We could not have known beta: The clustering behaviour of
US financial institution betas over time
Aaron van Gils1 Thesis Msc. Finance University of Groningen
June 2015
Supervisor: Dr. Jochen Mierau
Abstract
This study investigates whether US financial institution betas became more similar between 1988 and 2014 with a specific focus on recessions and years preceding recessions. Analyses are performed on the total sample as well as on banks categorised by size, bank type and leverage. Results show no empirical evidence for a declining trend in beta dispersion through time or in the onset of recessions. However, betas do increase during recessions and are higher for larger or more levered banks and investment banks. Additionally, large banks and investment banks have less dispersed betas, whereas leverage does not have any distinct effect.
Keywords: time varying beta, systemic risk, financial institutions, recessions
JEL classification: G12, G21, G28
1 University of Groningen, Faculty of Economics and Business
1. Introduction
The overly similar systemic risk exposure of banks is deemed to be a determinant of the severity of the recent crisis. Regulators learned that overall soundness of the financial system could not be assured by measuring the stability of individual banks but by focussing on system-wide inter-linkages of these banks (Suh, 2012). It is argued that banks often diversify their idiosyncratic risks in identical manners, leading to banks becoming more identical to one another (Wagner, 2010). The comovement of banks regarding market wide events has therefore become an increasingly hot topic in recent literature.
This study investigates whether this clustering behaviour of US financial institutions can be confirmed by increasingly similar betas over time. Ever since the capital asset pricing model (CAPM) exists a firm’s beta is the most commonly applied metric for measuring ones exposure to market movements as it shows the covariance of a stock’s return with the market return. Later on academics such as Barnes and Lopez (2006) tweaked beta’s application by using it for measuring levels of financial stress and other financial stability purposes. This application is possible due to beta’s time varying character, which allows it to react to systemic events and other major firm-related happenings. Since higher interconnected banks are deemed to be more alike and affected by similar events, their betas should be similar as well. This underlines that if banks became increasingly similar due to overlapping activities and diversification trends then bank betas should show higher similarity as well. However, despite the fact that a bank’s beta shows its exposure to systemic shocks in the market, it does not say anything about the aggregated systemic risk within the industry.
This study contributes to existing literature by relating the systemic risk exposure of individual banks to the aggregated systemic risk in the banking sector. The beta of an individual bank shows its comovement with the market and thereby its exposure to systemic risk. Consequently, banks with comparable betas will react similarly to market downturns. Therefore, the stability of the financial system will be severely undermined if bank betas show high similarities on a large scale. The deviation among the yearly betas of all banks thus serves as a reliable indicator of overall systemic stability in the banking industry: lower beta dispersion entails higher aggregated systemic risk. Therefore, the increasing similarity among banks found in recent literature suggests that beta deviation decreases through time. If this declining trend throughout the time series exists, then it would be interesting to investigate whether beta deviation substantially decreases in the onset of market wide downturns as well. Banks might tend to prepare for downturns by diversifying idiosyncratic risks away in identical ways to each other, which leads to identical systemic risk exposures and thus identical betas. Consequently, increasingly similar betas through time confirm theories on over-diversification of banks and subsequently enable the possibility of using decreasing deviations as an early warning signal for regulators who try to tackle recessions.
The deviation of the bank betas is measured on several levels. First of all, overall clustering behaviour within the financial sector is analysed by pooling all banks and investigating the beta deviations among them. However, since banks with significantly divergent characteristics react differently to systemic shocks in the market, it is valuable to categorise them based on their characteristics as well. Therefore, the financial institutions are divided into subportfolios based on their size, bank type, and leverage.
The results show that the betas for all banks, regardless of their characteristics, are highly affected by recessions, which leads to increasing betas during economic downturns. Despite this finding, no clustering trend is revealed through time or during recessions. This contradicts the existing theories on increasingly similar banks, although bank betas do show a remarkable decline from the 2009 credit crisis onwards in both value and dispersion. Furthermore, the results do not show any decrease in beta deviations in the years preceding recessions, meaning that the predictive power of beta clustering is not existent. Conclusively, this research shows that beta deviations could be a decent proxy for bank clustering since it clearly shows lower beta deviations for the large bank portfolio compared to the smaller bank portfolios. This is in accordance with Tharashev, Borio and Tsatsaronis (2010) and Wagner (2010), who state that larger banks are more similar due to interlinkages and analogous diversification strategies.
Therefore, this research scratches the surface of a new method for looking at bank clustering through certain time periods. In a sense this paper is related to the work of Weiss, Bostandzic and Neumann (2014) who investigate which factors drive systemic risks of banks in financial crises. However, this study applies another method for measuring systemic risk compared to them. The systemic risk is measured by focussing on beta developments and more specific the deviations among these betas. Surprisingly little research has been done regarding this specific aspect of bank betas. Secondly, this paper adds economic value by trying to provide extra tools for supervisors to effectively prevent recessions. Unfortunately, the results lack statistical power and are too insignificant to be applied for prediction purposes. However, it is recommended to perform additional studies on this topic since the 2008 crisis has proven that the market should be aware of the total systemic risks banks face within their financial system.
2. Literature review
The goal of Section 2 is to derive a foundation from existing literature on which the beta dispersion method can be build. Firstly, Section 2.1 explains systemic risk on individual bank level by showing the important characteristics of CAPM beta and its application to banks in specific. Subsequently, Section 2.2 elaborates on aggregated systemic risk in the banking industry and pays attention to the effect of a bank’s diversification on systemic risk. Additionally, Section 2.3 describes the effect of recessions on aggregated systemic risk and betas and Section 2.4 focuses on individual banks by consulting existing literature that tries to explain the characteristics of banks that cause higher systemic risk. Lastly, Section 2.5 combines the preceding sections to construct the research objectives.
2.1 The CAPM beta and its implications for banks
One of the most renowned models in finance is the CAPM.2 It has been studied, criticised and adjusted by many.3 Despite the persistent attention surrounding this model it still is the most widely applied asset-pricing model in practice. Mergner and Bulla (2008) state that neither recent anomalies in the literature nor multi-factor models have been able to take over the dominant position of the CAPM and its betas. Schuermann and Stiroh (2006) show that a quarter to half of the total variation in bank stock returns is explained by beta. This confirms that the banking industry is very adequately covered by the market model and is less sensitive to other (un)observed risk factors, which is mainly caused by the significantly different dynamics of this industry compared to non-banking industries.
Despite the fact that beta still is one of the most renowned concepts in finance, there has been a debate on its time varying behaviour. Fabozzi and Francis (1978) are the first to state that beta coefficients move randomly through time rather than remain stable as the OLS model presumed.4 According to them reasons for a shift in beta can
2 For more in depth literature on CAPM and its origin see Sharpe (1964), Lintner (1965), Mossin
(1966) and Black (1972).
