We show that the conservative estimate of the Value-at-Risk (VaR) for the sum of d random losses with given identical marginals and finite mean is equivalent to the corresponding conservative estimate of the Expected Shortfall (ES), in the limit as d → ∞. Examples of interest in quantitative risk management show that the equivalence holds also for relatively small risk portfolios. When the random losses Li have infinite first moment, we show that VaR can be arbitrarily large with respect to the… CONTINUE READING