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Alex Shkolnik presents “The Dispersion Bias” at the Financial Risks International Forum in Paris
March 26, 2018 - March 27, 2018
The explosive growth in the area of data-driven risk factor identification elevates the importance of analyzing and, to the extent possible, mitigating estimation error. Using random matrix theory, we show how a large, estimation-error-induced bias in the sample eigenvectors of factor-based covariance matrices affects portfolio construction and risk estimation. We develop a bias correction approach for the first sample eigenvector which corrects the problems of portfolio construction and risk estimation. Our approach is distinct from the regularization and eigenvalue shrinkage methods found in the literature. We provide theoretical guarantees on the improvement our correction provides as well as estimation methods for computing the optimal correction from data. We conclude with simulations illustrating the profound impact of our correction on financial portfolio construction and risk management.