Introduction
The global economy is currently facing a financial crisis of unprecedented scale, reminiscent of the Great Depression This turmoil began in the summer of 2007 with a credit crunch triggered by declining US house prices As many financial institutions worldwide were heavily invested in the US mortgage market, rising mortgage default rates forced banks to write down their portfolios, severely impacting their balance sheets and violating capital reserve ratios Consequently, the interbank loan market collapsed due to a lack of confidence in counterparties' capital reserves, compounded by their unclear investments in the distressed mortgage sector Current macroeconomic indicators reveal a stark reality: global stock markets have plummeted, world trade volumes have decreased, and numerous Western nations are officially in recession.
Figure 1: MSCI World index, period 04-04-2005/01-04-2009 Figure 2: World Trade Volumes
The ongoing crisis has led to significant challenges, including difficulties for companies in refinancing debt and widespread layoffs across various sectors The primary concern for financial institutions, private businesses, and households is the uncertainty regarding the future Despite governments worldwide injecting billions into the market to restore confidence, tangible improvements remain elusive Reflecting on the 2008 crisis raises important questions about the roles and responsibilities of key players, particularly within the financial sector This thesis aims to examine whether government interventions, such as bank bailouts during times of crisis, are justified and effective.
The core function of banks is to convert illiquid assets into liquid liabilities, facilitating the efficient allocation of capital that has historically supported economic prosperity As banks have become internationally active, society's dependency on them has increased, prompting government intervention as a lender of last resort during financial crises While government support is crucial for maintaining the stability of the financial sector, it raises concerns about moral hazard and the neglect of smaller banks Systemic risk, defined as the potential for a widespread financial meltdown triggered by an idiosyncratic event, necessitates careful government monitoring and intervention Research indicates that governments tend to bail out larger banks, deemed "too big to fail," due to their extensive linkages and roles in the payment system However, this approach can create adverse effects, such as encouraging riskier behavior among bankers This thesis aims to explore systemic risk in banking, emphasizing the impact of bank failures on the financial sector and providing regulators with insights to guide their bailout decisions amidst the complexities of financial contagion.
This thesis addresses the contagion effect of bank failures through the introduction of the Bank Contagion Index, a novel measurement based on heavy-tailed return distributions, as established by Campbell, Lo, and Mackinlay (1998) By applying Extreme Value Theory, we quantify how the failure of one bank can impact the stability of others within the financial system Our analysis covers the ten largest banks and five randomly selected smaller banks in Germany, Switzerland, and the US from 1975 to 2009 Findings indicate that interregional contagion is significantly lower than contagion within regions, with a noticeable increase in contagion effects over time Additionally, a comparison of market values with the Bank Contagion Index reveals unique insights specific to Germany.
“size matter” In the US, interestingly enough other factors are at play Finally we conclude that bail outs by government are necessary however they should be handled with care.
This thesis is structured into four key sections Section 2 offers a theoretical background and literature review on the financial crisis, highlighting various models developed to explain and predict such crises along with their related policy responses Section 3 presents our empirical study, detailing the fundamentals of Extreme Value Theory and introducing our innovative measurement approach alongside the dataset utilized Section 4 analyzes the findings of our research, while Section 5 concludes with insights derived from the study conducted.
Literature review and theoretical background
Introduction to financial crises
Over the past century, numerous financial and economic crises have occurred globally, with the earliest recorded instance in 1819 Historical patterns indicate that periods of economic growth are typically followed by downturns, yet recognizing this cycle often requires concrete evidence of future trends A notable aspect of financial crises is the tendency to overlook or deny their impending arrival, as illustrated by Chuck Prince, former CEO of Citigroup, who stated in July 2007, "As long as the music is playing, you've got to get up and dance We're still dancing." This thesis will primarily examine financial crises, acknowledging their broader impact on the real economy, as these crises frequently escalate into wider economic downturns Before delving into specific crises, we will define a financial crisis using Richard Portes' definition from the London Business School.
A financial crisis disrupts financial markets, hindering their ability to allocate capital effectively and causing a halt in financial intermediation and investment Each crisis is characterized by its unique background and causes, presenting challenges for regulators Nevertheless, various types of financial crises have been identified in the literature, which we will now explore in detail.
2 Starting year of “ the Panic” in the US.
3 Interview in the Financial Times of mr Prince by D Wighton., FT July 9 2007
4 Richard Portes., 1998, “An analysis of Financial crisis: lessons for the international Financial system”, FRB Chicago 8-10 october 1998
2.1.1 Different types of financial crises
A speculative attack on a currency often arises when investors lose confidence and begin to sell it off, particularly when the currency is pegged to another Fixed exchange rates are especially susceptible to such attacks due to the substantial reserves required to maintain them Notably, economist Paul Krugman (1979) was among the first to highlight that governments with significant currency reserves may actually be more vulnerable to these speculative assaults, presenting a model that illustrates this phenomenon.
The "Balance-of-Payments crisis" highlights the psychology of speculators in predicting and understanding speculative attacks on currencies A notable instance of such an attack occurred on Black Wednesday, September 16, 1992, when the Sterling Pound plummeted by 10% The market's disagreement on the pound's value against the European Exchange Rate Mechanism (ERM) led to a mass sell-off Despite the British treasury's efforts to stabilize the currency by purchasing pounds, they ultimately failed to maintain the peg As a result, Britain entered a significant recession following this speculative attack.
The attack on the Russian Ruble in mid-1997 exemplifies how a currency crisis can trigger a broader economic downturn Following the onset of the Asian financial crisis, the Ruble was artificially pegged to a Western currency, requiring substantial foreign currency reserves to sustain this rate As investors began to sell off the Ruble, the Russian government was forced to deplete nearly all its reserves to maintain the peg This depletion eroded investor confidence, resulting in a staggering 65% decline in the stock market in just one day Ultimately, what began as a currency attack escalated into a significant financial and economic crisis.
A bank run typically arises from a lack of confidence in a bank or the broader financial system, often observed during financial crises when individuals seek safer investments like government bonds This phenomenon, referred to as a "flight to quality," can lead to a bank run fueled by shifting expectations and irrational behavior, as highlighted by Diamond and Dybvig (1983) Their research suggests that bank runs can be triggered by various factors, reflecting the unpredictable nature of public sentiment and the urgency for individuals to withdraw their funds.
