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Parametrically computing efficient frontiers of portfolio selection and reporting and utilizing the piecewise-segment structure

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  • Yue Qi

Abstract

Portfolio selection is recognised as the birth-place of modern finance; portfolio optimisation has become a developed tool. However, efficient frontiers are piece-wisely made up by connected parabolic segments; such structure can be rendered only by parametric quadratic programming. Overlooking the structure can both get incomplete results and cause difficulties in e-constraint approaches or weighted-sums approaches. There has been no research to systematically parametrically compute efficient frontiers and report and analyse the structure up until now; in such an area, this article contributes to the literature. I utilise the software of parametric quadratic programming, set up practical portfolio selection models, build batches of 5-stock problems up to 1800-stock problems, analyse the structure, and report the findings. For example, the numbers of parabolic segments can quadratically increase with problem sizes, so fixed numbers of points are insufficient approximations of efficient frontiers. Contrary to common assumptions, an efficient frontier is not smooth in the presence of kinks. Moreover, I utilise the structure for rebalancing portfolios, propose two models to minimise rebalancing cost, transform them into linear programming or integer programming, and solve them. This article can help scholars and practitioners obtain a comprehensive picture of efficient frontiers and perceive the structure.

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  • Yue Qi, 2020. "Parametrically computing efficient frontiers of portfolio selection and reporting and utilizing the piecewise-segment structure," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(10), pages 1675-1690, October.
    • Handle: RePEc:taf:tjorxx:v:71:y:2020:i:10:p:1675-1690
    DOI: 10.1080/01605682.2019.1623477
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    Cited by:

    1. Qi, Yue & Liao, Kezhi & Liu, Tongyang & Zhang, Yu, 2022. "Originating multiple-objective portfolio selection by counter-COVID measures and analytically instigating robust optimization by mean-parameterized nondominated paths," Operations Research Perspectives, Elsevier, vol. 9(C).
    2. Francisco Salas-Molina & David Pla-Santamaria & Juan A. Rodriguez-Aguilar, 2023. "An analytic derivation of the efficient frontier in biobjective cash management and its implications for policies," Annals of Operations Research, Springer, vol. 328(2), pages 1523-1536, September.

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