PRACTICAL INVESTMENT CONSEQUENCES OF THE SCALARIZATION PARAMETER FORMULATION IN DYNAMIC MEAN–VARIANCE PORTFOLIO OPTIMIZATION

Pieter M. van Staden (), Duy-Minh Dang () and Peter A. Forsyth
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Pieter M. van Staden: David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada
Duy-Minh Dang: School of Mathematics and Physics, The University of Queensland, St Lucia, Brisbane 4072, Australia
Peter A. Forsyth: David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada

International Journal of Theoretical and Applied Finance (IJTAF), 2021, vol. 24, issue 05, 1-49

Abstract: We consider the practical investment consequences of implementing the two most popular formulations of the scalarization (or risk-aversion) parameter in the time-consistent dynamic mean–variance (MV) portfolio optimization problem. Specifically, we compare results using a scalarization parameter assumed to be (i) constant and (ii) inversely proportional to the investor’s wealth. Since the link between the scalarization parameter formulation and risk preferences is known to be nontrivial (even in the case where a constant scalarization parameter is used), the comparison is viewed from the perspective of an investor who is otherwise agnostic regarding the philosophical motivations underlying the different formulations and their relation to theoretical risk-aversion considerations, and instead simply wishes to compare investment outcomes of the different strategies. In order to consider the investment problem in a realistic setting, we extend some known results to allow for the case where the risky asset follows a jump-diffusion process, and examine multiple sets of plausible investment constraints that are applied simultaneously. We show that the investment strategies obtained using a scalarization parameter that is inversely proportional to wealth, which enjoys widespread popularity in the literature applying MV optimization in institutional settings, can exhibit some undesirable and impractical characteristics.

Keywords: Asset allocation; constrained optimal control; time consistent; mean–variance (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219024921500291

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