Advertisement

The Confrontation of Two Clustering Methods in Portfolio Management: Ward’s Method Versus DCA Method

  • Hoai An Le Thi
  • Pascal Damel
  • Nadège Peltre
  • Nguyen Trong Phuc
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 282)

Abstract

This paper presents a new methodology to cluster asset in the portfolio theory. This new methodology is compare with the classical ward cluster in SAS software. The method is based on DCA (Difference of Convex functions), an innovative approach in nonconvex optimization framework which has been successfully used on various industrial complex systems. The cluster can be used in an empirical example in the context of multi-managers portfolio management, and to identify the one that seems to best fit the objectives of portfolio management of a fund of funds or funds. The cluster is useful to reduce the choice of asset class and to facilitate the optimization of Markowitz frontier.

Keywords

clustering methods portfolio management DCA Ward’s method 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Calinski, T., Harabasz, J.: A dendrite method for cluster analysis. Communications in Statistics. Theory and Methods 3, 1–27 (1974)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Damel, P., Peltre, N., Razafitombo, H.: Classification, Performance and fund selection. In: Applied Econometrics Association 93th International Conference Exchange Rate and Risk Econometrics, Athènes Pireaus University (2006)Google Scholar
  3. 3.
    De Leeuw, J.: Applications of convex analysis to multidimensional scaling, Recent developments. In: Barra, J.R., et al. (eds.) Statistics, pp. 133–145. North-Holland Publishing Company, Amsterdam (1997)Google Scholar
  4. 4.
    Gordon, A.D.: How many clusters? An investigation of five procedures for detecting nested cluster structure. In: Hayashi, C., Ohsumi, N., Yajima, K., Tanaka, Y., Bock, H., Baba, Y. (eds.) Data Science, Classification, and Related Methods. Springer, Tokyo (1996)Google Scholar
  5. 5.
    Griffiths, A., Robinson, L.A., Willett, P.: Hierarchic Agglomerative Clustering Methods for Automatic Document Classification. Journal of Documentation 4(3), 175–205 (1984)CrossRefGoogle Scholar
  6. 6.
    Kaufman, L., Rousseeuw, P.J.: Finding Groups in Data. Wiley & Sons, New York (1990)CrossRefGoogle Scholar
  7. 7.
    Lance, G.N., Williams, W.T.: A general theory of classificatory sorting strategies 1. Hierarchical systems. The Computer Journal 9(4), 373–380 (1967)CrossRefGoogle Scholar
  8. 8.
  9. 9.
    Le Thi, H.A., Pham Dinh, T.: The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems. Ann. Oper. Res. 133, 23–46 (2005)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Le Thi, H.A., Belghiti, T., Pham Dinh, T.: A new efficient algorithm based on DC programming and DCA for Clustering. Journal of Global Optimization 37, 593–608 (2007)CrossRefMATHGoogle Scholar
  11. 11.
    Lozano, J.A., Larranaga, P., Grana, M.: Partitional cluster analysis with genetic algorithms: Searching for the number of clusters. In: Hayashi, C., Ohsumi, N., Yajima, K., Tanaka, Y., Bock, H., Baba, Y. (eds.) Data Science, Classification, and Related Methods. Springer, Tokyo (1996)Google Scholar
  12. 12.
    Mingoti, S.A., Felix, F.N.: Implementing Bootstrap in Ward’s Algorithm to estimate the number of clusters. Revista Eletrônica Sistemas & Gestão 4(2), 89–107 (2009)Google Scholar
  13. 13.
    Pham Dinh, T., Le Thi, H.A.: DC optimization algorithms for solving the trust region subproblem. SIAM J. Optim. 8, 476–505 (1998)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Pham Dinh, T., Le Thi, H.A.: Convex analysis approach to d.c. programming: Theory, Algorithms and Applications. Acta Mathematica Vietnamica (dedicated to Professor Hoang Tuy on the occasion of his 70th birthday) 2(1), 289–355 (1997)Google Scholar
  15. 15.
    Podani, J.: Explanatory variables in classifications and the detection of the optimum number of clusters. In: Hayashi, C., Ohsumi, N., Yajima, K., Tanaka, Y., Bock, H., Baba, Y. (eds.) Data Science, Classification, and Related Methods. Springer, Tokyo (1996)Google Scholar
  16. 16.
    Sarle, W.S.: Cubic Clustering Criterion, SAS Technical Report A-108. SAS Institute Inc., Cary (1983)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Hoai An Le Thi
    • 1
  • Pascal Damel
    • 1
  • Nadège Peltre
    • 2
  • Nguyen Trong Phuc
    • 3
  1. 1.L.I.T.A. Université de LorraineMontigny-lés-MetzFrance
  2. 2.C.E.R.E.F.I.G.E. Université de LorraineNancyFrance
  3. 3.Ecole supérieur de transport et communicationHanoiVietnam

Personalised recommendations