Physica A: Statistical Mechanics and its Applications
Loan and nonloan flows in the Australian interbank network
Highlights
► Statistical properties of high-value transactions between banks in Australia. ► The underlying causal mechanism connecting loan and nonloan payment flows. ► Payment flows cause imbalances, which drive compensating flows of overnight loans. ► The imbalances are closely counterbalanced by the flows of overnight loans. ► The loan and nonloan flow networks are dynamically linked.
Introduction
Financial systems are characterised by a complex and dynamic network of relationships between multiple agents. Network analysis offers a powerful way to describe and understand the structure and evolution of these relationships; background information can be found in Refs. [1], [2], [3]. The network structure plays an important role in determining system stability in response to the spread of contagion, such as epidemics in populations or liquidity stress in financial systems. The importance of network studies in assessing stability and systemic risk has been emphasised in Ref. [4] in the context of integrating economic theory and complex systems research. Liquidity stress is of special interest in banking networks. The topology of a banking network is recognised as one of the key factors in system stability against external shocks and systemic risks [5]. In this respect, financial networks resemble ecological networks. Ecological networks demonstrate robustness against shocks by virtue of their continued survival and their network properties are thought to make them more resilient against disturbances [6]. Often they are disassortative in the sense that highly connected nodes tend to have most of their connections with weakly connected nodes (see Ref. [7] for details). Disassortativity and other network properties are often used to judge stability of financial networks.
There has been an explosion in empirical interbank network studies in the last years thanks largely to the introduction of electronic settlement systems. One of the first, reported in Ref. [8], examines the Austrian interbank market, which involves about 900 participating banks. The data are drawn from the Austrian bank balance sheet database (MAUS) and the major loan register (GKE) containing all high-value interbank loans above ; smaller loans are estimated by means of local entropy maximisation. The authors construct a network representation of interbank payments for ten quarterly periods from 1999 to 2003. They find that the network exhibits small-world properties and is characterised by a power-law distribution of degrees. Specifically, the degree distribution is approximated by a power law with the exponent −2.01 for degrees ≳40. This result, albeit with different exponents, holds for the in- and out-degree distributions too (the exponent is −3.1 for out-degrees and −1.7 for in-degrees). A recent study of transactional data from the Austrian real-time interbank settlement system (ARTIS) reported in Ref. [9] demonstrates a strong dependence of network topology on the time-scales of observation, with power-law tails exhibiting steeper slopes when long time-scales are considered.
The network structure of transactions between Japanese banks, logged by the Bank of Japan Financial Network system (BOJ-NET), is analysed in Ref. [10]. The authors consider several monthly intervals of data from June 2001 to December 2002 and construct monthly networks of interbank links corresponding to 21 transactions or more, i.e. one or more transaction per business day on average. Truncating in this way eliminates about 200 out of 546 banks from the network. The resulting monthly networks have a low connectivity of 3% and a scale-free cumulative distribution of degrees with the exponent −1.1.
More than half a million overnight loans from the Italian electronic broker market for interbank deposits (e-MID), covering the period from 1999 to 2002, are analysed in Ref. [11]. There are about 140 banks in the network, connected by about 200 links. The degree distribution is found to exhibit fat tails with power-law exponent 2.3 (2.7 for in-degrees and 2.15 for out-degrees), the network is disassortative, with smaller banks staying on its periphery. In a related paper [12], the authors make use of the same dataset to uncover liquidity management strategies of the participating banks, given the reserve requirement of 2% on the 23rd of each month imposed by the central bank. Signed trading volumes are used as a proxy for the liquidity strategies and their correlations are analysed. Two distinct communities supporting the dichotomy in strategy are identified by plotting the correlation matrix as a graph. The two communities are mainly composed of large and small banks respectively. On average, small banks serve as lenders and large banks as borrowers, but the strategies reversed in July 2001, when target interest rates in the Euro area stopped rising and started to decrease. The authors also note that some mostly small banks tend to maintain their reserves through the maintenance period. The evolution of the network structure over the monthly maintenance period is examined in Ref. [13].
A study of the topology of the Fedwire network, a real-time gross settlement (RTGS) system operated by the Federal Reserve System in the USA, is reported in Ref. [14]. The study covers 62 days in the first quarter of 2004, during which time Fedwire comprised more than 7500 participants and settled 3.45×105 payments daily with total value $1.3 trillion. It reveals that Fedwire is a small-world network with low connectivity (0.3%), moderate reciprocity (22%), and a densely connected sub-network of 25 banks responsible for the majority of payments. Both in- and out-degree distributions follow a power law for degrees ≳10 (exponent 2.15 for in-degrees and 2.11 for out-degrees). The network is disassortative, with the correlation of out-degrees equal to −0.31. The topology of overnight loans in the federal funds market in the USA is examined in Ref. [15], using a large dataset spanning 2415 days from 1999 to 2006. It is revealed that the overnight loans form a small-world network, which is sparse (connectivity 0.7%), disassortative (assortativity ranging from −0.06 to −0.28), and has low reciprocity of 6%. The reciprocity changes slowly with time and appears to follow the target interest rate over the period of several years. A power law is the best fit for the in-degree distribution, but the fit is only good for a limited range of degrees. A negative binomial distribution, which requires two parameters rather than one for a power law, fits the out-degree distribution best.
A comprehensive survey of studies of interbank networks is given in Ref. [16]. The number of interbank markets being analysed continues to increase. For example, a study of the interbank exposures in Brazil for the period from 2004 to 2006 was reported in Ref. [17]. A topological analysis of money market flows logged in the Danish large-value payment system (Kronos) in 2006 was reported in Ref. [18], where customer-driven transactions are compared with the bank-driven ones. Empirical network studies have been used to guide the development of a network model of the interbank market based on the interbank credit lending relationships [19].
