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Identifying systemically important financial institutions: size and
other determinants∗
Kyle Moore†^ and Chen Zhou†,^ ‡
†Erasmus University Rotterdam
‡De Nederlandsche Bank
April 13, 2012
Abstract This paper analyzes the conditions under which a financial institution is systemically important. Measuring the level of systemic importance of financial institutions, we find that size is a leading determinant confirming the usual “Too Big To Fail” argument. Nevertheless, the relation is non-linear during the recent global financial crisis. Moreover, since 2003, other determinants of systemic importance emerge. For example, decisions made by financial institutions on their choice of asset holdings, methods of funding, and sources of income have had a significant effect on the level of systemic importance during the global financial crises starting in 2008. These findings help to identify systemically important financial institutions by examining their relevant banking activities and to further design macro-prudential regulation towards reducing the systemic risk in the financial system. JEL Classification: G01, G21, G28. ∗The research of Kyle Moore has received funding from the European Community’s Seventh Framework Pro- gramme FP7-PEOPLE-ITN-2008. The funding is gratefully acknowledged. We are also grateful for the research assistance provided by Lin Zhao. Views expressed do not necessarily reflect official positions of De Nederlandsche Bank.Email addresses: [email protected] (Moore, K.T.), [email protected] (Zhou, C.)
1 Introduction
The failure of a single financial institution has the potential to spark catastrophic losses in local, regional, and global financial systems. The global financial crisis initiated in 2008 has provided an example. Measures taken by the US government, in the onset of the crisis, attempted to save large financial institutions from possible default. Similarly, during the European debt crisis, the European Central Bank introduced aprogram designed to prop up banks struggling to raise funds. These intervention activities have lead to debates in both support and objection of rescuing certain distressed financial institutions. Arguments in favor stress that financial institutions receiving government support are systemically important. That is, their failure may trigger a relatively large number of simultaneous failures within the financial sector, and as a result, large losses to the entire economy. Nevertheless, the institutions that in practice receive most, if not all, the “bailout” attention are the large firms that are considered “Too Big to Fail”. This raises the question as to whether size is fundamental in determining the interconnectedness of the financial system. If size is not a sufficient measure in detecting bank interconnectedness, the consequent question most regulators would ask is: Which banks are “Too Systemically Important to Fail”? This paper aims to close this gap by empirically analyzing potential determinants of systemic importance of a financial institution. We analyze potential determinants of the systemic importance namely the size, leverage, and other components on individual institutions’ balance sheets. More specifically, we examine three categories comprising the assets composition, methods of funding, and sources of revenue. The implications of such a study will allow regulators to assess the systemic risk imposed by a single bank to the financial sector based on examining its banking activities. Regarding size as the determinant of systemic importance, we find strong support in favor of the TBTF hypothesis. However, the relation between size of a financial institution and its systemic importance is highly non-linear and depends on macroeconomic conditions. On the cross-section dimension, increases to systemic importance in relation to size are most pronounced for medium sized banks. On the time dimension, the relation varies according to the time period being analyzed. For example, in the period surrounding the financial crisis from 2007 to 2010, we find that size can only be considered as a proxy for systemic importance if the size is below a certain threshold level
the systemic risk in the financial industry must take into account more than just the size of a bank. Furthermore, in order to reduce the overall risk in the system, regulators should consider a balance between the systemic importance and individual risk - the dual contributors of systemic risk induced by a bank. The Systemic Impact Index introduced by Zhou (2010) measures the expected number of simul- taneous bank failures in the system conditional on the failure of a specific individual institution. This approach is able to capture the general instability of the system associated with the failure of a single institution. The notion of too-many-to-fail may raise regulators concern on the number of failures in the system stemming from a single failure; however, such a measure lacks information on the exact economic impact a failure would create. More specifically, the deterioration of social welfare within the system such as the amount of government assistance required to maintain a healthy banking system. We extend the definition of systemic impact to include two types of potential losses to the financial system. Conditional on a particular bank’s failure, the first measures the expected capital shortfall of other failed institutions, and the second measures the expected loss on insured deposits held by other failed banks. The two measures give additional insight into the social welfare effects of a particular bank failure. The first can be viewed as the recapitalization bailout costs of other banks in the event of a particular bank failure. The second is the liability the central authority faces if the other failed banks are not recapitalized, that is the total insured creditors’ demand on their guaranteed deposits. The paper proceeds as follows. We first introduce the related literature in Section 2. Sec- tion 3 describes the construction of the three measures of systemic importance. The potential determinants of systemic importance are explored in Section 4. The data collection and empirical methodology in analyzing the determinants of systemic importance are shown in Section 5 with the results explained in Section 6. Section 7 concludes the paper.
