IDEAS home Printed from https://ideas.repec.org/a/eee/jbfina/v31y2007i5p1545-1573.html
   My bibliography  Save this article

Noise sensitivity of portfolio selection under various risk measures

Author

Listed:
  • Kondor, Imre
  • Pafka, Szilard
  • Nagy, Gabor

Abstract

We study the sensitivity to estimation error of portfolios optimized under various risk measures, including variance, absolute deviation, expected shortfall and maximal loss. We introduce a measure of portfolio sensitivity and test the various risk measures by considering simulated portfolios of varying sizes N and for different lengths T of the time series. We find that the effect of noise is very strong in all the investigated cases, asymptotically it only depends on the ratio N/T, and diverges at a critical value of N/T, that depends on the risk measure in question. This divergence is the manifestation of a phase transition, analogous to the algorithmic phase transitions recently discovered in a number of hard computational problems. The transition is accompanied by a number of critical phenomena, including the divergent sample to sample fluctuations of portfolio weights. While the optimization under variance and mean absolute deviation is always feasible below the critical value of N/T, expected shortfall and maximal loss display a probabilistic feasibility problem, in that they can become unbounded from below already for small values of the ratio N/T, and then no solution exists to the optimization problem under these risk measures. Although powerful filtering techniques exist for the mitigation of the above instability in the case of variance, our findings point to the necessity of developing similar filtering procedures adapted to the other risk measures where they are much less developed or nonexistent. Another important message of this study is that the requirement of robustness (noise-tolerance) should be given special attention when considering the theoretical and practical criteria to be imposed on a risk measure.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Kondor, Imre & Pafka, Szilard & Nagy, Gabor, 2007. "Noise sensitivity of portfolio selection under various risk measures," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1545-1573, May.
  • Handle: RePEc:eee:jbfina:v:31:y:2007:i:5:p:1545-1573
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378-4266(07)00005-2
    Download Restriction: Full text for ScienceDirect subscribers only

    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. Eun, Cheol S & Resnick, Bruce G, 1984. "Estimating the Correlation Structure of International Share Prices," Journal of Finance, American Finance Association, vol. 39(5), pages 1311-1324, December.
    2. Jorion, Philippe, 1986. "Bayes-Stein Estimation for Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(3), pages 279-292, September.
    3. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    4. Frankfurter, George M. & Phillips, Herbert E. & Seagle, John P., 1971. "Portfolio Selection: The Effects of Uncertain Means, Variances, and Covariances," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6(5), pages 1251-1262, December.
    5. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    6. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    7. Louis K.C. Chan & Jason Karceski & Josef Lakonishok, 1999. "On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model," NBER Working Papers 7039, National Bureau of Economic Research, Inc.
    8. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    9. Szilard Pafka & Imre Kondor, 2001. "Noisy Covariance Matrices and Portfolio Optimization," Papers cond-mat/0111503, arXiv.org.
    10. Elton, Edwin J & Gruber, Martin J, 1973. "Estimating the Dependence Structure of Share Prices-Implications for Portfolio Selection," Journal of Finance, American Finance Association, vol. 28(5), pages 1203-1232, December.
    11. Frost, Peter A. & Savarino, James E., 1986. "An Empirical Bayes Approach to Efficient Portfolio Selection," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(3), pages 293-305, September.
    12. Pafka, Szilárd & Kondor, Imre, 2003. "Noisy covariance matrices and portfolio optimization II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 487-494.
    13. Yusif Simaan, 1997. "Estimation Risk in Portfolio Selection: The Mean Variance Model Versus the Mean Absolute Deviation Model," Management Science, INFORMS, vol. 43(10), pages 1437-1446, October.
    14. Laurent Laloux & Pierre Cizeau & Jean-Philippe Bouchaud & Marc Potters, 1999. "Random matrix theory and financial correlations," Science & Finance (CFM) working paper archive 500053, Science & Finance, Capital Fund Management.
    15. Gabor Papp & Szilard Pafka & Maciej A. Nowak & Imre Kondor, 2005. "Random Matrix Filtering in Portfolio Optimization," Papers physics/0509235, arXiv.org.
    16. Chan, Louis K C & Karceski, Jason & Lakonishok, Josef, 1999. "On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 937-974.
    17. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
    18. Martin R. Young, 1998. "A Minimax Portfolio Selection Rule with Linear Programming Solution," Management Science, INFORMS, vol. 44(5), pages 673-683, May.
    19. Dickinson, J. P., 1974. "The Reliability of Estimation Procedures in Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 9(3), pages 447-462, June.
    Full references (including those not matched with items on IDEAS)

    More about this item

    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:31:y:2007:i:5:p:1545-1573. 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: (Haili He). General contact details of provider: http://www.elsevier.com/locate/jbf .

    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.