Browsing by Subject "robust optimization"

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    Linearly constrained robust portfolio construction using Bauer-Householder bounds on the condition number
    (2026) Dalmeyer; Lara; Gebbie, Timothy
    We investigate and extend the result that the angle between the direction of expected returns and the optimal portfolio weights from unconstrained quadratic portfolio optimisations have an upper bound dependent on the condition number of the covariance matrix. This is known to imply that better conditioned covariance matrices produce weights from unconstrained mean-variance optimisations that are better aligned with each assets expected return. Here we relate the inequality between the angle spanning the expected returns vector α and the optimal weight vector θ – the so called α-weight angle and the condition number, to extend the result to include portfolio optimisations with gearing constraints to provide an extended family of robust optimisations, using the Bauer and Householder inequality. The Bauer and Householder inequality is an extension of the Kantorovich inequality which has been used to establish the unconstrained α-weight angle bounds. We use this to argue that the equally weighted portfolio is in general not preferable to the mean-variance portfolio even with poor forecast ability and a badly conditioned covariance matrix. A new shrinkage methodology directly using the α-weight angle is proposed and investigated, and shown to be superior to a collection of standard shrinkage methodologies known in the literature. We consider simulations for the behavior of the α-weight angle to demonstrate the theoretical results. We argue that even if there is naive knowledge about future expected returns, the new method is preferred.