Market Graph and Markowitz Model

Kalyagin, V. A.; Koldanov, A. P.; Koldanov, Petr A.; Zamaraev, Viktor

doi:10.1007/978-1-4939-0808-0_15

Cited by 14 publications

(8 citation statements)

References 17 publications

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“…The correlation matrices are not only important for network analysis and topological visualization but also serve as a bridge between financial network analysis and traditional finance theories. This is similar to modern portfolio theory (MPT) [18,19], which is based on the correlation relationships among assets. Network-based portfolio selection has been proposed for optimization and empirically proofed workable [20].…”

Section: Literature Review Of Financial Network Analysismentioning

confidence: 76%

Complexities in Financial Network Topological Dynamics: Modeling of Emerging and Developed Stock Markets

et al. 2018

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Policy makings and regulations of financial markets rely on a good understanding of the complexity of financial markets. There have been recent advances in applying data-driven science and network theory into the studies of social and financial systems. Financial assets and institutions are strongly connected and influence each other. It is essential to study how the topological structures of financial networks could potentially influence market behaviors. Network analysis is an innovative method to enhance data mining and knowledge discovery in financial data. With the help of complex network theory, the topological network structures of a market can be extracted to reveal hidden information and relationships among stocks. In this study, two major markets of the most influential economies, China and the United States, are systematically studied from the perspective of financial network analysis. Results suggest that the network properties and hierarchical structures are fundamentally different for the two stock markets. The patterns embedded in the price movements are revealed and shed light on the market dynamics. Financial policymakers and regulators can gain inspiration from these findings for applications in policy making, regulations design, portfolio management, risk management, and trading.

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Section: Literature Review Of Financial Network Analysismentioning

confidence: 76%

Complexities in Financial Network Topological Dynamics: Modeling of Emerging and Developed Stock Markets

et al. 2018

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“…In recent years, others have also examined portfolio construction via graph models. For example, Kalyagin et al (2014a) compared the Markowitz portfolio theory Markowitz (1952) to the market graph Boginski et al (2005). They reduced the pool of assets using historical returns, variance, and Sharpe ratio to build a market graph.…”

Section: Clustering For Index-trackingmentioning

confidence: 99%

Market Graph Clustering via QUBO and Digital Annealing

Hong

Miasnikof

Kwon

et al. 2021

JRFM

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We present a novel technique for cardinality-constrained index-tracking, a common task in the financial industry. Our approach is based on market graph models. We model our reference indices as market graphs and express the index-tracking problem as a quadratic K-medoids clustering problem. We take advantage of a purpose-built hardware architecture to circumvent the NP-hard nature of the problem and solve our formulation efficiently. The main contributions of this article are bridging three separate areas of the literature, market graph models, K-medoid clustering and quadratic binary optimization modeling, to formulate the index-tracking problem as a binary quadratic K-medoid graph-clustering problem. Our initial results show we accurately replicate the returns of various market indices, using only a small subset of their constituent assets. Moreover, our binary quadratic formulation allows us to take advantage of recent hardware advances to overcome the NP-hard nature of the problem and obtain solutions faster than with traditional architectures and solvers.

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“…Despite mathematical elegance and physical intuition, direct vertex clustering is an NP hard problem. Consequently, existing graph-theoretic portfolio constructions employ combinatorial optimization formulations [101,109,110,111,112,113], which too become computationally intractable for large graph systems. To alleviate this issue, we employ the minimum cut vertex clustering method to the graph of portfolio assets, to introduce the concept of portfolio cut.…”

Section: Portfolio Cutsmentioning

confidence: 99%

Graph Signal Processing -- Part III: Machine Learning on Graphs, from Graph Topology to Applications

Stanković¹,

Mandic²,

Daković³

et al. 2020

Preprint

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Many modern data analytics applications on graphs operate on domains where graph topology is not known a priori, and hence its determination becomes part of the problem definition, rather than serving as prior knowledge which aids the problem solution. Part III of this monograph starts by addressing ways to learn graph topology, from the case where the physics of the problem already suggest a possible topology, through to most general cases where the graph topology is learned from the data. A particular emphasis is on graph topology definition based on the correlation and precision matrices of the observed data, combined with additional prior knowledge and structural conditions, such as the smoothness or sparsity of graph connections. For learning sparse graphs (with small number of edges), the least absolute shrinkage and selection operator, known as LASSO is employed, along with its graph specific variant, graphical LASSO. For completeness, both variants of LASSO are derived in an intuitive way, and explained. An in-depth elaboration of the graph topology learning paradigm is provided through several examples on physically well defined graphs, such as electric circuits, linear heat transfer, social and computer networks, and spring-mass systems. As many graph neural networks (GNN) and convolutional graph networks (GCN) are emerging, we have also reviewed the main trends in GNNs and GCNs, from the perspective of graph signal filtering. We have in particular studied the diffusion process over graphs and have shown that the trend of various improvements on GCNs can also be understood from the graph diffusion perspective. Given that the existing GCNs have been introduced largely in a heuristic manner, the definition of different diffusion processes can also serve as a basis for a new design of GCNs. Tensor representation of lattice-structured graphs is next considered, and it is shown that tensors (multidimensional data arrays) are a special class of graph signals, whereby the graph vertices reside on a high-dimensional regular lattice structure. This part of monograph concludes with two emerging applications in financial data processing and underground transportation networks modeling. By means of portfolio cuts of an asset graph, we show how domain knowledge can be meaningfully incorporated into investment analysis. In the underground traffic example, we demonstrate how graph theory can be used to identify the stations in the London underground network which have the greatest influence on the functionality of the traffic, and proceed, in an innovative way, to assess the impact of a station closure on service levels across the city. Contents 1 Introduction 2 2 Geometrically Defined Graph Topologies 3 3 Graph Topology Based on Signal Similarity 4 4 Learning of Graph Laplacian from Data 8 4.1 Imposing Sparsity on the Connection Metric 10 4.2 Smoothness Constrained Learning of Graph Laplacian .

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Market Graph and Markowitz Model

Cited by 14 publications

References 17 publications

Complexities in Financial Network Topological Dynamics: Modeling of Emerging and Developed Stock Markets

Complexities in Financial Network Topological Dynamics: Modeling of Emerging and Developed Stock Markets

Market Graph Clustering via QUBO and Digital Annealing

Graph Signal Processing -- Part III: Machine Learning on Graphs, from Graph Topology to Applications

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