IDEAS home Printed from https://ideas.repec.org/a/eee/jbfina/v36y2012i9p2604-2615.html
   My bibliography  Save this article

Portfolio frontiers with restrictions to tracking error volatility and value at risk

Author

Listed:
  • Palomba, Giulio
  • Riccetti, Luca

Abstract

Asset managers are often given the task of restricting their activity by keeping both the value at risk (VaR) and the tracking error volatility (TEV) under control. However, these constraints may be impossible to satisfy simultaneously because VaR is independent of the benchmark portfolio. The management of these restrictions is likely to affect portfolio performance and produces a wide variety of scenarios in the risk-return space. The aim of this paper is to analyse various interactions between portfolio frontiers when risk managers impose joint restrictions upon TEV and VaR. Specifically, we provide analytical solutions for all the intersections and we propose simple numerical methods when such solutions are not available. Finally, we introduce a new portfolio frontier.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jbfina:v:36:y:2012:i:9:p:2604-2615
    DOI: 10.1016/j.jbankfin.2012.05.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378426612001422
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jbankfin.2012.05.014?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Campbell, Rachel & Huisman, Ronald & Koedijk, Kees, 2001. "Optimal portfolio selection in a Value-at-Risk framework," Journal of Banking & Finance, Elsevier, vol. 25(9), pages 1789-1804, September.
    2. Luca Riccetti, 2012. "Using tracking error volatility to check active management and fee level of investment funds," Global Business and Economics Review, Inderscience Enterprises Ltd, vol. 14(3), pages 139-158.
    3. Giulio Palomba, 2008. "Multivariate GARCH models and the Black-Litterman approach for tracking error constrained portfolios: an empirical analysis," Global Business and Economics Review, Inderscience Enterprises Ltd, vol. 10(4), pages 379-413.
    4. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1683, August.
    5. Isabelle Bajeux‐Besnainou & Riadh Belhaj & Didier Maillard & Roland Portait, 2011. "Portfolio Optimization Under Tracking Error And Weights Constraints," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 34(2), pages 295-330, June.
    6. Phelim Boyle & Weidong Tian, 2007. "Portfolio Management With Constraints," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 319-343, July.
    7. K. J. Martijn Cremers & Antti Petajisto, 2009. "How Active Is Your Fund Manager? A New Measure That Predicts Performance," The Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3329-3365, September.
    8. 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.
    9. Martijn Cremers & Antti Petajisto, 2006. "How Active is Your Fund Manager? A New Measure That Predicts Performance," Yale School of Management Working Papers amz2370, Yale School of Management, revised 01 May 2009.
    10. Nadima El-Hassan & Paul Kofman, 2003. "Tracking Error and Active Portfolio Management," Australian Journal of Management, Australian School of Business, vol. 28(2), pages 183-207, September.
    11. Gaivoronski, Alexei A. & Krylov, Sergiy & van der Wijst, Nico, 2005. "Optimal portfolio selection and dynamic benchmark tracking," European Journal of Operational Research, Elsevier, vol. 163(1), pages 115-131, May.
    12. 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.
    13. N Wagner, 2002. "On a model of portfolio selection with benchmark," Journal of Asset Management, Palgrave Macmillan, vol. 3(1), pages 55-65, July.
    14. Gordon Alexander, 2009. "From Markowitz to modern risk management," The European Journal of Finance, Taylor & Francis Journals, vol. 15(5-6), pages 451-461.
    15. Sid Browne, 1999. "Beating a moving target: Optimal portfolio strategies for outperforming a stochastic benchmark," Finance and Stochastics, Springer, vol. 3(3), pages 275-294.
    16. Luca RICCETTI, 2010. "Minimum Tracking Error Volatility," Working Papers 340, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    17. repec:bla:jfinan:v:58:y:2003:i:4:p:1651-1684 is not listed on IDEAS
    18. Rudolf, Markus & Wolter, Hans-Jurgen & Zimmermann, Heinz, 1999. "A linear model for tracking error minimization," Journal of Banking & Finance, Elsevier, vol. 23(1), pages 85-103, January.
    19. Alexander, Gordon J. & Baptista, Alexandre M., 2006. "Portfolio selection with a drawdown constraint," Journal of Banking & Finance, Elsevier, vol. 30(11), pages 3171-3189, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Huang, Jinbo & Li, Yong & Yao, Haixiang, 2022. "Partial moments and indexation investment strategies," Journal of Empirical Finance, Elsevier, vol. 67(C), pages 39-59.
    2. Alberto Russo, 2014. "A Stochastic Model of Wealth Accumulation with Class Division," Metroeconomica, Wiley Blackwell, vol. 65(1), pages 1-35, February.
    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. Ruggero Grilli & Gabriele Tedeschi & Mauro Gallegati, 2015. "Markets connectivity and financial contagion," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(2), pages 287-304, October.
