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

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  • 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.
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Suggested Citation

  • 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.
  • Handle: RePEc:eee:empfin:v:10:y:2003:i:5:p:603-621
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    References listed on IDEAS

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    1. 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.
    2. William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
    3. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
    4. 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.
    5. 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.
    6. Fama, Eugene F. & French, Kenneth R., 1997. "Industry costs of equity," Journal of Financial Economics, Elsevier, vol. 43(2), pages 153-193, February.
    7. 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.
    8. Rosenberg, Barr, 1974. "Extra-Market Components of Covariance in Security Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 9(02), pages 263-274, March.
    9. 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.
    10. 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.
    11. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    12. 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.
    13. 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(03), pages 293-305, September.
    14. 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.
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    More about this item

    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

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