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A Krylov subspace approach to large portfolio optimization

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  • Bajeux-Besnainou, Isabelle
  • Bandara, Wachindra
  • Bura, Efstathia

Abstract

With a large number of securities (N) and fewer observations (T), deriving the global minimum variance portfolio requires the inversion of the singular sample covariance matrix of security returns. We introduce the Break-Down Free Generalized Minimum RESidual (BFGMRES), a Krylov subspaces method, as a fully automated approach for deriving the minimum variance portfolio. BFGMRES is a numerical algorithm that provides solutions to singular linear systems without requiring ex-ante assumptions on the covariance structure. Moreover, it is robust to illiquidity and potentially faulty data. US and international stock data are used to demonstrate the relative robustness of BFGMRES to illiquidity when compared to the “shrinkage to market” methodology developed by Ledoit and Wolf (2003). The two methods have similar performance as assessed by the Sharpe ratios and standard deviations for filtered data. In a simulation study, we show that BFGMRES is more robust than shrinkage to market in the presence of data irregularities. Indeed, when there is an illiquid stock shrinkage to market allocates almost 100% of the portfolio weights to this stock, whereas BFGMRES does not. In further simulations, we also show that when there is no illiquidity, BFGMRES exhibits superior performance than shrinkage to market when the number of stocks is high and the sample covariance matrix is highly singular.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 36 (2012)
Issue (Month): 11 ()
Pages: 1688-1699

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Handle: RePEc:eee:dyncon:v:36:y:2012:i:11:p:1688-1699

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Web page: http://www.elsevier.com/locate/jedc

Related research

Keywords: Krylov subspaces; Singular systems; Algorithm; Sample covariance matrix; Global minimum portfolio;

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References

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  1. Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
  2. William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
  3. Vincenzo Tola & Fabrizio Lillo & Mauro Gallegati & Rosario N. Mantegna, 2005. "Cluster analysis for portfolio optimization," Papers physics/0507006, arXiv.org.
  4. Chan, Louis K C & Karceski, Jason & Lakonishok, Josef, 1999. "On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 937-74.
  5. Gilli, Manfred & Pauletto, Giorgio, 1998. "Krylov methods for solving models with forward-looking variables," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1275-1289, August.
  6. Louis K.C. Chan & Jason Karceski & Josef Lakonishok, 1999. "On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model," NBER Working Papers 7039, National Bureau of Economic Research, Inc.
  7. Oliver Ledoit & Michael Wolf, 2008. "Robust Performance Hypothesis Testing with the Sharpe Ratio," IEW - Working Papers 320, Institute for Empirical Research in Economics - University of Zurich.
  8. Golosnoy, Vasyl & Okhrin, Yarema, 2009. "Flexible shrinkage in portfolio selection," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 317-328, February.
  9. Olivier Ledoit & Michael Wolf, 2001. "Improved estimation of the covariance matrix of stock returns with an application to portofolio selection," Economics Working Papers 586, Department of Economics and Business, Universitat Pompeu Fabra.
  10. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
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Cited by:
  1. Dimitrios D. Thomakos & Fotis Papailias, 2013. "Covariance Averaging for Improved Estimation and Portfolio Allocation," Working Paper Series 66_13, The Rimini Centre for Economic Analysis.

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