Asset allocation: new evidence through network approaches

  • Gian Paolo ClementeEmail author
  • Rosanna Grassi
  • Asmerilda Hitaj
S.I.: Recent Developments in Financial Modeling and Risk Management


The main contribution of the paper is to unveil the role of the network structure in the financial markets to improve the portfolio selection process, where nodes indicate securities and edges capture the dependence structure of the system. Three different methods are proposed in order to extract the dependence structure between assets in a network context. Starting from this modified structure, we formulate and then we solve the asset allocation problem. We find that the optimal portfolios obtained through a network-based approach are composed mainly of peripheral assets, which are poorly connected with the others. These portfolios, in the majority of cases, are characterized by an higher trade-off between performance and risk with respect to the traditional global minimum variance portfolio. Additionally, this methodology benefits of a graphical visualization of the selected portfolio directly over the graphic layout of the network, which helps in improving our understanding of the optimal strategy.


Portfolio selection Networks Global minimum variance Dependence structure 

JEL Classification

G11 C6 



We would like to thank the anonymous referees for their careful reviews on an earlier version of this paper.

Supplementary material

10479_2019_3136_MOESM1_ESM.pdf (2.7 mb)
Supplementary material 1 (pdf 2735 KB)


  1. Bloomberg, L. P. (2018). Bloomberg terminal. Google Scholar
  2. Bloomfield, T., Leftwich, R., & Long, J. B, Jr. (1977). Portfolio strategies and performance. Journal of Financial Economics, 5(2), 201–218.Google Scholar
  3. Boginski, V., Butenko, S., Shirokikh, O., Trukhanov, S., & Lafuente, J. G. (2014). A network-based data mining approach to portfolio selection via weighted clique relaxations. Annals of Operations Research, 216(1), 23–34.Google Scholar
  4. Bongini, P., Clemente, G., & Grassi, R. (2018). Interconnectedness, G-SIBs and network dynamics of global banking. Finance Research Letters, 27, 185–192.Google Scholar
  5. Brandt, M. W., & Santa-Clara, P. (2006). Dynamic portfolio selection by augmenting the asset space. The Journal of Finance, 61(5), 2187–2217.Google Scholar
  6. Caccioli, F., Barucca, P., & Kobayashi, T. (2018). Network models of financial systemic risk: A review. Journal of Computational Social Science, 1(1), 81–114.Google Scholar
  7. Campbell, R., Huisman, R., & Koedijk, K. (2001). Optimal portfolio selection in a value-at-risk framework. Journal of Banking & Finance, 25(9), 1789–1804.Google Scholar
  8. Cerqueti, R., Ferraro, G., & Iovanella, A. (2018). A new measure for community structure through indirect social connections. Expert Systems with Applications, 114, 196–209.Google Scholar
  9. Cesarone, F., Gheno, A., & Tardella, F. (2013). Learning & holding periods for portfolio selection models: A sensitivity analysis. Applied Mathematical Sciences, 7(100), 4981–4999.Google Scholar
  10. Cesarone, F., Scozzari, A., & Tardella, F. (2013). A new method for mean-variance portfolio optimization with cardinality constraints. Annals of Operations Research, 205(1), 213–234.Google Scholar
  11. Choueifaty, Y., & Coignard, Y. (2008). Towards maximum diversification. Journal of Portfolio Management, 35(1), 40–51.Google Scholar
  12. Clemente, G., & Grassi, R. (2018). Directed clustering in weighted networks: A new perspective. Chaos, Solitons & Fractals, 107, 26–38.Google Scholar
  13. DeMiguel, V., Garlappi, L., & Uppal, R. (2007). Optimal versus naive diversification: How inefficient is the 1/n portfolio strategy? The Review of Financial studies, 22(5), 1915–1953.Google Scholar
  14. Embrechts, P., Lindskog, F., & McNeil, A. (2001). Modelling dependence with copulas. Rapport technique, Département de mathématiques, Institut Fédéral de Technologie de Zurich, Zurich.Google Scholar
  15. Epskamp, S., Cramer, A. O. J., Waldorp, L. J., Schmittmann, V. D., & Borsboom, D. (2012). qgraph: Network visualizations of relationships in psychometric data. Journal of Statistical Software, 48(4), 1–18.
  16. Fagiolo, G. (2007). Clustering in complex directed networks. Physical Review E, 76(2), 026107. Scholar
  17. Giudici, P., & Spelta, A. (2016). Graphical network models for international financial flows. Journal of Business & Economic Statistics, 34(1), 128–138.Google Scholar
  18. He, X. D., & Zhou, X. Y. (2011). Portfolio choice under cumulative prospect theory: An analytical treatment. Management Science, 57(2), 315–331.Google Scholar
  19. Hinich, M. J., & Patterson, D. M. (1985). Evidence of nonlinearity in daily stock returns. Journal of Business & Economic Statistics, 3(1), 69–77.Google Scholar
  20. Hitaj, A., & Zambruno, G. (2016). Are smart beta strategies suitable for hedge fund portfolios? Review of Financial Economics, 29, 37–51.Google Scholar
