Orthogonal portfolios to assess estimation risk

Abstract

This document presents the various advantages of using portfolio rules composed by linear combinations of the orthogonal components derived from the optimal solution to a linearly constrained mean–variance portfolio optimization problem. We argue that this practice has value in and of itself since it pushes forward the tractability of the out-of-sample performance measure, and the identification of risk sources in the portfolio. This structure is further used to propose new correction schemes based on shrinkage factors that improve out-of-sample performance, and to study its limiting behavior as both the sample size and the number of assets increase. Additionally, our results are compared with those corresponding to the theoretical and implementable three-fund rules of Kan and Zhou (2007) so the benefits of using orthogonal portfolio rules are highlighted.