    5. Grobys, Klaus, 2023. "Correlation versus co-fractality: Evidence from foreign-exchange-rate variances," International Review of Financial Analysis, Elsevier, vol. 86(C).
    6. Elena AMBROSETTI & Eralba CELA & Tineke FOKKEMA, 2011. "The Remittances Behaviour of the Second Generation in Europe: Altruism or Self-Interest?," Working Papers 368, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    7. Alessandro STERLACCHINI, 2012. "Patent Oppositions as Competitive Tools: An Analysis of the Major Players in the European Market of White Goods," Working Papers 374, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    8. 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.
    9. 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.
    10. Lenzu, Simone & Tedeschi, Gabriele, 2012. "Systemic risk on different interbank network topologies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(18), pages 4331-4341.
    11. Huang, Jinbo & Li, Yong & Yao, Haixiang, 2018. "Index tracking model, downside risk and non-parametric kernel estimation," Journal of Economic Dynamics and Control, Elsevier, vol. 92(C), pages 103-128.
    12. Ling, Aifan & Li, Junxue & Wen, Limin & Zhang, Yi, 2023. "When trackers are aware of ESG: Do ESG ratings matter to tracking error portfolio performance?," Economic Modelling, Elsevier, vol. 125(C).
    13. repec:ajn:abrjou:2019:p:17-28 is not listed on IDEAS
    14. Agata Gemzik-Salwach, 2012. "The Use Of A Value At Risk Measure For The Analysis Of Bank Interest Margins," "e-Finanse", University of Information Technology and Management, Institute of Financial Research and Analysis, vol. 8(4), pages 15-29, February.
    15. Eralba CELA & Tineke FOKKEMA & Elena AMBROSETTI, 2012. "Links Between Transnationalism Integration and Duration of Residence: The Case of eastern European Migrants in Italy," Working Papers 386, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    16. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Luca Riccetti, 2012. "Using tracking error volatility to check active management and fee level of investment funds," Global Business and Economics Review, Inderscience Enterprises Ltd, vol. 14(3), pages 139-158.
    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. Lorenz M. Roebers & Aras Selvi & Juan C. Vera, 2018. "Using Column Generation to Solve Extensions to the Markowitz Model," Papers 1812.00093, arXiv.org, revised Jun 2019.
    5. Lassance, Nathan & Vrins, Frédéric, 2023. "Portfolio selection: A target-distribution approach," European Journal of Operational Research, Elsevier, vol. 310(1), pages 302-314.
    6. 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.
    7. 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.
    8. Giuliano De Rossi & Gurvinder Brar, 2018. "Is high active share always good?," Journal of Asset Management, Palgrave Macmillan, vol. 19(7), pages 460-471, December.
    9. Luca RICCETTI, 2010. "Minimum Tracking Error Volatility," Working Papers 340, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    10. Sarantsev, Andrey, 2021. "Optimal portfolio with power utility of absolute and relative wealth," Statistics & Probability Letters, Elsevier, vol. 179(C).
    11. Tingting Yang & Xiaoxia Huang, 2022. "A New Portfolio Optimization Model Under Tracking-Error Constraint with Linear Uncertainty Distributions," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 723-747, November.
    12. 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.
    13. 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.
    14. Emilio Ricardo Carvalhais & Antonio Marcos Duarte Júnior, 2015. "Indexation of Fixed-Income Portfolios to the IMA-B," Brazilian Business Review, Fucape Business School, vol. 12(3), pages 116-142, May.
    15. Ahmed, Shamim & Bu, Ziwen & Symeonidis, Lazaros & Tsvetanov, Daniel, 2023. "Which factor model? A systematic return covariation perspective," Journal of International Money and Finance, Elsevier, vol. 136(C).
    16. Roy, Suvra & Nguyen, Harvey & Visaltanachoti, Nuttawat, 2023. "Be nice to the air: Severe haze pollution and mutual fund risk," Global Finance Journal, Elsevier, vol. 58(C).
    17. Yang, Jen-Wei, 2024. "Benchmark-based strategy for minimizing Riskiness," Finance Research Letters, Elsevier, vol. 60(C).
    18. Huang, Jinbo & Li, Yong & Yao, Haixiang, 2018. "Index tracking model, downside risk and non-parametric kernel estimation," Journal of Economic Dynamics and Control, Elsevier, vol. 92(C), pages 103-128.
    19. Diana Barro & Elio Canestrelli, 2014. "Downside risk in multiperiod tracking error models," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(2), pages 263-283, June.
    20. Giuseppe Galloppo, 2010. "A Comparison Of Pre And Post Modern Portfolio Theory Using Resampling," Global Journal of Business Research, The Institute for Business and Finance Research, vol. 4(1), pages 1-16.

    More about this item

    Keywords

    Risk management; Asset allocation; Portfolio frontiers; Tracking error volatility (TEV); Value at risk (VaR);
    All these keywords.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jbfina:v:36:y:2012:i:9:p:2604-2615. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jbf .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.