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Another Look at Portfolio Optimization under Tracking-Error Constraints

Author

Listed:
  • Philippe Bertrand

    (CERGAM - Centre d'Études et de Recherche en Gestion d'Aix-Marseille - AMU - Aix Marseille Université - UTLN - Université de Toulon)

Abstract

Research has shown that adding constraints to total portfolio volatility can substantially improve the performance of managed portfolios. Although other work has considered constant tracking-error volatility frontiers, in this study tracking error was allowed to vary but the risk aversion was fixed. The resulting optimal portfolios have several desirable properties.Today, the use of benchmark portfolios to evaluate the relative performance of portfolio managers is common practice in the financial management industry. This setup allows the investor to evaluate the added value in line with the risks taken. The relevant concept of risk is the relative risk as defined by the tracking-error volatility (TEV).The problem of minimizing the volatility of tracking error was originally solved in 1992. The optimal portfolios obtained had several undesirable properties, however, and introducing an additional constraint on the beta of the portfolio was suggested.In 2003, the problem was again tackled, this time in a study that pointed out that constant-TEV portfolios are described by an ellipse. Because of the flat shape of this ellipse, adding a constraint on total portfolio volatility can substantially improve the performance of the managed portfolio.This article looks at the problem from another angle. Instead of considering constant-TEV frontiers, the author allowed tracking error to vary but fixed the risk aversion. He found that the resulting optimal portfolios have several desirable properties.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Philippe Bertrand, 2010. "Another Look at Portfolio Optimization under Tracking-Error Constraints," Post-Print hal-01833085, HAL.
    • Handle: RePEc:hal:journl:hal-01833085
    DOI: 10.2469/faj.v66.n3.2
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    Cited by:

    1. Michael Maxwell & Michael Daly & Daniel Thomson & Gary van Vuuren, 2018. "Optimizing tracking error-constrained portfolios," Applied Economics, Taylor & Francis Journals, vol. 50(54), pages 5846-5858, November.
    2. Paskalis Glabadanidis & Leon Zolotoy, 2013. "Benchmark replication portfolio strategies," Journal of Asset Management, Palgrave Macmillan, vol. 14(2), pages 95-110, April.
    3. du Sart, Colin F. & van Vuuren, Gary W., 2021. "Comparing the performance and composition of tracking error constrained and unconstrained portfolios," The Quarterly Review of Economics and Finance, Elsevier, vol. 81(C), pages 276-287.
    4. L. Theron & G. van Vuuren, 2020. "Exploring the Behaviour of Actively Managed, Maximally Diversified Portfolios," Studies in Economics and Econometrics, Taylor & Francis Journals, vol. 44(2), pages 49-72, August.
    5. Giulio PALOMBA & Luca RICCETTI, 2013. "Asset Management with TEV and VaR;Constraints: the Constrained Efficient;Frontiers," Working Papers 392, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    6. Riccardo Lucchetti & Mihaela Nicolau & Giulio Palomba & Luca Riccetti, 2022. "Reconciling TEV and VaR in Active Portfolio Management: A New Frontier," Working Papers 461, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    7. Wade Gunning & Gary van Vuuren, 2019. "Exploring the drivers of tracking error constrained portfolio performance," Cogent Economics & Finance, Taylor & Francis Journals, vol. 7(1), pages 1684181-168, January.
    8. Gabriele Torri & Rosella Giacometti & Sandra Paterlini, 2024. "Penalized enhanced portfolio replication with asymmetric deviation measures," Annals of Operations Research, Springer, vol. 332(1), pages 481-531, January.
    9. Riccardo Lucchetti & Mihaela Nicolau & Giulio Palomba & Luca Riccetti, 2026. "Reconciling Tracking Error Volatility and Value-at-Risk in Active Portfolio Management: A New Frontier," Computational Economics, Springer;Society for Computational Economics, vol. 67(1), pages 83-112, January.

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