was based on an accuracy test and loss function on the following stock indices: the S&P 500, the Russell 2000 small cap and the DAX (Germany) from January 1, 2006, to December 31, 2020. Empirical analysis indicated the superiority of the MS approach in capturing tail risk for the overall testing period. In addition to the aforementioned findings, there was a gain in using the GJR-GARCH(1, 1) VaR in capturing tail risk, especially in turbulent periods.