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Contagion and self-fulfilling dynamics

Contagion and self-fulfilling feedback loops are propagation mechanisms at the heart of systemic financial crises. Contagion refers to the deterioration of fundamentals through the financial network, often through a cascade of insolvencies. A critical factor is the similarity of assets held by financial institutions. The commonality of assets erases some of the benefits of diversification because it facilitates contagion. The potential role of investment funds in aggravating contagion through fire sales has much increased over the past 20 years. Self-fulfilling feedback loops denote the shift from one equilibrium to another, possibly without a change in ‘fundamentals’. They arise from multiple equilibria and strong interdependencies in a financial network. Bank runs are a classic example. Simple metrics that track both types of systemic risk are principal components and cross-correlation coefficients of different types of financial assets.

The below is a summary based mainly on:

Jackson, Matthew and Agathe Pernoud (2020), “Systemic Risk in Financial Networks: A Survey”.
Montagna, Mattia, Gabriele Torri, and Giovanni Covi (2020), “On the Origin of Systemic Risk”, ECB Working Paper Series No 2502 / December 2020.
with quotes from
Choudhari, Sayuj and Richard Zhu (2020), “Diagnosis of systemic risk and contagion across financial sectors”.
Mirza, Harun, Diego Moccero, Spyros Palligkinis, and Cosimo Pancaro (2020) “Fire Sales by Euro Area Banks and Funds: What is Their Asset Price Impact?” ECB Working Paper Series No 2491 / November 2020.

The post ties up with this site’s summary on managing systemic risk.

Definition of financial systemic risk

“In the most general terms, systemic risk can be described as the risk of threats to financial stability that impair the functioning of a large part of the financial system with significant adverse effects on the broader economy.” [Montagna, Torri and Covi]

“[For model purposes] systemic risk is…the probability of a systemic event… [It is] the probability of a systemic event at time t, conditional on an information set that characterizes the state of the system available in a previous time…
A systemic event is defined as a scenario in which a large number of banks default or go into distress [at] the same time…A systemic event [should be] characterized by a clear and measurable indicator, [such as] the number of financial institutions going bust simultaneously over a certain time period.” [Montagna, Torri and Covi]

“[The figure below] represents the time series of the fraction of banks that experienced default or other credit events for the U.S. (left panel) and for the euro area (right panel)…The peaks of the series track closely…systemic banking crises…Two statistical properties are striking. First, there is…clusterization of banks distress and default events [and] strong correlation among banks’ default probabilities…Second, there is also large auto-correlation…Systemic events in the banking sector leave significant aftermaths. [Montagna, Torri and Covi]

The origin of financial systemic risk

“Financial interdependencies generate systemic risks…Because banks are interconnected, their values depend on each other…Financial networks are complex systems in which many institutions are interconnected in various ways.

  • First and foremost, institutions are linked through financial contracts: they lend to and borrow from each other to smooth idiosyncratic liquidity variations…
  • Second, even when financial institutions are not transacting directly, commonality in their exposures lead their values to be correlated.” [Jackson and Pernoud]

“The main drivers of systemic risk are the presence of correlated shocks from the real economy and market contagion that manifests in terms of fire sales of assets.” [Montagna, Torri and Covi]

Financial markets are ripe with externalities as the fates of institutions depend upon each other in a variety of ways. At a most basic level, insolvencies involve substantial costs which are then passed on via defaults and drops in equity values, especially if left to cascade…The externalities mean that the system as a whole can experience crises that are much broader and costlier than the independent failures that ignite them. Hence the term ‘systemic risk.’” [Jackson and Pernoud]

“The associated increasingly interconnected financial network among ever-larger nodes…paves the way for systemic risk. Interdependencies between financial institutions can act as amplification mechanisms and create channels for a shock in one part of the system to spread widely, leading to losses that are much larger than the initial changes in fundamentals.” [Jackson and Pernoud]

“The literature has highlighted two main distortions in banks’ investment decisions: they have an incentive to take on too much risk, and to correlate their portfolios with that of their counterparties…A bank’s investment decisions not only impact its own value, but also indirectly the values of its counterparties, and of its counterparties’ counterparties, and so on…Forces pushing towards correlation are regulations that limit the scope of investments, essentially pushing them to hold certain classes of assets, minimum amounts of certain assets, or to have a portfolio that meets certain risk characteristics. Banks also have forces that push them to the same lending strategies as their competitors.” [Jackson and Pernoud]

Two basic types of financial systemic risk

“We draw a distinction between two types of systemic risk: (i) contagion through various channels that generate externalities…and (ii) self-fulfilling feedback effects..

