IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v384y2007i2p468-474.html
   My bibliography  Save this article

Risk evaluation with enhanced covariance matrix

Author

Listed:
  • Urbanowicz, Krzysztof
  • Richmond, Peter
  • Hołyst, Janusz A.

Abstract

We propose a route for the evaluation of risk based on a transformation of the covariance matrix. The approach uses a ‘potential’ or ‘objective’ function. This allows us to rescale data from different assets (or sources) such that each data set then has similar statistical properties in terms of their probability distributions. The method is tested using historical data from both the New York and Warsaw stock exchanges.

Suggested Citation

  • Urbanowicz, Krzysztof & Richmond, Peter & Hołyst, Janusz A., 2007. "Risk evaluation with enhanced covariance matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 468-474.
    • Handle: RePEc:eee:phsmap:v:384:y:2007:i:2:p:468-474
    DOI: 10.1016/j.physa.2007.05.034
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437107005729
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2007.05.034?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. Malevergne, Y. & Sornette, D., 2007. "Self-consistent asset pricing models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 149-171.
    2. J. G. Kallberg & W. T. Ziemba, 1983. "Comparison of Alternative Utility Functions in Portfolio Selection Problems," Management Science, INFORMS, vol. 29(11), pages 1257-1276, November.
    3. Coelho, R. & Hutzler, S. & Repetowicz, P. & Richmond, P., 2007. "Sector analysis for a FTSE portfolio of stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 615-626.
    4. Merton, Robert C, 1987. "A Simple Model of Capital Market Equilibrium with Incomplete Information," Journal of Finance, American Finance Association, vol. 42(3), pages 483-510, July.
    5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    6. Andre F. Perold, 1984. "Large-Scale Portfolio Optimization," Management Science, INFORMS, vol. 30(10), pages 1143-1160, October.
    7. Morrel H. Cohen & Vincent D. Natoli, 2002. "Risk and Utility in Portfolio Optimization," Papers cond-mat/0212187, arXiv.org.
    8. Hal Varian, 1993. "A Portfolio of Nobel Laureates: Markowitz, Miller and Sharpe," Journal of Economic Perspectives, American Economic Association, vol. 7(1), pages 159-169, Winter.
    9. Arditti, Fred D & Levy, Haim, 1975. "Portfolio Efficiency Analysis in Three Moments: The Multiperiod Case," Journal of Finance, American Finance Association, vol. 30(3), pages 797-809, June.
    10. Wayne E. Ferson & Andrew F. Siegel, 2001. "The Efficient Use of Conditioning Information in Portfolios," Journal of Finance, American Finance Association, vol. 56(3), pages 967-982, June.
    11. Malgorzata Snarska & Jakub Krzych, 2006. "Automatic Trading Agent. RMT based Portfolio Theory and Portfolio Selection," Papers physics/0608293, arXiv.org.
    12. Akihiko Inoue & Yumiharu Nakano, 2005. "Optimal long term investment model with memory," Papers math/0506621, arXiv.org, revised May 2006.
    13. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 335-346.
    14. Krzysztof Urbanowicz & Janusz A. Holyst, 2005. "Application of noise level estimation for portfolio optimization," Papers physics/0503242, arXiv.org.
    15. P. Richmond, 2001. "Power law distributions and dynamic behaviour of stock markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(4), pages 523-526, April.
    16. Tola, Vincenzo & Lillo, Fabrizio & Gallegati, Mauro & Mantegna, Rosario N., 2008. "Cluster analysis for portfolio optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 235-258, January.
    17. W. T. Ziemba & C. Parkan & R. Brooks-Hill, 1974. "Calculation of Investment Portfolios with Risk Free Borrowing and Lending," Management Science, INFORMS, vol. 21(2), pages 209-222, October.
    18. Chunhachinda, Pornchai & Dandapani, Krishnan & Hamid, Shahid & Prakash, Arun J., 1997. "Portfolio selection and skewness: Evidence from international stock markets," Journal of Banking & Finance, Elsevier, vol. 21(2), pages 143-167, February.
    19. Peter Richmond & Sorin Solomon, 2001. "Power Laws Are Disguised Boltzmann Laws," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 333-343.
    20. Silvio M. Duarte Queiros & Celia Anteneodo & Constantino Tsallis, 2005. "Power-law distributions in economics: a nonextensive statistical approach," Papers physics/0503024, arXiv.org.
    21. Coelho, Ricardo & Gilmore, Claire G. & Lucey, Brian & Richmond, Peter & Hutzler, Stefan, 2007. "The evolution of interdependence in world equity markets—Evidence from minimum spanning trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 455-466.
    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. Ajay Singh & Dinghai Xu, 2016. "Random matrix application to correlations amongst the volatility of assets," Quantitative Finance, Taylor & Francis Journals, vol. 16(1), pages 69-83, January.
    2. Bertram, William K., 2008. "Measuring time dependent volatility and cross-sectional correlation in Australian equity returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3183-3191.

