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.