Physica A: Statistical Mechanics and its Applications
The topology of the federal funds market
Introduction
The recent turmoil in global financial markets underscores the continuing importance of the federal funds market. Its smooth functioning is of utmost importance for distributing liquidity throughout the financial system and for the practical implementation of monetary policy. Banks rely heavily on the federal funds market to offset liquidity shocks and manage their reserve positions over the two-week reserve maintenance period. In formulating monetary policy, the Federal Open Market Committee (FOMC) sets a target for the effective federal funds rate and directs the Federal Reserve Bank of New York to “create conditions in reserve markets” that will encourage federal funds to trade near the target. Creating such conditions became a significant challenge beginning in August 2007. Massive amounts of liquidity were injected into the market on several occasions. Nevertheless, the federal funds rate deviated from its target considerably more than usual both within and across days.
In this paper, we take an in-depth look at the structure of the federal funds market from the vantage point of network topology. Networks have proved useful in analyzing a wide array of structures and interactions across a multitude of fields. In recent years, the physics community has made significant progress toward understanding the structure and functioning of complex networks. The literature has focused on characterizing the structure of networked systems and how the properties of the observed topologies relate to stability, resiliency, and efficiency in the case of perturbations and disturbances. Recently, economists have started to show renewed interest in networks.
We represent the federal funds market as a network, in which financial institutions are nodes and loans are directed links, weighted by the value of the loans between the counterparties. Using a unique transaction-level data set spanning 1997–2006, we are able to analyze in unprecedented detail the characteristics of the overnight federal funds network and its evolution over the past decade. We find that the value sent between banks has increased even though the number of participants in the network has decreased. Like other complex networks, the federal funds network is sparse, exhibits the small-world phenomenon, and is disassortative. The number of counterparties per bank (degree) follows a fat-tailed distribution, with most banks having few counterparties and a small number having many. However, unlike other networks, the degree distribution is not necessarily best represented by a power law distribution. Using network-specific measures, we are able to shed new light on the small-bank–large-bank dichotomy of the federal funds market, whereby small banks generally lend funds to larger banks. Finally, we provide preliminary evidence that centrality measures, which determine the relative importance of banks in the network, are useful predictors of the interest charged between banks.
In Section 2, we begin with a quick overview of some of the institutional details of the federal funds market. In the subsequent section we review the literature on the federal funds market and network theory. Section 4 describes the data used in our study. Section 5 outlines some network terminology. Section 6 presents different ways to visualize the federal funds network. Section 7 contains the analysis and results of the paper. Section 8 concludes.
Section snippets
Federal funds market
The federal funds market is the market for immediately available reserve balances at the Federal Reserve. Depository institutions that maintain accounts at the Federal Reserve can borrow (buy) or lend (sell) reserve balances. Federal funds, or fed funds, are unsecured loans, and the rate at which these transactions occur is called the fed funds rate. Most trades are delivered on the same day, and the duration is typically overnight; but trades for longer terms (called term fed funds) also take
Literature review
The importance of the federal funds market has not escaped the notice of academic research. Ho and Saunders [3] develop a model in which banks have a target reserve balance that they achieve through participation in the federal funds market. Banks that are risk averse to having a deficient balance will have interest-rate–elastic-demand functions for purchasing federal funds. Since large banks have more options for obtaining necessary reserves, they are less risk averse. Large banks therefore
Data
We construct our networks from the transaction journal of the Fedwire Funds Service.4 The Fedwire Funds Service provides a real-time gross settlement system in which more than 7000 participants initiate funds transfers, which
Federal funds networks
A network is a collection of nodes joined in pairs by directed links. Links can have weights attached, measuring the strength of the relationship between nodes. Mathematically, a weighted directed network, , is defined by a set of nodes (vertices), a set of of links (edges), and a mapping . Each node is identified by an integer value ; the links are identified by a pair that represents a connection going from node to node to which a weight is
Visualizing the federal funds network
The federal funds loan network for September 29, 2006–the last business day of the third quarter–is illustrated in Fig. 4. A total of 479 banks were active in the market on that day. The largest bank–in total value of federal funds bought and sold–is located at the center of the graph. The first circle consists of the 165 banks with which the bank in the center did business. The second circle consists of the 271 banks that the banks of the first circle did business with. The banks in the second
Topological characteristics
We now turn to a detailed analysis of the topological features of the federal funds network. Our modus operandi is first to define the topological measures and then to present the results. For the results, we first focus on the statistics for 2006 and then turn to describing the trends observed since 1997. For the ease of exposition, we shall refer to market participants as banks even though institutions such as thrifts and government-sponsored enterprises are also important players in the
Conclusion
In this paper, we analyze the topology of the 2415 daily networks formed by overnight federal funds loans between commercial banks and other financial institutions over the period April 1, 1997, to December 29, 2006. These networks share many of the characteristics found in other complex networks. We identify two relationships between network statistics and factors external to the network. First, we find that reciprocity is correlated with the federal funds rate. Second, Bonacich centrality is
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The views expressed in this paper do not necessarily reflect those of the Federal Reserve Bank of New York or the Federal Reserve System.