• The collapse of asset prices:
In prosperous economic times, rising asset prices are driven by increased income and demand for consumption and investments However, it's crucial to maintain a balance between asset price growth and economic value creation, as higher asset prices should ideally stem from enhanced productivity or total output When credit availability and speculation inflate asset prices without corresponding productivity gains, a bubble forms, which can eventually burst, triggering a crisis Distinguishing between speculation and genuine productivity growth is challenging As asset prices decline, a chain reaction occurs, leading to homeowner defaults, reduced consumer spending, and decreased corporate investments This culmination of factors, coupled with waning economic growth and confidence, sets the stage for an economic crisis.
Crisis situations often exhibit multiple trigger factors simultaneously, complicating their anticipation and prevention Regulators strive to learn from each crisis to avoid recurrence; however, the prevailing optimism during economic booms can obscure the potential for downturns According to Burns and Mitchell (1946), a contraction typically follows a boom as part of the business cycle Friedman and Schwartz (1963) and Bernanke and Gertler (1989) argue that financial crises stem from economic fluctuations, highlighting the cyclical nature of markets Furthermore, Friedman et al (1963) emphasize that financial crises increase intermediation costs and restrict credit, ultimately leading to periods of low or negative growth and recession Conversely, some researchers, like Kindleberger (1978) and Diamond and Dybvig (1983), view financial crises as random events or self-fulfilling prophecies, unrelated to the real economy.
Financial crisis determinants are widely theorized, with various factors believed to have predictive power However, only a limited number of these factors are measurable and have successfully undergone empirical testing We categorize these determinants into two main groups: macroeconomic factors and financial factors.
The GDP growth rate serves as a key indicator of a country's economic health, with negative growth signaling increased vulnerability to crises, including potential banking system failures Research by Demirgúc-Kunt et al (1998) underscores the significance of GDP growth as a crucial predictor of economic crises.
Short-term interest rates play a crucial role in the banking sector, as banks typically maintain a balance sheet with long-term assets funded by short-term deposits and long-term liabilities This mismatch in maturities exposes banks to interest rate risk, particularly during periods of rising interest rates, when competitive pressures compel banks to pass these increases on to depositors Even if banks can transfer higher rates to borrowers, the impact on their balance sheets can be detrimental due to an increase in nonperforming loans, resulting in a negative interest rate effect Research by Mishkin (1996) indicates that most banking panics in the US were preceded by rising short-term interest rates, with factors influencing these increases including inflation rates, monetary policy restrictiveness, global interest rate trends, and the removal of interest rate controls, as noted by Galbis (1993) Additionally, Kaminsky and Reinhart (1999) highlight the use of short-term interest rates to defend exchange rates against speculative attacks.
Inflation stabilization in countries with a history of high inflation can pose challenges for the banking sector, as highlighted by English (1999) Chronic high inflation often correlates with a robust financial sector that benefits from payment floats Reducing inflation by cutting these profits can lead to difficulties for banks reliant on such revenues Central banks typically combat inflation by raising short-term interest rates, a strategy that may inadvertently trigger a financial crisis.
The capital ratios of banking systems play a crucial role in their resilience to external economic shocks, as those with lower ratios are more susceptible to banking crises While this may seem intuitive, it is often overlooked during periods of economic prosperity when confidence in the financial system tends to overshadow this essential aspect.
A decline in asset prices is a significant indicator that often precedes a financial or economic crisis, signaling the need for caution Monitoring asset price trends is crucial, as a downturn can serve as a warning sign of potential economic instability.
Countries with weak currencies often face challenges in their banking systems, as they must raise capital in foreign currencies while lending in their domestic currency This dual approach exposes banks to fluctuations in exchange rates, which can jeopardize their capital stability and lead to solvency issues Calvo (1996) highlighted the importance of the M2 to foreign exchange reserves ratio, demonstrating a significant correlation between this ratio and the likelihood of a financial crisis.
Policy implications
Section 2.1 provided an overview of the causes, consequences and frequency of financial crises Acknowledging the specific character of the financial sector by the government is essential In times of crisis clear and effective governmental intervention is crucial In this section we will look at the different recovery policies, their consequences and how they were used in the past and how they are best applied in the future Furthermore, we discuss the literature concerning necessary regulation to protect our financial and economic system. Special attention will be put in the Moral Hazard problem, which according to the literature is inherent to the world’s financial system
Effective policy responses during a crisis are contingent on the specific source of the crisis, as various crises necessitate different approaches While there is no universal solution that fits all scenarios, recent empirical research indicates that determining the efficacy of specific policies is challenging Nevertheless, there is a general agreement on fundamental policy responses and their potential impacts on the economy.
Governments and regulatory institutions possess macroeconomic tools to mitigate financial crises and restore economic stability Following a speculative exchange rate attack, research by Portes (1998) indicates that the most effective response is to abandon the fixed exchange rate and allow for currency devaluation However, governments often exhaust their capital reserves in attempts to defend their currency, ultimately increasing their vulnerability Portes also critiques the role of the International Monetary Fund, suggesting that it should not act as an International Lender of Last Resort during international financial crises.
Due to their inability to generate their own funds, they rely heavily on government support, which can lead to suboptimal decisions during times of crisis This dependence highlights the need for a reevaluation of their role and constitutional framework to ensure more effective financial management and decision-making on an international level.
IMF should be to act in a country-by-country way In worldwide systemic crises the LLR should be a domestic one which is coordinated with other troubled domestic LLR
Luc Laeven (2008) developed a comprehensive database documenting 42 systemic banking crises from 1970 to 2007, analyzing their timing, macroeconomic impacts, and policy responses This section focuses on the findings related to policy responses, with a detailed summary of the types and frequency of these interventions presented in Table 3 For additional insights into other results, readers are directed to Laeven's original article.
