Overlapping claims and the possibility of financial contagion: exploring the Finnish interbank markets

The current prevalence of financial crises makes is tempting to conclude that the financial sector is unusually susceptible to shocks. One possible theory says that we do not need large shocks to understand financial crises, since small local shocks in a particular part of the financial system can be spread by contagion to the rest of the financial sector and then infect the larger economy. Financial contagion could consequently be seen as a process by which eg a problem or crisis that begins in one region spreads to an economically linked region.

In some cases the basis of this contagion is informational. Recent literature has argued that asymmetric information can give rise to contagion between countries that are affected by common fundamentals. Think of asset markets in two different countries, for example. A change in prices may result from a common shock that affects asset values in both countries or it may be generated by an idiosyncratic shock that either has no effect on asset values or that affects only one of the two countries. Because of asymmetric information, the idiosyncratic shock can be mistaken for a common shock, a fall in prices in one country may lead to a self-fulfilling expectation that prices will fall in the other country. In that case, a costly and welfare reducing instability could possibly arise in the second country because of an unrelated crisis in the first country.

Naturally, this is not the only type of contagion. Allen and Gale (2007)[1] explore another type, the possibility of which arises from the overlapping claims that different regions or sectors of the banking system have on one another. In this set up, if one region suffers a banking crisis, the other regions suffer a loss because their claims on the troubled region fall in value. Sufficiently strong spillover effects will then cause a crisis in the troubled region's economic neighbours, so that in the extreme case a systemic event can result as the crisis passes from region to region infecting an increasing part of the financial system and maybe even the larger economy.

To understand the possibility of contagion through interlinkages the background literature offers some interesting models and thought experiments which nicely highlight the role of liquidity or liquidity preference in the process generating contagious effects. Think of consumers facing uncertainty about their intertemporal consumption preferences so that they are uncertain about the amount of savings they have to generate for consumption both tomorrow and further ahead. Once this uncertainty is resolved, the economy consists of early and late consumers.1 Allen, F and Gale, D (2007), Understanding Financial Crises, Calendron Lectures in Finance, Oxford University Press.

Uncertainty about consumption preferences creates demand for liquidity. Now, banks have a comparative advantage in providing liquidity. Consumers deposit their income in the banks, which invest it on behalf of the depositors, and, in exchange, depositors are promised funds for consumption at each subsequent period, depending on when the depositors choose to make withdrawals.

Banks' investment possibilities consist of short and long assets. The former pays next period a return of one unit, while the latter can be liquidated in the next period for a return of less than one unit or held to maturity for a return of more than one unit. Thus, liquidating the long asset is costly, so this is not very useful for providing consumption for those consumers who want to consumer early.

Imagine now that the economy consists of a number of regions and that the number of early and late consumers fluctuates randomly in each region. Regional demand for liquidity thus fluctuates, but the aggregate demand for liquidity is constant. The key feature in this set up is that it allows for interregional insurance, as regions with excess liquidity provide liquidity for regions short of liquidity.

One way to organize the provision of liquidity is through the exchange of interbank deposits. The implied interregional holdings of deposits work well as long as there is enough liquidity in the banking sector as a whole. Once there is excess demand for liquidity, however, the financial linkages created by these crossholdings may prove disastrous. Crossholdings are useful for allocating liquidity within the banking system, but they cannot increase the aggregate amount of liquidity. Consequently, if the economy-wide demand for liquidity exceeds the stock of short-term assets, the only way to increase it and, ultimately, consumption is to liquidate long-term assets. However, there are limits to such liquidation without provoking a bank run. If a run on a bank takes place, those banks holding deposits in the defaulting bank will suffer a capital loss, which may render them incapable of meeting their commitments to provide liquidity in their regions. Thus, crossholding of deposits is the mechanism through which a local financial crisis spreads by contagion in other regions.

