Marc Joëts
email: marcjoets@hotmail.fr.

Valérie Mignon

On the relationship between forward energy prices: a panel data cointegration approach ♠

Keywords: forward energy prices, oil, domestic fuel, panel cointegration. JEL classification: C23, Q40

The aim of this paper is to investigate the long-term relationship between the forward prices of crude oil and domestic fuel (FOD) on the period from August 2003 to April 2010. To this end, we rely on a panel data setting by considering a sample of 36 maturities for the forward prices. Using panel cointegration tests, our results show that oil and fuel prices are characterized by a strong homogeneous long-term equilibrium relationship for several maturities. Estimating a panel error correction model, we find that FOD prices are influenced by oil prices variations on both the short and the long run. The existence of a unique equilibrium model for all maturities may have important implications for financial arbitrage strategies based on energy prices relationships.

Introduction

The aim of this paper is to study the long-term relationship between forward prices of crude oil and domestic fuel (FOD). The empirical literature devoted to this relationship (and more generally to the relationship between oil and refined product prices), mainly relies on cointegration analysis in a time series context (see, [START_REF] Gj | Risk Management in the Oil Industry: Can Information on Long-Run Equilibrium Prices be Utilized?[END_REF] and Asche, Gj∅lberg and Vሷ lker (2003)). [START_REF] Gj | Risk Management in the Oil Industry: Can Information on Long-Run Equilibrium Prices be Utilized?[END_REF] analyze co-movements between the prices of crude oil and major refined products during the 1992-1998 period, and investigate whether deviations from a possible long-term equilibrium relationship can be used for short-term predictions and risk management. The authors conclude that crude and products spot prices are cointegrated, and rely on a vector error correction modeling. Asche et al. (2002) focus on the Northwest European market by considering a multivariate framework on the period from January 1992 to November 2000. They conclude in favor of a long-term relationship and show that the crude oil is weakly exogenous.

In this paper, we go further than these analyses based on spot price series by investigating the long-term link between forward prices of crude oil and domestic fuel for several maturities. To this end, we rely on a panel data framework including both cross-sectional and time dimensions. From a methodological viewpoint, it is well known that in small samples, traditional unit root and cointegration tests have low power against near stationary alternatives. By adding the individual dimension to the analysis, the use of panel data increases the power of the tests by raising the number of observations. Moreover, considering the various maturities for forward prices allow us to account for possible heterogeneity in the relationship between crude oil and domestic fuel prices. The novelty of the present study is that the cross-sectional dimension is characterized by different maturities, leading to rely on the term curve for our analysis. To our best knowledge, our paper is the first to investigate the relationships between energy prices for several terms in a panel context.

The rest of the paper is organized as follows. Section 2 presents the data and the panel unit root results. Section 3 is devoted to the empirical analysis of the link between oil and fuel forward prices, through the implementation of panel cointegration tests and estimation of error correction models. Section 4 concludes the paper.

Data and panel unit root tests

The data are extracted from Platt's Information Energy Agency. They concern monthly 1 forward prices of Brent ($/b) and FOD ($/t) for 36 maturities during the period from August 2003 to April 2010. In our panel data framework, each maturity constitutes one cross-section. Having 36 maturities, we thus have 36 different cross-sections. It should be noticed that the content of the FOD has changed on our studied period. Indeed, while the FOD was limited to content about 0.2% of sulfur since 1994, this content has been reduced to 0.1% in 2007 to preserve the atmosphere from SO ଶ . To account for this change, a new series has been constructed using a concatenation procedure 2 .

Figure 1 depicts the 12 month forward prices of Brent and FOD during the period from August 2003 to April 2010. The two series appear to be strongly correlated, and the fuel prices seem to influence Brent prices. This may be due to the absence of short-run substitutability possibilities regarding the energy fuel for heating. An increase in the demand for FOD induces a rise of fuel prices, previous to the Brent prices variations. This growth of FOD prices would lead to a rise of Brent prices, that may explain the gap between the two series. 1 Series have been seasonally adjusted. Moreover, as a robustness check, we have also considered daily series. Our results (available upon request to the author) show that are our conclusions are robust to the frequency. 2 To assess the robustness of our concatenation procedure, we have proceeded to various tests (cointegration and stability tests). All results are available upon request to the author. In order to investigate the long-term relationship between our two variables of interest, the first step is to test for the unit root hypothesis. As previously mentioned, it is well known that in small samples, traditional time-series unit root tests have low power against near stationary alternatives. To overcome this issue, we rely on panel data unit root tests that have the advantage of increasing the number of observations. We consider the following four tests: [START_REF] Levin | Unit root tests in panel data: Asymptotic and finite sample properties[END_REF], [START_REF] Im | Testing for Unit Roots in Heterogeneous Panels[END_REF], [START_REF] Maddala | A comparative study of unit root tests with panel data and a new simple test[END_REF][START_REF] Maddala | A comparative study of unit root tests with panel data and a new simple test[END_REF][START_REF] Choi | Unit Root Tests for Panel Data[END_REF]. These tests rely on Dickey-Fuller-type regressions and are based on the null hypothesis of an homogeneous unit root for all individuals ሺߩ = 0 ∀ ሻ. The alternative hypotheses are different, depending on the degree of heterogeneity considered. The tests are applied to series in levels (in logarithm) and to their first-differences. Results are reported in Table 1. They show that the two price series are non stationary in levels. Given that the null hypothesis is rejected when considered in their first differences, we can conclude that both price series are integrated of order 1 (I(1)). It is thus possible to investigate the presence of long-run relationships between Brent and FOD prices.