3 There have been different alternations of the model, accounting for size and value (Fama and French,
1992), momentum (Carhart, 1997), interest (Demsetz and Stratan, 1997), market volatility (Ang, Hodrick, Xing, and Zhang, 2006), the market’s volatility short and long-term components (Adrian and Rosenberg, 2008) and liquidity (Amihud, 2002).
4 For more in depth discussion on the time varying beta matter see Ferson, Kandal, and Stambaugh
be categorised into four main groups, namely: micro-economic variables, macro-economic influences, political factors and market factors. Since then, the time varying behaviour of beta has repeatedly been confirmed and overall consensus has been reached on yearly betas adequately representing a firm’s systemic risk.5 Handa, Kothari, and Wasley, (1989) acknowledge that betas estimated using interval returns of longer than a year lack statistical precision due to a higher standard error. Lewellen and Nagel (2006) show that beta indeed varies considerably with high-frequency changes on yearly basis and is relatively stable within a quarter or month. They also differentiate between betas based on daily, weekly and monthly data to eliminate possible noise in returns and find approximately identical results per method. Subsequently, Ang and Chen (2007) add the note that using rolling betas understates the variance of true conditional beta and therefore is less favourable.
Caporale (2012) applied the conditional beta to the banking sector by studying whether beta shifts could measure changing market expectations of US banking sector risk. The results show three large structural shifts. These shifts support the time-varying nature of beta. Caporale’s third structural break covers the period of the fourth quarter in 2000 to the first quarter in 2008 and has an average beta near historical lows. An odd discovery considering the fact that bank leverage and risk taking were rising. Therefore, Caporale believes that market expectations and reality have been severely mismatched during the onset of the 2007 financial crisis. As a concluding remark Caporale states that this mismatch could be an explanation for the severity of the stock market downturn.
In similar fashion, King (2009) studies yearly CAPM betas for banks. He finds declining betas across all countries in the period from 1990 to 2005, with Japan as the only exception. Similar to Caporale (2012) he suggests that the low betas indicate a mismatch between market expectations and reality. This mismatch is due to the high and stable returns of banks generated by new sources of income in years preceding the crisis. These sources of income resulted in higher returns for investors but were accompanied with higher risk that the market did not comprehend. According to King the market has not correctly priced this extra risk until the beginning of the financial crisis. US bank betas for example jump from 0.58 in 2005 to 0.84 in 2006 and continued to rise during the crisis until governmental support stabilised this trend.
5 For further confirmations of the time-varying nature of beta see e.g. Ferson and Korajczyk (1995),
2.2 Systemic risk in the total financial sector
Even more important than the systemic risk of individual banks, which is adequately shown by their betas, is the systemic risk within the total banking sector. As Suh (2012, p. 341) states: “The soundness of the financial system cannot be
guaranteed by simply ensuring the soundness of individual financial institutions.”
Rochet and Tirole (1996) state that the focus on systemic risk was low and they are one of the first who try to lighten the burden on central banks by building a framework that can more accurately analyse interbank lending and systemic risk. Their main recommendation is that higher accountability for lending banks can cause a shift in capital requirements, but difficult judgement calls of central banks remain necessary. Therefore, they believe that it is easier for central banks to bail out failing banks than focussing on the repercussions of systemic risks and interconnectedness.
Until the mortgage crisis in 2007 the attention on systemic risk in the banking sector never truly picked up steam. Actually, in the year preceding the mortgage crisis Bartram, Brown, and Hund (2007) stated that current policies were adequate to handle major macroeconomic events and their results showed only small potential increases in systemic risk. The 2007-2009 mortgage crisis proved them wrong. This crisis resulted in a continuous stream of new models and theories to support supervisors. These studies have a broad focus on potential contagion sources such as asset return correlations (Acharya, 2009; Huang et al., 2009), similarity of portfolio holdings (Cai et al., 2011), similar funding activities (Nijskens and Wagner, 2011) and asset commonalities (Allen et al., 2012).
appropriately accounted for clustering by ascribing similar risk profiles to banks. Wagner (2010) focuses on this question by discussing the remarkable paradox of diversification for banks (“pooling”).
According to Wagner diversification of banks increases their similarity to each other by exposing them to a relatively higher amount of identical systemic risks. For modelling purposes he focuses on two banks and their diversification activities. Normally, diversification is encouraged because it diminishes the likelihood of institutional failure and thus increases overall financial stability. However, this is not necessarily the case for banks. The diversification paradox for banks argues that a large degree of diversification increases similarity among banks, which leads to a monotonous financial system. The lacking variety among banks undermines financial stability and thus increases the aggregated systemic risk within the financial industry.6 Acemoglu et al. (2013) add to this argument that the financial network architecture stabilises the banking system when negative shocks are sufficiently small, but when shocks become more severe the interconnections become a liability and endanger the stability of the banking system.
The diversification trend especially holds for large banks. To illustrate this Wagner refers to a report of the Bank for International Settlements (BIS) that demonstrates increased correlations of large US bank share prices from 28% to 54% in the years 1995 to 2000. This increasing similarity shows a clustering tendency among larger banks in the period leading up to the dot-com bubble collapse. However, Weiss et al. (2014) state that a relation is unlikely since the dot-com bubble did not originate in the financial sector. Additionally, they show that the effect of banks on systemic risk differs per crisis.
Conclusively, research repeatedly shows that the major problem within the banking sector is the increasing similarity among banks caused by the identical ways in which banks diversify their risks away. This development leads to clustered banks, which impose higher systemic risks on the total industry and thereby on all banks operating within. This study contributes to existing literature by combining the systemic risk on individual bank level with the systemic risk on aggregated level. It focuses on the question whether the market correctly values higher systemic risk
6 See Stiglitz (2010), Allen et al. (2012), and Battiston, Delli Gatti, Gallegatie, Greenwald, and Stiglitz
within the financial industry by appointing increasingly similar systemic risk profiles to banks.
2.3 Recessions and systemic risk
The severe losses banks suffered in the 2007 credit crisis painfully showed the shortcomings and the increased complexity of the financial system. Formerly, banks’ main reason for existence was their ability to evaluate and manage risks more effectively than other institutions (Altunbas, Manganelli, and Marques-Ibanez, 2011). However, Altunbas et al. (2011) state that throughout time the increased deregulation and financial innovation made the banking sector more interconnected and dependent on financial markets. This reasoning is in line with the increase in aggregated systemic risk and the clustering behaviour described earlier. It even suggests that this behaviour becomes more extreme during downturns in the market.