  • Financial contagion…captures how a change in fundamentals can move through the network…A change in the value of bank i affects bank j…This then affects the values of banks connected to j, and so on: a change in one bank’s value spreads through the network and has far reaching consequences. This form of risk is the focus of much of the literature.
  • [Self-fulfilling feedback effects] stem from the multiplicity of equilibria and a possible shift from one equilibrium to another. Even in the absence of any change in the values of fundamental investments, network interdependencies can lead to self-fulfilling feedback effects whereby changes in beliefs become realized.” [Jackson and Pernoud]

The nature of contagion

Contagion is a cascade of insolvencies. A bank gets low returns on its investments and cannot pay its debts. As those liabilities are defaulted upon, this worsens the balance sheets of other institutions leading some of them to become insolvent. As more become insolvent, the values of others are further depressed and this cascades through the network…Insolvencies involve substantial bankruptcy costs…Each additional insolvency then leads to deadweight losses to the system, and the overall cost can greatly exceed the initial shock.” [Jackson and Pernoud]

When a bank becomes insolvent, it often has to sell, prematurely, significant amounts of assets in fire sales. Such dumping depresses prices for those assets, reducing the portfolio values of other banks holding similar assets. This can lead others to default, and their assets sales to create a downward spiral. This is particularly problematic when portfolios are correlated across banks. That leads both to stronger exposures, and greater pressures on prices…The effect of fire sales on market prices depends on market imperfections. One is that the financial market is not deep enough to absorb a liquidation of a large bank’s portfolio without price impact. There may also be asymmetric information, and market participants may infer something about underlying fundamentals when observing large-scale sales.” [Jackson and Pernoud]

Commonalities in exposures pave the way for another form of contagion: ‘guilt by similarity.’ People have doubts about the solvency of other enterprises that are similar to an insolvent one. Two key elements make such contagion possible: correlated portfolios across banks and uncertainty about the value of fundamentals and/or the banks’ portfolio structures.” [Jackson and Pernoud]

“An initial shock to yields causes [investment] funds to sell assets to address investor redemptions, while both banks and funds sell assets to keep their leverage constant. These fire sales generate second-round price effects…The contribution of funds to this impact is lower than that of banks. However, assets under management of investment funds have soared in recent years…[and] funds’ relative contribution has risen… Should this trend continue, funds will become an increasingly important source of systemic risk.” [Mirza, Moccero, Palligkinis, and Pancaro]

The nature of multiple equilibria and self-fulfilling dynamics

“Systemic risk can arise even in the absence of any change in fundamental values. As soon as a financial network allows for multiple equilibria, a mere shift in beliefs can move the system discontinuously from one equilibrium to another, with real economic consequences. Belief changes could arise from inferences, as mentioned above, that reflect real underlying correlations; but they could also arise via sunspots, bubbles, or exogenous events that can be conditioned upon by investors. The key idea is that if there are multiple equilibria, then which equilibrium applies depends on which one people expect.” [Jackson and Pernoud]

Bank runs and panics falls under [the] category of systemic risk, in which behavior becomes self-fulfilling. This source of risk stems from banks’ primitive role of transforming short-term deposits into long-term illiquid investments, which makes banks inherently fragile institutions: if enough depositors withdraw their funding before the bank realizes its investments, the bank cannot repay all of them and defaults…Merely expecting a bank to be insolvent and withdrawing their deposits, depositors can induce its insolvency. Importantly, this sort of risk need not be triggered by a decrease in the value of the bank’s fundamentals, but merely by a shift in beliefs about the health of the institution. It could even be that people know that a bank is healthy but are worried that others are unsure of its health.” [Jackson and Pernoud]

