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Active portfolio management with benchmarking: Adding a value-at-risk constraint

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  • Alexander, Gordon J.
  • Baptista, Alexandre M.

Abstract

We examine the impact of adding a value-at-risk (VaR) constraint to the problem of an active manager who seeks to outperform a benchmark while minimizing tracking error variance (TEV) by using the model of Roll [1992. A mean/variance analysis of tracking error. Journal of Portfolio Management 18, 13-22]. We obtain three main results. First, portfolios on the constrained mean-TEV boundary still exhibit three-fund separation, but the weights of the three funds when the constraint binds differ from those in Roll's model. Second, the constraint mitigates the problem that when an active manager seeks to outperform a benchmark using the mean-TEV model, he or she selects an inefficient portfolio. Finally, when short sales are disallowed, the extent to which the constraint reduces the optimal portfolio's efficiency loss can still be notable but is smaller than when short sales are allowed.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:dyncon:v:32:y:2008:i:3:p:779-820
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    References listed on IDEAS

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    Cited by:

    1. Robert Durand & John Gould & Ross Maller, 2011. "On the performance of the minimum VaR portfolio," The European Journal of Finance, Taylor & Francis Journals, vol. 17(7), pages 553-576.
    2. Ling, Aifan & Sun, Jie & Yang, Xiaoguang, 2014. "Robust tracking error portfolio selection with worst-case downside risk measures," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 178-207.
    3. 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.
    4. 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.
    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. Agarwal, Vikas & Gómez, Juan-Pedro & Priestley, Richard, 2012. "Management compensation and market timing under portfolio constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 36(10), pages 1600-1625.
    7. Hallerbach, W.G.P.M. & Pouchkarev, I., 2005. "A Relative View on Tracking Error," ERIM Report Series Research in Management ERS-2005-063-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    8. Das, Sanjiv R. & Statman, Meir, 2013. "Options and structured products in behavioral portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 137-153.
    9. Dias, Alexandra, 2014. "Semiparametric estimation of multi-asset portfolio tail risk," Journal of Banking & Finance, Elsevier, vol. 49(C), pages 398-408.
    10. Alexander, Gordon J. & Baptista, Alexandre M., 2011. "Portfolio selection with mental accounts and delegation," Journal of Banking & Finance, Elsevier, vol. 35(10), pages 2637-2656, October.
    11. Grauer, Robert R., 2013. "Limiting losses may be injurious to your wealth," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5088-5100.
    12. Alexander, Gordon J. & Baptista, Alexandre M., 2009. "Stress testing by financial intermediaries: Implications for portfolio selection and asset pricing," Journal of Financial Intermediation, Elsevier, vol. 18(1), pages 65-92, January.
    13. Al Janabi, Mazin A.M. & Arreola Hernandez, Jose & Berger, Theo & Nguyen, Duc Khuong, 2017. "Multivariate dependence and portfolio optimization algorithms under illiquid market scenarios," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1121-1131.
    14. Sheng, Jiliang & Wang, Xiaoting & Yang, Jun, 2012. "Incentive contracts in delegated portfolio management under VaR constraint," Economic Modelling, Elsevier, vol. 29(5), pages 1679-1685.
    15. Matteo Del Vigna, 2011. "Ambiguity made easier," Working Papers - Mathematical Economics 2011-07, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    16. Luca RICCETTI, 2010. "Minimum Tracking Error Volatility," Working Papers 340, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    17. Chiang, I-Hsuan Ethan, 2015. "Modern portfolio management with conditioning information," Journal of Empirical Finance, Elsevier, vol. 33(C), pages 114-134.
    18. Sheng, Jiliang & Wang, Jian & Wang, Xiaoting & Yang, Jun, 2014. "Asymmetric contracts, cash flows and risk taking of mutual funds," Economic Modelling, Elsevier, vol. 38(C), pages 435-442.
    19. 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.

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