Not only the aggregated systemic risk increases during recessions, bank betas also rise during crises and recessions. King (2009) and Caporale (2012) find that the 2008 recession broke the declining trend in bank betas. Bank betas’ behaviour during recessions makes it worthwhile to investigate whether the combined beta movements could support supervisors in predicting recessions. If bank betas show lower dispersions in years preceding recessions then this approach might yield valuable prediction possibilities. An analysis similar to on Estrella and Mishkin (1998), who successfully predict US recessions with financial variables, can be performed to see if bank clustering is a signal from the banking sector that warns for challenging times.
2.4 Important bank characteristics for measuring systemic risk
Not only interconnectedness contributes to the aggregated systemic risk of the financial sector, also bank specific characteristics play a significant role. It is of importance to account for these characteristics since banks with divergent characteristics are prone to react differently to systemic events. Table 1 shows the methods applied by different authors for measuring the most relevant bank characteristics.
higher dependency of larger banks on market wide events results in higher betas for large banks. Baele, De Jonghe, and Vander Vennet (2007) and De Jonghe (2010) confirm this bank size effect in their European studies. Another important argument introduced by them is that bigger banks are more capable and therefore willing to undertake noninterest activities, which results in higher overall market exposure and thus higher systemic risk. The other way around, Stiroh and Rumble (2006) argue that
This table presents the important characteristics for bank betas and the methods for deriving them that are applied by several authors. The table shows the characteristics bank size, core business and leverage. The columns show the author, the year of publication, the market in which the research has been conducted and the exact method applied for deriving the characteristic. The methods differ substantially due to the different purposes of the conducted researches.
Table 1: Portfolio categorisation methods in existing literature
SIZE
Author(s) Year Countries Applied measurement
Bertay, Demirgüç-Kunt, and Huizinga 2012 Global Log of total assets
Alternative: Log of total gross income Hovakimian, Kane, and Laeven 2012 US Book value of total assets
Berger and Bouwman 2011 US Gross total assets: small (< $1bn), medium ($1bn > $3bn), large (>$3bn)
De Jonghe 2010 Europe Log of total assets
Tharashev, Borio, and Tsatsarounis 2010 Global Book value liabilities/book value liabilities of all institutions in system
Viale, Kolari, Fraser 2009 US Monthly market capitalisation Baele, De Jonghe, and Vander Vennet 2007 Europe Log of total assets
Stiroh 2006 US Log of total assets: Small (<25 %), medium (25%<75%, large: >75%)
CORE BUSINESS
Author(s) Year Countries Applied measurement
Brunnermeier, Dong, and Palia 2012 US Noninterest income (trading and venture capital income)
Vallascas and Keasey 2012 Europe SIC codes
Demirgüç-Kunt and Huizinga 2010 Global Four categories based on Bankscope Stiroh and Rumble 2006 US Noninterest income/Net operating revenue
Stiroh 2004 US Noninterest income/Net operating revenue
De Young and Roland 2001 US Divide total revenues in five subcategories
LEVERAGE
Author(s) Year Countries Applied measurement
Acharya and Mora 2015 n.a. Model building with hypothetical debt and equity constraints
Hovakimian, Kane, and Laeven 2012 US Implied equity capital to total assets Vallascas and Keasey 2012 Europe Book value total assets/book value equity Adrian and Brunnermeier 2011 US Book value total assets/book value equity Berger and Bouwman 2011 US Capital ratio
the systemic risk of smaller banks is lower since small banks are depending more on local conditions instead of broad market forces.
The size-related findings of Stiroh and Rumble (2006) were derived from an analysis on the risk associated with noninterest income and its effect on bank betas (Stiroh, 2004). They show that noninterest income is more closely linked to market movements and therefore increases beta. Brunnermeier, Dong and Palia (2012) also emphasise the higher contribution of noninterest activities to systemic risk. These activities include investment banking, venture capital and trading activities.7 De Jonghe (2010) investigates this effect for European banks and finds that
“non-traditional banking activities increase banks’ tail betas and thus reduce banking system stability” (De Jonghe, 2010, p.389). Additionally, Demirgüc-Kunt and
Huizinga (2010) focus on the impact of bank activities and funding strategies on returns. They find that banks can be categorised on their core businesses. They use four categories, which are: commercial banks (also including bankholding companies), investment banks & securities houses, nonbank credit institutions and other banks (such as medium- and long-term credit banks and real estate and mortgage banks). Their results are obvious: from 1999 to 2007 investment banks gain 90% of their income via fee incomes, whereas fee income for commercial banks accounts for 30%. Nonbanking credit institutions and other banks are comparable to commercial banks with an average rate of approximately 40%. Furthermore, their research shows that banks that generate substantial noninterest income faced more severe difficulties when the market imploded during the crisis. DeYoung and Roland (2001) argue that the higher systemic risk of noninterest income activities is caused by lower switching costs, less stable bank-customer relationships, and relatively high fixed-to-variable operating cost ratios.
The third characteristic often accounted for is a bank’s leverage. Berger and Bouwman (2011) show that banks with lower equity capital are more prone to failure when a systemic event occurs. Additionally, Vallascas and Keasey (2012) reason that higher levered banks are more exposed to systemic shocks because a higher equity capital could be a buffer for unexpected losses caused by systemic shocks. To control for leverage they apply the method of Adrian and Brunnermeier (2011) who use the
7 Brunnermeier et al. (2012) highlight that the diversification trend in the United States started after the
ratio of total assets to equity. Acharya and Mora (2015) find that higher leverage creates a strong creditor discipline for an individual bank, but simultaneously leads to higher systemic risk when creditors liquidate banks. When this happens, higher leverage shows the weak-spots of the interdependence among banks. Indicating that highly levered banks face similar risks during a crisis or events such as bank runs.
On the contrary, Weiss et al. (2014) highlight that few studies focus on the determinants of systemic risk. They find some effects in the periods preceding the beginning of the subprime crisis and the fall of Lehman. However, their empirical results do not support that bank size, leverage, or noninterest income are determinants of systemic risk in financial crises when systemic risk is defined as the marginal expected shortfall (MES) or lower tail dependence (LTD). Despite their contradicting results, prevailing literature repeatedly proves that controlling for these characteristics is of importance when betas are the indicator of systemic risk.
2.5 Research objective
Recent literature shows consensus on banks becoming increasingly similar in systemic risk exposures. It is argued that these increasingly identical systemic risk profiles fuelled the severity of the most recent crisis. Especially large banks, investment banks and highly leveraged banks face higher similarity in their systemic risk exposures. If a clustering trend exists then regulators should take this into account when assessing risk on both individual bank and macro-economic level.
This study applies a new method for studying aggregated systemic risk within the financial sector. It investigates the development of bank betas over time, both market-wide and characteristic-specific, and assesses whether the dispersion of bank betas decreased over time. Additionally, this study investigates whether regulators can rely on bank betas’ clustering behaviour to predict upcoming economic downturns.