2 Literature Review
This paper relates to three strands of literature on systemic risk. The first strand deals with the theoretical models on systemic risk and systemic importance. A great deal of the literature models systemic risk through the direct links banks expose themselves to each other through the interbank markets, see, e.g. Rochet & Tirole (1996), Allen & Gale (2000), and Freixas et al. (2000). The banking system is wired together as a network supported by the interbank market. Liquidity constraints within the financial sector are reduced when banks have the ability and means to lend to each other. The downside of this activity is that banks open themselves up in the event of a bank failure. The magnitude of the chain reaction of failures introduced by the failure of one bank reflects the bank’s level of systemic importance (Furfine (2003)). This type of bank interconnectedness is derived from specific financial linkages between institutions and is referred to as direct channel linkages. Banks may also be connected through a common funding shock to the system that affects all those exposed to it. If the shock is of a large magnitude it will cause a subset of banks to fail simultaneously. A classic example is the standard bank run model described by Bryant (1980) and Diamond & Dybvig (1983). In this literature, a shock to the confidence of deposit holders, in the absence of deposit insurance, can lead to a swift withdrawal of bank capital regardless of its solvency. This, in turn, has the potential to spark simultaneous runs on other banks, healthy or otherwise. As a result, those models provide support for the potential of funding activities in determining a bank’s systemic importance. An indirect approach in modeling systemic risk can be considered via common shocks to the asset side of a financial institution’s balance sheet. Banks that hold similar portfolios, or highly correlated ones, will be indirectly linked in the event of such a shock, see, e.g. De Vries (2005) and Acharya (2009). Due to the nature of banks, the initial shock is likely to be amplified throughout the system as firms de-lever their positions to meet margin calls and capital requirements (Brunnermeier & Pedersen (2009)). Adrian & Shin (2010) provide empirical evidence for this. In this regard, the source or focus of the shock is not of primary importance since the linkages are a result of the similarities in banking characteristics. Therefore, the type and quantity of asset holdings of banks
facilitates.
3 Systemic Importance Measures
3.1 The Systemic Impact Index: SII
The systemic importance measure proposed by Zhou (2010) is based on an application of multi- variate Extreme Value Theory (EVT)^1. The SII measures the expected number of simultaneous failures given a single failure by measuring the conditional probability of one bank’s failure on the failure of a specific bank. A direct estimation of the probability of joint failure is difficult due to the scarcity of actual “bank failures”. We resolve this issue empirically by instead estimating the probability of bank distress. Evidence suggests that financial market data, such as a bank’s market price of equity, can serve as an early warning indicator of ratings changes for publicly traded bank holding companies (BHCs), see, e.g. Krainer & Lopez (2003). Therefore, we describe a distress event when the market price of a bank’s equity experiences a large (daily) loss. Consider a banking system consisting of N banks. Denote their equity returns as X 1 ,... , XN. A distress, or tail event, is defined as an event with a low probability p.^2 In other words, values of Xi below a certain threshold level are assumed to trigger a tail event for bank i. More explicitly, this threshold level is determined by the Value-at-Risk (VaR) of the bank and is defined as
P r(Xi < −V aRi(p)) = p, (1)
for some sufficiently low (tail) probability level p. While the choice of p is of concern for regulators and the internal risk management of the firm, we do not impose a specific p level here. Instead, we consider a constant p level across firms. Notice that this does not imply that the threshold levels are constant across firms, but rather that the probability of a tail event is invariant. Certain firms have a greater loss tolerance than others can thus enjoy a lower threshold for defining a tail event. Our description allows for heterogeneity in banks’ individual risk taking activities. (^1) See De Haan & Ferreira (2006) for an overview of multivariate EVT. (^2) For instance, a p of 0.001, using daily data, corresponds to a tail event once per 1/p = 1000 days, or about once per 4 years.
