IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/10089.html
   My bibliography  Save this paper

Improved estimation of the covariance matrix of stock returns with an application to portfolio selection

Author

Listed:
  • Ledoit, Olivier
  • Wolf, Michael

Abstract

This paper proposes to estimate the covariance matrix of stock returns by an optimally weighted average of two existing estimators. The sample covariance matrix and single-index covariance matrix. This method is generally known as shrinkage, and it is standard in decision theory and in empirical Bayesian statistics. Our shrinkage estimator can be seen as a way to account for extra-market covariance without having to specify an arbitrary multi-factor structure. For NYSE and AMEX stock returns from 1972 to 1995, it can be used to select portfolios with significantly lower out-of-sample variance than a set of existing estimators, including multifactor models.

Suggested Citation

  • Ledoit, Olivier & Wolf, Michael, 2000. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," DES - Working Papers. Statistics and Econometrics. WS 10089, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:10089
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/bitstream/handle/10016/10089/ws0077.pdf?sequence=1
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    2. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    3. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    4. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    5. William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
    6. Connor, Gregory & Korajczyk, Robert A, 1993. "A Test for the Number of Factors in an Approximate Factor Model," Journal of Finance, American Finance Association, vol. 48(4), pages 1263-1291, September.
    7. Roll, Richard, 1977. "A critique of the asset pricing theory's tests Part I: On past and potential testability of the theory," Journal of Financial Economics, Elsevier, vol. 4(2), pages 129-176, March.
    8. Fama, Eugene F. & French, Kenneth R., 1997. "Industry costs of equity," Journal of Financial Economics, Elsevier, vol. 43(2), pages 153-193, February.
    9. Roll, Richard & Ross, Stephen A, 1980. "An Empirical Investigation of the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 35(5), pages 1073-1103, December.
    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. Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-636, May-June.
    13. Kandel, Shmuel & Stambaugh, Robert F, 1995. "Portfolio Inefficiency and the Cross-Section of Expected Returns," Journal of Finance, American Finance Association, vol. 50(1), pages 157-184, March.
    14. Rosenberg, Barr, 1974. "Extra-Market Components of Covariance in Security Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 9(2), pages 263-274, March.
    Full references (including those not matched with items on IDEAS)

    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. Jon Poynter & James Winder & Tzu Tai, 2015. "An analysis of co-movements in industrial sector indices over the last 30 years," Review of Quantitative Finance and Accounting, Springer, vol. 44(1), pages 69-88, January.
    2. Zura Kakushadze & Willie Yu, 2016. "Multifactor Risk Models and Heterotic CAPM," Papers 1602.04902, arXiv.org, revised Mar 2016.
    3. Dimson, Elroy & Mussavian, Massoud, 1999. "Three centuries of asset pricing," Journal of Banking & Finance, Elsevier, vol. 23(12), pages 1745-1769, December.
    4. Sebastien Valeyre, 2020. "Refined model of the covariance/correlation matrix between securities," Papers 2001.08911, arXiv.org.
    5. Zura Kakushadze, 2015. "Heterotic Risk Models," Papers 1508.04883, arXiv.org, revised Jan 2016.
    6. Zura Kakushadze & Willie Yu, 2016. "Statistical Risk Models," Papers 1602.08070, arXiv.org, revised Jan 2017.
    7. Bruce N. Lehmann & David M. Modest, 1985. "Mutual Fund Performance Evaluation: A Comparison of Benchmarks and Benchmark Comparisons," NBER Working Papers 1721, National Bureau of Economic Research, Inc.
    8. Coën, Alain & Hübner, Georges, 2009. "Risk and performance estimation in hedge funds revisited: Evidence from errors in variables," Journal of Empirical Finance, Elsevier, vol. 16(1), pages 112-125, January.
    9. Don U.A. Galagedera, 2004. "A survey on risk-return analysis," Finance 0406010, University Library of Munich, Germany.
    10. Fernando Rubio, 2005. "Eficiencia De Mercado, Administracion De Carteras De Fondos Y Behavioural Finance," Finance 0503028, University Library of Munich, Germany, revised 23 Jul 2005.
    11. Guerard, John B. & Markowitz, Harry & Xu, GanLin, 2015. "Earnings forecasting in a global stock selection model and efficient portfolio construction and management," International Journal of Forecasting, Elsevier, vol. 31(2), pages 550-560.
    12. 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.
    13. Martin Gold, 2010. "Fiduciary Finance," Books, Edward Elgar Publishing, number 13813.
    14. Gregory Connor & Lisa R. Goldberg & Robert A. Korajczyk, 2010. "Portfolio Risk Analysis," Economics Books, Princeton University Press, edition 1, number 9224.
    15. Plachel, Lukas, 2019. "A unified model for regularized and robust portfolio optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 109(C).
    16. Attiya Y. Javid & Eatzaz Ahmad, 2008. "The Conditional Capital Asset Pricing Model: Evidence from Karachi Stock Exchange," PIDE-Working Papers 2008:48, Pakistan Institute of Development Economics.
    17. Nigel Meade & Gerry Salkin, 2000. "The selection of multinational equity portfolios: forecasting models and estimation risk," The European Journal of Finance, Taylor & Francis Journals, vol. 6(3), pages 259-279.
    18. Gillen, Benjamin J., 2014. "An empirical Bayesian approach to stein-optimal covariance matrix estimation," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 402-420.
    19. Michailidis, G., 2009. "Multivariate methods in examining macroeconomic variables effect on Greek stock market returns, 1997-2004," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 9(1).
    20. Attiya Y. Javed, 2000. "Alternative Capital Asset Pricing Models: A Review of Theory and Evidence," PIDE-Working Papers 2000:179, Pakistan Institute of Development Economics.

    More about this item

    Keywords

    Covariance matrix estimation;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • 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
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

    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:cte:wsrepe:10089. 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: . General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    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: Ana Poveda (email available below). General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    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.