There is a growing awareness among practitioners and academic researchers that asset returns are non-normally distributed and that the estimation of risk under the assumption of normality can be very bad. Since accurate estimates of risk exposure are a key ingredient for optimal portfolio allocation and asset pricing, methodology is needed to correctly estimate the risk of an investment in assets with non-normal returns. This thesis uses insights and methods from the robust statistics literature to propose methods that help the quantitative investment manager in adequately evaluating his risk exposure.