IDEAS home Printed from
   My bibliography  Save this paper

Risk measures and their applications in asset management


  • Birbil, S.I.
  • Frenk, J.B.G.
  • Kaynar, B.
  • N. Nilay, N.


Several approaches exist to model decision making under risk, where risk can be broadly defined as the effect of variability of random outcomes. One of the main approaches in the practice of decision making under risk uses mean-risk models; one such well-known is the classical Markowitz model, where variance is used as risk measure. Along this line, we consider a portfolio selection problem, where the asset returns have an elliptical distribution. We mainly focus on portfolio optimization models constructing portfolios with minimal risk, provided that a prescribed expected return level is attained. In particular, we model the risk by using Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). After reviewing the main properties of VaR and CVaR, we present short proofs to some of the well-known results. Finally, we describe a computationally efficient solution algorithm and present numerical results.

Suggested Citation

  • Birbil, S.I. & Frenk, J.B.G. & Kaynar, B. & N. Nilay, N., 2008. "Risk measures and their applications in asset management," Econometric Institute Research Papers EI 2008-14, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  • Handle: RePEc:ems:eureir:13050

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    2. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2002. "Portfolio Value-at-Risk with Heavy-Tailed Risk Factors," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 239-269.
    3. repec:wsi:ijtafx:v:08:y:2005:i:05:n:s0219024905003104 is not listed on IDEAS
    4. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
    5. Andrzej Ruszczynski & Alexander Shapiro, 2004. "Optimization of Risk Measures," Risk and Insurance 0407002, University Library of Munich, Germany.
    6. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    7. Huisman, R. & Koedijik, K.G. & Pownall, R.A.J., 1998. "VaR-x: Fat Tails in Financial Risk Management," Papers 98-54, Southern California - School of Business Administration.
    8. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    Full references (including those not matched with items on IDEAS)


    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:ems:eureir:13050. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (RePub). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.