3. Methodology
3.1 Beta dispersion through time
This study uses the dispersion among bank betas as measurement for systemic risk in the period 1988-2014. First of all, the yearly betas of all banks are calculated with daily data. Hereby the betas remain flexible enough to anticipate on significant changes in the bank’s systemic risk on the one hand and on the other hand the inaccuracy of too small intervals is eliminated. The formula for calculating beta is:
𝛽! = !"#(!! !,!!)
!"! (1)
Where 𝐶𝑜𝑣(𝑟!,𝑟!) is the covariance of stock i with the market index and 𝜎!"! is the
variance of the market index itself.
Secondly, all these yearly betas are combined into yearly portfolios, which results in 27 portfolios. By doing so the deviation among these betas can be analysed on a yearly basis in three ways, namely: (1) a plotted confidence interval graph,(2) the standard deviation of the betas within the yearly portfolio, and (3) the coefficient of variation (CV) of the betas within the yearly portfolio.The CV controls for the positive relation between beta and its standard deviation by rescaling the standard deviation with the portfolio’s mean beta, which increases comparability of the portfolios. Therefore this study mainly focuses on the CV instead of the standard deviation. CV is given by:
𝐶𝑉! = !!"#
!!"# (2)
Where σ!"# is the standard deviation of the portfolio betas in a particular year and µμ!"# 𝑖𝑠 the average beta of the portfolio in the same year.8 The mean used to calculate
the standard deviation and the CV is either the mean of all betas in a year, or the mean of betas within a characteristic-specific portfolio. The overall finding should be a decreasing beta variation among banks throughout the years since banks became gradually similar in activities and systemic risk exposures.
When looking at this development in more detail, an interesting analysis would be to compare the variation among bank betas during recessions and times of economic growth. One can assume a higher variation among betas when the economy expands and more clustered betas in the years leading up to a recession and during the recession. The clustered betas indicate similar systemic risk exposures of different banks, which lead to an undiversified financial system. This would prove that banks
8 A note of caution regarding differing negative observations among portfolios and means close to zero,
cover themselves in similar ways by diversifying away bank-specific risks and hence become particularly more exposed to identical systemic risks in the onset of a recession.
3.2 Recessions
To determine whether the economy is in a recession the method as applied by Estrella and Mishkin (1998) is used. The recession dates are obtained from the National Bureau of Economic Research (NBER). This results in 𝑅𝜏 = 1 when the economy is in a recession and in 𝑅𝜏 = 0 when this is not the case. Since these recession indicators are provided per month it is assumed that a year that contains at least one recessionary month can be categorised as being in a recession. This approach leads to the recessionary years 1990, 1991, 2001, 2008 and 2009. The hypothesis would then become that the CV of betas is smaller when 𝑅𝜏 = 1 than when 𝑅𝜏 = 0.
It has already been proven that bank betas rise during recessions. However, a new insight will be obtained if betas become more alike during downturns in the market. Since the standard deviations and CVs of the betas are not normally distributed the Mann-Whitney U-test is applied to see if the CV is significantly different during recessions, and years of economic expansion. This approach is based on Chaudhury (2014) who applies a similar method to analyse differences in betas through varying time periods. In accordance with Weiss et al. (2014) the economic explanations will emphasise on the 2007 financial crisis since this crisis originated within the financial sector.
3.3 Bank portfolios
A bank’s systemic risk can be significantly affected by bank characteristics. For comparability it is advisable to not only study all banks pooled together, but to also account for different characteristics and subdivide banks accordingly. Based on Section 2.3, the subportfolios will be based on bank-size, core activities, and leverage. Size, leverage and noninterest activities should positively relate to systemic risk.
The diversification argument (Wagner, 2010) plays an important role when analysing the beta dispersion within the portfolios. If the market correctly adjusts for the higher systemic risk of over-diversified banks then the larger bank and non-interest income bank portfolios should have more clustered betas and thus less beta dispersion. The investment bank portfolio is used as the embodiment of banks with higher noninterest income since overall consensus has been reached on investment banks having higher noninterest income (Demirgüc-Kunt and Huizinga, 2010)
The relation between leverage and bank beta’s CV is more complex. Logically, banks with higher leverage should have higher betas than less levered banks, but there is not much to say about their beta deviations. However, the danger of a systemic failure within the banking sector is aggravated by leverage when the market has been hit by a downturn already because counterparty risk makes high levered banks more heavily depended on each other (Acharya and Mora, 2015). This means that the beta deviation of the high-levered bank portfolio should decrease significantly during a recession compared to non-recessionary times.
A one-way ANOVA test on beta, beta’s standard deviation and beta’s CV is performed to test for significant differences among these portfolios in both betas and beta deviations. The Bartlett’s test is applied to test for equal variances among the different portfolios. If this test shows that the analysed portfolio characteristics have unequal variances the one-way ANOVA test will be replaced by the non-parametric Kruskal-Wallis analysis of variance. For representational purposes box-plots will be included in the appendices to show the nature and scale of the beta differences.
4. Data
4.1 Data
Only listed banks are used in this research since the co-movement of a bank’s return with the market return is required to estimate beta. Daily stock returns are used to increase the amount of possible observations on which the beta is calculated. This study focuses on banks that are listed in the United States (US) due to its dominant position in the financial industry. Additional advantages of focussing on the US only are the large dataset and the elimination of the effect of potential differences among banks caused by different countries of origin. The daily stock returns are taken from DataStream. For robustness purposes also the weekly stock returns are collected. In accordance with existing literature the S&P 500 will be the market proxy. The earliest date available in DataStream for the S&P 500 index is January 5, 1988, which will be used as starting date in the remainder of this paper.
Firstly, the ISIN numbers of all listed and delisted banks are obtained from Bankscope. The delisted banks are included to eliminate a potential survivorship bias. This results in a sample of 1,421 banks. Four banks are eliminated immediately due to unavailable stock returns. Subsequently, SIC codes are obtained for all the banks via DataStream. These codes, which are the most reliable industry descriptors according to Vallascas (2012), will be used to categorise the banks into three categories described by Demirguc-Kunt and Huizinga (2012) namely (1) commercial banks and bank holding companies, (2) investment banks and (3) other banks. SIC codes starting with 602- and 67- are labelled as ‘Commercial banks’, codes starting with 62- are categorised as ‘Investment banks’ and the SIC codes starting with 603- or 61- are ‘Other banks’. The fourth category ‘nonbank credit institutions’ is ignored since these institutions do not fit into the scope of this paper. 331 Banks are deleted from the sample due to missing SIC-codes. Additionally, insurance companies (2), real estate and unit investment trusts (4), unspecified investors and services (8) and federal sponsored credit institutions (3) are removed from the sample since they do not fit into one of the three subcategories.
