The use of dynamical networks to detect the hierarchical organization of financial market sectors

Two kinds of filtered networks: minimum spanning trees (MSTs) and planar maximally filtered graphs (PMFGs) are constructed from dynamical correlations computed over a moving window. We study the evolution over time of both hierarchical and topological properties of these graphs in relation to market fluctuations. We verify that the dynamical PMFG preserves the same hierarchical structure as the dynamical MST, providing in addition a more significant and richer structure, a stronger robustness and dynamical stability. Central and peripheral stocks are differentiated by using a combination of different topological measures. We find stocks well connected and central; stocks well connected but peripheral; stocks poorly connected but central; stocks poorly connected and peripheral. It results that the Financial sector plays a central role in the entire system. The robustness, stability and persistence of these findings are verified by changing the time window and by performing the computations on different time periods. We discuss these results and the economic meaning of this hierarchical positioning

Structural and topological phase transitions on the German Stock Exchange

We find numerical and empirical evidence for dynamical, structural and topological phase transitions on the (German) Frankfurt Stock Exchange (FSE) in the temporal vicinity of the worldwide financial crash. Using the Minimal Spanning Tree (MST) technique, a particularly useful canonical tool of the graph theory, two transitions of the topology of a complex network representing FSE were found. First transition is from a hierarchical scale-free MST representing the stock market before the recent worldwide financial crash, to a superstar-like MST decorated by a scale-free hierarchy of trees representing the market's state for the period containing the crash. Subsequently, a transition is observed from this transient, (meta)stable state of the crash, to a hierarchical scale-free MST decorated by several star-like trees after the worldwide financial crash. The phase transitions observed are analogous to the ones we obtained earlier for the Warsaw Stock Exchange and more pronounced than those found by Onnela-Chakraborti-Kaski-Kert\'esz for S&P 500 index in the vicinity of Black Monday (October 19, 1987) and also in the vicinity of January 1, 1998. Our results provide an empirical foundation for the future theory of dynamical, structural and topological phase transitions on financial markets

Asset Clusters and Asset Networks in Financial Risk Management and Portfolio Optimization

In this work we use explorative statistical and data mining methods for financial applications like risk management, portfolio optimization and market analysis. The outcomes are visualized and the relations are quantified by mathematical measures. Researchers, analysts and decision makers can visually explore the structures and can carry out management initiatives based on automatic measures provided by the system. There are example applications to equity and loan portfolios

