Capital injections and bank value
The case of German banks
J.J. Rodenburg
August, 2007
J.J. Rodenburg Student#: 1258222 j.j.rodenburg@student.rug.nl University of Groningen Master ThesisBusiness Administration, specialization Finance Faculty of Economics & Management and Organization Supervisors
Capital injections and bank value
The case of German banks
J.J. Rodenburg
August, 2007
Abstract
Banks are highly regulated and supervised and outright banking failures are rare. Supervisory authorities have several intervention measures to prevent distressed banks from going under. One of these measures are capital injections. In the literature, theoretical arguments can be found that justify the use of capital injections. However, little empirical evidence on this area exists. This research looks at capital injections from a valuation perspective using income statement, balance sheet and audit report data from all banks in Europe’s largest economy, namely Germany. In order to be able to compare different banks, they are valued using a discounted cashflow to equity model. The problem of lack of betas for non-listed banks is solved by using the probability of distress of a bank to estimate its cost of equity.
JEL classification: G12, G21, G33.
Preface
Contents
1. Introduction ... 5 2. Literature ... 6 2.1 Bailouts ... 7 2.2 Institutional background ... 8 3. Methodology ... 113.1 Cash flow to equity ... 12
3.2 Cost of equity... 13
3.2.1 A simple CAPM ... 13
3.2.2 β and probability of distress ... 14
3.2.3 Market return for non-listed banks ... 16
3.3 Continuing value ... 16
4. Data ... 17
4.1 Descriptive statistics ... 18
4.2 Logit model ... 20
5. Results ... 21
5.1 Bank value vs. capital injections... 23
5.2 Robustness ... 25
6. Conclusion... 25
1.
Introduction
The banking industry is undoubtedly the most highly regulated and supervised industry around. No matter whether countries put more effort on relying on market forces or government intervention and the different levels this can take, all countries regulate and supervise banks (Barth et al., 2003). Based on a survey of 120 banks in 24 developed countries, Goodhart (1995) finds that two out of every three failing banks is bailed out. The main argument to justify regulation and intervention is that bank failures may persuade externalities, i.e. their social costs may be greater than the private costs to the bank itself. Especially the contagion effect is feared i.e. the effect that one banking failure spreads out on to other banks like an oil stain and so leads to a banking crisis. This argument may well hold in theory but in practice this does not seem to be so straightforward. For instance, Kho, Lee and Stulz (2000) find that the LTCM crisis1 (in which the US Federal Service did not spend any governmental money) did not have a significant contagion effect in the banking sector. Furthermore they found negative stock returns on the announcement of the rescue for the banks that participated in the rescue. Here the market seems to address negative value to private bailouts and the threat that the crisis would move on to others turned out to be well overstated.
However, only little empirical research exists on both private bank bailouts, as in the LTCM case, and non-private bank bailouts, which is mainly caused by two things. First of all, if a bank is not listed it is difficult to measure the effects of a bailout and second, the parties involved are very discrete about giving information. This study tries to fill this gap in the literature. The first problem, the one of lacking data is solved by the ability to use a unique dataset provided by the Deutsche Bundesbank. The challenging part is how to measure the effectiveness of a bailout. To be able to do that a measure is needed which makes it possible to compare banks among each other. This is exactly the area to which this research is addressed. Here, a first attempt is made to develop a methodology to compare banks on their intrinsic bank value. The methodology used in this study bases value on all the future cashflows of a bank, and thus the capabilities of a bank to make money in the future, which are stated in a currency amount today. By doing this it becomes possible to compare this value to a form of bailouts which also can be stated in a currency amount, namely capital injections. The bank values are estimated from the income statement, balance sheet and audit report data for all German banks from 1993 to 2005.
The main idea is, simply put, that if capital injections exceed the total firm value of a bank it would be wiser for the party that gives the capital injection to buy the bank in distress, redeem its outstanding
1
debt and sell the assets. The main research question therefore is simple: From a valuation perspective,
do capital injections given to a distressed bank cost make sense?
The key focus of this research is developing a proper model to valuate the different banks. As a basis serves the discounted cashflow to equity model. Because most banks are not listed, the challenges in this model are to determine the appropriate discount rate and market return. The discount rate i.e. the cost of equity, is estimated in a unique way by adapting the CAPM model to a model where β is based on the probability of distress of a bank. The market return is estimated by closely looking at the main components of the balance sheets of German banks. This results in a measure that compares the specific bank risk versus the market risk with two important advantages. First, instead of using a general industry beta, this model estimates firm specific betas based on their individual risk profiles. Hence with this model bank values can be determined more precise. Second, because the model looks at intrinsic value that is both market-oriented and related to internal performance, it is universally applicable. For example, the model is suitable for different types of banks within a country as done in this research with German commercial, savings and cooperative banks but could also be used to make international analyses with different banks between countries.
This research continues as follows. The next section present a theoretical framework providing a discussion of literature findings that motivate the rationale behind the research question stated above and gives some institutional background on banking supervision and intervention in Germany. Methodology is explained in section three and data in section four. Results are depicted in section five. Finally, section six concludes.
2.
