IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0067503.html
   My bibliography  Save this article

Directional Variance Adjustment: Bias Reduction in Covariance Matrices Based on Factor Analysis with an Application to Portfolio Optimization

Author

Listed:
  • Daniel Bartz
  • Kerr Hatrick
  • Christian W Hesse
  • Klaus-Robert Müller
  • Steven Lemm

Abstract

Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices derived from the statistical Factor Analysis model exhibit a systematic error, which is similar to the well-known systematic error of the spectrum of the sample covariance matrix. Moreover, we introduce the Directional Variance Adjustment (DVA) algorithm, which diminishes the systematic error. In a thorough empirical study for the US, European, and Hong Kong stock market we show that our proposed method leads to improved portfolio allocation.

Suggested Citation

  • Daniel Bartz & Kerr Hatrick & Christian W Hesse & Klaus-Robert Müller & Steven Lemm, 2013. "Directional Variance Adjustment: Bias Reduction in Covariance Matrices Based on Factor Analysis with an Application to Portfolio Optimization," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-14, July.
    • Handle: RePEc:plo:pone00:0067503
    DOI: 10.1371/journal.pone.0067503
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0067503
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0067503&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0067503?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
    ---><---

    References listed on IDEAS

    as
    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. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    3. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1683, August.
    4. Michael E. Tipping & Christopher M. Bishop, 1999. "Probabilistic Principal Component Analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 611-622.
    5. 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.
    6. Laurent Laloux & Pierre Cizeau & Marc Potters & Jean-Philippe Bouchaud, 2000. "Random Matrix Theory And Financial Correlations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 391-397.
    7. Bernd Scherer, 2004. "Resampled efficiency and portfolio choice," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 18(4), pages 382-398, December.
    8. Schäfer Juliane & Strimmer Korbinian, 2005. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
    9. Gregory Connor & Lisa R. Goldberg & Robert A. Korajczyk, 2010. "Portfolio Risk Analysis," Economics Books, Princeton University Press, edition 1, number 9224.
    10. McLachlan, G.J. & Bean, R.W. & Ben-Tovim Jones, L., 2007. "Extension of the mixture of factor analyzers model to incorporate the multivariate t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5327-5338, July.
    11. 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.
    12. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1684, August.
    13. D. Goldfarb & G. Iyengar, 2003. "Robust Portfolio Selection Problems," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 1-38, February.
    14. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    15. Kourtis, Apostolos & Dotsis, George & Markellos, Raphael N., 2012. "Parameter uncertainty in portfolio selection: Shrinking the inverse covariance matrix," Journal of Banking & Finance, Elsevier, vol. 36(9), pages 2522-2531.
    16. Shanken, Jay, 1992. "On the Estimation of Beta-Pricing Models," Review of Financial Studies, Society for Financial Studies, vol. 5(1), pages 1-33.
    17. Pagan, Adrian R. & Schwert, G. William, 1990. "Testing for covariance stationarity in stock market data," Economics Letters, Elsevier, vol. 33(2), pages 165-170, June.
    18. Campbell, Rachel A.J. & Forbes, Catherine S. & Koedijk, Kees G. & Kofman, Paul, 2008. "Increasing correlations or just fat tails?," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 287-309, March.
    19. Longin, Francois, 2005. "The choice of the distribution of asset returns: How extreme value theory can help?," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 1017-1035, April.
    20. Donald Rubin & Dorothy Thayer, 1982. "EM algorithms for ML factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 47(1), pages 69-76, March.
    21. Jiang, Chonghui & Ma, Yongkai & An, Yunbi, 2010. "An analysis of portfolio selection with background risk," Journal of Banking & Finance, Elsevier, vol. 34(12), pages 3055-3060, December.
    22. Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
    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. Daniel Bartz & Kerr Hatrick & Christian W. Hesse & Klaus-Robert Muller & Steven Lemm, 2011. "Directional Variance Adjustment: improving covariance estimates for high-dimensional portfolio optimization," Papers 1109.3069, arXiv.org, revised Mar 2012.
    2. Wolfgang Karl Hardle & Yegor Klochkov & Alla Petukhina & Nikita Zhivotovskiy, 2022. "Robustifying Markowitz," Papers 2212.13996, arXiv.org.
    3. Plachel, Lukas, 2019. "A unified model for regularized and robust portfolio optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 109(C).
    4. Zhu, Bo & Zhang, Tianlun, 2021. "Long-term wealth growth portfolio allocation under parameter uncertainty: A non-conservative robust approach," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
    5. 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.
    6. Candelon, B. & Hurlin, C. & Tokpavi, S., 2012. "Sampling error and double shrinkage estimation of minimum variance portfolios," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 511-527.
    7. Liusha Yang & Romain Couillet & Matthew R. McKay, 2015. "A Robust Statistics Approach to Minimum Variance Portfolio Optimization," Papers 1503.08013, arXiv.org.
    8. Fan, Jianqing & Liao, Yuan & Shi, Xiaofeng, 2015. "Risks of large portfolios," Journal of Econometrics, Elsevier, vol. 186(2), pages 367-387.
    9. Füss, Roland & Miebs, Felix & Trübenbach, Fabian, 2014. "A jackknife-type estimator for portfolio revision," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 14-28.
    10. Jianqing Fan & Jingjin Zhang & Ke Yu, 2008. "Asset Allocation and Risk Assessment with Gross Exposure Constraints for Vast Portfolios," Papers 0812.2604, arXiv.org.
    11. Yan, Cheng & Zhang, Huazhu, 2017. "Mean-variance versus naïve diversification: The role of mispricing," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 48(C), pages 61-81.
    12. Long Zhao & Deepayan Chakrabarti & Kumar Muthuraman, 2019. "Portfolio Construction by Mitigating Error Amplification: The Bounded-Noise Portfolio," Operations Research, INFORMS, vol. 67(4), pages 965-983, July.
    13. Santos, André Alves Portela & Ferreira, Alexandre R., 2017. "On the choice of covariance specifications for portfolio selection problems," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 37(1), May.
    14. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    15. Johannes Bock, 2018. "An updated review of (sub-)optimal diversification models," Papers 1811.08255, arXiv.org.
    16. Branger, Nicole & Lučivjanská, Katarína & Weissensteiner, Alex, 2019. "Optimal granularity for portfolio choice," Journal of Empirical Finance, Elsevier, vol. 50(C), pages 125-146.
    17. De Nard, Gianluca & Zhao, Zhao, 2023. "Using, taming or avoiding the factor zoo? A double-shrinkage estimator for covariance matrices," Journal of Empirical Finance, Elsevier, vol. 72(C), pages 23-35.
    18. Kremer, Philipp J. & Lee, Sangkyun & Bogdan, Małgorzata & Paterlini, Sandra, 2020. "Sparse portfolio selection via the sorted ℓ1-Norm," Journal of Banking & Finance, Elsevier, vol. 110(C).
    19. Ding, Wenliang & Shu, Lianjie & Gu, Xinhua, 2023. "A robust Glasso approach to portfolio selection in high dimensions," Journal of Empirical Finance, Elsevier, vol. 70(C), pages 22-37.
    20. Hongxin Zhao & Yilun Jiang & Yizhou Yang, 2023. "Robust and Sparse Portfolio: Optimization Models and Algorithms," Mathematics, MDPI, vol. 11(24), pages 1-20, December.

    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:plo:pone00:0067503. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.