Table 3: Different policy responses and the number of times used in the period 1970-2007 15
Intervention type number of crisis
Large-Scale government intervention in banks 36
The government typically provides liquidity support in times of financial crisis, having offered direct assistance in 30 out of 42 cases analyzed Additionally, nationalization, deposit insurance, and IMF programs serve as indirect forms of support The decision to intervene in a struggling bank or banking system often hinges on the costs associated with inaction While some banks are deemed "too big to fail," this designation does not solely correlate with their size This analysis highlights the proactive role of governments and regulators in coordinating solutions to restore the financial system, including reestablishing normal credit flow and strengthening banks' balance sheets.
Governments often adjust the macroeconomic environment to foster a quicker and more sustainable economic recovery, typically through measures such as lowering income taxes and interest rates According to Laeven (2008), there exists a trade-off for governments between the speed and durability of recovery and the associated fiscal costs Despite this, governments frequently prioritize rapid recovery over fiscal concerns, making it challenging to assess the effectiveness of their decisions, particularly since the potential outcomes of not pursuing an expedited recovery are difficult to simulate.
Governments must navigate a delicate balance when intervening in the financial industry, as such actions can either mitigate the impact on the real economy or exacerbate future risks While intervention can prevent widespread economic contagion, it may also lead to moral hazard, where decision-making is adversely affected Understanding the significance of predictable policy is crucial, as it highlights the potential negative consequences of intervention, particularly the emergence of moral hazard.
Effective policy resolution relies heavily on good communication and predictability During crises, uncertainty breeds anxiety, leading individuals to behave erratically Therefore, governments must establish clear communication to foster predictable behavior among the populace The 2008 financial crisis exemplifies the consequences of unclear policy communication, as evidenced by the significant spike in credit spreads following ambiguous announcements regarding a rescue package by the US government and the Federal Reserve.
Figure 10 Jump in Libor-OIS spread
The bankruptcy of Lehman Brothers, a major New York investment bank previously considered "too big to fail," caused a slight increase in credit spreads due to market anxiety over the government's decision not to provide a bailout This uncertainty was briefly alleviated by a subsequent intervention in American Insurance Group (AIG), but concerns resurfaced following Federal Reserve Chairman Ben Bernanke's testimony regarding a $700 billion stimulus package, which raised further questions about the government's knowledge of the financial situation As credit spreads continued to rise, Taylor (2009) highlighted the critical importance of clear government decision-making during crises, emphasizing that effective response policies can only succeed if the markets understand them and maintain confidence in their implementation Taylor also provided valuable recommendations for policymakers to enhance the effectiveness of their strategies.
The Libor-OIS credit spread serves as a key indicator of banks' confidence in one another and the overall economy, with high spreads reflecting significant uncertainty Government intervention must stem from a well-defined diagnosis of economic issues, accompanied by a solid rationale for the actions taken Additionally, it is essential to establish a predictable and effective framework for assisting financial institutions during times of crisis.
Historically, inconsistent government interventions led to market uncertainty and unpredictability, a trend that has resurfaced globally To enhance stability, policymakers must adopt a consistent approach and clearly communicate their rationale behind decisions However, predictable policy resolutions can lead to individuals adjusting their decision-making to capitalize on government interactions This phenomenon will be further explored in the following section.
Moral hazard has a tremendous impact on the financial sector by influencing the decisions made by an agent, depending on whether there is insurance in place or not (see Dow 2000).
Moral hazard occurs when individuals or entities take greater risks because they are insulated from the consequences, exemplified by a car owner who neglects safe driving due to having insurance coverage To mitigate this issue, insurance companies have implemented "own risk" policies However, moral hazard is not limited to insurance; it also affects banks and financial regulators This article will explore two types of moral hazard: one at the corporate level (micro) and the other at the industry level (macro), analyzing their causes and consequences.
Moral hazard in the corporate banking sector arises from remuneration packages that heavily incentivize trading performance As banks increasingly engage in trading activities alongside traditional lending, traders' compensation often hinges on the profits they generate, typically through performance-based bonuses This structure creates a situation where traders are encouraged to take excessive risks, as their potential losses do not impact their remuneration negatively A notable instance of this behavior is the Barings Bank collapse, where trader Nick Leeson's risky bets led to the bank's downfall Additionally, the Black-Scholes formula illustrates how the value of traders' options is influenced by the volatility of underlying assets; greater risk-taking results in higher volatility and, consequently, higher option values.
At the industry level, the principal-agent problem intensifies, manifesting between bank management and regulators, which poses significant risks to the entire financial sector Historically, governments have intervened to bail out large banks during financial crises, highlighting the "too big to fail" phenomenon, which varies by country Regulators face a dilemma: either rescue an insolvent bank, risking moral hazard, or allow it to fail, potentially eroding depositor confidence and triggering mass withdrawals Additionally, the critical role of major banks in global payment systems compels regulators to act, as the repercussions of disrupting these networks are deemed too severe to ignore.
Empirical study
Extreme Value Theory
Many financial studies assume a normal distribution of asset returns due to its simplicity and the valuable insights it provides However, empirical data often reveals that return distributions can be more extreme than what a normal distribution predicts, as highlighted by Campbell, Lo, and Mackinlay (1998) For instance, Caserta and de Vries (2003) analyzed the return distribution of the AEX, demonstrating significant deviations from normality in daily log-returns during the observed period.
1983 till March 2009 The peaks in the distribution are respectively the crashes of:1987(black Monday), 1998(Russian debt crisis), 2001(9/11 terrorist attacks), 2008(Credit crisis)
Figure 12 Daily logarithmic returns of the AEX, 01-01-1983 / 01-03-2009
Note: the circled parts are the crises: Black Monday, Russian debt crisis, 9/11 terrorist attacks, 2008 crisis
Figure 13 Randomly generated returns with a normal distribution
Note: the normal distribution has the mean and standard deviation of the AEX return for the period: 1983-2009
When comparing the distributions of figures 12 and 13, which represent randomly generated returns with a normal distribution, it becomes evident that the AEX log-returns exhibit more extreme characteristics During financial crises, traditional normal distribution models significantly underestimate the likelihood and consequences of such extreme events This distinctive feature of asset price distribution can be effectively analyzed using Extreme Value Theory Recently, both regulators and investors have recognized the importance of this approach.
