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Honey, I shrunk the sample covariance matrix

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Author Info

  • Olivier Ledoit
  • Michael Wolf

Abstract

The central message of this paper is that nobody should be using the sample covariance matrix for the purpose of portfolio optimization. It contains estimation error of the kind most likely to perturb a mean-variance optimizer. In its place, we suggest using the matrix obtained from the sample covariance matrix through a transformation called shrinkage. This tends to pull the most extreme coefficients towards more central values, thereby systematically reducing estimation error where it matters most. Statistically, the challenge is to know the optimal shrinkage intensity, and we give the formula for that. Without changing any other step in the portfolio optimization process, we show on actual stock market data that shrinkage reduces tracking error relative to a benchmark index, and substantially increases the realized information ratio of the active portfolio manager.

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File URL: http://www.econ.upf.edu/docs/papers/downloads/691.pdf
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Bibliographic Info

Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 691.

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Date of creation: Jun 2003
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Handle: RePEc:upf:upfgen:691

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Web page: http://www.econ.upf.edu/

Related research

Keywords: Covariance matrix; Markovitz optimization; shrinkage; tracking error;

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References

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  1. 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, 08.
  2. 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 1263-91, September.
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Cited by:
  1. Brandt, Michael W & Santa-Clara, Pedro & Valkanov, Rossen, 2005. "Parametric Portfolio Policies: Exploiting Characteristics in the Cross Section of Equity Returns," University of California at Los Angeles, Anderson Graduate School of Management qt4ft420b6, Anderson Graduate School of Management, UCLA.
  2. Michael W. Brandt & Pedro Santa-Clara & Rossen Valkanov, 2004. "Parametric Portfolio Policies: Exploiting Characteristics in the Cross Section of Equity Returns," NBER Working Papers 10996, National Bureau of Economic Research, Inc.
  3. Loriana Pelizzon & Massimiliano Caporin, 2012. "Market volatility, optimal portfolios and naive asset allocations," Working Papers 2012_08, Department of Economics, University of Venice "Ca' Foscari".
  4. Caicedo-Llano, Juliana & Dionysopoulos, Thomas, 2008. "Market integration: A risk-budgeting guide for pure alpha investors," Journal of Multinational Financial Management, Elsevier, vol. 18(4), pages 313-327, October.
  5. Michael Wolf, 2006. "Resampling vs. Shrinkage for Benchmarked Managers," IEW - Working Papers 263, Institute for Empirical Research in Economics - University of Zurich.
  6. Gopal K. Basak & Ravi Jagannathan & Tongshu Ma, 2004. "A Jackknife Estimator for Tracking Error Variance of Optimal Portfolios Constructed Using Estimated Inputs1," NBER Working Papers 10447, National Bureau of Economic Research, Inc.

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