링크 예측을 이용한 금융시장 복잡계 네트워크 분석

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 산업공학과, 2020. 8. 장우진.Financial risk sets off a chain reaction in the market and leads to a collapse of the system, called a domino effect. Since the U.S. subprime mortgage crisis in 2008 hit economies across the world, it has emerged important research fields to understand and analyze the financial system properly to deal with financial risk. Econophysics is an interdisciplinary research field to explain the stylized facts in financial systems that are unexplainable by traditional financial theories. In particular, the complex network models that represent a system by nodes and links are widely applied regardless of research areas. However, since the existing complex network models for financial markets usually end up in confirming empirical results such as a structural change in the network and diffusion paths of risk, based on historical data, it has limitations to suggest direct alternatives. To cope with these limitations, this dissertation proposes a link prediction model based on the real effective exchange rate (REER) that reveals the relationships clearly between the compositions. At first, it is confirmed that the network successfully mimics the market to ensure the validity of the network structure prediction. The results show that the return of REER has fat-tailed distributions whose tails are not exponentially bounded and follow a power-law. Also, for the analysis, the changes are focused on cross-sectional topology and time-varying properties of the network during the U.S. subprime mortgage crisis, the European debt crisis, and the Chinese stock market turbulence. The result implies that the network appropriately describes the market by showing the significant increments in out-degrees and in-degrees of the originating continents of the crises. Secondly, the Weighted Causality Link Prediction (WCLP) model is proposed to predict future possible links by measuring the similarities between different nodes. This model has differentiations that it measures the strength of directed Granger causality directions as effect sizes based on $F$-statistics, while the existing models are based on correlations. The experiment is conducted under the hypothesis that the intensity of connections is different from each other and maintains longer when the effect size is larger. The higher prediction accuracy is observed rather than that of unweighted or correlation-based weighted models by showing the statistical significance of higher Area Under Curve (AUC) in every aspects. Finally, a decision making model for investment is proposed based on the results of the link prediction. Once the portfolio is composed of stocks located in the periphery of the PMFG, it distributes the risk due to the low correlation between assets. However, the correlation does not represent the relationship by time lags since it implies only the extent of association between them. Therefore, this dissertation proposes the Weighted Causality Planar Graph (WCPG) that is improved from the Planar Correlation Planar Graph (PCPG) model. It differs from the existing models in that it considers directions and strength of links based on the similarity score between assets. As a result, the proposed model improves the performance in terms of risk-adjusted return compared to the benchmarks. Especially, it has an advantage in long-term investment for over 6 months. In conclusion, the contributions of this dissertation involve the development of an effective link prediction model based on the effect size and the attempt to suggest a decision-making model for investment.