Extreme Value Theory (EVT) offers a compelling framework for risk management, particularly in calculating Value at Risk (VaR), as it effectively models the probability of significant losses without relying on the distribution shape of asset prices EVT employs a semi-parametric approach, where the tails above a high threshold align with a Pareto distribution while allowing flexibility in the moderate part of the distribution function Its ability to capture the co-movement of extreme events in multidimensional contexts, including tail dependency, makes EVT particularly valuable Recent applications of multivariate EVT, such as those by Hartmann et al (2004) and Huang (1992), have successfully modeled tail dependencies in financial markets EVT has also been instrumental in addressing portfolio diversification challenges, as noted by Hyung and de Vries (2002) Our research focuses on the multivariate approach, specifically examining stress linkages among banks during crises, starting with a discussion of univariate EVT, which underpins our study.
3.1.1 Univariate EVT: fat tails and the tail index
Financial return distributions often exhibit fat tails, prompting interest in effectively capturing and predicting these extremes Extreme Value Theory (EVT) facilitates this modeling, exemplified by its application in determining optimal dike heights to safeguard nations like the Netherlands from severe flooding Today, the principles of EVT are increasingly applied in finance, particularly in periods of economic instability This article provides an overview of univariate EVT, highlighting its significance in risk assessment and management.
Recognizing the existence of fat tails in F(x) is the first step in EVT We use Feller (1971) definition of fat tails:
25 The explanation is based on Caserta and de Vries (2003)
F(x) is heavy tailed if for sufficiently large x:
1 as x → ∞ , α > 0 , (1) and the slowly varying function L(x) is such that for any x>0
Looking at the tail part of the distribution only x − α is asymptotically important As the limit of L(tx)/L(t) = 1,
The power function x − α represents the Pareto distribution, where α denotes the tail index that reflects the size of the tail A smaller tail index indicates fatter tails, distinguishing it from a normal distribution, which has exponential-like tails that decrease more rapidly This unique characteristic enables the estimation of the heavy tail area within the distribution, such as calculating the Value-at-Risk at a specified probability level p.
When considering Value at Risk defined as for low level of p and p 0, the
This method allows for the calculation of Value at Risk (VaR) at a lower confidence level (p) using an existing VaR at an intermediate confidence level Typically, one selects k equal to p, where n represents the number of observations and k denotes the count of higher-order statistics, ensuring a reliable tail approximation.
To estimate the tail index α, we utilize the Hill estimator, which is particularly effective for analyzing independent and identically distributed observations, denoted as X₁, X₂, , Xn The Hill estimator provides a reliable method for quantifying the tail behavior of a distribution.
Where: X ( ) 1 ≥ X ( ) 2 ≥ ≥ X ( ) k ≥s≥ X ( k + 1 ) ≥ ≥ X ( n ) are the order statistics of X 1 ,X 2 X n
The Pareto distribution applies above a certain threshold, denoted as S, and the selection of order statistics, k, is essential for determining the correct tail index Ideally, k should approach infinity while the product of k and n should tend toward zero as n increases However, since n represents a finite number of observations, the Hill plot can be utilized to identify k by examining the first stable segment following the initial variable portion This initial segment is influenced by the limited number of observations, while the middle section may introduce bias It is important to recognize the trade-off between variance and bias when selecting k, as choosing a value that is too low or too high can impact results Additionally, a higher tail index, α, indicates less extreme tail behavior.
Extreme Value Theory (EVT) enables the prediction of behavior in the far tail of heavy-tailed distributions by analyzing the not-so-far tail This approach utilizes available data from the not-so-far tail to extrapolate insights into the far tail Building on the principles of univariate EVT, we will now explore multivariate EVT, which has been applied to assess contagion effects within the banking industry.
Multivariate Extreme Value Theory (EVT) enables the analysis of joint tail behavior among multiple risk factors and their interdependencies This approach is particularly useful for assessing the contagion effects of one bank on others within the same region The methodology is straightforward: univariate EVT is applied to evaluate individual risk behavior, while the dependence function L(x₁, x₂, , x_d) captures the co-movements Essentially, any joint distribution can be broken down into its marginal distributions and a dependence function, allowing multivariate EVT to examine the joint probability of extreme co-movements To better understand this, we can first explore the two-dimensional case, which serves as the foundation for multivariate EVT.
Assume a system with two banks: with loss returns X and Y Following de Haan and Ferreira(2006) the two-dimensional EVT assumes that there exists a G ( ) x , y such that:
We can express the marginal tail indices:
Using these marginal tail indices we can remove the marginal information by simply changing the x into 1
(7) no longer contains marginal information
Notice that VaR X ( ) px ≈ VaR X ( ) p ∗ x − α 1 1 and VaR Y ( ) px ≈ VaR Y ( ) p ∗ y − α 1 2
We can rewrite (7) as follow:
( ) L ( ) x y p py VaR orY px VaR X
The marginal information, represented by the tail indices α1 and α2, does not affect L(x,y), indicating that the two-dimensional Extreme Value Theory (EVT) conditions model the marginals through one-dimensional EVT while capturing tail dependence with the L(x,y) function By applying L(x,y) for x = y = 1, a straightforward measure of tail dependency can be estimated.
According to de Haan and Ferreira (2006), the value of L(1, 1) ranges from 1 to 2, where L(1, 1) = 1 signifies complete tail dependency, indicating that if variable X is in crisis, variable Y will also be in crisis Conversely, L(1, 1) = 2 represents tail independence, meaning the crisis status of Y is unaffected by whether X is in crisis.
Our research focuses on the impact of a bank's failure on the broader financial system, necessitating a multi-dimensional measure akin to the two-dimensional scenario We represent the losses from d individual risk factors as X = (X1, , Xd), where each risk factor adheres to a univariate Extreme Value Theory (EVT) framework, possessing its unique tail index αi for 1≤i≤d By employing the Value at Risk (VaR) measure as a threshold, we can analyze these multi-dimensional calculations effectively.
( d d d d ) L ( x x x d ) p p x VaR X or or p x VaR orX p x VaR
Again, from L(1,1 ,1 )the tail dependency follows This time the values will be delimited between 1 and the number of individual risk factors d.
3.1.3 Conditional probability of joint failure
The Conditional Probability of Joint Failure (CPJF) is a key metric for assessing two-dimensional tail dependence, particularly in analyzing the independence of interregional banking systems By utilizing the L(1, 1) function, CPJF estimates the likelihood of simultaneous failures between two banks, given that one of them has already failed.
