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Large Scale Covariance Estimates for Portfolio Selection

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Abstract

We propose an estimator of the Covariance Matrix (SWSE) of a large number of assets. This estimator improves the Similarity Weighted Estimator (SWE) introduced in Munnix et al. (2014), by combining it with the shrinkage estimator of the sample covariance matrix towards the market factor developed by Ledoit and Wolf (2003). We compare the performance of our estimator to some alternatives already available form the literature and the industry. For this purpose we analyse both statistical and economic measures associated to the Global Minimum Variance (GMV) Portfolio, composed by the stocks included in the S&P 500 index and computed using the different estimators considered in our comparison.

Suggested Citation

  • Francesco Lautizi, 2015. "Large Scale Covariance Estimates for Portfolio Selection," CEIS Research Paper 353, Tor Vergata University, CEIS, revised 07 Aug 2015.
  • Handle: RePEc:rtv:ceisrp:353
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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. William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
    3. Haff, L. R., 1979. "An identity for the Wishart distribution with applications," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 531-544, December.
    4. 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.
    5. Hlawitschka, Walter, 1994. "The Empirical Nature of Taylor-Series Approximations to Expected Utility," American Economic Review, American Economic Association, vol. 84(3), pages 713-719, June.
    6. 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.
    7. 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..
    8. Ryan Sullivan & Allan Timmermann & Halbert White, 1999. "Data‐Snooping, Technical Trading Rule Performance, and the Bootstrap," Journal of Finance, American Finance Association, vol. 54(5), pages 1647-1691, October.
    9. Ledoit, Oliver & Wolf, Michael, 2008. "Robust performance hypothesis testing with the Sharpe ratio," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 850-859, December.
    10. Peter R. Hansen & Asger Lunde & James M. Nason, 2011. "The Model Confidence Set," Econometrica, Econometric Society, vol. 79(2), pages 453-497, March.
    11. Liu, Lily Y. & Patton, Andrew J. & Sheppard, Kevin, 2015. "Does anything beat 5-minute RV? A comparison of realized measures across multiple asset classes," Journal of Econometrics, Elsevier, vol. 187(1), pages 293-311.
    12. Kan, Raymond & Zhou, Guofu, 2007. "Optimal Portfolio Choice with Parameter Uncertainty," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(3), pages 621-656, September.
    13. Balduzzi, Pierluigi & Lynch, Anthony W., 1999. "Transaction costs and predictability: some utility cost calculations," Journal of Financial Economics, Elsevier, vol. 52(1), pages 47-78, April.
    14. Roland Weigand, 2014. "Matrix Box-Cox Models for Multivariate Realized Volatility," Working Papers 144, Bavarian Graduate Program in Economics (BGPE).
    15. 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.
    16. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    17. M.C. M�nnix & R. Sch�fer & O. Grothe, 2014. "Estimating correlation and covariance matrices by weighting of market similarity," Quantitative Finance, Taylor & Francis Journals, vol. 14(5), pages 931-939, May.
    18. Green, Richard C & Hollifield, Burton, 1992. "When Will Mean-Variance Efficient Portfolios Be Well Diversified?," Journal of Finance, American Finance Association, vol. 47(5), pages 1785-1809, December.
    19. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    20. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    21. Olivier Ledoit & Michael Wolf, 2014. "Nonlinear shrinkage of the covariance matrix for portfolio selection: Markowitz meets Goldilocks," ECON - Working Papers 137, Department of Economics - University of Zurich, revised Feb 2017.
    22. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
    23. 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.
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    More about this item

    Keywords

    Portfolio selection; large scale covariance matrix; precision matrix; shrinkage; minimum variance; market dynamics;
    All these keywords.

    JEL classification:

    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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