금융 시장에서 발생하는 위험은 하나의 금융 체계(System)에서 연쇄 작용으로 이어지며 이것은 곧 시스템의 붕괴로 이어진다. 세계 경제에 큰 타격을 주었던 미국의 서브프라임 모기지 사태 이후 위기 대처 능력 제고를 위해 금융 체계를 올바르게 이해하고 분석하는 것이 매우 중요한 과제로 떠올랐다. 전통적인 금융 위험 관리 이론으로 설명되지 않는 정형화된 사실(stylized facts)들의 발견으로 새롭게 등장한 연구 분야가 경제물리학(Econophysics)이다. 특히, 점(노드)과 선(링크)으로 하나의 체계를 나타내는 복잡계 네트워크 모형은 분야를 막론하고 다양하게 응용되고 있다. 하지만 금융 시장에 대한 기존의 복잡계 네트워크 모형은 대부분 과거 데이터를 기반으로 네트워크 구조 변화, 위험의 확산 경로와 같은 실증적 연구결과를 확인하는 데 그쳐 위험에 대비한 능동적인 대안을 제시하는데 제약이 존재한다. 본 학위논문은 이러한 결점을 보완하고자 네트워크 구성 요소 간 관계가 명확하게 드러나는 환율 데이터 기반의 네트워크 링크 예측 모형을 제시하였다. 먼저, 네트워크 구조 예측의 타당성을 확보하기 위해 네트워크가 시장을 성공적으로 모방하는지 확인하였다. 그 결과 실질실효환율 데이터는 두꺼운 꼬리(Fat-tailed) 분포를 가지며 꼬리 분포가 멱함수(Power-law) 분포를 따르는 것을 확인하였다. 또한, 미국의 서브프라임 모기지 사태, 유럽 부채 위기, 중국 주식 시장 위기 동안 네트워크의 단면(cross-sectional) 토폴로지와 시간에 따라 변화하는 성질을 관찰하였다. 위기 발생 대륙에서 증가하는 링크의 수량을 봤을 때 제시된 그레인저-인과관계(Granger causality) 네트워크가 시장을 적절히 나타내고 있었다. 두 번째로, 네트워크에서 새롭게 생겨날 수 있는 링크를 예측하기 위해 구성 요소 간 유사도를 측정하는 Weighted Causality Link Prediction (WCLP) 모형을 제시하였다. 기존의 많은 네트워크 모형이 구성 요소 간 상관관계에 기반하였다면, 본 모형은 그레인저 인과관계를 측정하여 네트워크의 방향성을 함께 고려하고, 연결 강도를 통계량에 기반한 효과 크기(Effect size)로 나타내었다는 점에서 그 차별성이 있다. 네트워크의 링크는 서로 다른 연결 강도를 가지며 효과 크기가 클 수록 오래 유지된다는 가설 하에 실험을 진행하였다. 그 결과, 높은 수신자 조작 특성 곡선의 면적 (Area Under the receiver operating characteristic Curve, AUC) 값을 가져 비가중치(Unweighted) 또는 상관관계 기반 유클리드 거리(Euclidean distance)를 가중치를 이용한 기존 모형들에 비해 통계적으로 개선된 예측 성능을 보였다. 마지막으로, 네트워크 링크 예측 결과를 기반으로 미국 금융 시장에서의 투자 의사 결정 모형을 제시하였다. PMFG의 주변부에 위치하는 종목으로 포트폴리오가 구성되면, 자산 간의 낮은 상관관계는 포트폴리오 위험의 분산화를 가능하게 한다. 하지만 상관관계는 두 변수 간 연관된 정도만을 나타내므로 시차를 두고 나타나는 인과관계를 나타내지 못한다는 단점이 있다. 따라서 본 학위논문에서는 기존의 Partial Correlation Planar Graph (PCPG) 모형에서 개선 된 새로운 그래프를 제시하고, Weighted Causality Planar Graph (WCPG)라고 명명한다. WCPG는 링크 예측을 통해 얻은 자산 간 유사도를 이용하여 만들어지며 방향성과 세기가 함께 고려된다는 점에서 기존 모형과 차별성이 있다. 그 결과, 위험 조정 수익률 측면에서 제시된 모형이 기존의 네트워크 모형 대비 개선된 성능을 보이며 특히 6개월 이상의 장기 투자에서 강점을 가졌다. 결론적으로 본 학위논문은 효과적인 링크 예측 모형을 효과 크기와 결부하여 개선된 모형을 제시하고 투자 의사 결정을 위한 모형에 응용하였다는 점에서 그 의의를 찾을 수 있다.Chapter 1 Introduction 1 1.1 Problem Description 1 1.2 Motivations of Research 5 1.3 Organization of the Thesis 7 Chapter 2 Literature Review 9 2.1 Network models 9 2.2 Link Prediction 11 2.3 Portfolio optimization 12 Chapter 3 Time-varying Granger Causality Network 15 3.1 Overview 15 3.2 Architecture of Time-varying Granger Causality Network 16 3.2.1 Granger Causality Direction 16 3.2.2 Granger Causality Network 18 3.2.3 Measures of Granger Causality Network 20 3.3 Data description 21 3.4 Results 25 3.4.1 Cross-sectional Topology of REER Networks 25 3.4.2 Time-varying Properties of REER Networks 38 3.5 Summary and Discussion 44 Chapter 4 Link Prediction 47 4.1 Overview 47 4.2 Benchmarks for Link Prediction 48 4.2.1 Unweighted Measures 48 4.2.2 Weighted Measures 57 4.3 Proposed measures 59 4.4 Results 61 4.4.1 Evaluation of Link Prediction 61 4.4.2 Result of Link Prediction 63 4.5 Summary and Discussion 69 Chapter 5 Application of Link Prediction 71 5.1 Overview 71 5.2 Benchmark models 72 5.2.1 Classical models 72 5.2.2 Planar Maximally Filtered Graph(PMFG) 73 5.3 Weighted Causality Planar Graph(WCPG) 76 5.3.1 Realization of WCPG 76 5.4 Data description 78 5.5 Results 79 5.5.1 Evaluation measures 79 5.5.2 Evaluation of portfolio strategies 82 5.6 Summary and Discussion 92 Chapter 6 Concluding Remarks 95 6.1 Contributions and Limitations 95 6.2 Future Work 98 Bibliography 101 Appendix 117 국문초록 125Docto

