Financial Risk & Network Theory

This essay examines lessons from systemic breakdowns, and presents a framework for Adaptive Stress Testing to proactively manage systemic risks. The framework is inspired by evolutionary ecosystems, including ecology, economics, technology, psychology, and sociology. Adaptive Stress Testing harnesses network intelligence to integrate early warning signals. We pre-diagnose systemic fragilities by tapping into the marketplace of ideas, and then identify key metrics to monitor market-based early warning signals. We apply the Technology Adoption Lifecycle model to develop a theory of social diffusion of disruptive information in financial markets. We start by taking a macro view of risk in its hidden potential form, and then focus on phase transition signals as risk becomes visible. This process allows us to better understand key systemic risks, and to more effectively sense and respond to emerging risks.

Abstract

The network pattern of financial linkages is important in many areas of banking and finance. Yet bilateral linkages are often unobserved, and maximum entropy serves as the leading method for estimating counterparty exposures. This paper proposes an efficient alternative that combines information-theoretic arguments with economic incentives to produce more realistic interbank networks that preserve important characteristics of the original interbank market. The method loads the most probable links with the largest exposures consistent with the total lending and borrowing of each bank, yielding networks with minimum density. When used in a stress-testing context, the minimum-density solution overestimates contagion, whereas maximum entropy underestimates it. Using the two benchmarks side by side defines a useful range that bounds the cost of contagion in the true interbank network when counterparty exposures are unknown.

Paper co-authored by:

• Kartik Anand, Financial Stability Department, Bank of Canada
• Ben Craig, Deutsche Bundesbank and Federal Reserve Bank of Cleveland
• Goetz von Peter, Bank for International Settlements

Abstract

European banks’ cross exposures via marketable securities are largely visible via collateral supporting ECB operations. The network thus inferred is referred to as the interbank securities network. Owing to the geographical comprehensiveness (all banks active in the euro area), detail on the type of cross-bank exposures and high frequency of the information, the analysis of structural developments in euro area banking is possible, in particular facilitating information for policy decisions. For this purpose a number of system-wide metrics are developed and their usefulness for policy making explained. Notably, information available since 2009 suggests that integration in the interbank system has been faltering, and that the interbank structure is increasingly organised in national components.

Abstract

Intro/Problem

Partially as a result of recent regulatory policy, financial regulators1 have been tasked with increased levels of market surveillance and oversight, aimed at ensuring healthy market liquidity and identifying potentially destabilising risks. Included within this mandate is promoting financial stability, mitigating risks which may be of a nature to harm the market as a whole. One of the more prominent areas of concern during the 2008-2009 financial crisis was swaps linked to credit risks, including credit default swap (CDS) contracts. These swaps can be especially difficult to monitor given that they embed multiple risk dimensions, including risks to trade counterparty and to reference entity. Because of a general lack of both regulatory and public data prior to the crisis, international policymakers have called for increased data transparency, and, subsequently, effective methods to use this data for robust financial oversight.

Literature/ Background Risk

Regulatory literature over the last few years has expanded its use of network analysis, and its associated metrics, in order to assess the means by which a bank engages in risk transfer not just between itself and counterparties, but how it fits within the risk transfer network as a whole. Some examples of this use of network tools include the Fed’s monitoring of credit risks passed between the bank dealer network, an IMF working paper on systemic risk as implied by FDIC swap exposures, and the Bank of England’s work on cross-border balance sheet exposures. However, many commonly used network metrics, such as measures of centrality and aggregated accounts of risk flows, are not always well calibrated to the specifics of a given financial market (e.g. jump-to-default risks in credit swaps are not shared by products like interest rate or FX swaps). Results or risk rankings generated by network metrics often only portray one of a number of concerns that may arise from bank activity. In their most general forms, these measures typically focus on a single risk dimension, such as risk to market movements or risk to market volatility, rather than on the relationships between risk dimensions. As seen recently, these relationships can often have the most prominent effects in the area of system stability2.

Visual Analysis

One approach in addressing some of the oversight gaps resulting from a reliance on metrics alone has been to integrate then with visual analytics. This technique merges analytical reasoning with interactive visual interfaces. A key advantage of using visual techniques is the transformation of multidimensional data into a visual representation which can clarifies important relationships inherent to the network structure and to the idiosyncratic characteristics of nodes/edges. When done well, Perer and Shneidermen (2008) have suggested that integration of these tools can dramatically speed up insight for visualisation users, in our case regulators and policy-makers. For the case study included in this paper, risk transfers effected by individual financial entities along with entity classes (at a determined aggregate level), will be matched with network measures which proxy for entity importance to the network on a global level.

