Recent experience with emerging market investments and hedge funds has highlighted the fact that risk parameters are unstable. To address this problem, we introduce a procedure for identifying multivariate outliers and use the outliers to estimate a new covariance matrix. We suggest that a covariance matrix estimated from outliers characterizes a portfolio’s riskiness during market turbulence better than a full-sample covariance matrix. We also introduce a procedure for blending an inside-sample covariance matrix with one from an outlier sample. This procedure enables one to express views about the likelihood of each risk regime and to differentiate one’s aversion to them. Our framework collapses to the Markowitz mean–variance model if (1) we set the probabilities of the inside and outlying covariance matrixes equal to their empirical frequencies, (2) we are equally averse to both risk regimes, and (3) we estimate the inside and outlying covariances around the full sample’s mean.