The last characteristic accounted for is leverage. For this characteristic the method applied by Adrian and Brunnermeier (2011) is used as starting point.They determine leverage as the ratio of the book value of total assets to the book value of total equity. This paper deviates from their approach by obtaining leverage from DataStream via code WC08221 and thus using the ratio of total debt to total financing of the firm. This leads to the removal of two more banks due to unavailable data. The portfolios are constructed in identical ways as the size portfolios and account for yearly varying leverage levels. Six observations are deleted due to extremely high leverage levels caused by distress in the months preceding bankruptcy.
4.2 Penny stock and illiquidity adjustments
Similar to Fama and French (1992) penny stocks are excluded due to their uncommon return characteristics. These stocks have a higher likelihood of including noise in the return observations, which obscures the true reaction to market events. This undesired characteristic is mainly caused by the major impact of the minimum tick of $1/8 dollar on the share price. The requirements for a stock to be included are:
1. The stock should have a market capitalisation larger than 5 million dollars at the end of June in the preceding year.
2. If requirement (1) is not met, the stock should have a share price larger than $1 at the end of June in the preceding year.
In accordance with Fama and French June is selected as month of choice to correct for differences in financial years and reporting dates.
Another important reason for excluding small stocks is their tendency to be illiquid. Illiquid stocks include noise in the observations as they lack the ability to adequately react to market developments in a timely manner. Since daily returns are used for the yearly beta estimations the observations per year will be 250, which is the total amount of trading days during a year. To eliminate as much illiquidity noise as possible the liquidity criteria of Amihud (2002) is followed, which is a minimum of 200 trading days (or 80%) for inclusion.
limitedly represented within the sample with even only one observation in 1988 and 1989. Furthermore, investment banks have, on average, a larger size. Commercial banks and other banks show similar statistics for almost all years. Moreover, it holds for all bank types that the portfolio is largest in the early 2000s and beta is highest in 2009.
COMMERCIAL BANKS INVESTMENT BANKS OTHER BANKS
Year N Size Lvrg Beta N Size Lvrg Beta N Size Lvrg Beta 1988 15 1,151 47.1 0.57 1 4,181 61.3 1.01 3 1,509 54.2 0.65 1989 15 1,099 45.7 0.78 1 5,084 58.2 1.63 4 1,637 55.1 0.86 1990 21 1,194 46.3 0.96 3 5,753 53.4 0.99 5 1,597 54.0 1.08 1991 33 681 36.4 0.82 3 1,049 44.3 1.28 7 548 44.0 0.79 1992 34 724 36.0 0.78 4 1,042 45.6 1.56 6 551 40.7 0.75 1993 42 393 32.8 0.87 4 1,299 45.7 1.89 6 440 40.2 0.65 1994 41 414 36.6 0.66 6 1,134 44.1 1.41 7 335 43.4 0.81 1995 56 420 35.6 0.66 8 1,256 45.1 1.44 12 346 41.9 0.74 1996 70 436 37.9 0.64 7 1,038 56.0 1.29 14 359 40.8 0.62 1997 124 424 38.5 0.47 9 1,510 49.9 1.11 43 392 40.8 0.46 1998 204 450 40.3 0.64 11 1,520 51.7 1.45 77 419 44.0 0.69 1999 210 488 47.3 0.38 19 2,402 56.6 1.18 62 464 50.9 0.41 2000 216 551 46.7 0.48 21 3,557 55.3 1.21 67 487 52.8 0.49 2001 205 571 47.2 0.55 18 4,159 57.5 1.35 66 486 53.5 0.50 2002 252 636 49.8 0.56 17 5,987 56.7 1.06 84 486 53.2 0.50 2003 309 696 52.4 0.56 17 7,476 54.7 1.11 100 503 55.5 0.49 2004 286 745 53.1 0.85 16 8,825 55.0 1.24 76 528 55.6 0.76 2005 274 848 52.9 1.04 14 11,627 60.7 0.96 75 591 55.7 0.87 2006 272 910 51.2 1.00 14 14,774 62.4 1.51 74 690 55.1 0.84 2007 259 965 54.9 0.97 15 17,876 56.4 1.42 73 686 57.0 0.84 2008 234 1,064 57.7 0.95 12 12,515 49.4 1.58 61 794 61.3 0.88 2009 234 1,134 52.4 1.46 11 6,707 46.2 1.84 61 792 59.3 1.15 2010 237 1,186 46.6 1.05 10 8,418 44.8 1.30 61 932 53.5 0.83 2011 225 1,195 42.6 1.13 10 6,711 48.5 1.57 61 889 50.8 0.87 2012 227 1,323 41.5 1.01 10 8,359 46.8 1.43 63 906 47.9 0.80 2013 246 1,437 39.8 0.85 10 8,756 36.4 1.23 69 977 48.4 0.71 2014 234 2,282 39.8 0.82 7 23,831 43.6 1.38 61 1,248 52.1 0.64
This table shows the descriptive statistics of the three different bank categories: commercial banks, investment banks, and other banks. The portfolios are shown per year after all corrections have been implemented. Observations (N) are the total amount of banks per category, size is their median size (total assets in billion dollars), Leverage (Lvrg) is debt in percentage of total assets and Beta is the average beta of the banks within the portfolio (based on S&P 500 as market proxy).
Table 2: Descriptive statistics bank categories
5. Results
In this section I will present the empirical results. Section 5.1 will focus on the overall effect of recessions on bank betas and the potential of predicting recessions with beta behaviour. The following sections observe whether betas show a development over time for: all banks (5.2), portfolios based on size (5.3), portfolios based on bank type (5.4) and portfolios based on leverage level (5.5). Section 5.6 concludes with robustness checks for weekly returns, quarterly betas, more illiquid stocks, and differently categorised portfolios.