CDS Market

CDS instruments provide insurance against the default of a given institution (commonly known as the reference entity), and require regular payment streams from the counterparty purchasing protection. After an event of company default, where the company cannot fully satisfy it debt obligations, the CDS seller agrees to make the purchaser “whole,” paying against losses accrued on a given set of bonds or the equivalent bond notional. Historically, most of these transactions have been bilateral, with both counterparties having present and/or future, state-contingent, payment obligations. This system of relationships is one of the largest examples of credit intermediation within the financial world3, and takes three primary forms: the assumption of credit risk by dealers from their clients, the distribution of risks between dealers, and the reallocation by dealers of risks back to their clients. In the visualisations developed in the paper, the focus will be on interdealer trading, as reported to data repositories4, including how client risks get intermediated between dealers.

Hive Plot

Given that CDS contracts have historically relied on bilateral relationships, network visualisations, when used, have typically focused on how trade relationships and exposures distribute risk by way of ones counterparties (see Yellen, 2013 and Haldane, 2009). Corresponding network measures often then capture, quantitatively, the risks depicted in the associated network diagrams. These measures encapsulate individual forms of risk transfer such as the most prominent vectors of risk between entities (betweenness centrality), entities with greatest distribution of risk (closeness centrality) or even measures of an entity’s importance to risk at a global level (eigenvector centrality). Credit risk summaries at the level of a node, on the other hand, depend critically on a counterparty’s concentration and default correlation to a specific reference entity, risk that is sourced by the product itself. Though market participants rely on contractual valuation models that take into account the joint risk of counterparty and credit risk default, often with difficulty5, this problem is even more acute for regulators who must be able to grasp these joint exposures not just for a single financial firm, but for firms which differ by size, geographical reach and business practices. Establishing a concise method of depicting these variations across firms, while also prioritising risk as it may affect financial stability, is a crucial product of regulatory oversight.

In this paper, we propose a less-commonly used graphical representation, the hive plot (Krzywinski, 2012), matched with numerical summaries, as one way of achieving this efficient rendering. Figure # provides a sample hive plot, where axes consolidate entities by business practices (dealers versus clients) and by counterparty risk versus product risk (the latter by reference entity axis). The individual nodes and edges in the chart display the relationship between counterparties, and can be filtered by a selection of reference entities. To clarify with an example, a buy-side institution (for example, a hedge fund) may purchase CDS protection from a dealer, who then offsets this position through a trade with a second dealer. Both dealers are shown twice, to allow for explicit depiction of the interdealer trade. Finally, the second dealer “closes the loop” by buying protection from a second end user outside the interdealer core of the market (perhaps an asset manager). Detailed depictions like this provide valuable context for an analyst to understand market behaviour and evaluate risks, namely counter party and reference entity, in unison.

Applications

In our paper we will outline how network risks of multiple types (risks within the inter-dealer network, risks between dealers and their clients, risks due to reference entity characteristics) evolve during crisis events, during natural periods of risk re-allocation (such as the credit index roll) and how margin and clearing may mitigate some of these concerns.

Conclusions

Our paper suggests that the use of visual tools can play a significant role when integrated with traditional network analytical techniques; this integration is especially powerful when a network visualisation is especially attuned to the idiosyncratic characteristics of a market structure – in our case the hive plot and bilateral CDS relationships. This visual technique allows for the integration of several risk dimensions, such as distinguishing between type and importance of counterparty, along with the importance of product risk, and therefore clarifies financial stability weaknesses. In order to demonstrate the value and potential uses of these visual techniques, we have shown how application to the bilateral CDS market, especially during periods of market instability, can focus regulators on the sources and vectors of potentially cascading failures, along with ways of mitigating these concerns.

1 By “regulator” we implicitly encompass a number of different parties, the most obvious being that of public government market regulators like the SEC, CFTC or FSA. In addition, however, this could include SRO’s such as FINRA or NFA within the US, and exchanges tasked with market oversight.

2 For instance, risk associated to AIG’s CDS position was exacerbated by the positive relationship between negative market movements in its CDS sales and its own credit-worthiness, requiring unfulfillable margin calls by its counterparties.

3 The most recent estimate of global credit derivatives notional exposure (H1 2013) by the Bank of International Settlements is approximately $24tr.

4 The data is sourced from the largest credit swap data repository during the period of study, the Depository Trust and Clearing Corporation (DTCC).

