GEOMETRIC INSIGHTS INTO ROBUST PORTFOLIO CONSTRUCTION

Lara Dalmeyer () and Tim Gebbie
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Lara Dalmeyer: Department of Statistical Sciences, University of Cape Town, Rondebosch, Cape Town 7700, South Africa
Tim Gebbie: Department of Statistical Sciences, University of Cape Town, Rondebosch, Cape Town 7700, South Africa

International Journal of Theoretical and Applied Finance (IJTAF), 2024, vol. 27, issue 07n08, 1-46

Abstract: We investigate and extend the result that an α-weight angle from unconstrained quadratic portfolio optimizations has 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 optimizations that are better aligned with each asset’s expected return. Here, we relate the inequality between the α-weight angle and the condition number to extend the result to include portfolio optimizations with gearing constraints to provide an extended family of robust optimizations. 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.

Keywords: Mean-variance optimization; Kantorovich inequality; gearing constraints; robust optimization (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0219024924500249

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