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Sample covariance matrices tend to underestimate the risk of optimized portfolios. In this article, we identify special portfolios, termed “eigenportfolios,” that capture these systematic biases. Further, we present a methodology for estimating eigenportfolio biases and for adjusting the covariance matrix to remove these biases. We show that this procedure effectively removes the biases of optimized portfolios. We demonstrate that the adjusted covariance matrices are effective at reducing the out-of-sample volatilities of optimized portfolios.