A Krylov subspace approach to large portfolio optimization
AbstractWith 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 InfoArticle provided by Elsevier in its journal Journal of Economic Dynamics and Control.
Volume (Year): 36 (2012)
Issue (Month): 11 ()
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Web page: http://www.elsevier.com/locate/jedc
Krylov subspaces; Singular systems; Algorithm; Sample covariance matrix; Global minimum portfolio;
Find related papers by JEL classification:
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
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