Literature
Hawkins and Turner (1999) identify three sets of causes of bank failure. The first set is microeconomic and focuses on poor banking practices and other microeconomic problems like principal-agent problems and overstaffing. The second set is macroeconomic and comprises macroeconomic shocks of an unpredicted magnitude as they argue that banks should be prudent enough to be able to deal with the volatility that is normal for their market. The third set is system-related and are causes that are not favorable for the environment in which banks act.
In case of trouble, exit out of the market is only one of many options a bank has, hence it is not just a matter of life or death. Oshinsky and Olin (2005) find three alternative outcomes for troubled banks besides failure: recovery, merger and continuation as a troubled bank.
borrowers and, a more direct way, capital injections. In turn, a capital injection can come in the form of extending long-term loan guarantees, buying equity or buying bank loans at a favourable price, where the latter two are direct capital injections (Gorton and Huang, 2002). According to Daniel (1997) usually nonperforming loans are bought at face value.
2.1 Bailouts
In their model of lender of last resort assistance Goodhart and Huang (1999) weigh social costs against moral hazard. They find that concerns about contagion generally weigh more strongly than moral hazard considerations and therefore a government has incentive to bailout banks. Still they argue that governments should use “constructive ambiguity” to make their decisions.
According to Cordella and Yeyati (1999) governmental bailouts have two effects. The first one is the so-called value effect. They argue that in order to prevent banking distress banks should limit their risk exposure and thus limit their profit maximization as more risk leads to more return. A bailout scheme by the central banks would allow banks to engage in more risky projects with higher return thereby creating more value. The offsetting effect of such a bailout scheme is that it creates moral hazard as the risk exposure of a bank is not verifiable by the central bank. Cordella and Yeyati (1999) find that their framework provides a rationale for a publicly announced bailout scheme in the situation of an adverse economic shock by the central bank. Furthermore they argue that a policy of bailing out banks with certainty always dominates the “constructive ambiguity” approach.
Gorton and Huang (2002) argue that governments cannot just simply close a bank in distress and sell its assets to private investors. It is costly for private agents to be prepared to purchase the assets of the banking system as a large part of their resources should be highly liquid in order to be readily available if such an event occurs. Instead, the government can create this liquidity, use it to intervene and thereby improve welfare.
Diamond (2001) argues that the only case when bailouts are justified is when banks are undercapitalized and have lending relationships and viable borrowers. In all other cases, a bailout is merely a governmental subsidy without social value. In addition, Diamond and Rajan (2002) show that a poorly targeted bailout can cause a banking system to collapse. They argue that a natural sequence of bailouts leads to an escalating set of bailouts which ends when the government runs out of sources and the system breaks down.
while in the second round the latter two criteria were essential parts of the decision-making process. This seems to favor the argument of “constructive ambiguity” in bailing out banks.
Based on previous theoretical studies there seems to be a case for bailing out banks. With the exception of Cordella and Yeyati (1999) previous studies seem to agree that supervising institutions need to carefully evaluate under what circumstances and which banks to bailout. However, Cordella and Yeyati (1999) favour bailing banks out with certainty only in the situation of an adverse economic shock. Except for the research by Montgomery and Shimizutani (2005) on the banking crisis in Japan not much empirical research exists on bail outs. The confidential dataset provided by the Deutsche Bundesbank gives the opportunity to analyse capital injections made under different economic circumstances over a longer period of time. In addition, by using valuation theory to approximate the bank values the present study makes it possible to compare different types of banks.
2.2 Institutional background
system (Masciandaro, 2005). A schematic view of the organization concerned with banking is given in figure 1.
Figure 2-1. The organization of banking supervision in Germany
source: own figure
For Germany, Kick and Koetter (2007) describe four categories of intervention. The first category takes the form of compulsory notifications of regulatory authorities. These notifications are specified in the KWG. Category two includes official warnings or disagreements of the BaFin. The third category consists of interventions by the respective banking sector’s insurance scheme in the form of capital injections as well as binding measures issued by the BaFin e.g. restrictions concerning lending and deposit taking. The fourth and final category requires the exit of a bank from the market. This can either happen through forced closure by the BaFin or through restructuring mergers. Koetter et al. (2005) find evidence for restructuring mergers and Elsas (2004) indicates that in Germany no bank closed in the cooperative bank sector in the period 1992-2001. Therefore in practice the preferred measure for category four seems restructuring mergers.
