Covariance Matrix Regularization for Portfolio Selection: Achieving Desired Risk

Sammanfattning: The modus operandi of most asset managers is to promise clients an annual risk target, where risk is measured by realized standard deviation of portfolio returns. Moreover, Markowitz (1952) portfolio selection requires an estimate of the covariance matrix of the returns of the financial instruments under consideration. To address both these problems, we develop a data-driven method for covariance matrix regularization. The data-driven method critically depends on a novel risk targeting loss function. In addition, the risk targeting loss function is analyzed under large-dimensional asymptotics, resulting in an asymptotically optimal covarinace matrix regularization. In an ex-post analysis, using historical price data from multiple future markets, the data-driven method outperforms other regularization methods compared against.