Filtering financial networks and optimal portfolio selection

Abstract

Financial markets can be represented as complex networks of agents connected by different intensities of interaction. In this Ph.D. thesis I study correlation-based networks. The complete system of relations available from large financial datasets is notoriously characterized by an inextricable mass of redundant information-too complex to approach without adopting some optimizing filtering tools. Filtering graphs such as Minimum Spanning Trees (MSTs) and Planar Maximally Filtered Graphs (PMFGs)-widely known and adopted in the field of econophysics-provide a simple and "light" structure which retains the most important connections and discards redundancies, preserving meaningful properties of the original complex system. In this work I have studied dynamical MSTs and PMFGs: a great deal of analysis has been dedicated to elaborate appropriate measures of dynamical interactions between the nodes of a graph improving the conditioning of the associated adjacency matrix and the resilience of individual interactions to sudden shocks, i.e. their ability to rapidly absorb the effect of anomalous disturbances. At first I have focused the attention on filtered subgraphs' robustness over time and the sectorial composition of their edges, unveiling the interactions within and between sectors of economic activity observable through empirical evidence. I have then verified how different economic sectors differently populate the various regions of the graphs: stocks have been initially mapped in terms of centrality/peripherality using classic measures (degree, betweenness, eccentricity, closeness, eigenvector centrality). I showed how the center of the networks is primarily dominated by Financial stocks and secondarily by stocks providing the market with specific inputs of production (Basic Materials, Capital Goods or Conglomerates sectors); the periphery is mainly populated by sectors specialized in final products (Consumer Non Cyclical and Healthcare) and sectors providing general inputs of production (Transportation, Energy and Utilities). The analysis of the classic measures of centrality has revealed the existence of two principal components of centrality/peripherality dividing the map into four extremes: central stocks connected with many central stocks opposed to peripheral stocks connected with few peripheral stocks; stocks connected with many peripheral stocks opposed to stocks connected with few central stocks. Correspondingly two new composite centrality/peripherality indices have been devised. Most networks are characterized by a large number of "unimportant" nodes and only a very small number of "important" ones. While classic measures are fairly effective in detecting the few most central/important nodes-however failing to discriminate between global centers and peripheral centers-they are also quite ineffective in clearly differentiating the status of all other nodes: in the literature a large number of studies have been dedicated to the centrality of nodes whereas the notion of peripherality has received only marginal attention. The composite indices of centrality/peripherality introduced in this thesis fill the gap and accurately identify the particular positioning of all nodes, particularly those located in the extreme peripheries. On the basis of the centrality map, investment simulations have been carried out over a period of 28 market years (1982-2009): portfolios have been set up by grouping together stocks located in given regions of the map and their performance has been thoroughly evaluated through traditional measures (yearly returns, yearly excess returns, probability of positive returns and excess returns, information ratio and Sharpe information ratio, beta coefficients) calculated out-of-sample; the results are finally compared with those obtained through traditional investment alternatives. The main result is that central portfolios appear to concentrate a great deal of financial risk not associated with any other improved outcome, systematically performing worse than benchmark alternatives, whereas peripheral portfolios-with stocks selected from different peripheries of the network-prove successful in efficiently diversifying the risk, with strikingly encouraging results in the decade 2000-2009-period characterized by multiple financial crises. Peripheral portfolios systematically perform competitively with-and often better than-benchmark alternatives. The results have been confirmed by an independent set of simulations where peripheral nodes have been detected through an alternative methodology selecting the mutually farthest nodes. To the best of my knowledge this study is the first rigorous attempt to apply filtered graphs to solve portfolio selection problems. This work is largely based on articles published on scientific journals or submitted and currently under review by referees.{u00B2}{u207B}{u2077} Show more