Figure 2-2. The organization of the voluntary deposit protection schemes
Guarantee system of the Association of German
Banks
Bundesbank BaFin
Year-end reports
Guarantee system of the German association of cooperative banks and
credit unions
Guarantee system of the Savings bank finance group (regional guarantee
funds) Individual private banks Individual cooperative banks Individual savings banks
Different banking pillars Voluntary deposit protection schemes
Contributions
Capital injection in case of distress
Contributions
Capital injection in case of distress
Contributions
Capital injection in case of distress
source: own figure
As can be seen in figure 2-2 each banking pillar has its own head federation. For commercial banks this is the Association of German Banks (“Bundesverband Deutscher Banken”, BDB from hereon), for cooperative banks the Association of Cooperative Banks and Credit Unions (“Bundesverband der
Deutschen Volksbanken und Raiffeisenbanken”, BVR from hereon) and for savings banks the German Savings Bank Association (“Deutscher Sparkassen und Giroverband”, DSGV from hereon).2 All head federations have a voluntary deposit guarantee scheme exceeding legal requirements. While the system of the BDB is aimed at deposit insurance, the system of the BVR and DSGV is aimed at the
2
protection of each single institution. The individual banks of the BDB and BVR make yearly contributions to their corresponding insurance scheme. In case of distress the head organization may decide to support a bank in the form of a capital injection. The system of the DSGV works a little different. They have a Joint Liability Scheme made up of eleven regional savings bank guarantee funds, the Guarantee Fund of the Central Savings Banks and Central Giro Institutions, and the Guarantee Fund of the Central Building Societies. The members of the DSGV make contributions to their corresponding sub guarantee fund. Of this sum a part is actually paid and a part remains readily claimable by the guarantee fund. In the case of distress, the sub guarantee funds can decide to assist a member. If the funds do not reach, the claimable part has to be paid by the other members. When this also does not suffice the other sub guarantee funds will help thereby following the same procedure. Furthermore, ‘negative’ amounts of capital injections are present in the sample. Mostly, these occur a few years after a capital injection. Clear and specific information on these procedures is lacking, but the fact that not every positive amount is followed by a negative one indicates that banks repay parts of the capital they received only when they are capable of doing so.
Concluding, in Germany banking supervision and intervention is done by multiple institutions and federations that closely work together on some level. Capital injections on the other hand, are executed and supervised solely by the respective banking pillars head organizations, who only report their actions to the BaFin and Bundesbank at year end. Next the methodology of the model to investigate the effects of capital injections and choice of explanatory variables is discussed.
3.
Methodology
This section discusses the methods used in this research to find an answer to the research question. The methodology used to derive the value of a bank and compare this to the capital injected is discussed.3 In this research bail outs in the form of capital injections are compared to the intrinsic value of the capital receiving bank. Depending on the distribution of the sample two tests are appropriate here: the paired sample t-test and the Wilcoxon signed rank test. The methodology and assumptions for these tests are well-known and will therefore not be explained further4.
Numerous approaches determine the value of a bank. The most well known are i) market oriented or multiple approaches, ii) asset oriented approaches, iii) cash flow oriented approaches, iv) residual income oriented approaches and v) the replicating portfolio approach (Koller, Goedhart and Wessels, 2005 and Gross, 2006). The most widely used methods are the multiple and cash flow oriented approach. The former is often used to place the latter in the proper context (Koller et al, 2005).
3
All analyses are performed with the statistical software package Stata.
4
According to Damodaran (2004) and Gross (2006) this is also true for banks. Advantages of cash flow oriented approaches are that they represent an intrinsic value that is both market-oriented and related to internal performance. Moreover, Damodaran (2004) and Koller et al. (2005) recommend using the discounted equity cash flow model for valuing banks. Therefore in this paper we use the discounted cash flow to equity (DCFE) model. This model takes the following form:
1 1(1 ) (1 ) t n t n t n t ei e ei ECF NI Value k k k = + = = + + +
∑
(3.1)where EFCtis expected free cash flow to equity in period t, kei the cost of equity for bank i, NIt+1 the
expected net income in the first year after the explicit forecast period ends and n is the length of the forecast period. The first term of equation 3.1 represents the value of the explicit forecasting period and the second the value of the continuing value (CV). The value of a bank is determined by three main components: EFCt, kei, and CV. Next these three components will be described further.
3.1 Cash flow to equity
As stated in equation 3.1, forecasting is used to estimate future cash flows. In the present study however, the value of a bank is determined for a point in time in the past. Therefore instead of using forecasted cash flows actual cash flows are used as they are readily available. According to Damodaran (2004) the free cash flow to equity can be calculated as:
Equity Cash Flow=Net Income−Increase in Equity+Other Comprehensive Income (3.2) Using the balance sheets of the banks from the Bundesbank this is done in the way stated in appendix A-1. To arrive at the true bank value the amount of capital that has been injected has to be subtracted. The capital injections are amortized evenly over the forecasting period.
As this study uses historical data the term forecasting seems a bit out of place. The goal here is to determine the length of n. Using every period available will introduce the bias that the share of the continuing value will differ significantly among the different observations.5 Using a short period will decrease the precision of the research and a long period will decrease the number of observations significantly. A good way to estimate the appropriate forecasting period is to look at the time a bank needs to recover as cash flows can be expected to become much more stable after the recovery period. In Germany, when a bank receives a capital injection, to bail out a nonperforming loan, it also receives access to a credit line which it can use in case other large borrowers default. The average number of years this credit line stays open gives a good approximation of the recovery period. The mean number of years is 3.01 with a standard deviation of 2.22. The median is 2 years. Therefore the number of
5
years taken for n in this research will be three, four and five years. In addition, bank values will also be calculated for every forecast period available (one to eleven) to see how results hold.
