On the Validity of Value-at-Risk: Comparative Analyses with Expected Shortfall

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Backtesting for Risk-Based Regulatory Capital (2004, background): “This seems to lead to the general opinion that, although expected shortfall has nice theoretical properties, it is much harder to backtest than value-at-risk (see Yamai and Yoshiba (2002)), the main reason why expected shortfall is still absent in Basle II.”
Value-at-risk versus expected shortfall: A practical perspective (2005, methodology): “11 Yamai and Yoshiba (2002a) illustrate this problem using simple examples of far-out-of-the-money option and a concentrated credit portfolio.”
Estimating Value at Risk and Expected Shortfall Using Expectiles (2007, background): “ES is defined as the conditional expectation of the return given that it exceeds the VaR (see Yamai and Yoshiba, 2002).”
Hybrid Historical Simulation VaR and ES: Performance in Developed and Emerging Markets (2009, unknown): “They, along with many others (see Acerbi et al. 2001, Yamai and Yoshiba, 2002 and Inui and Kijima, 2005), advocated the use of ES as an alternative risk measure with good theoretical properties.”
Optimal Financial Portfolios (2007, unknown): “The definition is îî ïð ñ ò ó ô õö ï÷ø ù ðú ÷ ñ ó ô õû ïð ú ÷ ù ÷ø ñ (20)”