5.1 Beta characteristics during recessions and the preceding years.
Table 3 shows that the betas of financial institutions rise during recessions regardless of their size, core business or leverage level. These results are in accordance with King (2009) and Caporale (2012) and justify my approach. This confirms that the market acknowledges the volatile positions of banks when the economy hits a downturn. Recessions are of particular danger to banks since the broad exposure to all kinds of industries and individuals is embedded in their business
Portfolio Mean Standard deviation Coefficient of variation R𝜏=0 R𝜏=1 t-statistic R𝜏=0 R𝜏=1 z-score R𝜏=0 R𝜏=1 z-score All banks 0.79 0.99 -8.27*** 0.48 0.53 -0.38 0.64 0.56 0.94
Portfolios based on size
Large 1.09 1.41 -7.48*** 0.32 0.37 -0.50 0.31 0.29 1.00 Medium 0.86 1.02 -5.16*** 0.42 0.45 -0.44 0.56 0.49 0.50 Small 0.36 0.48 -3.76*** 0.40 0.44 -0.38 1.11 0.86 1.50
Portfolios based on bank type
Commercial 0.80 1.00 -7.31*** 0.46 0.52 -0.50 0.62 0.55 1.19 Investment 1.28 1.50 -2.45** 0.49 0.47 0.34 0.38 0.35 0.34 Other 0.68 0.84 -3.26*** 0.43 0.51 -1.00 0.63 0.61 -0.19
Portfolios based on leverage
High 0.88 1.06 -3.79*** 0.44 0.49 -0.50 0.50 0.46 -0.19 Medium 0.79 1.00 -6.05*** 0.48 0.50 0.50 0.64 0.54 1.50 Low 0.71 0.88 -4.03*** 0.47 0.49 0.19 0.78 0.63 1.44 The mean, standard deviation and coefficient of variation are given for every portfolio’s beta during non-recessionary years and recessions. The non-recessionary years are 1990, 1991, 2001, 2008 and 2009. The first column shows the names of the portfolios. The second column shows the mean in recessions (R𝜏=1) and during non-recessionary years (R𝜏=0). The t-statistic shows if there is a significant difference between these means. The third and fourth column do the same for the standard deviation and CV. Since the standard deviation and the CV are non-parametric the z-score of the Mann-Whitney U-test is shown. For both tests ***, ** and * show significance at 1%, 5% and 10% level.
Table 3: Beta characteristics during recessions and non-recessionary years
models. Consequently, the dependency of banks and their income on the welfare of the overall economy is confirmed throughout all portfolios.
When looking at the portfolios in more detail the first interesting observation is the average beta of exactly 1.00 for commercial banks during recessions. The increase in beta from 0.80 to 1.00 might be explained by the ways in which banks shred risky, firm specific, investments during recessions. The beta of 1.00 then indicates that, on average, these banks move perfectly correlated with the market. This follows naturally since a well-diversified portfolio remains after eliminating firm specific risks, leaving only truly systemic risks in play.
The second finding that strikes the eye is the positive relation between bank size and the effect of a recession on a bank’s beta. My results seem to confirm the findings of Wagner (2010) since the effect of a recession is substantially bigger for large banks compared to smaller banks. This could be caused by the overexposure to identical systemic risks, caused by over-diversification, and the higher degree of interconnectedness. The higher integration of larger banks can lead to trouble since systemic shocks will cause similar reactions among these larger banks. In contrast to smaller, more locally dependent, banks that have varying bank or region specific options to eliminate market risks, large banks diversify away risks in manners that increase the similarity of their remaining systemic risk exposures. This leads to higher aggregated systemic risks within the total banking sector. The larger increase in betas of large banks confirms the finding of Wagner (2010) that banks and regulators should be aware of the fact that diversification might help on individual bank level, but imposes significantly more danger to the overall financial system.
The second and third column show the standard deviation and coefficient of variation of the betas within a portfolio. The standard deviations show no significant difference between recessions and non-recessionary years. An explanation for the higher beta standard deviation during recessions could be the positive linear relation between beta size and its standard deviation. A more appropriate comparison tool would therefore be the coefficient of variation.9 However, the coefficient of variation shows no significant decrease during recessions either. A major argument for these weak results is the small amount of possible observations. The standard deviations
9 The coefficient of variation is justified due to the linear relation between beta’s mean and standard
and coefficients of variation show the dispersion of the betas within a portfolio. Since the portfolios are constructed on a yearly basis the observations for this analysis are limited to a maximum of 27. Therefore, when applying beta deviation as measure, it is impossible to state that banks become more alike during recessions.
Additionally, Table 4 shows that, regardless of the method used to control for years preceding recessions, no typical beta-clustering trend is observed in the onset of recessions either. None of the deviations is significantly smaller in the years leading up to a recession, which is strong evidence that financial institution betas do not have a predictive ability regarding market wide recessions. Therefore, predictions similar to Estrella and Mishkin (1998) become irrelevant. This might be because betas only account for market movements that have already occurred. This reactive nature is confirmed by the fact that beta is only significantly higher in P𝜏=1 for the large bank portfolio with a t-statistic of -3.82. All other portfolios lose their significant differences.
Another argument, discussed in more detail by Ang and Cheng (2007), could be the lagging nature of beta. To specify: yearly betas also represent the observations
This table shows the standard deviations and coefficients of variation for betas in the years preceding recessions compared to the other years. P𝜏=1 represents the years preceding a recession, P𝜏=0 represents all remaining years. The left columns include the years 1989, 1990, 2000, 2007 and 2008, in the P𝜏=1 group since these years precede a recessionary year. The right columns exclude 1990 and 2008 from the preceding year group given that these are recessionary years themselves. The z-score indicates whether there is a significant difference between these years. None of the results are significant.
Table 4: Beta deviations in years preceding recessions
Including recessionary years Preceding years only
Portfolio Standard deviation Coefficient of variation Standard deviation Coefficient of variation P𝜏=0 P𝜏=1 z-score P𝜏=0 P𝜏=1 z-score P𝜏=0 P𝜏=1 z-score P𝜏=0 P𝜏=1 z-score All banks 0.63 0.59 0.69 0.49 0.49 0.13 0.62 0.66 -0.54 0.49 0.50 0.15
Portfolios based on size
Large 0.34 0.31 -0.50 0.32 0.26 0.75 0.33 0.35 -1.16 0.30 0.32 -0.62 Medium 0.42 0.43 -0.25 0.55 0.72 0.44 0.42 0.44 -0.08 0.54 0.59 -0.69 Small 0.42 0.38 1.06 1.07 1.02 0.38 0.41 0.37 0.85 1.05 1.18 -0.69
Portfolios based on bank type
Commercial 0.47 0.47 -0.06 0.62 0.58 0.81 0.47 0.46 0.31 0.61 0.64 -0.39 Investment 0.49 0.50 -0.22 0.37 0.39 -0.44 0.48 0.56 -1.00 0.37 0.43 -0.80 Other 0.43 0.49 -1.00 0.62 0.63 -0.44 0.43 0.51 -0.93 0.62 0.71 -1.16
Portfolios based on leverage
in the beginning of a year, for example January. Hence, when a recession hits at year’s end, the recessionary symptoms are starting to be reflected in betas from the last quarter of a year onwards. The impact of these observations would be diminished by the older and irrelevant observations from January. For predictive purposes it might therefore be better to focus on betas with shorter time intervals. However, the robustness analysis in Section 5.6 shows that the differences remain insignificant when using quarterly betas, which leads to the overall conclusion that financial institutions betas do not have any predictive power regarding upcoming recessions.