5 See the controversies regarding the use of Gaussian copulas to estimate correlation risks in credit markets.

Paper co-authored by:

• Sriram Rajan, Office of Financial Research
• Richard Haynes, US Treasury Department
• Mark Paddrik, Office of Financial Research

Recent years have seen rapid advances in the techniques used to measure the susceptibility of financial systems to systemic risk. Of particular note is the in- creased use of network based measures to empirically examine the effects of the failures of banks on the rest of the financial system. In this paper we employ these techniques to examine the spread of contagion in the American financial system in period around the 1873 banking panic. There are two purposes to this work. Firstly it enhances our understanding of the mechanisms at play during the 1873 crisis. Previous studies of this period have used written accounts and aggregated data to understand the behaviour of banks and the financial system. No analysis has employed the latest techniques in network analysis with the available data to quantitatively examine how the structure of the financial system, and the positions of the banks, might allow crises to spread. Our study aims to resolve debates in the economic history literature with regard to how this crisis propagated. Historical studies differ on this point, some argue that the crisis principally stemmed from New York and its effects were only significantly felt there. Others argue that the state of the periphery played a much more significant role. There are also arguments regarding the actual susceptibility of banks to failure – whether the crisis spread through loss of confidence or actual weakness in balance sheets.

The second purpose of this work is to increase our understanding of modern financial crisis. One of the key difficulties in understanding how balance sheet information translates into financial weakness in modern banks is the complex asset positions and off balance sheet activities which modern banks frequently adopt. An advantage of studying the period of history this paper focuses on, as opposed to the most recent financial crisis, is that the assets holdings of banks were much simpler. There was at the time no national over-night interbank lending system – the physical constraints of communication and transportation across long distances made this impossible. Similarly the number of derivative contracts, and in particular derivatives on financial firms or positions, was much smaller. In particular CDS were not traded for another 100 years and off balance sheets activities such as CDO’s and SPV’s were unheard of. As a result this historical financial system provides a much cleaner test bed for the analysis of contagion and systemic risk.

We base our analysis on data from the Annual Report of the Comptroller of the Currency. These reports are available from the Federal Reserve Archive and detail the full balance sheets of all U.S. national banks from 1863 onwards. In this paper we focus on the years surrounding the 1873 panic: 1872-1874. During this period there were approximately two-thousand banks spread between forty-two states and territories. One-hundred and eighty-two of these banks were located in fifteen reserve cities and a further forty-nine were based in the central reserve city of New York. Based on this we construct networks of financial connections. In similar work focusing on current financial systems maximum entropy techniques have been used to produce configurations of relationships based on minimal assumptions. This has been shown, however, to create an overly connected network which, in turn, is less susceptible to systemic risk than the real financial systems which are being modeled. To remedy this we incorporate the nature of the regulatory system and technological constraints to refine the network. During this period state banks were required to keep a portion of their deposit holdings in reserve city banks, such as those in St. Louis or Boston, whilst reserve city banks had to keep a portion of their reserves in the banks of the central reserve city – New York. The balance sheet data specifically lists the amount each bank is owed form reserve city banks and the amount owed form other national banks. This allows us to place constraints on viable network structures.

We also exploit the constraint that communication and the transfer of funds were not instantaneous at this time. In the modern financial system electronic communication technology means that if a bank wishes to lend money the physical location of the counter-party within a given jurisdiction has little impact. For a bank in New York, lending to a bank in Boston or San Francisco has little material difference. In the 1800’s, however, the amount of time it would take to transport and then recover funds from the latter over the former causes significant liquidity risks. The lack of communications technology also meant that the amount of information available about geographically distant banks was far less. As such we may model banks as having a preference for geographically close counter-parties. We use a range of specifications for the effect of distance in modeling this factor. In constructing the most likely network we numerically minimise the distance between counter-parties whilst maintaining compliance with regulations and balance sheet quantities. Due to the very large space of possible networks we employ a stochastic approach to this minimisation. As a result many viable networks are generated and then tested to provide robust conclusions.

We use historical data to construct a series of stress tests to analyse the vulnerability of the generated financial networks to the shocks. The scenarios are based on movements in the stock markets, defaults on railroad bonds, withdrawal of specie and the failure of counter party banks. The analysis is repeated across each of the three years of data. Analysis of 1872 allows us to consider the run up to the crisis and how close the banking system came to failure a year earlier than it actually occurred. By analysing 1874 we may determine if the actions taken after the crisis were adequate to reduce the risk of banks suffering adverse events. We focus our analysis on two aspects – the susceptibility of New York banks to shocks and the likelihood of contagion across the rest of the system. New York was the financial center at the time and so failure of banks in this city could have a significant effect on the stock market and international trade. Banks in the rest of the country were relatively smaller, however, their failure could cause serious issues for the communities they helped to support.