3.2 Cost of equity
Equity is valued by discounting cash flows to equity at the cost of equity. In its essence the cost of equity is a hurdle rate or a mix of danger and opportunity. There are four main methods to estimate the cost of equity; i) the capital asset pricing model (CAPM) model, ii) the arbitrage pricing theory (APT), iii) the Fama-French three-factor model and iv) proxy models. The CAPM model uses variance as a measure of risk and specifies that only that portion of variance that is not diversifiable is rewarded. This non-diversifiable risk is measured by how much an asset moves with the market i.e. its covariance with the market. The beta of an asset is a standardized measure of this covariance. In APT a number of factors and random noise fully specify a security’s actual return. However, there is little agreement about how many factors exist, what these factors represent and how to measure those (Koller et al., 2005). The Fama-French three-factor model is based on empirical evidence and measures if a company’s returns are correlated to small over big stocks and high versus low market to book values and adds premiums accordingly. The proxy model argues that in an efficient market differences in returns over long periods must be due to market risk differences. Out of these models the CAPM model is the most widely used, because it is easy to apply and based on purely economic theory (Koller et al., 2005).
3.2.1 A simple CAPM
In the basic CAPM model the required return or the cost of equity kei can be calculated in the following
way:
( ( ) )
ei f ei m f
k =R +
β
E R −R (3.3)where Rfis the riskfree rate (for instance Euribor/Fibor) and E(Rm) the expected return on the market
index. The equity beta βei can be calculated as:
2 ij ei j Cov
β
σ
= (3.4)where Covij is the covariance of asset return i with market return j and σ2j the variance of market return
j. In the present study, two of the three components of the basic CAPM model of equation 3.3, namely market return and return β are not available for most German banks6. The use of average unlevered
6
industry betas of listed banks would introduce a significant estimation bias. This problem is circumvented here in a unique way. By basing β on the probability of distress (PD) of a bank and the market, the CAPM model can be used to determine the cost of equity of a bank. The estimation of β is discussed below.
3.2.2 ββββ and probability of distress
As stated above, essentially CAPM uses the co-movement or sensitivity of the return of an asset with the market (gathered by β) as a measure of risk to estimate the required return for that asset. An asset with a βof one has the same risk level as the market, a β higher (lower) has an above (below) average risk level and an asset with a zero β is riskless.
In short, β uses the co-movement of an asset with the market to find out how much risk it adds to the market portfolio. In CAPM this co-movement is measured by looking at the stock returns of firms and the return of a market. The relation between risk and return is that risk is the unexpected part of the actual total return (Ross, Westefield and Jaffe, 2005). Risk can be broken down into unsystematic and systemic (market) risk. Mathematically this can be put down in the following formula:
R=R+m+
ε
(3.5)where R is actual return, R the expected part of the return, m the systematic risk and ε the unsystematic risk. Because R is expected and thus fixed, the variance of R comes from the variance in ε and m i.e. the total risk of a firm. Therefore, in absence of measurable returns β can be proxied by a measure that encompasses total risk of an asset and the market. The total risk
ϕ
of a bank can be denoted asϕ
ε
=+
m (3.6)
The PD of a bank captures the probability that a given bank will become distressed within a certain period. Moreover, the PD aggregated across all banks is an estimator for the distress rate of that year. That is, the PD of a given bank related to the distress rate of all banks (the market) gives the co-movement of that bank with the market. If the risk factors used to estimate the PD proxy for
ϕ
the variance of the PD can be used as a measure of risk just as return is used in the basic CAPM model. From the discussion above follows that the PD λ is a function ofϕ
:) (
λ
ϕ
= f (3.7)downfalls or shortcomings in the above risk factors and that distress can come in the forms mentioned in section 2.2. In order to determine the general rate of distress all these forms of distress should be incorporated in the model. A distress rate λit is estimated for bank i at time t under the condition that
no default has occurred prior to time t:
( ; )
it P Ti t Ti t Xit
λ
= = ≥α
(3.8)where Ti is a random variable that stands for the year when the capital injection of bank i occurs, Xit is
a vector of explanatory variables and αa vector of coefficients.
The hazard model takes the form of a logistic regression. Such a regression models how a {0,1} dichotomy depends on one or more explanatory variables (Hamilton, 2004). Here 1 represents a distressed event for bank i in year t and 0 when no such event has happened. The hazard model takes the following form:
( ) it Sit
λ
= Φ with∑
= + + + = m j i t j it j it X S 1 0 0 , 0α
λ
λ
α
(3.9)where λ0t is a time effect and λi0 a random effect.
Here Sit is referred to as the score which forms an order of the banks according to their risks. The score
is translated into a PD with the link function Ф. Several link functions exist to estimate a hazard model. However, Porath (2004) finds no significant differences between the outcomes of the most widely used link functions.7 Here the logit link function is used, due to its computational simplicity:
( ) 1 it it S it S e S e Φ = + (3.10)
The explanatory variables that are included in the vector of coefficients of the hazard model are equal to the ones used in Porath (2004) and Kick and Koetter (2007) since they have been found to provide the best fit and results. The different risk factors are represented by i) Tier 1 capital to risk-weighted assets, ii) hidden reserves8 allocated as liable equity to balance sheet total, iii) not as liable equity allocated hidden reserves to balance sheet total, iv) contingent liabilities to total assets, v) dummy for hidden charges, vi) credit with increased risk to total audited credit, vii) return on equity and viii) business climate growth rate. Lagged values are taken so that the model predicts a capital injection based on the risk factors of the preceding year. For the time effect λ0t year dummies are included. The
variance of λit is used to calculated β using equation 3.4.
