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Regression, multicollinearity and Markowitz

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  • Ortiz, Roberto
  • Contreras, Mauricio
  • Mellado, Cristhian

Abstract

This paper shows that the usual drawbacks of the Markowitz model (high optimal weights, high volatility and low out-of-sample performance) can be overcome by correcting for the multicollinearity of individual assets that directly affect the estimation of portfolio weights. That improves the stability, predictability and out-of-sample performance of the Markowitz model, allowing it to provide better results than the 1/n rule.

Suggested Citation

  • Ortiz, Roberto & Contreras, Mauricio & Mellado, Cristhian, 2023. "Regression, multicollinearity and Markowitz," Finance Research Letters, Elsevier, vol. 58(PC).
  • Handle: RePEc:eee:finlet:v:58:y:2023:i:pc:s1544612323009224
    DOI: 10.1016/j.frl.2023.104550
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    References listed on IDEAS

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    1. DeMiguel, Victor & Martin-Utrera, Alberto & Nogales, Francisco J., 2013. "Size matters: Optimal calibration of shrinkage estimators for portfolio selection," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3018-3034.
    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. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    4. Olivier Ledoit & Michael Wolf, 2017. "Nonlinear Shrinkage of the Covariance Matrix for Portfolio Selection: Markowitz Meets Goldilocks," The Review of Financial Studies, Society for Financial Studies, vol. 30(12), pages 4349-4388.
    5. Klein, Roger W. & Bawa, Vijay S., 1976. "The effect of estimation risk on optimal portfolio choice," Journal of Financial Economics, Elsevier, vol. 3(3), pages 215-231, June.
    6. Barry, Christopher B, 1974. "Portfolio Analysis under Uncertain Means, Variances, and Covariances," Journal of Finance, American Finance Association, vol. 29(2), pages 515-522, May.
    7. Gabor Papp & Szilard Pafka & Maciej A. Nowak & Imre Kondor, 2005. "Random Matrix Filtering in Portfolio Optimization," Papers physics/0509235, arXiv.org.
    8. Brown, S., 1979. "The Effect of Estimation Risk on Capital Market Equilibrium," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 14(2), pages 215-220, June.
    9. MacKinlay, A Craig & Pastor, Lubos, 2000. "Asset Pricing Models: Implications for Expected Returns and Portfolio Selection," The Review of Financial Studies, Society for Financial Studies, vol. 13(4), pages 883-916.
    10. Roberto Ortiz & Mauricio Contreras & Cristhian Mellado, 2022. "Improving the volatility of the optimal weights of the Markowitz model," Economic Research-Ekonomska Istraživanja, Taylor & Francis Journals, vol. 35(1), pages 2836-2858, December.
    11. Olivier Ledoit & Michael Wolf, 2019. "The power of (non-)linear shrinking: a review and guide to covariance matrix estimation," ECON - Working Papers 323, Department of Economics - University of Zurich, revised Feb 2020.
    12. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    13. Mark Britten‐Jones, 1999. "The Sampling Error in Estimates of Mean‐Variance Efficient Portfolio Weights," Journal of Finance, American Finance Association, vol. 54(2), pages 655-671, April.
    14. 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.
    15. Goto, Shingo & Xu, Yan, 2015. "Improving Mean Variance Optimization through Sparse Hedging Restrictions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 50(6), pages 1415-1441, December.
    16. Shapour Mohammadi, 2022. "A test of harmful multicollinearity: A generalized ridge regression approach," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(3), pages 724-743, February.
    17. 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.
    18. Best, Michael J & Grauer, Robert R, 1991. "On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results," The Review of Financial Studies, Society for Financial Studies, vol. 4(2), pages 315-342.
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    More about this item

    Keywords

    Markowitz mean–variance optimization G11; Estimation of optimal portfolio weights G11; Financial econometrics C58; Multicollinearity C58;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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