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A unified approach to portfolio selection in a tracking error framework with additional constraints on risk

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  • Stucchi, Patrizia

Abstract

Most methods of performance evaluation and most allocation strategies are based on tracking error, that is the excess return of the managed portfolio with respect to the benchmark return. Analysis of the tracking error in a mean-variance framework has been performed by Roll (1992) who also investigated the impact of additional beta constraints, while Jorion (2003) considers constraints on total risk (portfolio variance). Alexander and Baptista (2010) add a constraint on the alpha of minimum tracking error variance portfolios. In other recent works, Alexander and Baptista (2008) and Palomba and Riccetti (2012) analyze the problem with Value at Risk (VaR) constraints under return normality assumption. This paper investigates the relationships between all these different approaches and provides a unified treatment. Moreover, analysis of the frontier of Conditional VaR constrained tracking error variance has been performed.

Suggested Citation

  • Stucchi, Patrizia, 2015. "A unified approach to portfolio selection in a tracking error framework with additional constraints on risk," The Quarterly Review of Economics and Finance, Elsevier, vol. 56(C), pages 165-174.
    • Handle: RePEc:eee:quaeco:v:56:y:2015:i:c:p:165-174
    DOI: 10.1016/j.qref.2014.09.008
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    References listed on IDEAS

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    1. Alexander, Gordon J. & Baptista, Alexandre M., 2010. "Active portfolio management with benchmarking: A frontier based on alpha," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2185-2197, September.
    2. Palomba, Giulio & Riccetti, Luca, 2012. "Portfolio frontiers with restrictions to tracking error volatility and value at risk," Journal of Banking & Finance, Elsevier, vol. 36(9), pages 2604-2615.
    3. Alexander, Gordon J. & Baptista, Alexandre M., 2008. "Active portfolio management with benchmarking: Adding a value-at-risk constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 779-820, March.
    4. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    5. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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    Cited by:

    1. 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.
    2. Andrey Sarantsev, 2021. "Optimal Portfolio with Power Utility of Absolute and Relative Wealth," Papers 2105.08139, arXiv.org, revised Jul 2021.
    3. Yang, Jen-Wei, 2024. "Benchmark-based strategy for minimizing Riskiness," Finance Research Letters, Elsevier, vol. 60(C).
    4. 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.
    5. Sarantsev, Andrey, 2021. "Optimal portfolio with power utility of absolute and relative wealth," Statistics & Probability Letters, Elsevier, vol. 179(C).
    6. Sant’Anna, Leonardo R. & Filomena, Tiago P. & Caldeira, João F., 2017. "Index tracking and enhanced indexing using cointegration and correlation with endogenous portfolio selection," The Quarterly Review of Economics and Finance, Elsevier, vol. 65(C), pages 146-157.

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    More about this item

    Keywords

    Portfolio frontiers; Tracking error; Risk management; Value at Risk (VaR); Conditional VaR (CVaR);
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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