7
Porath (2004) estimates a logit, probit and complementary log-logistic link function.
8
3.2.3 Market return for non-listed banks
In essence, a bank (like any firm) can be regarded as a set of assets grouped together. From this line of reasoning it follows that the average return for banks can be calculated by taking the weighted average of the return of the different assets within a given bank. By taking the averages of all banks in the market the market return can be proxied. In appendix A-2 the main categories of the assets, their share of total assets as well as a proxy for the corresponding return of German banks can be found. These numbers are calculated using the balance sheets from the Bundesbank database. The proxies for business loans and bonds and other interest bearing securities as well as consumer loans securitized by mortgages are considered fairly straightforward as they are just their corresponding interest rates which can be found on the Deutsche Bundesbank Statistics Website. Note here that for business loans interbank rates are taken. Interbank rates are a readily available statistic while business loan rates are not. As both rates turn out to approach each other quite close interbank rates are an appropriate proxy. A year is approximated as the average duration of other loans and thus the one year interbank rate is chosen. Average consumer loans statistics are not readily available. As can be seen in table 3-2 the unaccounted part of consumer loans make up for more than 40 percent of total assets, which is by far the largest part and therefore not to be left out of consideration. To proxy for the consumer loans interest rate the total average interest rate (calculated by dividing total interest income by total interest bearing assets) is used. In total consumer loans, business loans and bonds and other interest bearing securities account for more than 90 percent of total assets and thus the weighted average is considered to be a an appropriate and very close approximation of the average market return for banks.
3.3 Continuing value
The most basic form of the discounted equity cash flow model stated in equation 3.1 takes the following form: 1(1 ) t t t t e ECF Value k =∞ = = +
∑
(3.11)However, practically this model cannot be applied, as cashflows have to be discounted until infinity. By assuming that the growth rate will remain constant forever at some point in time in the future it becomes possible to estimate the terminal value of a company (Damodaran, 2004 and Koller et al., 2005). Koller et al. (2005) recommend the following value driver formula to estimate CV:
1(1 ) ( ) g t RONE e NI CV k g + + = − (3.12)
where NIt+1 is the expected net income in the first year after the explicit forecast period ends, g the
For simplicity, we assume that banking is a competitive industry and therefore the return in net new equity will eventually converge to the cost of equity. This argument can partly be justified by the fact that, amongst other factors, competition has lead to a wave of consolidation in the German Banking industry. Porath (2004) finds that in the period 1995-2002 the number of saving and cooperative banks decreased by 40 percent. In addition Hempell (2002) finds that the consolidation has not lead to less competitive behavior.
By assuming the RONE is equal to ke the growth term and RONE term disappear from the equation.9
This does not mean that the growth in NI will be zero. It simply means that the new growth adds nothing to value, since the return associated with this growth is equal to the cost of equity (Koller et al. 2005). This leads to the following formula for calculating CV:
e t k NI CV +1 = (3.13)
4.
Data
The financial data for the German banks is obtained from income statements, balance sheets and audit reports provided by the Bundesbank for all German Banks from 1993 to 2005. The data is collected at year end. For instance, in December 1995 the value of a bank is calculated using a five year forecast horizon by using the equity cash flows of 1996 until 2000 and net income of 2001. Interest rate statistics are taken from the Deutsche Bundesbank Statistics Website.
In total there are 3908 banks in the sample which covers the period 1993 until 2005. The sample comprises the following banking groups; i) commercial banks, ii) savings banks, iii) cooperative banks, iv) large banks (e.g. Deutsche Bank AG), v) cooperative central banks and vi) central savings banks.
Cooperative central banks, large banks and central savings banks received a negligible amount of capital injections. Therefore these three groups are dropped from the sample. Due to lack of data for all variables some additional observations are lost. This leaves 3885 banks over a time span of 13 years. In total the sample contains 1563 capital injections.
9
Assume RONE = ke, then
1(1 e) g t k e NI CV k g + − = − or 1( e ) k g t k e e NI CV k g + − =
4.1 Descriptive statistics
The next step is to take a closer look at the data to get better understanding of the characteristics of banks and capital injections. Table 4-1 gives an overview of the number of existing banks and the capital injections made yearly per banking pillar. Here it can be seen that between 1993 and 2005 on average 5.0 percent of the commercial banks received some form of capital injection, for savings banks this was 0.7 percent and for cooperative banks this was about 5.1 percent.
Table 4-1 Number of banks and capital injections
Three variables are created for the capital injections: cash capital injections, credit lines opened and the average of both. Their trend is shown in appendix A-3. Here we see an enormous peak of the credit lines in 2003. Further inspection of the data learns that this peak is caused by a single outlier for which a large credit line was opened. Even though this is just reality this outlier is dropped from the sample as it has a very big influence on the complete sample. A new figure is given in the form of figure 4-1. All values are stated in millions of Euros and from hereon this will be done unless stated otherwise.
