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Fast Quadratic Programming for Mean-Variance Portfolio Optimisation

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Abstract

In this paper, a vectorised quadratic convex optimisation algorithm based on Matlab’s quadprog built-in function is proposed. We target specifically a classic problem confronted by portfolio analysts, that of optimising asset allocation when choosing among several asset classes, in the context of Markowitz’s modern portfolio theory. Simulating return trajectories for several asset classes, we formulate the optimisation routine in such a way that is able to handle multiple scenarios at the same time, instead of on a one-by-one basis, reducing computational times significantly, without introducing observable estimation errors. A sensitivity analysis is offered with respect to the optimal batch size.

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Notes

  1. Among others, frequently reported are the large estimation errors in the variance-covariance matrix that might lead to counter-intuitive portfolios, as a result of its backward-looking approach and the questionable suitability of variance as the most appropriate portfolio risk measure

  2. Equivalent to Eq. 5 is the return maximisation problem of \({\max \limits } \mathbf {r}^{T} \mathbf {w}, \text {s.t.} \frac {1}{2}\mathbf {w}^{T} {\Sigma } \mathbf {w} = \sigma _{0}\) and the risk minimisation problem of \(\min \limits \frac {1}{2}\mathbf {w}^{T} {\Sigma } \mathbf {w}, \text {s.t.} \mathbf {r}^{T}\mathbf {w} = r_{0}\).

  3. The problem presented here is the sparse interior-point where bounds are combined with linear constraints. For the full predictor-corrector problem, where bounds and constraints are not combined, see references stated above.

  4. The assumptions of normality and independence can be of course challenged by using more advanced models that incorporate serial correlation in asset returns. Nevertheless, a more thorough study of the stylised facts of asset returns is beyond the scope of this study.

  5. All simulation runs and statistical analysis were performed on a Macbook Pro Core i5, 2.4 GHz with 8 GB RAM.

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Authors and Affiliations

  1. Department of Econometrics, Business Statistics, Monash University, Wellington Rd, Clayton, Victoria, 3800, Australia

    Vasileios E. Kontosakos

  2. Group Risk, Allianz SE, Königinstrasse 28, 80802, Munich, Bavaria, Germany

    Vasileios E. Kontosakos

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Correspondence to Vasileios E. Kontosakos.

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Kontosakos, V.E. Fast Quadratic Programming for Mean-Variance Portfolio Optimisation. SN Oper. Res. Forum 1, 25 (2020). https://doi.org/10.1007/s43069-020-00025-0

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