Robust mean-variance portfolio through the weighted $$L^{p}$$ L p depth function

Portfolios constructed by the classical mean-variance model are very sensitive to outliers. We propose the use of a non-parametric estimation method based on statistical data depth functions. Specifically, we exploit the notion of the weighted $$L^{p}$$ L p depth function to obtain robust estimates of the mean and covariance matrix of the asset returns. This approach has the advantage to be independent of parametric assumptions, and less sensitive to changes in the asset return distribution than traditional techniques. The proposed procedure is evaluated and compared with standard and other robust techniques through simulated and real data. Results indicate effective improvements of the proposed method in terms of out-of-sample performance.