Figure 4-1 Trend of average capital injection
In figure 4-1 we see that the trend of bailouts evolves around five million Euros. This is quite small compared to the average amount of total assets of around 675 million for all German banks (stated in table 4-2). Clear peaks can be seen at the time of the East Asian Financial crisis (1997) and the burst of the internet bubble (1999/2000). Furthermore, an at first sight contradictory trend is found, namely a peak in capital injections always goes together with a plunge in credit lines. In addition, for 2002 the opposite is found. It appears that in times of economic distress e.g. the East Asian Financial crisis and the burst of the internet bubble there is a higher need for direct capital i.e. capital injections and not for credit lines. In the aftermath of such events offering credit lines suffices which explains why a peak in credit lines follows a few years after a peak in capital injections.
1 capital steadily increase over time and, contrary to figure 4-1, capital injections relative to total assets and Tier 1 capital are downward sloping.
Figure 4-2. Average Tier 1 capital and assets and relative capital injections
Table 4-2 shows the descriptive statistics for the complete sample of German banks, i.e. commercial, savings and cooperative banks pooled together. Here we can see that the average German bank has about 675 million Euros in assets. On average free cash flow to equity is four times larger than net income and the average capital injection given is a little less than 6 million Euros.
Table 4-2 Descriptive statistics of total sample
As can be seen in table 4-2 the data shows high variation and is skewed to the right. For this reason the median is also given. The median values are about four to five times smaller than the mean values. In addition the data is highly leptokurtic. In terms of shape, this means that the mass of the distribution is concentrated on the left of the distribution, has a sharp peak around the mean and fat tails. In terms of probability, the probability of values near the mean and extreme values are higher than a normally distributed variable. To get some more insight into the data the sample is split up in multiple ways and descriptive statistics are calculated again. These results are presented in appendix A-4 and A-5. In appendix A-4 the sample is split up between banks that did and did not receive a capital injection. Here it can be seen that, as expected, net income of banks that were bailed out is much lower than that of banks that were not bailed out. Appendix A-5 splits the banks up according to banking pillar. This significantly lowers the variation of the variables. To get a grasp of the relative performance of the different banks, free cash flows are divided by total assets. This gives an overview of the cash generating performance. In addition, to account for bank size in the capital injections they are divided by total assets. The results are presented in appendix A-6. Here it can be seen that the capital injection variables show much less variation. This cannot be said about the free cash flows divided by total assets. There seem to be structural differences in the cash generating capabilities of banks of the different banking pillars. We can clearly conclude that all variables are non-normally distributed. However, due to the large sample size the effects of non-normality in this research are expected to be virtually inconsequential (Brooks, 2002).
Figure 4-3 Development of interest rates
In figure 4-3 we see a downward sloping trend, except for a peak at the turn of the century, which is assumed to be caused by the burst of the internet bubble.
4.2 Logit model
The results of the logit model based on the one from Porath (2004) are presented in table 4-3. As can be seen all variables have the expected sign and are statistically significant, with the exception of Tier 1 capital to risk-weighted assets and log of total assets which show the right sign, but are not significant. A higher share of hidden reserves as well as a higher return on equity and an increase in the business climate lower the probability of a bailout. On the other hand, a large share of contingent liabilities, hidden charges, a large share of credit with increased risk and an earlier failure lower the probability of a bailout significantly.
Table 4-3. Results logit model
A correlation matrix is given in appendix A-7. Here it can be seen that the variables show no high correlations hence multicollinearity is not expected to be a problem.
The predictive power of these models can be determined with help of the receiver operating characteristic (ROC) curve. It plots the fraction of true positives against the fraction of false positives. The area under the ROC curve (AUR) is a graphical measure of the discriminative power of the dependent variable of the model. Thus in this case the AUR gives a graphical measure of how well the models can predict a capital injection. If the AUR is one, the variable has maximal positive discriminative power. If it is zero, it has maximal negative discriminative power and when it equals 0.5 it has no discriminative power. According to Hosmer and Lemshow (2000) a model with an AUR score of 0.7874 has good discriminative power.
The trend of the probability of distress is presented in figure 4-4. Here also a high peak can be observed caused by the bursting of the internet bubble. In the last years the probability of distress has dropped considerably.
The predicted probability of distress is used to calculated betas through equation 3.4. A summary of beta is given in appendix A-8. The beta shows a fairly large variation and suffers from some extreme outliers. A closer inspection of the data reveals that the most extreme betas are for banks with only a small number of PD observations. Therefore the extreme values of betas are considered to be outliers caused by data insufficiency. To compensate for this the cost of equity is truncated at the 2.5 and 97.5 percent level.
Betas are used in the CAPM model to calculate the cost of equity. The trend of the cost of equity is also shown in figure 4-4. Logically this trend follows the one of the risk free rate, the market return and the probability of distress.
5.