The SII is defined as
SIIi(p) = E(
j 6 =i
IXj <−V aRj (p)|Xi < −V aRi(p))
= ∑ j 6 =i
P (Xj < −V aRj (p)|Xi < −V aRi(p)), (2)
where IA is the indicator function that is equal to 1 if A occurs and 0 otherwise. If the distress of one bank is likely to be accompanied by similar distresses in other banks, this bank is said to be systemically important^3. This measure is able to capture the degree to which an individual bank distress or failure can influence the rest of the banking system, however, it is unable to distinguish the economic size of the impact. A distress in a bank which is accompanied by distress or failure in other small banks, or a similar impact to large banks, are indistinguishable under this measure. Hence, it is necessary to extend this measure to account for the economic size of the impact.
3.2 Extension to a Weighted SII: Social Welfare Measures
We propose two different weighting measures to capture the systemic importance of a bank in terms of social welfare loss given its distress. The first extension is the expected capital shortfall in the system given a particular bank is distressed. The capital shortfall (CS) of a bank can be approximated by the product of its equity and the Expected Shortfall (ES) of its equity return given the return falls below a certain V aR level as
CSi = Equityi · ESi, (3)
where Equityi is the equity for bank i, and the ES of bank i is given by
ESi(p) = −E(Xi|Xi < −V aRi(p)), (4) (^3) This measure cannot discern any causality. For instance, a system consisting of only two banks has a corresponding SII 1 = SII 2. Acharya (2009) argues that causality is not necessary in determining systemic importance. If a bank’s failure is often associated with other’s failure, it ultimately enjoys a high chance of being bailed out. Such a bank should be regarded as systemically important from a social welfare point-of-view.
follows: SIiDEP (p) = ∑ j 6 =i
DEPj · P (Xj < −V aRj (p)|Xi < −V aRi(p)), (6)
where DEPj is the sum of the customer demand and time deposits held by bank j.
4 Potential Determinants of Systemic Importance
Our systemic importance measure does not reflect the likelihood of an individual bank distress or failure, but rather the expected additional costs given such an event. The operations and features of a bank that increase its individual tail risk do not necessarily increase its interconnectedness. The two contributors to systemic risk, the individual risk and the systemic importance, can work in parallel or against one another. Consequently, certain determinants, such as size, may induce an opposite effect on systemic importance in comparison to individual risk of failure. We discuss the potential determinants of systemic importance and make hypotheses as to their impacts.
4.1 Size
Banks have an incentive to hold diversified portfolios. While this may be an optimal strategy in terms of lowering individual risk, it induces a negative externality on the system. The benefits of diversification, minimizing a portfolio’s exposure to idiosyncratic risk, are countered by an increase to systemic connectedness when other banks hold similar portfolios. A shock to a certain class of assets will affect all banks that hold these assets. If a large fraction of banks are holding a comparable collection of assets, then a large negative shock will cause these banks to all become distressed simultaneously (Ibragimov et al. (2011)). Therefore, larger banks holding more diversified portfolios are typically recognized as being more stable, whereas when one fails the probability that this shock also affects other banks is high. On the contrary, smaller banks hold a smaller set of assets, and are thus more isolated from the rest of the system. Therefore, size may be positively associated with SI, opposite the relation to individual risk.
4.2 Leverage
The risk taking of a bank is determined, to a large degree, by its leverage position. While taking on leverage allows for banks to increase their return on equity, excessive leveraging by financial institutions is considered as a potential cause of financial crises. Balance sheet leverage, the focus in this paper, exists whenever the value of assets exceeds the value of equity of the bank. The increase of a bank’s leverage is caused by either acquiring more funding by borrowing, or by a negative shock to its asset value. As a bank’s leverage ratio increases the bank is able to earn a higher return on equity, however, this is at the expense of an increasing risk to the debt holders. Due to the riskiness imparted by high leverage, banks may choose to limit their exposures to highly levered institutions, thereby isolating them in the system^4. Therefore, a high leverage position may lead to a disconnected position within the financial system.