Denote, A ={ X > Var X ( ) p }, as X being in crisis, similarly, B ={ Y > Var Y ( ) p } as Y being in crisis.
= , we can now calculate CPJF as:
Since 1 ≤ L ( ) 1 , 1 ≤ 2we have that, 0≤CPJF ≤1.
A Conditional Probability Joint Function (CPJF) value of 0 indicates tail independency, while a value of 1 signifies complete tail dependency In scenarios of complete tail dependency, the likelihood of both variables, X and Y, being in crisis is certain if either one is in crisis The CPJF is particularly effective for assessing the dependence between banks during crises This study utilizes CPJF to analyze and compare the regional and interregional dependencies of banks from different areas, revealing significant differences in dependency levels between banks within a single region and those across different regions.
The Banking Contagion Index
Introducing our innovative Banking Contagion Index (BCI), which quantifies the systemic impact of a bank's failure The BCI estimates the potential number of banks that could fail if a specific bank collapses, allowing us to identify which bank's failure would have the most detrimental effect on the financial system This critical information aids regulators in making informed decisions regarding bailouts during potential bank failures To understand the theoretical foundation of the BCI, consider a scenario with three banks in the system.
0 , , lim L x x x p p x VaR orX p x VaR orX p x VaR X
For bank X i , the BCI is defined as:
BCI =lim p → ∞ E (number of crises in X 2 and X 3|X 1 in crisis) (11)
Denote, I i =1 { X i > VaR i ( ) p }as X i being in crisis for i=1,2,3, by rewriting (11) we obtain:
Note that (12) can be rewritten as the sum of two separate expectations:
Rewriting (13) in terms of probabilities, by using (10) we obtain:
The ( I 2 =1 orI 1 =1 ) part is the same as the denominator of (9), hence we can use
L in (14) Doing so for all parts we proved that:
Such an analysis also applies for higher number of banks, d ≥3.
In essence we proved that the effect of X i on the sector with all banks can be estimated using the two-dimensional function of L ( ) 1 , 1 for each individual linkage of X i on X ≠ i
Assume a dataset with d banks, the BCI is obtained as follow:
1 Construct a matrix of d by d , for the i-th row and j-th column we put the estimate
L for the combinations X i and X j as L i , j ( ) 1 , 1
2 The diagonal is always 1, as X i and X i are complete dependent
2 , , the result is what we call the
A Bank Contagion Index (BCI) close to d−1 signifies a strong influence of bank j on the overall banking system, indicating that the failure of bank j could lead to numerous other bank failures Conversely, a BCI near 0 suggests that bank j has minimal impact on the system, meaning its failure would likely result in few or no additional bank failures.
Data
To effectively apply the BCI, it is essential to include a sample of at least three banks, necessitating a substantial number of observations due to the use of Extreme Value Theory (EVT) We selected three countries—Germany, Switzerland, and the United States—each with distinct financial sector concentrations Germany features numerous small banks alongside a few large institutions, while the U.S has a diverse banking sector with many mid-sized banks and several major players Switzerland strikes a balance, hosting two prominent banks, Credit Suisse and UBS, along with several smaller entities Our data, sourced from Datastream, comprises log-returns of daily stock prices from 27 banks per country, spanning the period from 1980 to 2009 However, due to mergers and market exits, complete data for the entire period is not always available We curated two optimal datasets: one maximizing the number of banks and another ensuring full-period data availability The selection process also accounted for the frequency of observations, as smaller banks often exhibit low trading activity, resulting in periods of unchanged stock prices For EVT analysis, it is crucial to minimize identical observations; thus, we included only banks with an acceptable number of zero observations, ensuring that 85% of all observations met this criterion.
In the United States, we focused on the top 10 largest publicly traded banks, along with five randomly selected smaller banks for our analysis Set 1 comprises banks like Lehman Brothers, Merrill Lynch, and Washington Mutual, which either went bankrupt or were acquired during the 2008 financial crisis, concluding our study after their exit from the stock exchange In contrast, Set 2 excludes these three banks, as the sample period is limited to the time before their disappearance.
Co-operative banks in Germany are widely favored and are not publicly listed Our research spans two distinct periods, though we lack data prior to the 2008 financial crisis, as only four publicly traded banks remained after 2002, which was insufficient for our analysis We designated the acquisition of Dresdner Bank by Allianz AG as the endpoint for our second data set.
The Swiss banking sector is primarily composed of small private banks that are not publicly listed, resulting in data availability for only nine banks in the first dataset Due to mergers, only four banks were identified in the second dataset Notably, the banks "Union Bank Swiss" and "Swiss Bank" were treated as separate entities in the first set but merged into the "United Bank of Switzerland" (UBS) in the second set.
The US banking dataset includes both retail banks and commercial/investment banks, highlighting the significant role of major investment banks that operate independently from retail banking While these pure investment banks are crucial to the overall banking sector and the interbanking market, the leading banks in Germany and Switzerland also engage in investment banking activities, yet they maintain a presence in the retail market, distinguishing them from pure investment banks.
To conduct comprehensive analyses comparing the Business Confidence Index (BCI) across different periods, it is essential to create a "minimal size" dataset that includes data available in both datasets This dataset serves as a reference point for comparison, allowing the BCI values from dataset 2 to be evaluated against the results of the "minimal size" dataset For a visual representation of the sample selection, please refer to Figure 14.
Nr of obs Maximum number
Of Minimal size dataset banks
Our samples have the following characteristics:
• For the US: o One dataset with 15 banks and 3828 daily log-returns
The following banks are classified as investment banks due to their lack of retail operations: JP Morgan, Morgan Stanley, and Lehman Brothers This analysis is based on a dataset comprising 12 banks and 6,042 daily log-returns.
Period: 01-01-1986 till 01-03-2009 o Minimal Size dataset with 12 banks and 3828 daily log-returns
• For Germany this results: o One dataset with 11 banks and 3696 daily log-returns.
