Advertisement

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)

Abstract

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.

Keywords

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

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).

References

  1. 1.
    Buser SA (1977) Mean-Variance portfolio selection with either a singular or non-singular variance-covariance matrix. Journal of Financial and Quantitative Analysis 12:347–361Google Scholar
  2. 2.
    Cheung CS, Kwan C, Mountain D (2009) On the nature of mean-variance spanning. Finance Research Letter 6:106–113Google Scholar
  3. 3.
    DeRoon F, Nijman T (2001) Testing formean-variance spanning: A survey. Journal of Empirical Finance 8:111–155Google Scholar
  4. 4.
    Eun CS, Lai S, Huang W(2008) International diversification with large- and small-cap stock. Journal of Financial and Quantitative Analysis 43:489–524Google Scholar
  5. 5.
    Fang SH (2007) A mean-variance analysis of arbitrage portfolios. Physica A: Statistical Mechanics and its Applications 375:625–632Google Scholar
  6. 6.
    Fan J, Zhang J, Yu K (2008) Asset Allocation and Risk Assessment with Gross Exposure Constraints for Vast Portfolios. Working Paper 2008Google Scholar
  7. 7.
    Glabadanidis P (2009) Measuring the economic significance of mean-variance spanning. The Quarterly Review of Economics and Finance 49:596–616Google Scholar
  8. 8.
    Gouri’eroux C, Jouneau F (1999)Econometrics of efficient fitted portfolios. Journal of Empirical Finance 6:87–118Google Scholar
  9. 9.
    Huberman G, Kandel S (1987) Mean variance spanning. Journal of Finance 42:873–888Google Scholar
  10. 10.
    Jiang CF, Dai YL (2008) Analytic solutions of efficient frontier and efficient portfolio with singular covariance matrix. Journal of Systems Science and Mathematical Sciences 28:1134–1147Google Scholar
  11. 11.
    Kan R, Zhou G (2008) Tests of mean-variance spanning, Working paper. University of Toronto and Washington University in St. LouisGoogle Scholar
  12. 12.
    Korki B, Turtle HJ (2002) A mean-variance analysis of self-financing portfolios. Management Science 48:427–433Google Scholar
  13. 13.
    Korki B, Turtle HJ (1994) A note on the analytics and geometry of limiting mean-variance investment opportunity sets. Review of Quantitative Finance and Accounting 9:289–300Google Scholar
  14. 14.
    Los CA (1998) Optimal multi-currency investment strategies with exact attribution in three Asian countries. Journal of Multinational Financial Management 8:169–198Google Scholar
  15. 15.
    Markowitz H, Lacey R, Plymen J (1994) The general mean-variance portfolio selection problem (and discussion). Philosophical Transactions: Physical Sciences and Engineering 347:543-549Google Scholar
  16. 16.
    Michaud RO (1998) Efficient asset management: A practical guide to stock portfolio optimization and asset allocation. 1st edn, Havard Business School Press, BostonGoogle Scholar
  17. 17.
    Magnus JR, Neudecker H (1999) Matrix differential calculus with applications in statistics and econometrics. 1st edn, John Wiley & Sons, New YorkGoogle Scholar
  18. 18.
    Okhrin Y, Schmid W (2006) Distributional properties of portfolio weights. Journal of Econometrics 134:235–256Google Scholar
  19. 19.
    Petrella G (2005) Are Euro area small cap stocks and asset class? Evidence from mean variance spanning tests. European Financial Management 11:229–253Google Scholar
  20. 20.
    Ross S (1978) Mutual fund separation in financial theory: The separating distributions. Journal of Economic Theory 17:254–286Google Scholar
  21. 21.
    Ryan PJ, Lefoll J (1981) A comment on mean-variance portfolio selection with either a singular or a non-singular variance-covariance matrix. Journal of Financial and Quantitative Analysis 16:389–396Google Scholar
  22. 22.
    Schott JR (2005) Matrix Analysis for Statistics. 2nd edn, John Wiley & Sons, New YorkGoogle Scholar
  23. 23.
    Szegö GP (1980) Portfolio theory: With application to bank asset management. 2nd edn, Academic Press, New YorkGoogle Scholar
  24. 24.
    VöRös J (1987) The explicit derivation of the efficient portfolio frontier in the case of degeneracy and general singularity. European Journal of Operational Research 32:302–310Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

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

Personalised recommendations