Establishing basic topological features of interbank networks is essential for understanding these complex systems. Fundamentally, however, interbank money markets are flow networks, in which links between the nodes correspond to monetary flows. The dynamics of such flows has not been examined in depth in previous studies, which mostly viewed interbank networks as static or slowly varying. But the underlying flows are highly dynamic and complex. Moreover, monetary flows are inhomogeneous; loan flows are fundamentally different from the flows of other payments. Payments by the banks’ customers and the banks themselves cause imbalances in the exchange settlement accounts of the banks. For some banks, the incoming flows exceed the outgoing flows on any given day; for other banks, the reverse is true. Banks with excess reserves lend them in the overnight money market to banks with depleted reserves. This creates interesting dynamics: payment flows cause imbalances, which in turn drive compensating flows of loans. Understanding this dynamic relationship is needed for advancing our ability to model interbank markets effectively.
In this paper, our objective is to define empirically the dynamics of interbank monetary flows. Unlike most studies cited above, we aim to uncover the fundamental causal relationship between the flows of overnight loans and other payments. We choose to specialise in the Australian interbank market, where we have privileged access to a high-quality dataset provided by the Reserve Bank of Australia (RBA). Our dataset consists of transactions settled in the period from 19 to 23 February 2007 in the Australian interbank market. We separate overnight loans and other payments (which we call nonloans) using a standard matching procedure. The loan and nonloan transactions settled on a given day form the flow networks, which are the main target of our statistical analysis. We compare the topology and variation of the loan and nonloan networks and reveal the causal mechanism that ties them together. We investigate the dynamical stability of the system by testing how individual flows vary from day to day. Basic network properties such as the degree distribution and assortativity are examined as well.
Section snippets
Data
High-value transactions between Australian banks are settled via the Reserve Bank Information and Transfer System (RITS) operated by the RBA since 1998 on an RTGS basis [20]. The transactions are settled continuously throughout the day by crediting and debiting the exchange settlement accounts held by the RBA on behalf of the participating banks. The banks’ exchange settlement accounts at the RBA are continuously monitored to ensure liquidity, with provisions for intra-day borrowing via the
Overnight loans
The target interest rate of the RBA during the week of our sample was per annum. If the target rate is known, it is easy to extract the overnight loans from the data by identifying reversing transactions on consecutive days. A hypothetical interest rate can be computed for each reversing transaction and compared with the target rate. For instance, suppose a transaction of value from bank A to bank B on day 1 reverses with value , from bank B to bank A, on day 2. These transactions
Nonloans
We display the distributions of the incoming and outgoing nonloan transactions, for which the bank is the destination and the source respectively, for the six largest banks in Fig. 4. The distributions are similar to the total distribution shown in Fig. 1, with the notable exception of BA (see below). There is also an unusually large number of A$106 and A$400 transactions from W to T on Monday. Note that the daily imbalance for each bank is mostly determined by the highest value transactions;
Loan and nonloan imbalances
In order to maintain liquidity in their exchange settlement accounts, banks ensure that incoming and outgoing transactions roughly balance. However, they do not control most routine transfers, which are initiated by account holders. Therefore, the imbalances arise. On any given day, the nonloan imbalance of bank is given by where is a list of values of individual nonloan transaction from bank to bank , settled on the day. The nonloan imbalances are
Flow variability
For each individual source and destination, we define the nonloan flow as the totality of all nonloan transactions from the given source to the given destination on any given day. The value of the flow is the sum of the nonloan transaction values and the direction is from the source to the destination. On any given day, the value of the flow from bank to bank is defined by where is a list of values of individual nonloan transactions from to on the day.
Net flows
The net flow between any two banks is defined as the difference of the opposing flows between these banks. The value of the net flow equals the absolute value of the difference between the values of the opposing flows. The direction of the net flow is determined by the sign of the difference. If , the net flow value from to is given by For instance, if the flow from D to AV is larger than the flow in the opposite direction, then the net
Conclusions
In this paper, we study the properties of the transactional flows between Australian banks participating in RITS. The value distribution of transactions is approximated well by a mixture of two log-normal components, possibly reflecting the different nature of transactions originating from SWIFT and Austraclear. For the largest banks, the value distributions of incoming and outgoing transactions are similar. On the other hand, the central bank displays a high asymmetry between the incoming and
Acknowledgment
We thank the Reserve Bank of Australia for supplying the data. AS acknowledges generous financial support from the Portland House Foundation.
References (26)
- et al.
Trading strategies in the Italian interbank market
Physica A: Statistical Mechanics and its Applications
(2007) - et al.
A network analysis of the Italian overnight money market
Journal of Economic Dynamics and Control
(2008) - et al.
The topology of interbank payment flows
Physica A: Statistical Mechanics and its Applications
(2007) - et al.
The topology of the federal funds market
Physica A: Statistical Mechanics and its Applications
(2010) - et al.
The role of banks in the Brazilian interbank market: does bank type matter?
Physica A: Statistical Mechanics and its Applications
(2008) - et al.
A network model of the interbank market
Physica A: Statistical Mechanics and its Applications
(2010) Statistical Analysis of Network Data: Methods and Models
(2009)Social and Economic Networks
(2008)Scale-Free Networks: Complex Webs in Nature and Technology
(2007)- et al.
Economic networks: what do we know and what do we need to know?
Advances in Complex Systems
(2009)
Systemic risk in banking ecosystems
Nature
Ecology for bankers
Nature
Mixing patterns in networks
Physical Review E
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