Period: 04-07-1984 till 02-09-1998 o One dataset with 9 banks and 6882 daily log-returns
Period: 01-01-1975 till 10-07-2002 o Minimal Size dataset with 9 banks and 3696 daily log-returns
• For Switzerland the results: o One dataset with 9 banks and 2522 daily log-returns
Period: 08-03-1983 till 01-04-1993 o One dataset with 4 banks and 3431 daily log-returns
Period: 01-01-1996 till 01-03-2009 o Minimal Size dataset with 4 banks and 2522 daily log-returns
From March 8, 1983, to April 1, 1993, a cross-regional analysis was conducted to examine interregional dependence among banks The study utilized a uniform dataset covering the period from January 1, 1986, to December 31, 2001, ensuring a comprehensive collection of observations for each country involved This dataset included 13 American banks, 9 German banks, and 3 Swiss banks, providing a robust foundation for the analysis.
For a complete overview of the datasets, including bank names we refer to Appendix B.1.
Results
Interregional dependency
The analysis of dependency among banks, both within a country and across countries, reveals that regional dependency is greater than cross-regional dependency Utilizing the CPJF as a two-dimensional measure for tail dependency, we calculated average CPJF values for each bank's dependency on others to facilitate comparisons with cross-regional analyses The findings of these evaluations are presented in Table 6, while detailed individual CPJF values can be found in Appendix B.3.
Table 6 Average CPJF for within country dependency
Average CPJF Bank nr Average CPJF
The estimation of the CPJF cross-regional is conducted similarly to the regional CPJF, with each bank pair comprising institutions from different countries Table 5 presents the average CPJF, while individual CPJFs are detailed in appendix B.3 It is important to note that the sample size, analysis period, and choice of k remain consistent across both analyses A comparison between regional and cross-regional dependency is only valid when utilizing the same data set.
Table 7 Average CPJF for Cross-regional dependency
Germany Swiss US Swiss US Germany
The analysis reveals that regional dependency significantly surpasses cross-regional dependency, particularly evident in the US and Germany, where regional dependency is, on average, twice as high While Switzerland's data deviates from expectations, this may be attributed to a limited number of banks during the selected period Despite variations in CPJF among individual banks, the stable difference between regional and cross-regional CPJF remains notable Furthermore, the US and Germany demonstrate a stronger interdependence compared to Switzerland, as indicated by consistently higher average CPJF values in comparisons involving the US and Germany versus those with Switzerland This study underscores the importance of recognizing the pronounced regional dependency, which is crucial for our subsequent analyses, particularly in assuming cross-regional independence for BCI computation.
Regional dependency
This thesis aims to establish a relationship between a bank's market value and the potential damage its failure could inflict on the financial sector Utilizing a multivariate Extreme Value Theory (EVT) approach, we developed the Banking Contagion Index (BCI) to estimate the likelihood of other banks failing if a specific bank collapses The BCI for banks in the US, Germany, and Switzerland is presented in Tables 8, 9, and 10, alongside each bank's market value, which reflects the average market capitalization during the sample period The BCI is calculated by aggregating individual dependencies, with detailed results available in Appendix B.4.
Table 8 BCI results for different datasets, US
US Set 1 US Set 2 US Minimal Size
Bank name BCI MV Bank name BCI MV Bank name BCI MV
Merrill.Lynch 6,45 17853 Fifth.Third 4,64 8719 Wells.Fargo 5,29 30500 JP.Morgan 6,45 35981 Wells.Fargo 4,57 30500 PNC.FINL 5,245 7824
Wells.Fargo 6,43 30500 PNC.FINL 4,49 7824 BBT 5,24 5932
BBT 6,42 5932 JP.Morgan 4,48 35981 JP.Morgan 5,19 35981
PNC.FINL 6,40 7824 Northern.Trust 4,44 4564 Northern.Trust 5,055 4564 Morgan.Stanley 6,29 26005 BBT 4,22 5932 Fifth.Third 4,925 8719 Northern.Trust 6,22 4564 Morgan Stanley 4,20 26005 Morgan Stanley 4,85 26005 Fifth.Third 6,02 8719
Table 9 BCI results for different datasets, Germany
Germany Set 1 Germany set 2 Germany minimal size
30 Number of shares outstanding * Share price, available through Datastream
Bank name BCI MV Bank name BCI MV Bank name BCI MV
Deutschebank 3,41 19978 Deutschebank 2,20 19978 Deutschebank 2,61 19978 Dresdnerbank 3,33 11875 Dresdnerbank 2,09 11875 Dresdnerbank 2,59 11875 Commerzbank 3,28 6327 Commerzbank 2,06 6327 Commerzbank 2,49 6327 Bayer.HYP 2,96 12732 Bayer.HYP.VBK 1,81 8734 Bayer.HYP.VBK 2,17 8734 Bayer.HYP.VBK 2,91 8734 Vereins.Westbank 1,26 882 Vereins.Westbank 1,62 882 Landesbank 2,36 2396 IKB.deutsche 1,16 892 IKB.deutsche 1,61 892
Table 10 BCI results for different datasets, Swiss
Swiss Set 1 Swiss Set 2 Swiss minimal size
Bank name BCI MV Bank name BCI MV Bank name BCI MV
Union bank Swiss 2,69 27552 Banque.canton 0,58 VP.bank 0,69
VP.bank 2,52 807 UBS 0,54 Credit.Suisse 0,68
Swiss bank 2,47 18283 VP.bank 0,53 Banque.canton 0,49
Credit.Suisse 2,43 26398 Credit.Suisse 0,52 UBS 0,29
When analyzing the Bank Comparison Index (BCI) for each bank within a set, it's crucial to compare the BCI value to the total number of banks in that set minus one The BCI reflects the number of other banks that are likely to fail if a particular bank fails Therefore, comparing BCI values across sets with varying numbers of banks can lead to misleading conclusions if the total number of banks is not taken into account.
Recent data from the US, including the onset of the 2008 crisis, reveals several key insights regarding bank contagion risk The absolute Bank Contagion Index (BCI) values are notably high, with set 1 ranging from 5.46 to 7.14 across 15 banks, significantly surpassing those in Germany, where only one-third of banks would fail under worst-case scenarios compared to over half in the US Additionally, the relative differences in contagion effects among US banks are minimal; for set 1, the disparity between the highest and lowest contagion effects is just 1.5, which is low compared to Germany Furthermore, the market value of banks does not primarily influence BCI values, possibly due to distinctions between retail and investment banks A robustness check comparing the minimal size set with set 2 showed consistent rankings, while a comparison of set 2 with the minimal size set indicated a decrease in BCI values, suggesting that systemic linkages have weakened in more recent times.
