Abstract
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.
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Notes
This sensitivity has generally been attributed to the tendency of the optimization to magnify the effects of estimation error. Michaud in Michaud and Michaud (2008) referred to “portfolio optimization” as “error maximization”. Efforts to improve parameters estimation procedure include among others the papers (Ledoit and Wolf 2004; Martellini and Ziemann 2009). Empirical analyses have shown that the use of improved estimators for moments and co-moments leads to higher out-of-sample performance compared to the sample estimation, see among others Hitaj and Zambruno (2016).
As well-known, a closed-form solution of the GMV problem exists if short selling is allowed.
Notice that an ultrametric distance can be associated to the correlation coefficient in order to assure that weights range in a limited interval (see, for instance, Giudici and Spelta 2016; Mantegna 1999; Onnela et al. 2003). In our case, this transformation does not affect the results in terms of optimal portfolio.
By basic properties of the determinants, the eigenvalues of \(\varvec{{\varOmega }}\) can be obtained by those of \(\varvec{{\varSigma }}\) by a multiplicative factor:
$$\begin{aligned} \det {(\varvec{{\varOmega }}-\lambda \varvec{I})}= & {} \det {\left( \frac{\varvec{{\varSigma }}}{\sum _{i=1}^{N}\sigma _{i}^{2}}-\lambda {{\mathbf {I}}}\right) }= \det {\left( \frac{\varvec{{\varSigma }}-\left( \sum _{i=1}^{N}\sigma _{i}^{2}\right) \lambda {\mathbf {I}}}{\sum _{i=1}^{N}\sigma _{i}^{2}}\right) }\\= & {} \left( \frac{1}{\sum _{i=1}^{N}\sigma _{i}^{2}}\right) ^n\det {\left( \varvec{{\varSigma }}-\left( {\sum }_{i=1}^{N}\sigma _{i}^{2}\right) \lambda {\mathbf {I}}\right) }. \end{aligned}$$https://www.hedgefundresearch.com/hfr-database. Observations before than 1st of April 2003 are not available for the hedge funds under analysis.
For the sake of simplicity, we set the average risk-free rate at zero in the empirical analysis.
In case of negative average portfolio excess return this measure is not appropriate and different modifications have been proposed in literature (see Scholz 2007).
We point out that OR ratio is very sensitive to values of \(\epsilon \) which can be different from investor to investor. In the empirical analysis \(\epsilon \) is set equal to 0.
We remind that detailed results are reported in the Supplementary Material.
References
Bloomberg, L. P. (2018). Bloomberg terminal.
Bloomfield, T., Leftwich, R., & Long, J. B, Jr. (1977). Portfolio strategies and performance. Journal of Financial Economics, 5(2), 201–218.
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.
Bongini, P., Clemente, G., & Grassi, R. (2018). Interconnectedness, G-SIBs and network dynamics of global banking. Finance Research Letters, 27, 185–192.
Brandt, M. W., & Santa-Clara, P. (2006). Dynamic portfolio selection by augmenting the asset space. The Journal of Finance, 61(5), 2187–2217.
Caccioli, F., Barucca, P., & Kobayashi, T. (2018). Network models of financial systemic risk: A review. Journal of Computational Social Science, 1(1), 81–114.
Campbell, R., Huisman, R., & Koedijk, K. (2001). Optimal portfolio selection in a value-at-risk framework. Journal of Banking & Finance, 25(9), 1789–1804.
Cerqueti, R., Ferraro, G., & Iovanella, A. (2018). A new measure for community structure through indirect social connections. Expert Systems with Applications, 114, 196–209.
Cesarone, F., Gheno, A., & Tardella, F. (2013). Learning & holding periods for portfolio selection models: A sensitivity analysis. Applied Mathematical Sciences, 7(100), 4981–4999.
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.
Choueifaty, Y., & Coignard, Y. (2008). Towards maximum diversification. Journal of Portfolio Management, 35(1), 40–51.
Clemente, G., & Grassi, R. (2018). Directed clustering in weighted networks: A new perspective. Chaos, Solitons & Fractals, 107, 26–38.
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.
Embrechts, P., Lindskog, F., & McNeil, A. (2001). Modelling dependence with copulas. Rapport technique, Département de mathématiques, Institut Fédéral de Technologie de Zurich, Zurich.
