A Krylov subspace approach to large portfolio optimization
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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- Tola, Vincenzo & Lillo, Fabrizio & Gallegati, Mauro & Mantegna, Rosario N., 2008.
"Cluster analysis for portfolio optimization,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 32(1), pages 235-258, January.
- 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.
- 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.
- 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.
- 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.
- 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.
- Golosnoy, Vasyl & Okhrin, Yarema, 2009. "Flexible shrinkage in portfolio selection," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 317-328, February.
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
- 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.
- Ledoit, Olivier & Wolf, Michael, 2000. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," DES - Working Papers. Statistics and Econometrics. WS 10089, Universidad Carlos III de Madrid. Departamento de Estadística.
- 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.
- 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.
- William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
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