Interestingly the BCI rank is not explained by the market value rank in US results For set 1
SunTrust ranks highest among the banks analyzed, holding only one-fifth of Citigroup's market value, which is in third place Both Washington Mutual and Lehman Brothers exhibited low BCI values and declared bankruptcy during the 2008 financial crisis, with Lehman Brothers' collapse receiving significant media attention due to its perceived "too big to fail" status However, our analysis indicates that the Federal Reserve's decision to let Lehman Brothers fail aligns with the low rankings of both banks Despite their high absolute BCI values, the potential failure of Washington Mutual or Lehman Brothers would likely have less severe repercussions compared to the failure of SunTrust or Citigroup, highlighting the systemic importance of larger institutions.
In set 1, pure investment banks exhibit a low score relative to their market value, likely due to their minimal retail activities, which reduces their societal connection Conversely, retail banks like Keycorp and Comerica demonstrate a high Bank Community Index (BCI) despite their lower market values, as they focus primarily on retail banking with limited investment banking involvement.
Looking at set 2 the position within the top 5 of set 1 has completely changed In set 2
Citigroup holds the highest Bank Competitive Index (BCI), while Bank of America (BoA) ranks fifth In recent years, Citigroup's significance within the financial system has increased, a trend corroborated by minimal size set results Additionally, Fifth Third Bank has improved its position, achieving a BCI just below that of BoA, despite having a market value that is five times larger.
31 Washington Mutual and Lehman Brothers filed for chapter 11 on 26-09-2008 and 15-09-2008 respectively
Looking at the bottom of set 2 we see that “Morgan Stanley” took over the last position of
The analysis of Northern Trust reveals that the overall Bank Contagion Index (BCI) values in set 2 are lower than those in the minimal size set, indicating a reduced influence of bank failures on the system in recent years, similar to trends observed in Germany However, when comparing the absolute BCI values relative to the total number of banks, the US market exhibits significantly higher values than the German market, suggesting that the US financial system is more sensitive to the potential failure of a single bank.
In Germany, the Bank Credit Index (BCI) values for the three sets of banks are considered reasonable, with set 1 showing a range of 1.43 to 3.41 across 11 banks, while set 2, consisting of 9 banks, has a lower range of 0.85 to 2.20, resulting in a maximum BCI of 8 Notably, the relative differences among German banks are significant, as the lowest BCI in both sets is nearly half of the highest BCI Additionally, the market value of banks serves as a reliable indicator of BCI, with rankings based on BCI closely mirroring those based on market value A robustness check comparing the minimal size set with set 2 yielded satisfactory results, as their rankings were nearly identical However, a comparison between set 2 and the minimal size set reveals a decline in BCI values in the more recent sample, suggesting a decrease in systemic linkages over time.
In Germany, market value emerges as the key factor in assessing the impact of potential bank failures, as indicated by the BCI values that rise with increasing market value Notably, Commerzbank, despite its lower market value, maintains a high BCI, likely due to its status as the second-largest bank by total assets The rankings remain stable over time, with only Suedboden and hvbREAL exchanging positions A comparison between the second dataset and the minimal size set reveals a decline in efforts to mitigate systemic risk, while the BCI values of the top four banks remain closely aligned A significant drop in BCI occurs beyond these top banks, correlating with a decrease in market value Consequently, regulators should prioritize the solvency of these four major German banks, highlighting that in this context, size is indeed a critical factor.
In analyzing the banking sector in Germany, we encounter several key observations: Firstly, the interpretation of results is challenging due to limited data availability, leading to mixed outcomes, notably influenced by the merger of Union Banks Swiss and Swiss bank into UBS Secondly, the absolute BCI values across three sets are relatively low, with the Swiss market's values falling between those of the US and Germany Additionally, the relative differences among Swiss banks are minimal, particularly in set 2, where distinctions are negligible Furthermore, a correlation between market value and the BCI is only evident in set 1, as the top four banks, excluding VP Bank, exhibit the highest market values, while results for the other sets are inconsistent due to their limited number of banks Lastly, a comparison between set 2 and a smaller dataset reveals a decline in BCI values in the more recent sample, suggesting a reduction in systemic linkages over time.
For set 1 we see again that the rank of the BCI relates to the market value ranking Except the
The "VP Bank" ranks among the top four banks with the highest market value, highlighting a significant disparity between the leading banks—“Union Bank Swiss,” “Swiss Bank,” and “Credit Suisse”—and their smaller counterparts, which are only one-tenth their size Interestingly, the ranking shifts in the second set, with “Banque Canton,” previously last, now taking the top spot UBS, formed from the merger of “Swiss Bank” and “Union Bank Swiss,” maintains a strong position Analyzing the BCI over time indicates a decrease in contagion effects in Switzerland, which is promising for regulators; however, the lack of comprehensive data limits the robustness of these findings compared to those from other countries.
Our analysis across the three selected countries reveals several key insights Notably, there has been a decrease in the Bank Confidence Index (BCI) value for all countries, suggesting a reduction in systemic risk However, the overall BCI values remain high, indicating persistent systemic risk within the banking sector, with even smaller banks exerting a considerable influence The United States stands out as the most concerning case, exhibiting high BCI values across all banks Contrary to our initial expectations, bank size does not consistently serve as the primary indicator of failure impact; while size is crucial in Germany, in the US, the bank's profile plays a significant role Specifically, investment banks tend to have lower BCI values compared to retail banks, despite some investment banks boasting much higher market values.
Conclusion
A robust financial system is crucial for economic prosperity, as it efficiently allocates capital; however, disruptions in this allocation can severely impact the real economy, as evidenced by the 2008 financial crisis This thesis explores the interconnectedness of stressed banks and introduces a novel measurement approach using Extreme Value Theory (EVT) in a multivariate context to assess the failure impact of one bank on the entire system Previous research has indicated that asset return distributions exhibit heavy tails, which can be effectively estimated through EVT Given our focus on the extreme events associated with stressed banks, EVT was the appropriate choice The intricate connections between banks increase the industry's vulnerability to contagion.