Can Google Trends search queries contribute to risk diversification?

Portfolio diversification and active risk management are essential parts of financial analysis which became even more crucial (and questioned) during and after the years of the Global Financial Crisis. We propose a novel approach to portfolio diversification using the information of searched items on Google Trends. The diversification is based on an idea that popularity of a stock measured by search queries is correlated with the stock riskiness. We penalize the popular stocks by assigning them lower portfolio weights and we bring forward the less popular, or peripheral, stocks to decrease the total riskiness of the portfolio. Our results indicate that such strategy dominates both the benchmark index and the uniformly weighted portfolio both in-sample and out-of-sample.Comment: 11 pages, 3 figure

Cryptocurrency market structure: connecting emotions and economics

We study the dependency and causality structure of the cryptocurrency market investigating collective movements of both prices and social sentiment related to almost two thousand cryptocurrencies traded during the first six months of 2018. This is the first study of the whole cryptocurrency market structure. It introduces several rigorous innovative methodologies applicable to this and to several other complex systems where a large number of variables interact in a non-linear way, which is a distinctive feature of the digital economy. The analysis of the dependency structure reveals that prices are significantly correlated with sentiment. The major, most capitalised cryptocurrencies, such as bitcoin, have a central role in the price correlation network but only a marginal role in the sentiment network and in the network describing the interactions between the two. The study of the causality structure reveals a causality network that is consistently related with the correlation structures and shows that both prices cause sentiment and sentiment cause prices across currencies with the latter being stronger in size but smaller in number of significative interactions. Overall our study uncovers a complex and rich structure of interrelations where prices and sentiment influence each other both instantaneously and with lead-lag causal relations. A major finding is that minor currencies, with small capitalisation, play a crucial role in shaping the overall dependency and causality structure. Despite the high level of noise and the short time-series we verified that these networks are significant with all links statistically validated and with a structural organisation consistently reproduced across all networks.Comment: 17 pages, 5 figures, 2 table

Sectoral analysis of the US stock market through complex networks

PURPOSE: This study was carried out to analyze the structure of the aggregated network at the level of economic sectors and to reveal the central/peripheral sectors.DESIGN/METHODOLOGY/APPROACH: The study uses the method of complex networks, with the two-step procedure employed to construct the network of economic sectors. First, the MST approach is utilized based on the cross-correlation of 496 stock price returns of the S&P500 Index. Then, the network is aggregated at the level of economic sectors. In addition, to analyze the graph, the network theory, multi-dimensional scaling (MDS), and relative importance approaches are employed.FINDINGS: The results indicate that the sectoral network has a core/periphery structure. Based on the centrality measures, the ranking of sectors is provided. Of the 11 sectors, 3 are classified as central nodes, 4 as peripheral nodes, and the remaining 4 are classified as intermediate. In addition, the network configuration analysis demonstrates that the graph consists of two parts with a star-like structure, connected through the industrials sector.PRACTICAL IMPLICATIONS: An analysis of the cross-correlation network of aggregated assets at the level of economic sectors can be applied to ascertain the direction of stock price movements in the stock market. The division of sectors in the network into central and peripheral nodes has important implications for the management of an optimal portfolio of stocks.ORIGINALITY/VALUE: This study contributes to complex network theory and portfolio strategy design. A unique procedure is proposed to construct the network of economic sectors using the MST-based approach. Detection of the stock market network structure is vital for investors and regulators alike.peer-reviewe

Will the US Economy Recover in 2010? A Minimal Spanning Tree Study

We calculated the cross correlations between the half-hourly times series of the ten Dow Jones US economic sectors over the period February 2000 to August 2008, the two-year intervals 2002--2003, 2004--2005, 2008--2009, and also over 11 segments within the present financial crisis, to construct minimal spanning trees (MSTs) of the US economy at the sector level. In all MSTs, a core-fringe structure is found, with consumer goods, consumer services, and the industrials consistently making up the core, and basic materials, oil and gas, healthcare, telecommunications, and utilities residing predominantly on the fringe. More importantly, we find that the MSTs can be classified into two distinct, statistically robust, topologies: (i) star-like, with the industrials at the center, associated with low-volatility economic growth; and (ii) chain-like, associated with high-volatility economic crisis. Finally, we present statistical evidence, based on the emergence of a star-like MST in Sep 2009, and the MST staying robustly star-like throughout the Greek Debt Crisis, that the US economy is on track to a recovery.Comment: elsarticle class, includes amsmath.sty, graphicx.sty and url.sty. 68 pages, 16 figures, 8 tables. Abridged version of the manuscript presented at the Econophysics Colloquim 2010, incorporating reviewer comment