4.3 Funding
The funding decision of a financial institution plays an important role in determining its stability. Banks, unlike non-financial corporations, issue debt liabilities with maturities that are significantly shorter than the assets they hold. This reliance on short term funding, ranging from immediately callable retail deposits to slightly longer term money market funds, leave the bank exposed to maturity mismatch and considerable liquidity risk (Goodhart (1988)). The maturity mismatch of the investments to the funding decision leaves even solvent banks exposed to a quick withdrawal of funds by panicked investors. Acharya et al. (2010) and? find that a reliance on wholesale funding leads to an increase in the bank’s downside tail risk. Guarantees on retail deposits have removed some of the liquidity risk, however, this did not stop retail depositors from initiating a bank run such as that on Northern Rock’s funds in September 2007. Runs on the short term funding of banks are the result of a lack of confidence in particular financial institutions, which is regarded as a funding shock. When a common funding shock hits the banking sector, it leads to an erosion of creditor confidence. Banks relying heavily on short term funding may simultaneously face a run on their short term funding. Even if the shock is (^4) See, e.g. BCBS (1999b): Banks. Interactions with Highly Leveraged Institutions, Basel Committee on Banking Supervision, BIS, Basel, January.
banks that have decided to generate income from non-interest bearing activities.
5 Data and Methodology
5.1 Data for Constructing the Systemic Importance Measures
To construct the three systemic important measures, daily equity prices on US bank holding com- panies (BHCs) from 1999 to the end of 2010 are collected from Datastream^5. Corresponding annual balance sheet data for the total equity and customer demand deposits for each firm is matched with the Bankscope database^6. Data are divided into three non-overlapping periods, 1999-2002, 2003-06, and 2007-10. The choice of having a four year period for our analysis is to ensure a sufficient number of observations for the estimation of the conditional probabilities in the three SI measures. We filter out any institution not traded on at least 55% of the days within a certain period. Therefore, the minimum number of trading days for an institution within each period is 570. When estimating the conditional probabilities in the SII measure, Zhou (2010) did not correct for the possibility that the co-movement of bank equity returns can be due to a common market factor. This may lead to an overestimation of the SI measures. In order to remove the dependence imposed by a common market factor, we make correction by analyzing the banks excess returns over the market. We calculate the residual equity returns over the market return^7 using the single-factor market model: Ri,t = αi + βiRm,t + i,t. (7) The error term, i,t, is assumed to follow the standard assumptions of Ordinary Least Squared (OLS) regression and are cross-sectionally uncorrelated. The excess returns are calculated as
ˆi,t = Ri,t − αˆi − βˆiRm,t, (8) (^5) Equities selected are traded on both the NYSE and the NASDAQ exchanges. (^6) Equity and balance sheet accounting data are matched between the BvD Bankscope and Datastream by using the corresponding Bankscope number for each firm 7 The market returns for the period 1999 - 2010 refers to the returns of the SP500 index.
which are used in the construction of the three SI measures. The scope of financial institutions included in the analysis is further filtered by the inter-period availability of balance sheet data. The yearly accounting data are smoothed by averaging over four years. We require that firms included in the regression analysis have balance sheet data for at least three out of the four years in each period. In the end the number of selected BHCs are 194 for the period of 1999-2002, 298 for 2003-2006, and 375 for the period 2007-2010.
5.2 Estimation of the SI measures: an EVT approach
The key element in estimating all three SI measures (see (2) (4) and (5)), is the estimation of the conditional probability that bank j fails given that bank i fails for each pair i and j. We follow the approach in de De Jonghe (2010) and Zhou (2010) which applies multivariate EVT. Multivariate EVT provides models such that the limit of the conditional probability is at a constant level as p → 0, i.e. τi,j := lim p→ 0 P (Xj < −V aRj (p)|Xi < −V aRi(p)). (9)
Thus the conditional probability can be approximated by its limit τi,j. Suppose we have n obser- vations on the two return series as (Xi,s, Xj,s) for 1 ≤ s ≤ n. The limit τi,j can be estimated by taking p = k/n for sample size n, where k := k(n) is an intermediate sequence such that k(n) → ∞ and k(n)/n → 0 as n → ∞. A non-parametric estimate of τi,j is then given as
τˆi,j :=^1 k ∑^ n s=
(^1) Xj,s<Xj,(n−k),Xi,s<Xi,(n−k) , (10)
where Xi,(n−k) is the (k + 1)th lowest return among Xi, 1 ,... , Xi,n.^8 Practically, the theoretical conditions on k is not relevant for a finite sample analysis. Thus, how to choose a proper k in the estimator is a major issue in estimation. Instead of taking an arbitrary k, a usual procedure is to calculate the estimator of τi,j under different k values and draw a line plot against the k values. With a low k value, the estimation exhibits a large variance, while for a high k value, since the estimation uses too many observations from the moderate level, it (^8) For the estimator of τi,j , usual statistical properties, such as consistency and asymptotic normality, has been proved, see, e.g. De Haan & Ferreira (2006).
