A Geometric Approach to Asset Allocation with Investor Views

Herein, a geometric approach that incorporates investor views into portfolio construction is presented. In particular, the proposed approach utilizes the notion of generalized Wasserstein barycenter (GWB) to combine statistical information regarding asset returns with investor views to obtain an updated estimate of asset drifts and covariance as inputs to a mean–variance optimizer. Quantitative comparisons of the proposed geometric approach with the conventional Black–Litterman (BL) model (and a closely related variant) are presented. The proposed geometric approach provides investors with more flexibility in specifying their confidence in their views than conventional BL model-based approaches. Additionally, the geometric approach rewards investors more for making correct decisions than conventional BL model-based approaches. We provide empirical and theoretical justifications for our claim.