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Cluster analysis for portfolio optimization

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  • Vincenzo Tola
  • Fabrizio Lillo
  • Mauro Gallegati
  • Rosario N. Mantegna

Abstract

We consider the problem of the statistical uncertainty of the correlation matrix in the optimization of a financial portfolio. We show that the use of clustering algorithms can improve the reliability of the portfolio in terms of the ratio between predicted and realized risk. Bootstrap analysis indicates that this improvement is obtained in a wide range of the parameters N (number of assets) and T (investment horizon). The predicted and realized risk level and the relative portfolio composition of the selected portfolio for a given value of the portfolio return are also investigated for each considered filtering method.

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File URL: http://arxiv.org/pdf/physics/0507006
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number physics/0507006.

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Date of creation: Jul 2005
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Handle: RePEc:arx:papers:physics/0507006

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Web page: http://arxiv.org/

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Cited by:
  1. Nikolaus Hautsch & Lada M. Kyj & Roel C.A. Oomen, 2009. "A blocking and regularization approach to high dimensional realized covariance estimation," SFB 649 Discussion Papers SFB649DP2009-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Yves Dominicy & Hiroaki Ogata & David Veredas, 2013. "Inference for vast dimensional elliptical distributions," ULB Institutional Repository 2013/136282, ULB -- Universite Libre de Bruxelles.
  3. Golosnoy, Vasyl & Okhrin, Yarema, 2009. "Flexible shrinkage in portfolio selection," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 317-328, February.
  4. Alina Lucia Trifan, 2009. "Testing Capital Asset Pricing Model For Romanian Capital Market," Annales Universitatis Apulensis Series Oeconomica, Faculty of Sciences, "1 Decembrie 1918" University, Alba Iulia, vol. 1(11), pages 43.
  5. Nicolo Musmeci & Tomaso Aste & Tiziana Di Matteo, 2014. "Clustering and hierarchy of financial markets data: advantages of the DBHT," Papers 1406.0496, arXiv.org.
  6. Leonidas Sandoval Junior & Adriana Bruscato & Maria Kelly Venezuela, 2012. "Building portfolios of stocks in the S\~ao Paulo Stock Exchange using Random Matrix Theory," Papers 1201.0625, arXiv.org, revised Mar 2013.
  7. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2011. "Financial Risk Measurement for Financial Risk Management," CREATES Research Papers 2011-37, School of Economics and Management, University of Aarhus.
  8. M. Tumminello & F. Lillo & R. N. Mantegna, 2008. "Correlation, hierarchies, and networks in financial markets," Papers 0809.4615, arXiv.org.
  9. Sandoval, Leonidas Junior & Bruscato, Adriana & Venezuela, Maria Kelly, 2012. "Building portfolios of stocks in the São Paulo Stock Exchange using Random Matrix Theory," Insper Working Papers wpe_270, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
  10. Sandoval, Leonidas & Franca, Italo De Paula, 2012. "Correlation of financial markets in times of crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 187-208.
  11. Jang, Wooseok & Lee, Junghoon & Chang, Woojin, 2011. "Currency crises and the evolution of foreign exchange market: Evidence from minimum spanning tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 707-718.
  12. R\'emy Chicheportiche, 2013. "Non-linear dependences in finance," Papers 1309.5073, arXiv.org.
  13. M. Tumminello & T. Di Matteo & T. Aste & R. N. Mantegna, 2007. "Correlation based networks of equity returns sampled at different time horizons," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 55(2), pages 209-217, 01.
  14. Bajeux-Besnainou, Isabelle & Bandara, Wachindra & Bura, Efstathia, 2012. "A Krylov subspace approach to large portfolio optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 36(11), pages 1688-1699.
  15. Tabak, Benjamin M. & Serra, Thiago R. & Cajueiro, Daniel O., 2010. "Topological properties of stock market networks: The case of Brazil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3240-3249.
  16. Nikolaus Hautsch & Lada M. Kyj & Peter Malec, 2013. "Do High-Frequency Data Improve High-Dimensional Portfolio Allocations?," SFB 649 Discussion Papers SFB649DP2013-014, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  17. Leonidas Sandoval Junior & Italo De Paula Franca, 2011. "Correlation of financial markets in times of crisis," Papers 1102.1339, arXiv.org, revised Mar 2011.

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