Efficient Subset Selection in Large-Scale Portfolio with Singular Covariance Matrix

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 242)


In the classic mean-variance model, the covariance matrix is supposed to be positive definite or nonsingular. However, the degenerate portfolio can arise from multi-collinearity and correlation of assets returns in large-scale portfolio. In this paper, we investigate the issue of which assets can be removed from the original portfolio. We propose a new concept of efficient subset of portfolio for meanvariance optimizing investor. Applying the generalized inverse matrix, we derive some conditions for determining the efficient subset. In addition, a new three fund separation result is also obtained as an economic interpretation, which in fact gives an extension of the mean-variance spanning.


Large-scale portfolio Efficient subset Singular covariance matrix Mean-variance spanning 


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This work was supported in part by the national natural science foundation of China (No.71101095) and Natural Science Foundation of Guangdong Province (No.2008276).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Mathematical Finance Research CenterShenzhen UniversityShenzhenP. R. China

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