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Reconciling Tracking Error Volatility and Value-at-Risk in Active Portfolio Management: A New Frontier

Author

Listed:
  • Riccardo Lucchetti

    (Università Politecnica delle Marche, Dipartimento di Scienze Economiche e Sociali)

  • Mihaela Nicolau

    (Danubius International University, School of Economics Sciences and Business Administration)

  • Giulio Palomba

    (Università Politecnica delle Marche, Dipartimento di Scienze Economiche e Sociali)

  • Luca Riccetti

    (Università di Macerata, Dipartimento di Economia e Diritto)

Abstract

This article introduces the Risk Balancing Frontier (RBF), a new portfolio boundary in the absolute risk-total return space: the RBF arises when two risk indicators, the Tracking Error Volatility (TEV) and the Value-at-Risk (VaR), are both constrained not to exceed pre-set maximum values. By focusing on the trade-off between the joint restrictions on the two risk indicators, this frontier is the set of all portfolios characterized by the minimum VaR attainable for each TEV level. First, the RBF is defined analytically and its mathematical properties are discussed: we show its connection with the Constrained Tracking Error Volatility Frontier (Jorion in Financ Anal J, 59(5):70–82, 2003. https://doi.org/10.2469/faj.v59.n5.2565 ) and the Constrained Value-at-Risk Frontier (Alexander and Baptista in J Econ Dyn Control, 32(3):779–820, 2008. https://doi.org/10.1016/j.jedc.2007.03.005 ) frontiers. Next, we explore computational issues implied with its construction, and we develop a fast and accurate algorithm to this aim. Finally, we perform an empirical example and consider its relevance in the context of applied finance: we show that the RBF provides a useful tool to investigate and solve potential agency problems.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:compec:v:67:y:2026:i:1:d:10.1007_s10614-024-10684-4
    DOI: 10.1007/s10614-024-10684-4
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    References listed on IDEAS

    as
    1. Manuel Ammann & Heinz Zimmermann, 2001. "Tracking Error and Tactical Asset Allocation," Financial Analysts Journal, Taylor & Francis Journals, vol. 57(2), pages 32-43, March.
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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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