5.2 Beta development of all US financial institutions over time
The results show no evidence of structural clustering behaviour in the US banking industry throughout the years when using plotted confidence intervals, standard deviations or coefficients of variation analyses. Fig. 1 shows the development of all US financial institution betas over time. The grey areas represent recessionary years, the dots are the mean betas and the error lines embody the 95% confidence intervals. An important note needs to be made regarding the larger
.5 1 1.5 Be ta '88 '89 '90 '91 '92 '93 '94 '95 '96 '97 '98 '99 '00 '01 '02 '03 '04 '05 '06 '07 '08 '09 '10 '11 '12 '13 '14 Year 95% confidence intervals
This figure shows the development of all US financial institution betas over the time period 1988 – 2014. The y-axis represents the betas, whereas the x-y-axis shows the years. They grey areas represent recessions. The plotted dots are the beta means per year for all US financial institutions. The vertical error lines are a visual representation of the beta dispersion and embody the 95% confidence intervals
Figure 1: The development of all US financial institution betas over time
intervals in the early years (1988-1994); these are mainly caused by the lower amount of observations during these years.
Four remarkable trends are observed. The first finding is the jump in betas in 1998, which was caused by the global financial meltdown. Although this crisis did not originate in the US, it did affect the systemic risk of the US banks. The overall economy did not face a recession, but the high interconnectedness of (global) banks became visible during this systemic risk spike. Therefore, the most interesting development around this beta jump is the post crisis beta level of only 0.44, which indicates the returning underestimation of the systemic risk exposures of banks. Second are the low betas until 2004 and the following jump in the years 2004 (from 0.56 to 0.84) and 2005 (from 0.84 to 1.01). This is exactly the same result as Caporale (2012) and King (2009) find in their US bank beta analysis. It indicates that the market underestimated systemic risk and only started to account for the increased systemic risks of banks from 2004 onwards. The third remarkable finding is the larger confidence interval in 2009, which shows that there was a higher variety among betas in the primetime of the credit crunch. This contradicts the hypothesis that betas become more alike in times of an economic recession. The last remarkable trend is the decline in betas in 2013 and 2014 to the pre-crisis level of 2005. This trend either suggests that banks are less exposed to systemic risks since the effects of the crisis have worn off or that the market falls into old habits and underestimates the systemic risks of the banking sector again.
5.3 Beta development of US financial institutions based on bank size
The most obvious result is the positive relation between bank size and beta. This is in accordance with theories of Stiroh and Rumble (2006), Baele et al. (2007), and De Jonghe (2010). Additionally, the results show that the standard deviations significantly differ among the different size portfolios and that large banks have lower beta dispersion. Nonetheless, no clustering trend is observed within any of the portfolios when analysing the confidence intervals, standard deviations or coefficients of variation through time.
Fig. 3 shows the development of bank betas categorised on bank size. The significantly lower betas of small banks confirm the theory of Stiroh and Rumble (2006), which states that smaller banks are more dependent on local economic conditions instead of overall market trends. The higher betas for large banks subsequently show the higher risk caused by interdependency of larger banks
This graph shows the development over time of the standard deviation and coefficient of variation of all financial institution betas. The time horizon is shown on the x-axis and ranges from 1988 – 2014. The coefficient of variation shows the standard deviation in percentage of its mean. The year 1999 shows the coefficient of variation’s inability to compare when the mean is close to zero. For all other years the coefficient of variation provides insights in variation trends of beta.
Figure 2: Standard deviation and coefficient of variation of all financial institution betas
.4 .6 .8 1 1.2 C o eff ic ie n t o f v ar ia tio n o f b e ta s .3 .4 .5 .6 .7 .8 Sta nd ar d d e vi ati on o f b e ta s 1990 1995 2000 2005 2010 2015 Year
(Wagner, 2010). The consequent higher reliance on the well being of the overall market is in line with this argument.10
Regarding beta deviations, differences in variances are confirmed by the Bartlett’s test, showing differences in variances at every significance level with a chi-squared value of 124.87. The standard deviations of the betas in the three different size based portfolios differ significantly, with 0.34 for larger banks and 0.42 and 0.41 for medium sized and smaller banks respectively. The differences are proven significant at the 1% level with an F-statistic of 5.84. These results confirm the diversifying tendency of larger banks that eventually leads to their similar systemic risk exposures (Wagner, 2010). Additionally, it proves that the beta deviation method successfully shows which betas are more alike and therefore could be of value when investigating bank clustering.11
10 See Appendix B for a visual representation of the beta distribution per portfolio and the statistical
significant confirmation of the positive relation between bank size and beta.
11 Appendix C shows that the absolute standard deviation of the betas in the large bank portfolio is also
smaller than the standard deviation of betas in the smaller bank portfolios. This underlines the strong clustering tendency of larger banks.
This figure shows the beta development of three US financial institution portfolios based on size over the time period 1988 – 2014. The y-axis represents the betas, whereas the x-axis shows the years. The grey areas represent recessions. The large bank symbol is a circle, the medium sized banks are shown by a triangle and the small bank symbol is a hollow square. The symbols represent the yearly beta means. The vertical error lines are a visual representation of the beta dispersion and embody the 95% confidence intervals. The larger confidence intervals in the early years are due to fewer available observations.
Figure 3: The development of financial institution betas categorised on bank size
0 .5 1 1.5 2 Be ta '88 '89 '90 '91 '92 '93 '94 '95 '96 '97 '98 '99 '00 '01 '02 '03 '04 '05 '06 '07 '08 '09 '10 '11 '12 '13 '14 Year
Large Medium Small
Fig. 4 shows that the bank clustering theories do not hold when measuring increasing similarity by means of the beta’s coefficient of variation. The potential contributors to increasing aggregated systemic risk are the larger banks, however the CV for both medium sized and large banks stabilises from 2001 onwards. This finding contradicts the hypothesis that banks became more alike in recent years. It is worth mentioning that even the crisis of 2008 and 2009 did not alter the CV of medium sized and large banks. This indicates that betas of larger banks do not cluster in downturns nor show other remarkable behavior in economical recessions. The CVs for smaller banks are unpredictable through time, which is probably caused by their higher dependency on local economies. It can be assumed that smaller banks react to systemic events in different ways, if they react at all, since every local economy has a different relation with the overall market and its systemic shocks.
This figure shows the beta deviations of three US financial institution portfolios based on size over the time period 1988 – 2014. The y-axis shows the coefficients of variation of the betas within the portfolios in absolute values. The x-axis shows the years. The grey areas represent recessions. The large bank symbol is a square, the medium sized banks are shown by a triangle and the small bank symbol is a circle.
Figure 4: Coefficient of variation development of bank betas in portfolios based on size
0 .5 1 1.5 2 C o eff ic ie n t o f v ar ia tio n 1990 1995 2000 2005 2010 2015 Year
5.4 Beta development of US financial institutions based on bank type
Fig. 5 shows that investment banks have higher betas than commercial and other banks in every year. Furthermore, commercial and other banks show high similarity in both betas and their dispersion through time. The higher betas for investment banks are statistically significant.12 These results confirm that higher dependency on noninterest income indeed results in more systemic risk (Stiroh, 2004; Demirgüc-Kunt and Huizinga, 2010). Regarding the beta dispersions, note that the confidence intervals in Fig. 5 show larger intervals for investment banks due to fewer observations. Hence, comparing the intervals of the different bank type portfolios does not yield any economic relevant insights, but analysing the portfolio intervals over time does.
