single intuitive number, defined here as the “crash volatility”, to characterize the true left-tail risk as an alternative to … the usual downside deviation. The crash volatility can be fed into a typical mean-variance optimizer, allowing the … optimizer to finally “see” the risk effect of the non-Gaussian distribution. An example using Amaranth's returns before it lost …

This study investigates the simplicity and adequacy of tail-based risk measures-valueat-risk (VaR) and expected … shortfall (ES)-when applied to tail targeting of the extreme value (EV) model. We implement Lévy-VaR and ES risk measures as … 2007-2008, we fnd that the simplicity of tail-based risk management with a tail-targeting EV model is more attractive …