MUNI E C O N SUPTECH WORKSHOP III Tomáš Výrost Network-based asset allocation strategies • SUPTECH WORKSHOP III • Network-based asset allocation strategies 1/21 Introduction Motivation Background and motivation Prior research on stock market networks ■ Dynamic conditional correlation networks (Lyócsa et ai., 2012). ■ Granger causality - temporal proximity and preferential attachment (výrost et ai., 2015). ■ Return and volatility spillovers (Lyócsa et ai., 2015). Question: is network analysis purely academical? ■ Networks capture the structure of relationships. ■ Does the additional information have practical meaning? ■ How to incorporate the information on structure into investment decisions? • SUPTECH WORKSHOP III • Network-based asset allocation strategies 2/21 Introduction Motivation Research outline Objective: to explore the potential benefits the information on the interconnectedness of returns within the topological structure of a network brings to portfolio management. Analysis has several steps: 1. construction of return series for each asset and calculation correlations among returns 2. construction of time-varying correlation networks and quantification of relative importance of assets within the network 3. construction of benchmark and network-information augmented investment portfolios 4. evaluation of performance of constructed portfolios by various measures • SUPTECH WORKSHOP III • Network-based asset allocation strategies 3/21 Introduction Motivation Literature review ■ Classical theory: Markowitz (1952), Black and Litterman (1991) ■ P0St-m0dern theory: downside risk (Rom and Ferguson, 1994), higher moments (Kane, 1982; de Athayde and FLores, 2004), improved COVariance estimators (Tola et al., 2008; Pantaleo et al., 2011). ■ Network interconectedness studies: biluo et ai. (2012), Dieboid and Yilmaz (2014, 2015), Baitinger and Papenbrock (2016), Kaya (2015), Lopez de Prado (2016) ■ Portfolio weights vs. network centrality: Peraita and zaren (2016) • SUPTECH WORKSHOP III • Network-based asset allocation strategies 4/21 Data and methodology Data and return series construction 45 assets, weekly returns and yields, 12 month rolling windows, 1 week drift. Sample covers January 1999 - December 2015. ■ 11 stock indices BVSP, DAX, FTSE100, KOSPI, MERV, N225, SMI, SP500, SSE, TSE, TWII ■ / commodities Brent, Cocoa, Copper, Cotton, Gold, Natural gas, Silver ■ 8 FX pairs AUD/USD, CAD/USD, CHF/USD, CNY/USD, EUR/USD, GBP/USD, JPY/USD, NOK/USD ■ 19 bond/money market instruments bAAA, bBBB, bCPF-lM, bCPNF-lM, bEMEA-corp, bEMER-corp, bEMER-corp-high, bEMER-EURO-corp, bEUR-HY, bGER-lY, bGER-5Y, bGER-20Y, bGER-corp, bJPN-lY, bJPN-5Y, bJPN-20Y, bUS-lY, bUS-5Y, bUS-20Y • SUPTECH WORKSHOP III • Network-based asset allocation strategies 5/21 Data and methodology Data and return series construction The long-run correlation coefficient (Andrews, 1991; Panopouiou etai, 2010) id PhJ = hJ is for a sample of length T obtained from — T-l m=—T+l m M tT (to where rT (m) = and quadratic spectral kernel weighting function k rn M 25 / sin (fiirx/5) 12A2 6ttx/5 — cos (fiirx/5) zt = rri^] ^or returns r^, rBandwidth parameter M — 3. • SUPTECH WORKSHOP III • Network-based asset allocation strategies 6/21 Data and methodology Networks What are stock market networks? ■ Proposed by Mantegna (1999). ■ Network is a graph G(V, E), describing individual stocks (V) and their relationships (E). ■ Relationships are typically measured as correlation, transformed into distances: Pij,i = l,di(i,j) = 0 Pj,k,i = 0, k) = \/2 • SUPTECH WORKSHOP III • Network-based asset allocation strategies 7/21 Data and methodology Networks Complete graphs and complexity ■ Minimum spanning tree (MST) - Mantegna (1999). Connected acydic undirected graph with a minimal sum of edge weights. The most common subgraph, \ V\ - 1 edges. ■ Planar maximally filtered graph (PMFG) -Tumminello et al. (2005,2010). Maximal connected planar undirected graph with a minimal sum of edge weights, 3\V| - 6 edges. ■ Threshold graphs (THR). Keep all edges with weights above a selected threshold. K 3,3 • SUPTECH WORKSHOP III • Network-based asset allocation strategies 8/21 Data and methodology Networks • SUPTECH WORKSHOP III • Network-based asset allocation strategies 9/21 Data and methodology Networks • SUPTECH WORKSHOP III • Network-based asset allocation strategies 10/21 Data and methodology Networks Centrality measures ■ Betweenness: counts the number of times a vertex lies on the shortest path between other vertices in the network. Vertices with high betweenness mediate the interconnection between other vertices and act as spillover hubs. ■ Eigenvalue centrality: not onlythe number of connections, their quality also is relevant. Few links to important vertices vs. higher number of connections with inconsequential vertices. ■ Expected force: classical centrality measures are good for most important vertices, but not others. Evaluates spreading power of a node (either own interconectendess, or strong neighbors). • SUPTECH WORKSHOP III • Network-based asset allocation strategies 12/21 Data and methodology Portfolio optimization and evaluation Portfolio strategies Return maximization: arg maxaT£(r) aeRM cxTD{r)cx < aTl = l on > 0,i = 1,2,...,M Risk minimization: arg min cxTD(r)cx cxeRM cxTl = 1 on > 0,i = 1,2,...,M Alternative: &z > &j =^ ®i < OLj,i,j = 1,2,..., M • SUPTECH WORKSHOP III • Network-based asset allocation strategies 13/21 Data and methodology Portfolio optimization and evaluation Evaluating portfolio performance ■ Descriptive statistics: minimum, maximum, quartiLes, standard deviation, average drawdown (DD), expected shortfall (ES), Burke ratio (BR) and Sharpe ratio (SR) ■ Model confidence set of Hansen et al. (2011): block-bootstrap with 5,000 replications, test for a superior subset, run on portfolio returns and Sharpe ratios. ■ Break-even transaction cost as in Peralta and Zareei (2016): \ J2 (!+^) l-BETdJ2 a - 1 = 0 / • SUPTECH WORKSHOP III • Network-based asset allocation strategies 14/21 Results Return maximization 2000 2002 2004 2006 200S 2010 2012 2014 2016 • SUPTECH WORKSHOP III • Network-based asset allocation strategies 15/21 Results Return maximization SD DD ES10 ES5 ESI BR Turnover BETC M SR SR10 SR5 SRI V00: Benchmark (B) 3.630 11.462 -6.405 -10.186 -11.876 0.118 0.364 0.0076 0.278 0.077 0.043 0.027 0.023 Individual strategies Betweenness V01: MST 2.106 4.748 -2.505 -8.669 -10.311 0.132 1.177 0.0013 0.154 0.073 0.061 0.018 0.015 V02: PMFG 2.289 6.748 -2.675 -6.385 -10.731 0.066 1.363 0.0007 0.103 0.045 0.039 0.016 0.010 V03: Threshold 2.222 4.448 -2.859 -5.407 -8.697 0.198 1.534 0.0013 0.217 0.098 0.076 0.040 0.025 Eigenvalue V04: Complete 1.966 5.119 -2.028 -8.123 -10.591 0.100 1.126 0.0010 0.128 0.065 0.063 0.016 0.012 V05: MST 2.351 6.164 -17.414 -0.128 -18.118 0.078 1.459 0.0005 0.100 0.043 0.006 0.781 0.006 V06: PMFG 2.251 4.375 -2.338 -7.730 -11.434 0.197 1.517 0.0013 0.224 0.100 0.096 0.029 0.020 V07: Threshold 2.137 7.841 -3.235 -9.094 -9.887 0.021 1.510 0.0001 0.047 0.022 0.015 0.005 0.005 Expected force V08: Complete 1.386 4.615 -2.124 -4.304 -5.220 0.179 0.151 0.0089 0.144 0.104 0.068 0.033 0.028 V09: MST 2.916 7.819 -2.116 -3.883 -20.577 0.028 1.521 0.0005 0.086 0.029 0.041 0.022 0.004 V10: PMFG 2.349 6.143 -3.343 -5.166 -7.875 0.199 1.504 0.0016 0.255 0.109 0.076 0.049 0.032 VI1: Threshold 2.597 9.235 -2.646 -9.531 -17.262 0.062 1.463 0.0007 0.112 0.043 0.042 0.012 0.006 Combination strategies V12: Betweenness + B 2.336 6.265 -4.157 -6.641 -7.650 0.167 0.701 0.0030 0.218 0.093 0.052 0.033 0.028 V13: Eigenvalue + B 2.211 6.132 -3.879 -5.687 -7.097 0.162 0.704 0.0027 0.201 0.091 0.052 0.035 0.028 V14: Exp. force + B 2.305 6.526 -4.118 -6.637 -7.617 0.162 0.628 