  21. Hu, D., Zhao, J. L., Hua, Z., & Wong, M. C. (2012). Network-based modeling and analysis of systemic risk in banking systems. MIS Quarterly, 36(4), 1269–1291.Google Scholar
  22. Isogai, T. (2016). Building a dynamic correlation network for fat-tailed financial asset returns. Applied Network Science, 1(1), 1–7.Google Scholar
  23. Isogai, T. (2017). Dynamic correlation network analysis of financial asset returns with network clustering. Applied Network Science, 2(1), 2–8.Google Scholar
  24. Jobson, J. D., & Korkie, B. (1980). Estimation for markowitz efficient portfolios. Journal of the American Statistical Association, 75(371), 544–554.Google Scholar
  25. Keating, C., & Shadwick, W. F. (2002). A universal performance measure. Journal of Performance Measurement, 6(3), 59–84.Google Scholar
  26. Krokhmal, P., Palmquist, J., & Uryasev, S. (2002). Portfolio optimization with conditional value-at-risk objective and constraints. Journal of Risk, 4, 43–68.Google Scholar
  27. Ledoit, O., & Wolf, M. (2004). Honey, I shrunk the sample covariance matrix. The Journal of Portfolio Management, 30(4), 110–119.Google Scholar
  28. Maillard, S., Roncalli, T., & Teïletche, J. (2010). The properties of equally weighted risk contribution portfolios. The Journal of Portfolio Management, 36(4), 60–70.Google Scholar
  29. Mantegna, R. N. (1999). Hierarchical structure in financial markets. The European Physical Journal B-Condensed Matter and Complex Systems, 11(1), 193–197.Google Scholar
  30. Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77–91.Google Scholar
  31. Martellini, L., & Ziemann, V. (2009). Improved estimates of higher-order comoments and implications for portfolio selection. The Review of Financial Studies, 23(4), 1467–1502.Google Scholar
  32. McAssey, M. P., & Bijma, F. (2015). A clustering coefficient for complete weighted networks. Network Science, 3(2), 183–195.Google Scholar
  33. Merton, R. C. (1980). On estimating the expected return on the market: An exploratory investigation. Journal of Financial Economics, 8(4), 323–361.Google Scholar
  34. Michaud, R. O., & Michaud, R. (2008). Estimation error and portfolio optimization: a resampling solution. Journal of Investment Management, 6(1), 8–28.Google Scholar
  35. Minoiu, C., & Reyes, J. A. (2013). A network analysis of global banking: 1978–2010. Journal of Financial Stability, 9(2), 168–184.Google Scholar
  36. Neveu, A. R. (2018). A survey of network-based analysis and systemic risk measurement. Journal of Economic Interaction and Coordination, 13(2), 241–281.Google Scholar
  37. Onnela, J., Chakraborti, A., Kaski, K., Kertesz, J., & Kanto, A. (2003). Asset trees and asset graphs in financial markets. Physica Scripta, 2003(T106), 48.Google Scholar
  38. Onnela, J. P., Chakraborti, A., Kaski, K., Kertész, J., & Kanto, A. (2003). Dynamics of market correlations: Taxonomy and portfolio analysis. Physical Review E, 68, 056110.Google Scholar
  39. Peralta, G., & Zareei, A. (2016). A network approach to portfolio selection. Journal of Empirical Finance, 38, 157–180.Google Scholar
  40. Pozzi, F., Di Matteo, T., & Aste, T. (2013). Spread of risk across financial markets: Better to invest in the peripheries. Scientific Reports, 3, 1665.Google Scholar
  41. R Development Core Team: R. (2018). A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
  42. Schmidt, R., & Stadtmüller, U. (2006). Non-parametric estimation of tail dependence. Scandinavian Journal of Statistics, 33(2), 307–335.Google Scholar
  43. Scholz, H. (2007). Refinements to the sharpe ratio: Comparing alternatives for bear markets. Journal of Asset Management, 7(5), 347–357.Google Scholar
  44. Serrour, B., Arenas, A., & Gómez, S. (2011). Detecting communities of triangles in complex networks using spectral optimization. Computer Communications, 34(5), 629–634.Google Scholar
  45. Tabak, B., Takami, M., Rocha, J. M., Cajueiro, D. O., & Souza, S. R. (2014). Directed clustering coefficient as a measure of systemic risk in complex banking networks. Physica A: Statistical Mechanics and its Applications, 394, 211–216.Google Scholar
  46. Tumminello, M., Coronnello, C., Lillo, F., Miccichè, S., & Mantegna, R. (2007). Spanning trees and bootstrap reliability estimations in correlation based networks. International Journal of Bifurcation and Chaos, 17(7), 2319.Google Scholar
  47. Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5(4), 297–323.Google Scholar
  48. Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of ‘small-world’networks. Nature, 393(6684), 440.Google Scholar
  49. Yin, G., & Zhou, X. Y. (2004). Markowitz’s mean-variance portfolio selection with regime switching: From discrete-time models to their continuous-time limits. IEEE Transactions on automatic control, 49(3), 349–360.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dipartimento di Discipline Matematiche, Finanza Matematica ed EconometriaUniversità Cattolica del Sacro CuoreMilanoItaly
  2. 2.Dipartimento di Statistica e Metodi QuantitativiUniversità degli Studi di Milano - BicoccaMilanoItaly

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