by ranking them as Xi,(1) ≥ Xi,(2) ≥ · · · ≥ Xi,(n), the Hill estimator is defined as
1 /αˆi := k^1 ∑^ k i=
log(−Xi,(n−i+1)) − log(−Xi,(n−k)). (13)
For the statistical properties of the Hill estimator, see Hill (1975). With the estimation of the V aR and the tail index, we obtain the estimate of the expected shortfall on the return series of each bank. Together with the market capitalization, they can be used in weighing the conditional probabilities which yield the estimate of the SI measure in terms of expected capital shortfall. The other SI measure, SIDEP^ , is formed in a similar way by using the bank’s total deposits to weigh the conditional probabilities.
5.3 Data for Potential Determinants
Two variables applied in the empirical analysis, size (Size) and leverage (Leverage), are defined by the logarithm of total assets and the ratio of total liability to total equity, respectively. To capture a non-linear property of the size of the institution, we also consider its quadratic form Size^2. The analysis of the remainder of the balance sheet items considered in the regression analysis are separated into three categories, funding sources, assets holdings, and income strategy. The funding sources of banks is dissected into short-term and long-term components as a ratio of the total funding. Including both variables introduces a multi-collinearity problem. Thus we choose to include the short-term component (ST F ) in the regression. The short-term funding is then sub-divided into three variables: money market funding, demand deposits (Demand), and saving deposits (Savings) as a ratio of the total short-term funding. Again, to avoid any multi- collinearity, only Savings and Demand are included in the regression along with ST F. In order to analyze the asset structure of the bank we look at the fraction of total assets that are held as loans (Loans) versus those held as securities. We omit the variable for securities, to avoid multi-collinearity. Loans is then divided into two non-disjoint variables, the fraction of loans that are mortgages (M ortgage), and the fraction of loans that are non-performing (P roblem). For the third category, the total gross income of each financial institution is divided into interest
or non-interest bearing activities. The total gross interest income of the firm as a fraction of the total gross income (Interest) is included in the regression.
6 Empirical Results
We conduct our empirical analysis in three disjoint periods between 1999 and 2010. Each captures a different and unique economic climate. The most recent period (2007-2010) manifest the time surrounding the financial crisis which is in direct contrast to the previous period (2003-2006) when the economy was experiencing a boom. These two periods allow for a comparison of determinants of systemic importance under different economic conditions. The earliest period (1999-2002) covers the time surrounding the bursting of the dot-com bubble and its subsequent deflation. Moreover, it also contains the introduction of bill that repealed, in part, the Glass-Steagall Act and began a wave of consolidation in the financial sector. Table 1 provides the summary statistics of our SI measures in each period. We observe that the interconnectedness within the system in 2007-2010 is in general higher than that in the previous two periods. Table 2 lists the most systemic banks by each measure for 2007-2010 period. These three lists differ from each other, while the “big banks” (Bank of America, Wells Fargo, Citigroup, etc.) appear only when the weighted measure is applied^9. We observe that our weighted measures report different systemically important financial institutions (SIFIs) compared to that identified by the unweighted SII measure. Therefore it is necessary to take the exact economic impact into account when measuring banks systemic importance. Table 3 shows the correlation matrix among the measures for each of the three periods. The correlation between the non-weighted SII and the two SI measures weighted by social welfare losses vary between periods, whereas the correlation of the two social welfare measures are close to 1. The low correlations between the two weighted measures and the SII measure may be a result of the different methods to account the impact to the system. On the contrary the high correlation (^9) If the expected shortfall on equity and the loss to customer deposits for the conditionally failed bank were also included as weights, then the list would essentially represent the 15 largest banks. This is partly due to the fact that the the probability of simultaneous failure conditional on the failure of a certain bank is relatively low. Therefore, the weight placed on the conditional bank dominates the measure.