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. http://www.jstatsoft.org/v48/i04/
Fagiolo, G. (2007). Clustering in complex directed networks. Physical Review E, 76(2), 026107. https://doi.org/10.1103/physreve.76.026107.
Giudici, P., & Spelta, A. (2016). Graphical network models for international financial flows. Journal of Business & Economic Statistics, 34(1), 128–138.
He, X. D., & Zhou, X. Y. (2011). Portfolio choice under cumulative prospect theory: An analytical treatment. Management Science, 57(2), 315–331.
Hinich, M. J., & Patterson, D. M. (1985). Evidence of nonlinearity in daily stock returns. Journal of Business & Economic Statistics, 3(1), 69–77.
Hitaj, A., & Zambruno, G. (2016). Are smart beta strategies suitable for hedge fund portfolios? Review of Financial Economics, 29, 37–51.
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.
Isogai, T. (2016). Building a dynamic correlation network for fat-tailed financial asset returns. Applied Network Science, 1(1), 1–7.
Isogai, T. (2017). Dynamic correlation network analysis of financial asset returns with network clustering. Applied Network Science, 2(1), 2–8.
Jobson, J. D., & Korkie, B. (1980). Estimation for markowitz efficient portfolios. Journal of the American Statistical Association, 75(371), 544–554.
Keating, C., & Shadwick, W. F. (2002). A universal performance measure. Journal of Performance Measurement, 6(3), 59–84.
Krokhmal, P., Palmquist, J., & Uryasev, S. (2002). Portfolio optimization with conditional value-at-risk objective and constraints. Journal of Risk, 4, 43–68.
Ledoit, O., & Wolf, M. (2004). Honey, I shrunk the sample covariance matrix. The Journal of Portfolio Management, 30(4), 110–119.
Maillard, S., Roncalli, T., & Teïletche, J. (2010). The properties of equally weighted risk contribution portfolios. The Journal of Portfolio Management, 36(4), 60–70.
Mantegna, R. N. (1999). Hierarchical structure in financial markets. The European Physical Journal B-Condensed Matter and Complex Systems, 11(1), 193–197.
Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77–91.
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.
McAssey, M. P., & Bijma, F. (2015). A clustering coefficient for complete weighted networks. Network Science, 3(2), 183–195.
Merton, R. C. (1980). On estimating the expected return on the market: An exploratory investigation. Journal of Financial Economics, 8(4), 323–361.
Michaud, R. O., & Michaud, R. (2008). Estimation error and portfolio optimization: a resampling solution. Journal of Investment Management, 6(1), 8–28.
Minoiu, C., & Reyes, J. A. (2013). A network analysis of global banking: 1978–2010. Journal of Financial Stability, 9(2), 168–184.
Neveu, A. R. (2018). A survey of network-based analysis and systemic risk measurement. Journal of Economic Interaction and Coordination, 13(2), 241–281.
Onnela, J., Chakraborti, A., Kaski, K., Kertesz, J., & Kanto, A. (2003). Asset trees and asset graphs in financial markets. Physica Scripta, 2003(T106), 48.
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.
Peralta, G., & Zareei, A. (2016). A network approach to portfolio selection. Journal of Empirical Finance, 38, 157–180.
Pozzi, F., Di Matteo, T., & Aste, T. (2013). Spread of risk across financial markets: Better to invest in the peripheries. Scientific Reports, 3, 1665.
R Development Core Team: R. (2018). A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org.
Schmidt, R., & Stadtmüller, U. (2006). Non-parametric estimation of tail dependence. Scandinavian Journal of Statistics, 33(2), 307–335.
Scholz, H. (2007). Refinements to the sharpe ratio: Comparing alternatives for bear markets. Journal of Asset Management, 7(5), 347–357.
Serrour, B., Arenas, A., & Gómez, S. (2011). Detecting communities of triangles in complex networks using spectral optimization. Computer Communications, 34(5), 629–634.
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.
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.
Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5(4), 297–323.
Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of ‘small-world’networks. Nature, 393(6684), 440.
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.
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We would like to thank the anonymous referees for their careful reviews on an earlier version of this paper.
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Clemente, G.P., Grassi, R. & Hitaj, A. Asset allocation: new evidence through network approaches. Ann Oper Res 299, 61–80 (2021). https://doi.org/10.1007/s10479-019-03136-y
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DOI: https://doi.org/10.1007/s10479-019-03136-y