    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. Gautam Mitra & Frank Ellison & Alan Scowcroft, 2007. "Quadratic programming for portfolio planning: Insights into algorithmic and computational issues," Journal of Asset Management, Palgrave Macmillan, vol. 8(3), pages 200-214, September.
    2. Adcock, C.J., 2014. "Mean–variance–skewness efficient surfaces, Stein’s lemma and the multivariate extended skew-Student distribution," European Journal of Operational Research, Elsevier, vol. 234(2), pages 392-401.
    3. Gourieroux, C. & Monfort, A., 2005. "The econometrics of efficient portfolios," Journal of Empirical Finance, Elsevier, vol. 12(1), pages 1-41, January.
    4. Kerstens, Kristiaan & Mounir, Amine & Van de Woestyne, Ignace, 2011. "Geometric representation of the mean-variance-skewness portfolio frontier based upon the shortage function," European Journal of Operational Research, Elsevier, vol. 210(1), pages 81-94, April.
    5. Walter Briec & Kristiaan Kerstens & Octave Jokung, 2007. "Mean-Variance-Skewness Portfolio Performance Gauging: A General Shortage Function and Dual Approach," Management Science, INFORMS, vol. 53(1), pages 135-149, January.
    6. Arturo Lorenzo Valdés & Antonio Ruiz Porras, 2014. "Un modelo Tgarch con una distribución t de student asimétrica y las hipótesis de racionalidad de los inversionistas bursátiles en Latinoamérica," Archivos Revista Economía y Política., Facultad de Ciencias Económicas y Administrativas, Universidad de Cuenca., vol. 19, pages 66-97, Enero.
    7. Haim Levy & Enrico G. De Giorgi & Thorsten Hens, 2012. "Two Paradigms and Nobel Prizes in Economics: a Contradiction or Coexistence?," European Financial Management, European Financial Management Association, vol. 18(2), pages 163-182, March.
    8. Hollstein, Fabian & Nguyen, Duc Binh Benno & Prokopczuk, Marcel, 2019. "Asset prices and “the devil(s) you know”," Journal of Banking & Finance, Elsevier, vol. 105(C), pages 20-35.
    9. Haim Levy, 2010. "The CAPM is Alive and Well: A Review and Synthesis," European Financial Management, European Financial Management Association, vol. 16(1), pages 43-71, January.
    10. Kazemilari, Mansooreh & Mardani, Abbas & Streimikiene, Dalia & Zavadskas, Edmundas Kazimieras, 2017. "An overview of renewable energy companies in stock exchange: Evidence from minimal spanning tree approach," Renewable Energy, Elsevier, vol. 102(PA), pages 107-117.
    11. Gautier Marti & Frank Nielsen & Miko{l}aj Bi'nkowski & Philippe Donnat, 2017. "A review of two decades of correlations, hierarchies, networks and clustering in financial markets," Papers 1703.00485, arXiv.org, revised Nov 2020.
    12. J. Francisco Rubio & Neal Maroney & M. Kabir Hassan, 2018. "Can Efficiency of Returns Be Considered as a Pricing Factor?," Computational Economics, Springer;Society for Computational Economics, vol. 52(1), pages 25-54, June.
    13. Aouni, Belaid & Colapinto, Cinzia & La Torre, Davide, 2014. "Financial portfolio management through the goal programming model: Current state-of-the-art," European Journal of Operational Research, Elsevier, vol. 234(2), pages 536-545.
    14. Levy, Haim & Levy, Moshe, 2021. "Stocks versus bonds for the long run when a riskless asset is available," Journal of Banking & Finance, Elsevier, vol. 133(C).
    15. Leung, Mark T. & Daouk, Hazem & Chen, An-Sing, 2001. "Using investment portfolio return to combine forecasts: A multiobjective approach," European Journal of Operational Research, Elsevier, vol. 134(1), pages 84-102, October.
    16. Haim Levy, 2017. "What is the Economic Cost of the Investment Home Bias?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 49(5), pages 897-929, August.
    17. Vanduffel, Steven & Yao, Jing, 2017. "A stein type lemma for the multivariate generalized hyperbolic distribution," European Journal of Operational Research, Elsevier, vol. 261(2), pages 606-612.
    18. Zhang, Yiting & Lee, Gladys Hui Ting & Wong, Jian Cheng & Kok, Jun Liang & Prusty, Manamohan & Cheong, Siew Ann, 2011. "Will the US economy recover in 2010? A minimal spanning tree study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 2020-2050.
    19. Bai, Zhidong & Liu, Huixia & Wong, Wing-Keung, 2016. "Making Markowitz's Portfolio Optimization Theory Practically Useful," MPRA Paper 74360, University Library of Munich, Germany.
    20. Joro, Tarja & Na, Paul, 2006. "Portfolio performance evaluation in a mean-variance-skewness framework," European Journal of Operational Research, Elsevier, vol. 175(1), pages 446-461, November.

    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:phsmap:v:384:y:2007:i:2:p:468-474. 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.