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

摘要

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 mean-variance 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.