Whether and to what extent a financial crisis spreads depends critically on the pattern of inter-connectedness generated by the crossholdings. An interbank network can be characterized as complete if each region is connected to all other regions, and incomplete if each region is connected only to a possible small subset of other regions.[1] In a complete network, the amount of interbank deposits that any bank holds is spread relatively evenly over a large number of banks so that the initial impact of a financial crisis in any one region may be attenuated. On the other hand, the initial impact of a financial crisis in an incomplete network is concentrated in the few neighbouring regions, with the result that they succumb to the crisis relatively easily. The crisis prompts a premature liquidation of long-term assets in the regions being infected, implying a consequent loss of value, so that previously unaffected regions find that they, too, are affected. There is a free rider problem in explaining the process of contagion, as each bank is trying to meet external demand for liquidity by drawing down its deposits in other banks. While banks in this process are effectively passing the buck to other banks, the end result is that all the interbank deposits disappear and no one gets additional liquidity.

More often than not, a reluctance of banks to lend to each other and tightened lending policies in interbank markets are symptomatic of an increasing risk of an emerging or an already ongoing process of a contagious financial crisis. Hence, an important question is if we can by using actual interbank market data identify processes possibly related to contagious crises, and, if so, which banks and how large crossholdings are most critical for the potential emergence of a contagious financial crisis.

An interesting forthcoming Bank of Finland discussion paper, Financial Interlinkages and Risk of Contagion in the Finnish Interbank Market by Mervi Toivanen takes steps to answer these questions. The author uses current data from the Finnish interbank market as well as data from the crisis period in the first half of the 1990s to evaluate through simulation methods the likelihood of contagion in the current state of the market and to evaluate the ability of the methods she employs to detect interlinkages in the problem period of the early 1990s which most likely would have triggered contagious effects resulting in a banking crisis.

As Toivanen observes, many empirical studies on financial crises and contagion have concentrated on (national) banking systems, basically following one of two approaches. One uses simulation methods to study the effects of a bank failure. Often such simulation studies conclude by not being able to disregard significant contagion effects, but also find adverse systemic outcomes in the form of eg substantial weakening of the banking sector unlikely.

The second approach focuses on a wide variety of shocks and other sources of risk. This approach incorporates alternative methods from simulation to the application of standard risk management techniques to study the effects of contagion, but the common feature of these exercises is the network structure of banks' interbank exposures. Descriptive studies of the banking sector's counterparty risks as well as studies building on distance-to-default indicators to analyse contagion risks should be included in the second approach.

Toivanen points out in her study that, since Finnish banks do not have to disclose their counterparties, very little is known about the actual structure of bilateral exposures in Finland and how these financial linkages impinge upon the contagion risk. Consequently, to carry out her simulation exercise, Toivanen needs to generate bilateral exposures or the whole distribution of interbank loans and deposits. She exploits an existing methodology by Upper et al[2] to generate bilateral exposures through maximized entropy. Entropy is heavily used in information theory, where it measures the uncertainty associated with a random variable. More specifically, Shannon entropy, as it is called in information theory, quantifies, in the sense of expected value, the information contained in a message or, equivalently, the average information content one is missing when one does not know the value of the random variable.

It is this latter characterization of entropy that gives us the intuition behind the method of maximizing entropy in the present context: interbank loans and deposits are spread over banks as equally as is consistent with their observed interbank exposures. This is a close analogue to the concept of 'complete interbank network' referred to above, where the basic idea is that banks symmetrically hold claims on all other banks in the economy, conditioned on the size-structure of the banks.

Toivanen shows in her simulation study that the risk of a contagion that results in a banking crisis is very low in the current state of the Finnish interbank markets. More specifically, five deposit banks out of ten are potential triggers for contagion, but the breadth and depth of the contagion depends on the first failing bank. In addition to large commercial banks, some of the middle-sized banks are also capable of triggering a contagion with systemically important implications. Of some interest is the result that the five banks identified by Toivanen as potential triggers for contagious effects retain their status in this respect across different time periods.

Upon repeating the simulations on data prior to the early 1990s, the author concludes that the risk of a systemically important contagion increased in the banking sector from 1988 to 1990. Moreover, in comparison with the historical evidence the method of maximum entropy is able to pick up those financial institutions that posed a threat to the stability of the Finnish banking system. All in all, the analysis as well as the results presented in Toivanen's forthcoming paper are very interesting and contribute importantly to our understanding of financial crises as well as to our tools for analysing and monitoring the evolution of the state of the financial system. As this study should be seen as part of a wider research agenda aiming to gain deeper understanding of the process and effects of contagion and financial crises, further research efforts are clearly welcome.