Results
The results of the banking valuation model are presented in appendix A-9a to c. Bank values are calculated with equation 3.1 using forecast periods of three, four and five years respectively. In addition, the main components of equation 3.1; free cash flows and continuing value are presented. For the free cash flow these are simply averages of the free cash flows used in the bank value calculation following equation 3.2. For the size of the continuing value equation 3.7 is used. The trends of the three variables are given in appendix A-10a to l.
A first glance at appendix A-9 reveals that the bank values show much more variation for commercial banks than for the other two banking pillars. Appendix A-10 shows that this variation is not caused by high variation in free cashflows (see appendix A-10f) but by an equal variation in continuing value (appendix A-10j). Moreover, appendix A-10j reveals that the peaks and plunges follow the same pattern for all three the graphs, only a year sooner per forecast year i.e. a peak or plunge for the graph of the five year forecast period occurs one and two year before the graphs of the four and three year forecast period respectively. There are two possible explanations. First it might be the case that the net income of commercial banks shows higher variation than cooperative and savings banks. This is confirmed in appendix A-5. Secondly in appendix A-9 it can be seen that the number of observations is much lower for commercial banks compared to the other two banking pillars. It might therefore be the case that the average of the continuing value for commercial banks is also more sensitive to positive and negative outliers. A closer look at the data confirms the latter explanation10, therefore both explanations are expected to be of influence.
10
Another interesting finding is that average cashflows of savings banks are decreasing while for commercial and cooperative banks they are increasing over time. A possible explanation is that commercial and cooperative banks (both privately owned) manage their banks better and are better in generating cash flows than the managers of the public owned savings banks.
As can be seen in appendix A-8 the pattern does not change with the length of the forecast period. Also the share of the continuing value remains around the same level in the different forecasting periods. Therefore the preferred specification remains the total sample of commercial, savings and cooperative banks with a forecast horizon of three years. An overview of the average bank values, free cashflows and continuing values is presented in table 5-1 and the trend in figure 5-1.
Table 5-1. Bank values, free cash flows and continuing values
In table 5-1 we can see that the average bank value is about nine times its average cashflow and the share of the continuing value is about sixty percent.
Figure 5-1 Trend of bank value, average free cashflow and continuing value
Table 5-2. Number of observations and average bank values
In table 5-2 we can clearly see the survivor bias. The number of banks decreases while the bank values increase year by year. The longer a bank stays around the higher its values. Important to note is that the decrease in observations of banks that received capital injections over the years is not higher than non-distressed banks. From equation 3.1 we know that the value of a bank depends on its free cash flows and net income. Therefore we can also conclude that these banks are becoming more profitable. Interesting to see is that the value of distressed banks increases stronger than banks that were not in distress. This is a first indication that capital injections do help a bank to recover but over the long time and given that a bank survives. For instance, the average bank value of a bank that received a capital injection is over 25 percent higher if a bank survives one year. A more thorough way to empirically investigate this is to compare the bank values directly to the amount of capital injected. This is done next.
5.1 Bank value vs. capital injections
The next step is to compare the bank values of the banks that received a capital injection to the bailout made, where it is argued that in order for a bailout to make sense the bank value should be higher than the capital injected. The results are presented in table 5-3. With the exception of 1997 we see positive mean differences for each year. However, some statistical evidence is appropriate. Therefore the significance of the differences is tested.
Table 5-3. Bank value compared to capital injection
The t-test assumes that that the differences between the paired values have been randomly drawn from the source population andthat the source population from which these differences have been drawn can be reasonably supposed to have a normal distribution. Since the appropriateness of the t-test here is doubtful, a Wilcoxon signed rank test is also performed. The results of the paired sample t-test and the Wilcoxon signed rank test are presented in appendix A-12a and b and a summary is given at the bottom of table 5-3. The signed rank test confirms that the difference between bank value and capital injection is statistically significant from zero and the paired sample t-test confirms that this difference is both positive and statistically significant. Though the results of the latter need to be handled with some care. At first sight it can be concluded that bank values are significantly higher than the capital injections made.
smaller than the actual value of the bank. It becomes evident that bank size is only one of many factors in determining the size of a capital injection. Though this is a interesting subject, developing a model for determining the efficient size of a capital injection is beyond the scope of this research.
From the literature section we know that in Germany capital injections are done by the insurance schemes of the head organization of the corresponding banking pillar. These are three separate, independent organizations and therefore also the bailout strategies are independent of each other. Thus, the next step is to investigate whether the same holds for the different banking pillars. The results are presented in appendix A-13 and A-14. As can be seen the t-test and signed rank test for commercial and cooperative banks confirm earlier findings. Interesting to see is that the null hypothesis of the signed rank test for savings banks cannot be rejected. Also the null hypotheses of the t-tests for savings banks cannot be rejected, which already where questionable due to the low number of observations. Nonetheless for savings banks we find that in 8 of the 18 cases the amount of capital injected is larger than the value of the bank. Moreover, the mean difference is highly negative. In short the results for savings banks differ extremely from the results for commercial and cooperative banks. Where does this difference come from? First of all it needs to be noted that due to the relative small number of observations averages are sensitive to outliers. Besides statistical differences there are also some structural differences in the characters of savings banks which may explain this negative difference. This explanation starts with the observation that the banks that received a capital injection which was larger than the value of the bank were about 30 percent bigger11 than the average savings bank. As stated before savings banks are public institutions and especially these large savings banks play important roles in the financing of regional public projects. Therefore, in order to maintain autonomy in local decision making, from a political standpoint, a case can be made for these large capital injections.
