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The VaR risk measure specifies a probability, Rho, e.g., in the interval [ 0.01, 0.1]. The VaR of a portfolio is the ending wealth level such that at most a fraction Rho of the outcomes that might actually occur, have an ending wealth < VaR. VaR is popular because it is relativiely easy to understand. It is criticised for several reasons: a) It is expensive to compute optimal VaR portfolios when there are lots of scenarios. b) VaR is not a "coherent risk measure." It may suggest that holding a portfolio of just one bond with a 0.04 chance of default is better than holding a 50/50 mix of two independent but equivalent bonds, each with a 0.04 chance of default (and say Rho = 0.05). c) it does not take into account long tails, e.g., a low probability (<< Rho) of losing a huge amount of wealth.