Fear and pulling back of investments can occur not only on the part of depositors and outside investors, but also on the part of banks. Uncertainty about economic conditions can lead banks to doubt how sound many businesses will be. This can feed on itself, as if banks fear a recession they can pull back their capital and require ever higher interest rates. This can lead to defaults, and banks to begin to doubt each other’s health and to stop contracting with each other, making it more difficult for banks to rebalance their portfolios. This leads to further tightening and potential spiralling, and possibly to a complete credit freeze.” [Jackson and Pernoud]

“Self-fulfilling default cascades differ from classic bank runs as they are generated by network interdependencies, rather than purely by beliefs. They appear in any network of exposures between banks for which there are multiple equilibrium values for interbank claims…Financial contracts between banks can lead to self-fulfilling chains of defaults. Recall that interbank contracts make bank values interdependent. The anticipation of one bank failing to pay its debts can depress the value of other banks, and feedback to the original bank, making its default self-fulfilling…As a bank adds counterparties it becomes susceptible to drops in values or defaults from more sources – which tends to increase the potential for cascades.” [Jackson and Pernoud]

The fragility of networks

Positive correlation in investments across banks erases some of the benefits of diversification in counterparties, and facilitates contagion. More generally, increasing the correlation in portfolios of investments leads to increased probabilities of co-defaults…Positive correlation in investments across banks erases some of the benefits of diversification in counterparties, and facilitates contagion. More generally, increasing the correlation in portfolios of investments leads to increased probabilities of co-defaults…Of course, the worst case is when the banks have similar and under-diversified portfolios – for instance, all holding similar mortgages or loans – as then they are correlated and risky.” [Jackson and Pernoud]

Financial networks have an intriguing property of being ‘robust-yet-fragile’. Interdependencies between banks, in the form of lending or liquidity provision for instance, allow for risk-sharing, which can help individual institutions be less susceptible to individual liquidity or portfolio shocks…However, very large shocks can cause an institution to fail despite the diversification, and then interdependencies can transmit the shock more widely and more extensively.” [Jackson and Pernoud]

“There exists multiple equilibria for bank values if and only if there is a cycle composed of banks that are sufficiently interconnected, such that a bank’s solvency depends on the solvency of its predecessor in the cycle…This becomes self fulfilling: there is an equilibrium in which all banks are insolvent and no debts are paid. There is also an equilibrium in which all debts are paid.” [Jackson and Pernoud]

“[One can] distinguish between two shock regimes: shocks that are small enough to be absorbed by total excess liquidity in the system, and those that are not. In the former regime, interdependencies unambiguously alleviate the risk of contagion: the network structure most resilient to contagion is the complete network, in which each bank’s total liabilities are spread equally across all other banks. This leads to maximal risk sharing, and minimal expected number of defaults. However, if shocks are larger than the total excess liquidity in the system, interdependencies just facilitate its propagation.” [Jackson and Pernoud]

Without network information, one cannot even identify which banks are at risk of insolvency…The main input into many stress tests is balance sheet data, which describes the amount of each type of financial assets and liabilities held by each bank…Such ‘local’ data can completely miss which banks are most likely to start a default cascade, or be caught up in one.” [Jackson and Pernoud]

Two simple trackers of contagion and self-fulfilling dynamics

“Two [simple and timely] measures of systemic risk that require only easily-available time series data: principal component analysis [and] cross-correlation…[of] daily and monthly returns on hedge fund indexes and broad-based market indexes.

  • Principal component analysis…helps to measure and identify systemic risk through analyzing return data for evidence of market friction across Hedge Funds, Banks, Brokerages, and Insurers…Principal component analysis involves the eigenvalue decomposition between data sets…[i.e.] the amount of variation brought by each data set…If the fractional variation of the first or first few eigenvalues was very high and quickly approached 1..there [would be] less variation among them and their movements [would become] similar. Therefore, principal component analysis is…used to measure the connectedness of institutions within a market as well as the market fragility.
  • The cross-correlation coefficient…indicates the levels of correlation between two assets with a possible time lag…In periods of [high] systemic risk, these correlations between assets [are] increasing as market friction increases…Cross-correlation coefficients between types of financial data are used to identify…systemic risk…The single comparison used in cross-correlations, which cannot be done in principal components analysis, is helpful for creating more highly defined mappings of systemic risk.” [Choudhari and Zhu]

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