0.0030 0.214 0.093 0.052 0.032 0.028 V15: MST + B 2.377 6.942 -4.027 -6.925 -8.180 0.145 0.739 0.0025 0.196 0.082 0.049 0.028 0.024 V16: PMFG + B 2.316 6.154 -3.968 -5.919 -7.248 0.187 0.757 0.0029 0.236 0.102 0.059 0.040 0.033 V17: Threshold + B 2.274 7.352 -4.157 -6.265 -7.171 0.154 0.764 0.0025 0.202 0.089 0.049 0.032 0.028 VI8: Complete+ B 2.177 6.056 -3.867 -5.897 -6.843 0.165 0.392 0.0051 0.207 0.095 0.054 0.035 0.030 • SUPTECH WORKSHOP III • Network-based asset allocation strategies 16/21 Results Risk minimization 2000 2002 2CC- 2006 200S 2010 2012 2014 2016 • SUPTECH WORKSHOP III • Network-based asset allocation strategies 17/21 Results Risk minimization SD DD ES10 ES5 ESI BR Turn BETC M SR SR10 SR5 SRI over R00: Benchmark (B) 0.431 0.902 -0.708 -1.332 -1.581 0.131 0.352 0.0007 0.029 0.067 0.041 0.022 0.018 Individual strategies Betweenness R01: MST 0.842 1.884 -0.864 -2.810 -4.240 0.214 0.499 0.0018 0.098 0.117 0.113 0.035 0.023 R02: PMFG 0.875 2.118 -0.855 -3.022 -5.647 0.188 0.502 0.0018 0.091 0.105 0.106 0.030 0.016 R03: Threshold 0.826 2.029 -1.262 -1.973 -2.679 0.179 0.754 0.0009 0.083 0.100 0.066 0.042 0.031 Eigenvalue R04: Complete 0.762 1.741 -0.878 -1.904 -3.249 0.249 0.580 0.0015 0.098 0.128 0.112 0.051 0.030 R05: MST 0.769 2.021 -0.962 -2.614 -3.419 0.148 0.747 0.0008 0.064 0.083 0.067 0.024 0.019 R06: PMFG 0.784 1.896 -1.156 -2.033 -2.726 0.237 0.727 0.0012 0.094 0.120 0.081 0.046 0.034 R07: Threshold 0.744 1.901 -0.887 -2.465 -3.354 0.178 0.824 0.0008 0.073 0.098 0.082 0.030 0.022 Expected force R08: Complete 0.757 1.811 -1.012 -2.226 -2.975 0.232 0.054 0.0170 0.101 0.133 0.100 0.045 0.034 R09: MST 0.844 2.178 -0.800 -3.579 -5.523 0.158 0.742 0.0008 0.072 0.085 0.090 0.020 0.013 RIO: PMFG 0.855 2.030 -0.947 -1.584 -4.132 0.202 0.759 0.0012 0.097 0.113 0.102 0.061 0.023 Rll: Threshold 0.819 1.705 -0.902 -1.840 -3.715 0.233 0.770 0.0012 0.102 0.125 0.113 0.055 0.027 Combination strategies R12: Betweenness + B 0.563 1.404 -0.656 -2.080 -2.638 0.196 0.335 0.0016 0.060 0.107 0.091 0.029 0.023 R13: Eigenvalue + B 0.509 1.197 -0.665 -1.864 -2.244 0.198 0.347 0.0015 0.056 0.109 0.084 0.030 0.025 R14: Exp. force + B 0.541 1.178 -0.591 -2.043 -2.637 0.205 0.313 0.0018 0.061 0.113 0.103 0.030 0.023 R15: MST + B 0.541 1.417 -0.560 -2.262 -2.827 0.180 0.357 0.0014 0.053 0.099 0.095 0.023 0.019 R16: PMFG + B 0.551 1.286 -0.604 -2.067 -2.679 0.219 0.354 0.0016 0.062 0.112 0.103 0.030 0.023 R17: Threshold + B 0.527 1.253 -0.734 -1.757 -2.163 0.201 0.384 0.0013 0.057 0.109 0.078 0.032 0.026 R18: Complete+ B 0.526 1.195 -0.686 -1.767 -2.227 0.229 0.248 0.0024 0.064 0.122 0.093 0.036 0.029 • SUPTECH WORKSHOP III • Network-based asset allocation strategies 18/21 Results Conclusion Conclusion ■ We propose simple network-based asset allocation extensions of standard Markowitz portfolio strategies. ■ We consider four types of network topologies and three centrality measures. ■ Information on the topological structure of a network improves risk-return characteristics of standard benchmark portfolios. • SUPTECH WORKSHOP III • Network-based asset allocation strategies 19/21 Results Conclusion Conclusion (cont.) With no transaction costs, simple extensions generally improve risk-return characteristics. In return maximization, improvements are costly (increased turnover and transaction costs). In risk minimization, improvements are retained (cheaper than pure Markowitz strategy). Improvements irrespective of the employed network model or centrality measure used. Best improvements in left-tail risk-adjusted returns. Combination portfolios (50% benchmark + 50% network) are recomended. • SUPTECH WORKSHOP III • Network-based asset allocation strategies 20/21 Results Conclusion MUNI ECON SUPTECH WORKSHOP III Tomáš Výrost Network-based asset allocation strategies • SUPTECH WORKSHOP III • Network-based asset allocation strategies