To conclude, from a valuation perspective bailouts make sense as it appears to be a cheaper solution than buying the bank, redeem its debt and sell its assets. This and the results from above that, given that a bank survives, a capital injection on first sight seems to helps a bank to recover seem to advocate for the functionality of capital injections. On the other hand, judging on the fact that a lot of banks that receive a capital injection fall out there seems to be a cut-off point well before the point where bank value minus capital injection equals zero. The voluntary insurance schemes should use “constructive ambiguity” in appointing assistance as suggested by Goodhart and Huang (1999). However, as the survivor bias for banks that received a capital injection is not higher than non-distressed banks it can be concluded that the voluntary insurance schemes are succeeding in this area. Next, the results from above are checked for robustness.
11
5.2 Robustness
To check for the validity of the methodology used, some robustness checks are appropriate. In section 3.1 is determined that the average recovery period is a good estimation of the ideal period on which the free cashflows to equity can be discounted (the first element of equation 3.1). This turned out to be three, four and five years. In order to check for the robustness of the results in section 5.1 the same tests for the four and five year forecast period are done. It needs to be noted that two opposing effects can be expected. First of all, due to the survivor bias the bank values of the four and five year cashflow period will be higher. This should cause the tests to reject the null hypothesis of equal means more strongly. The other effect is that due to the same survivor bias the samples for the four and five year cashflow period will be smaller which may cause the tests to have insignificant results. The results for the paired t-test and Wilcoxon signed rank test can be found in tables 5-4 and 5-5 respectively.
Table 5-4. Paired sample t-test for 4 & 5 year forecast
At first sight in table 5-4 and 5-5 it can be seen that the results closely resemble the ones for the three year forecast periods stated in tables 5-3, A-12 and A-13. Interesting to see is that of the 18 savings banks that were present in the sample with the three year cashflow period a third disappeared in the next two years. Most of these banks that exited the market had negative differences between bank value and capital injection. An explanation might be that in the longer term economic rationales might outweigh any political incentive to keep assisting distressed savings banks as it simply becomes too costly. Furthermore we see that the decreasing effect on the sample size appears to be larger than the increasing value effect caused by the survivor bias. Nevertheless, the conclusion can be drawn that the results for the bank values compared to the amount of capital injected are quite robust.
Table 5-5. Signed rank test for 4 & 5 year forecast
6.
Conclusion
outstanding debt and sell the assets. By using data gathered by the Deutsche Bundesbank all German commercial, savings and cooperative banks are valued on a yearly basis for the period 1993 to 2005 with a discounted cashflow to equity model. In this model two of the main elements, the free cashflow to equity and the continuing value are relatively easy to estimate. The third important element, the cost of equity which is used as the hurdle rate is a lot more challenging to estimate for banks that are not listed.
In this research the cost of equity is calculated in an unique way based on the traditional CAPM model. The methodology developed in this research differs from the traditional CAPM in two ways. First of all, the traditional CAPM uses variance as a measure of risk which is measured by how much an asset moves with the market, thereby looking at the return of the asset and the market. In absence of these returns, this research uses a new approach and measures risk directly. Central in this model is the argument that the variance in return between assets and between assets and the market is determined by the differences in systematic and unsystematic risk. By incorporating all risk factors of a bank this risk can be measured with a hazard model that estimates the probability of distress. It then becomes possible to estimate a probability of distress for each bank year and since the sample includes all banks in Germany a yearly average forms an estimator of the distress rate of the market of that year. From this line of reasoning it follows that the β of a bank can be estimated with the variance of the probability of distress between banks and between banks and the market.
The second issue is the market return. In essence, a bank (like any firm) can be regarded as a set of assets grouped together. Therefore, the average return for banks can be calculated by taking the weighted average of the return of the different assets within a given bank. By taking the averages of all banks in the market the market return can be proxied.
Positive differences between bank value and capital injection, which are both statistically significant and robust, are found for the sample as a whole. When the same tests are applied to the different banking pillars the outcome is that for savings these results are not as clear cut. Concerning this matter, valid political grounds exist to assist certain savings banks beyond the economically feasible level. Furthermore a significant survivor bias is found. Bank value increases significantly the longer a bank stays around, while the number of observations drops steadily. Interesting to see is that the survivor bias for banks that received a capital injection is more or less equal to the survivor bias of non-distressed banks. This suggests that a capital injection does not decrease the chances of survival for a bank. On the other hand, it does not increase them either, which should be one of the goals a capital injection ought to strive for.
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Deutsche Bundesbank Statistics Website
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http://www.bankenverband.de/index.asp (June 2007) Association of Cooperative Banks and Credit Unions
http://www.bvr.de/public.nsf/index.html?ReadForm (June 2007) German Savings Bank Association
