Value at risk (VaR) and Conditional VaR (CVaR) are two common measures of risk that are related to the loss distribution. It is generally believed that if the true loss distribution is heavy-tailed, as compared to the normal, then the risk is higher. We show that in general this is not the case. We derive formulas for VaR and CVaR for mixtures and show that there are instances where the normality assumption overestimates (and the mixture distribution underestimates) the observed market risk. We show examples using market data from different financial firms to confirm our conclusions.