Paper co-authored by:

• Daniel Ladley, Department of Economics, University of Leicester
• Peter L. Rousseau, Department of Economics, Vanderbilt University

We are witnessing interesting times rich of information, readily available for us all. Using, understanding and filtering such information has become a major activity across science, industry and society at large. Our society has become a global information processing system where news propagate and impact on the real economy at increasingly fast rates with increasingly large effects. It is therefore important to have tools that can analyse this information while it is generated and that can provide ways to reduce complexity and dimensionality while keeping the integrity of the dataset. Information content and flow are often associated with large degrees of redundancy both in time (repeating and scaling patterns) and across different variables (similarity, dependency and causality). Redundancy is often used to convey strength to the meaning or, more simply, it is the signal of recurring patterns with high statistical significance and therefore important.

In this talk we propose to use such redundancy to build an information based network that retains the relevant part of the data-interdependency structure. The structure of this network is a representation of the information in the dataset and such information can be efficiently analysed by using network-theoretic tools. The idea of using redundancy – namely correlation coefficients – to filter information in large-scale datasets by building networks of relevant links has been very actively studied in the literature mostly by means of two approaches: 1) the minimum spanning tree (MST)1,2 and 2) the planar maximally filtered graph (PMFG)3,4. The common idea underneath these two approaches is to retain the largest and most significant possible sub-graph while imposing global constraints on the topology of the resulting network. In particular, in the MST approach, the links with largest weights (e.g. correlations) are retained while constraining the sub-graph to be globally a (spanning) tree. Similarly, in the PMFG construction the largest weights (e.g. correlations) are retained while constraining the sub-graph to be globally a planar graph. The PMFG has richer information content than the MST with a larger number of edges (3N-6 instead of N-1, with N being the number of vertices) and the presence of 3- and 4-cliques. Planar filtered graphs are powerful tools to study complex datasets. It has been shown in5 that by making use of the 3-clique structure of the PMFG a clustering can be extracted allowing dimensionality reduction that keeps both local information and global hierarchy in a deterministic manner without the use of any prior information.

We show that applications to financial data-sets can meaningfully identify industrial activities and structural market changes6. Planar filtered graphs can be used to diversify financial risk by building a well-diversified portfolio that effectively reduces investment risk by investing in stocks that occupy peripheral, poorly connected regions in the financial filtered networks7. Another appealing advantage of planar filtered networks, such as the PMFG, concerns graphical modeling (e.g. Markov Random Fields) where the structure of the network ensures that exact inference algorithms can be performed in an efficient fashion8.

However, the algorithm so far proposed to construct the PMFG is numerically costly with O(N3) computational complexity and cannot be applied to large-scale data. There is therefore scope to search for novel algorithms that can provide, in a numerically efficient way, such a reduction to planar filtered graphs. We introduce a new algorithm, the TMFG (Triangulated Maximally Filtered Graph)that efficiently extracts a planar subgraph which optimises an objective function. The method is scalable to very large datasets and it can take advantage of parallel and GPUs computing. The method is adaptable allowing online updating and learning with continuous insertion and deletion of new data as well changes in the strength of the similarity measure9.

1 R.C. Prim, Bell-System Technical Journal 36 (1957) 1389-1401.

2 R.N. Mantegna, Eur. Phys. J. B 11 (1999) 193-197.

3 T. Aste, T. Di Matteo, S. T. Hyde, Physica A 346 (2005) 20.

4 M. Tumminello, T. Aste, T. Di Matteo, R. N. Mantegna, PNAS 102, n. 30 (2005) 10421.

5 W.-M. Song, T. Di Matteo, and T. Aste, PLoS ONE 7 (2012) e31929.

6 N. Musmeci, T. Aste, T. Di Matteo, “Clustering and hierarchy of financial markets data: advantages of the DBHT”, arXiv: 1406.0496 [qfin.ST] submitted 2014.

7 F. Pozzi, T. Di Matteo and T. Aste, Scientific Reports 3 (2013) 1665.

8 Amir Globerson Tommi Jaakkola. Approximate inference using planar graph decomposition. In Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference, Vol.19, page 473. MIT Press, 2007.

9 G. Previde Massara, T. Di Matteo, and T. Aste, draft (2014)

Paper co-authored by:

• T. Aste, Department of Computer Science, University College London and Systemic Risk Centre, London School of Economics and Political Sciences
• T. Di Matteo and N. Muscmeci, Department of Mathematics, King’s College London
• G. Previde Massara, Department of Computer Science, University College London