From this regression we observe that above and below these two thresholds, increasing or de- creasing the size of the bank has less impact to its systemic importance. We conclude that for this period size is only a determinant of systemic importance for medium sized firms. When firms become too large, or small, the SI ceases to increase with size. Banks that grow larger increase their systemic importance, but only up to a limit. Above this limit threshold, large banks have a similar level of systemic importance. Zhou (2010) provides empirical evidence that size is not necessarily a determinant of systemic importance. However, the analysis was based only on data from 28 large US banks. Interestingly, we find also find that the 30 largest banks in our sample do not significantly differ in systemic importance giving support to this result. Our sample covers also medium and small banks, and thus provides a more complete picture on testing TBTF. Our results have direct policy implications. The Obama administration in early 2010 announced their intention that the implementation of policy based on the concept of TBTF would cease. At the same time, the governor of the Bank of England has publicly stated his desire to limit the size of banks. In either case, it is necessary to know if and when size is an important determinant of systemic importance. Based on our findings, a regulator imposing a TBTF policy should consider not the relative size of large banks, but rather a frontier size, above which all institutions become TBTF. The analysis shows that limiting the size of banks, is only effective if the appropriate size limit is imposed. While the relation between the systemic importance of a bank and its leverage is negative, it is not significant for the weighted measure. As aforementioned, a bank’s leverage ratio may increase in two ways: increasing the debt level or decreasing the asset value. Given the negative market conditions in this period, it is more likely that leverage increases as a result of depressed asset values. Leverage increasing in this way would have a similar effect on all banks in the system and can be regarded as being “involuntary”. Therefore, the argument on the potential negative impact of leverage discussed in Section 4.2 may not apply during the global financial crisis. This partially explains the insignificant result during this period. The hypothesis that traditional banking practices are less risky, not only to the idiosyncratic risk, but also to the systemic risk is confirmed in our analysis: the coefficient on the fraction of
income generated by interest is negative with a significance at the 95% level. Our finding supports regulating non-traditional banking activities since they help to mitigate both individual risk as well as the interconnectedness of the system.
6.2 Economic Boom and US Housing Bubble: 2003-
When conducting analysis in the 2003-2006 period which corresponds to the rapid expansion in the US, the impact of asset holdings and income strategy has on the systemic importance of institutions is essentially unchanged. However, three differences are observed. First, the partial linear effect of size on the bank’s SI weighted by capital shortfall is apparent in Figure 3, however, with only single breakpoint for this period. This occurs in the neighborhood around the point where Size = 7.4 (see Figure 4). We find that when Size < 7 .2 the coefficient on the size is no longer significant. Conversely, it is highly significant in the positive direction when Size is greater than 7.2. This gives strong support for the TBTF hypothesis. Second, the coefficient on the leverage variable is highly significant in this period in the negative direction. In this period the economy is booming. Increased leverage positions are not due to a common negative shock on asset prices, as during the crisis, but rather a choice by the bank to increase its level of debt. We have conjectured that banks choosing to increase their leverage have a lower SI because of taking on a more isolated position. In addition, as these highly levered banks sought out more risky investment opportunities their operations and asset holdings became increasingly unique and less susceptible to common shocks. De Jonghe (2010) finds that leverage contributes positively to the systemic importance of financial institutions, which is opposite to what we find. The difference in our findings may be attributed to the different SI measures employed. The systemic risk of a bank in De Jonghe (2010) is defined as the probability that a bank receives an extreme negative return on its equity at the same time that the banking index suffers from an extreme drop in value. This measure is similar to the PAO of Segoviano & Goodhart (2009), in the sense that it only reports the probability of a spillover effect, and not the expected losses to the system as in our paper. Moreover, we find that the ratio of problem loans to total loans is significant in determining