Financial contagion is unique due to its rapid spread and significant impact on various industries, making prevention crucial To address this issue, we developed the Banking Contagion Index (BCI), which predicts the number of banks likely to fail within a system when a specific bank collapses The BCI effectively differentiates between banks that exert high and low contagion effects, utilizing the tail dependency function L(x, y) established by de Haan and Ferreira.
In 2006, we estimated the tail dependency between banks X and Y, revealing that the impact of bank Xi's failure on the overall system can be quantified by summing the tail dependencies of its individual linkages with other banks This analysis focuses on the tail dependency of daily log returns for each bank within the system Our empirical study examines the Banking Concentration Index (BCI) across three distinct regions: the US, Germany, and Switzerland, chosen for their varying banking sector concentrations To accurately estimate the BCI, we utilized daily log returns over an extended period, emphasizing the need for large datasets due to our application of extreme value theory Each region was analyzed using three samples: one with the maximum number of observations, another with the maximum number of banks, and a combined dataset for robustness checks This combined dataset also facilitated a temporal comparison of the BCI, allowing us to track the evolution of failure linkages over time.
Our analysis revealed that cross-regional dependency in bank failures is lower than regional dependency across three regions, using the Conditional Probability of Joint Failure measure We aimed to assess the significance of bank size on failure impact by comparing the Bank Concentration Index (BCI) rankings with market value rankings In Germany, our findings support the hypothesis that larger banks have a greater failure impact, while the US banking sector lacks a clear correlation between market value and failure impact Notably, pure investment banks appear to exert less influence than traditional retail banks Over time, we observed a decrease in failure impact for both countries, which is encouraging for regulators However, the consistently high absolute values of the BCI underscore the need for stability across the banking sector, regardless of bank size or type Due to limited data for the Swiss market, we could only conclude that the failure impact has diminished over an extended period.
Overall, the findings align with our expectations, indicating that large banks generally have a greater impact in the event of a failure compared to smaller banks Nevertheless, as evidenced by the situation in the US, there are notable exceptions to this trend.
The existence of contagion in banking underscores the critical need for robust financial regulation, as evidenced by historical attempts to mitigate crises, starting with the G-10's Basel Committee on Banking Supervision in the 1980s The introduction of the Basel 1 accord in 1988 established minimal capital requirements for G-10 banks, yet it failed to prevent significant financial crises and faced criticism for complicating competition between developed and developing nations The subsequent Basel 2 accord in the 1990s improved upon its predecessor but remained contentious among stakeholders Post-2008, the necessity for stringent regulation is paramount, as bank failures can have far-reaching impacts on the financial sector Regulators in Germany prioritize bank size in assessing failure risk, while U.S regulators consider both size and bank activities for capital requirements The BCI (Bank Contagion Index) values serve as a tool for governments to determine bailout strategies, with high BCI values indicating the need for intervention due to potential systemic effects, whereas low BCI values suggest minimal impact and no intervention However, even low BCI values highlight the importance of all banks, raising concerns about moral hazard, as banks may engage in riskier behaviors if bailouts are expected Thus, stringent regulation remains essential to address these moral hazard challenges effectively.
The introduction of the Bank Contagion Index (BCI) provides an objective measure of how the failure of one bank impacts others in the banking sector This thesis serves as an example of the diverse analyses that can be conducted using the BCI Future research should emphasize the significance of sample size, as demonstrated by our Swiss dataset, which indicates that meaningful results are only achievable with a dataset comprising at least seven banks While we utilized market value to assess bank size, it may be beneficial to consider total assets, as this is more commonly used in the banking industry, potentially yielding different insights regarding the impact of size on failure Additionally, future studies should explore the BCI's ability to identify which banks are likely to fail if a specific bank fails, necessitating modifications to the BCI framework to enhance understanding of interbank linkages Lastly, applying the BCI to the banking sectors of developing countries is essential to uncover potential differences or similarities with developed markets Ultimately, the BCI aims to contribute to understanding bank interconnections and inform policy responses during financial crises.
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██ Countries in official recession (two consecutive quarters)
██ Countries in unofficial recession (one quarter)
██ Countries with economic slowdown of more than 1.0%
██ Countries with economic slowdown of more than 0.5%
██ Countries with economic slowdown of more than 0.1%
(Between 2007 and 2008, as estimates of December 2008 by the International MonetaryFund) 32
Example of a hill plot for Bank of America, data from dataset 1 (see Appendix B.1 for the banks included in dataset 1).
The circled part is the first stable part after the variation at the beginning Note that we should chose k%0 which gives a value for the tail index of 2.3.
Number of obs 3828 Number of obs 6042
Number of obs 3696 Number of obs 6882
Bayer.HYP 1 Bayer.HYP.VBK 1
Dresdnerbank 5 hvbREAL 5 hvbREAL 6 IKB.deutsche 6
Number of obs 2522 Number of obs 3431
Bank number Bank name Bank number Bank name Bank number Bank name
1 BoA 1 Bayer.HYP.VBK 1 VP.bank
Plots of estimation L(1,1), see section 3.1.2, in order to get k for each regional dataset: US:
Plots of estimator L(1,1) in order to get k for each cross- regional dataset:
Plots of estimation L(1,1) in order to get k for each minimal size dataset:
Appendix B.3: Conditional Probability of Joint Failure results
In each table, N represents the total number of observations, while K indicates the number of higher order statistics The figures in the main rows and columns correspond to the bank names provided in Appendix B.1.
Individual results for CPJF analyses, US:
Individual results for CPJF analyses, Germany:
Individual results for CPJF analyses, Swiss:
Interregional results for CPJF analyses:
Appendix B.4: Banking Contagion Index results
In these tables we report the estimate of the tail dependence measure L(1,1) for
In the context of tail dependence, the function L(1,1)=1 indicates complete tail dependence, while L(1,1)=2 signifies complete tail independence The BCI, or Bank Correlation Index, is calculated by summing the values of each row, representing the expected number of system failures given that a specific bank has failed Here, N denotes the total number of observations, and K refers to the higher order statistics considered in the analysis.
The number on the axes corresponds to the bank number as given in Appendix B.1