IDEAS home Printed from https://ideas.repec.org/p/anc/wpaper/358.html
   My bibliography  Save this paper

Portfolio Frontiers with Restrictions to Tracking Error Volatility and Value at Risk

Author

Listed:
  • Giulio PALOMBA

    ([n.a.])

  • Luca RICCETTI

    (Universita' Politecnica delle Marche, Dipartimento di Economia)

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 can not always be simultaneously satisfied because the VaR is independent of the benchmark portfolio. The management of these restrictions is likely to affect portfolio performances 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 restrictions upon TEV and VaR are jointly imposed. Analytical solutions for the intersections are provided and short numerical methods are proposed when solutions are not available. Finally, a new portfolio frontier is introduced.

Suggested Citation

  • Giulio PALOMBA & Luca RICCETTI, 2011. "Portfolio Frontiers with Restrictions to Tracking Error Volatility and Value at Risk," Working Papers 358, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
  • Handle: RePEc:anc:wpaper:358
    as

    Download full text from publisher

    File URL: http://docs.dises.univpm.it/web/quaderni/pdf/358.pdf
    File Function: First version, 2011
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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. Luca RICCETTI, 2010. "Minimum Tracking Error Volatility," Working Papers 340, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    5. 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.
    6. 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.
    7. 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.
    8. 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 1651-1684, August.
    9. 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.
    10. N Wagner, 2002. "On a model of portfolio selection with benchmark," Journal of Asset Management, Palgrave Macmillan, vol. 3(1), pages 55-65, July.
    11. Gordon Alexander, 2009. "From Markowitz to modern risk management," The European Journal of Finance, Taylor & Francis Journals, vol. 15(5-6), pages 451-461.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Phelim Boyle & Weidong Tian, 2007. "Portfolio Management With Constraints," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 319-343, July.
    18. K. J. Martijn Cremers & Antti Petajisto, 2009. "How Active Is Your Fund Manager? A New Measure That Predicts Performance," Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3329-3365, September.
    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. Alberto Russo, 2014. "A Stochastic Model of Wealth Accumulation with Class Division," Metroeconomica, Wiley Blackwell, vol. 65(1), pages 1-35, February.
    2. 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).
    3. Huang, Jinbo & Li, Yong & Yao, Haixiang, 2022. "Partial moments and indexation investment strategies," Journal of Empirical Finance, Elsevier, vol. 67(C), pages 39-59.
    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. 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.
    6. 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.
    7. Rangga Handika & Mahjus Ekananda, 2019. "Benefits and Consequences of Diversification: Evidence from Financialzed Commodity Portfolios," Asian Business Research Journal, Sophia, vol. 4(1), pages 17-28.
    8. 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.
    9. 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.
    10. 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.
    11. Grobys, Klaus, 2023. "Correlation versus co-fractality: Evidence from foreign-exchange-rate variances," International Review of Financial Analysis, Elsevier, vol. 86(C).
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    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. 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. 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.
    3. 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).
    4. Lassance, Nathan & Vrins, Frédéric, 2023. "Portfolio selection: A target-distribution approach," European Journal of Operational Research, Elsevier, vol. 310(1), pages 302-314.
    5. 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.
    6. 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.
    7. Menoncin, Francesco & Vigna, Elena, 2017. "Mean–variance target-based optimisation for defined contribution pension schemes in a stochastic framework," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 172-184.
    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. 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.
    10. 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.
    11. Füss, Roland & Miebs, Felix & Trübenbach, Fabian, 2014. "A jackknife-type estimator for portfolio revision," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 14-28.
    12. Giuzio, Margherita & Ferrari, Davide & Paterlini, Sandra, 2016. "Sparse and robust normal and t- portfolios by penalized Lq-likelihood minimization," European Journal of Operational Research, Elsevier, vol. 250(1), pages 251-261.
    13. Lassance, Nathan & Vrins, Frédéric, 2021. "Portfolio selection with parsimonious higher comoments estimation," Journal of Banking & Finance, Elsevier, vol. 126(C).
    14. Behr, Patrick & Guettler, Andre & Truebenbach, Fabian, 2012. "Using industry momentum to improve portfolio performance," Journal of Banking & Finance, Elsevier, vol. 36(5), pages 1414-1423.
    15. Chiang, I-Hsuan Ethan, 2015. "Modern portfolio management with conditioning information," Journal of Empirical Finance, Elsevier, vol. 33(C), pages 114-134.
    16. Harris, Richard D.F. & Stoja, Evarist & Tan, Linzhi, 2017. "The dynamic Black–Litterman approach to asset allocation," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1085-1096.
    17. 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.
    18. 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.
    19. 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.
    20. Massimo Biasin & Roy Cerqueti & Emanuela Giacomini & Nicoletta Marinelli & Anna Grazia Quaranta & Luca Riccetti, 2019. "Macro Asset Allocation with Social Impact Investments," Sustainability, MDPI, vol. 11(11), pages 1-19, June.

    More about this item

    Keywords

    asset allocation; portfolio frontiers; tracking error volatility; value at risk;
    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:anc:wpaper:358. 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: Maurizio Mariotti (email available below). General contact details of provider: https://edirc.repec.org/data/deancit.html .

    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.