12 See Appendix D for the confirmation of the significant difference between investment bank betas
and betas of commercial and other banks. Additionally, Appendix E shows that this effect still holds when controlled for the size effect and thereby eliminates the argument that investment banks in this sample only have higher betas due to their bigger size.
This figure shows the beta development of three US financial institution portfolios based on bank type over the time period 1988 – 2014. The y-axis represents the betas, whereas the x-axis shows the years. The grey areas represent recessions. The commercial bank symbol is a circle, the investment banks are shown by a triangle and the other bank symbol is a square. The symbols represent the yearly beta means. The vertical error lines are a visual representation of the beta dispersion and embody the 95% confidence intervals. The larger confidence interval for investment banks is caused by the lower amount of banks available for this portfolio. The larger confidence intervals and the missing confidence intervals for investment banks in the early years are due to fewer available observations.
Figure 5: The development of financial institution betas categorised on bank type
-1 0 1 2 3 Be ta '88 '89 '90 '91 '92 '93 '94 '95 '96 '97 '98 '99 '00 '01 '02 '03 '04 '05 '06 '07 '08 '09 '10 '11 '12 '13 '14 Year
Commercial bank Investment bank Other bank
Conversely, Fig. 6 shows that the investment bank portfolio has lower beta CVs from 2001 onwards, with a small bump in 2005. The CV is always lower for the investment bank portfolio compared to the commercial or other bank portfolios. The Bartlett’s test hypothesis of equal variances allows for the appliance of the ANOVA test at the 5% and 1% confidence level with a probability of 0.097. The results show that the mean coefficient of variation is 0.37 for investment banks, 0.61 for commercial banks and 0.63 for other banks with an F-statistic of 19.62.
Although a clear trend through time is absent for commercial and other banks, the decline of investment banks’ beta deviation in 2008 and 2009 is remarkable. Betas of commercial and other banks seem to become increasingly different in this period but investment bank betas show an opposite trend.13 Despite the fact that Table 1 shows that there is no significant difference in investment bank beta dispersion for recessions and non-recessionary years it is worth noting that the trend in 2008-2009 could confirm clustering behaviour of banks that are more dependent on overall
13 For further visualisation of beta dispersion see Appendix F, which shows the drop in investment
bank beta’s standard deviation during the 2007-2009 crisis in more detail
This figure shows the beta deviations of three US financial institution portfolios based on bank type over the time period 1988 – 2014. The y-axis shows the coefficient of variation of the betas within the portfolios in absolute values. The x-axis shows the years. The grey areas represent recessions. The commercial bank symbol is a circle, the investment banks are shown by a triangle and the other bank symbol is a square.
Figure 6: Coefficient of variation development of bank betas in portfolios based on bank type
Figure 6: Coefficient of variation development of bank betas in portfolios based on bank type
.2 .4 .6 .8 1 1.2 C o eff ic ie n t o f v ar ia tio n 1990 1995 2000 2005 2010 2015 Year
market movements in recent years. Hence, although the results are not statistically significant, they show a lower beta deviation for investment banks compared to other bank types in the last third of the time period. This indicates that investments banks contributed to an increase of aggregated systemic risk. However, despite the 2008-2009 decline for investment bank beta dispersion, it is too optimistic to state that banks with a higher ratio of noninterest income are less dispersed by means of beta.
5.5 Beta development of US financial institutions based on leverage
Fig. 7 shows that leverage has a positive relation with beta but no clear clustering trend is observed. The results prove that the positive relation between leverage and beta also holds for banks despite the different meaning of leverage for banks compared to other firms in terms of their business models (Fama and French, 1992). The betas are 0.91 for highly levered, 0.83 for medium levered, and 0.73 for
This figure shows the beta development of three US financial institution portfolios based on leverage levels over the time period 1988 – 2014. The y-axis represents the betas, whereas the x-axis shows the years. The grey areas represent recessions. The low-levered bank symbol is a circle, the medium levered banks are shown by a triangle and the highly levered bank symbol is a square. The symbols represent the yearly beta means. The vertical error lines are a visual representation of the beta dispersion and embody the 95% confidence intervals. The larger confidence intervals in the early years are due to fewer available observations.
Figure 7: The development of financial institution betas categorised on leverage level
0 .5 1 1.5 2 Be ta '88 '89 '90 '91 '92 '93 '94 '95 '96 '97 '98 '99 '00 '01 '02 '03 '04 '05 '06 '07 '08 '09 '10 '11 '12 '13 '14 Year
low-levered banks. The differences are significant with an F-statistic of 36.80.14 These findings are in line with the capital buffer argument of Vallascas (2012).
As expected, there is no clear difference between the beta dispersions of the leverage-based portfolios. This means that, despite the positive relation between leverage and systemic risk, highly levered banks do not cluster more than less levered banks. Still, the average CVs do differ; with 0.49 for highly levered, 0.62 for medium levered, and 0.75 for low-levered banks. The differences are significant with an F-statistic of 123.18 but Fig. 8 shows that these differences are solely caused by the early years since the portfolios show identical deviations from 2005 onwards. These observations underline that the effect of leverage on beta dispersion is ambiguous.15
Acharya and Mora (2015)state that during recessions higher leverage leads to higher bank-interdependence and a higher degree of control due to creditor discipline. This subsequently increases aggregated systemic risk. However, Fig. 8 shows that the
14 The chi-squared outcome of the ANOVA test is 4.4230 with a probability of 0.110, therefore it
allows for equal variances. See Appendix G for the visual representation of the betas.
15 Appendix H shows that the results have no economic relevance if the standard deviations per
portfolio are not adjusted to scale. The variations among the different portfolios appear to be random and are therefore diminishable.
This figure shows the beta deviations of three US financial institution portfolios based on leverage levels over the time period 1988 – 2014. The y-axis shows the coefficient of variation of the betas within the portfolios in absolute values. The x-axis shows the years. The grey areas represent recessions. The low-levered bank symbol is a circle, the medium levered banks are shown by a triangle and the highly levered bank symbol is a square.
This figure shows the beta deviations of three US financial institution portfolios based on leverage levels over
Figure 8: Coefficient of variation development of bank betas in portfolios based on leverage
Figure 8: Coefficient of variation development of bank betas in portfolios based on leverage
0 .5 1 1.5 2 C o eff ic ie n t o f v ar ia tio n 1990 1995 2000 2005 2010 2015 Year