ݏݐݏ݁ܶ ݊ܫ ݉ℎݐ݅ݎ݈ܽ݃ ା ݊ܫ ݁ܿ݊݁ݎ݂݂݁݅݀ ܪ ∶ ݐܷ݅݊ ݐܴ ݏݑ݁݊݁݃݉ሺℎ ܴܣሻ ݊݅ݒ݁ܮ & ݊݅ܮ ሺ݂݊݀ ௧ ሻ 0.305ሺ0.62ሻ -28.44ሺ0. 0 * ሻ ݊݅ݒ݁ܮ & ݊݅ܮ ݐ݊݁ݎܾሺ ௧ ሻ ܪ ∶ ݐܷ݅݊ ݐܴ ݏݑ݁݊݁݃ݎ݁ݐ݁ሺℎ ܴܣ ݎ݁݀݊ݑ ܪ ଵ ሻ -1.862ሺ0.03ሻ -39.65ሺ0. 0 * ሻ ,݉ܫ ݊ܽݎܽݏ݁ܲ & ܵℎ݅݊ ሺ݂݊݀ ௧ ሻ ,݉ܫ ݊ܽݎܽݏ݁ܲ & ܵℎ݅݊ ݐ݊݁ݎܾሺ ௧ ሻ ܨܦܣ -݈ܽܽ݀݀ܽܯ & ݑܹ ሺ݂݊݀ ௧ ሻ ܨܦܣ -݈ܽܽ݀݀ܽܯ & ݑܹ ݐ݊݁ݎܾሺ ௧ ሻ ܨܦܣ -݅ℎܥ ܼ -ݐܽݐܵ ሺ݂݊݀ ௧ ሻ ܨܦܣ -݅ℎܥ ܼ -ݐܽݐܵ ݐ݊݁ݎܾሺ ௧ ሻ 3.160ሺ0

Econometric results

Before proceeding to the cointegration analysis, it is relevant to assess whether the relationships between our series of interest are or not homogeneous for all maturities. To this end, we rely on the nested homogeneous Hsiao (1985)'s test. We also provide a causality analysis through the use of the Hurlin (2008)'s test.

When working within a panel data framework, investigating the homogeneity or the heterogeneity of the data generating process (existence or not of individual effects) is of crucial importance. The Hsiao-type test allows us, by successive Fisher tests, to distinguish between a (totally) homogeneous panel data framework and a (totally) heterogeneous setting by specifying the heterogeneous type. Roughly speaking, this test consists in testing the equality between coefficients of the model estimated for all cross-section units, to investigate whether the underlying model is the same in the cross-section dimension. This test is based on the following regression between the log-returns series:

݂݈݊݀∆ ,௧ = ߙ + ߚ ݐ݊݁ݎܾ݈∆ ,௧ + ߝ ,௧
where , i = 1, … , N, t = 1, … , T, α ୧ ∈ R ,ε ୧,୲ ~i. i. dሺ0, σ க ଶ ሻ.∆lfodn ୧,୲ and ݐ݊݁ݎܾ݈∆ ,௧ denote the log-returns series.

Results are given in Table 2 and conclude in favor of the homogeneous hypothesis: the model is the same for all maturities (from 1 to 36). In this homogenous framework, we now proceed to the implementation of a causality test to investigate which series causes the other. We consider the Hurlin (2008)'s test based on the null hypothesis of no-Granger causality. Under the alternative hypothesis, a heterogeneous causality 3 is considered, using the average of individual Wald statistics associated to the Granger's test of the no causality hypothesis for units ݅ = 1, … , ܰ. Results reported in Table 3 4 show that there exists heterogeneous feedback causality. This bidirectional link can be explained by (i) a refining relationship between the two energies, and (ii) the absence of substitutability possibilities for FOD regarding heating at short term. To investigate the existence of a long-term relationship between our two price series, we consider the seven cointegration tests proposed by [START_REF] Pedroni | Critical Values for Cointegration Tests in Heterogeneous Panels with MultipleRegressors[END_REF][START_REF] Pedroni | Panel cointegration, asymptotic and finite sample properties of pooled time series tests with an application to the PPP hypothesis[END_REF]) and the Kao (1999)'s test. All these tests are based on the null hypothesis of no cointegration. The tests proposed by 3 Under this hypothesis, there exist two subgroups of units: one with causal relationships from x to y, but not necessarily with the same data generating process; and another subgroup where there are no causal relationships from x to y.

4

In order to assess the sensitivity of our results to the choice of the common lag-order, we compute all these statistics for several lag. Only the results corresponding to the optimal lag are reported in Table 3.

ݐݏ݁ܶ ܪ ଵ : ߙ = ߙ, ߚ = ߚ, ∀ ሻݕݐ݅݁݊݁݃݉ሺℎ ݏݒ ܪ ଵ ଵ : ߙ ≠ ߙ, ߚ ≠ ߚ, ∀ ሺℎéݐéݕݐ݅݁݊݁݃ݎሻ ܨ -ݏݐܽݐݏ  -݁ݑ݈ܽݒ 1.110 0.249
Kao examine the cross-sectional cointegration vectors in the homogeneity case, while Pedroni allows for heterogeneity under the alternative hypothesis.

For the Pedroni's tests, the following relationship is estimated:

݂݈݊݀ ௧ = ߙ + ߜ ݐ + ߚ ݐ݊݁ݎܾ݈ ௧ + ߝ ௧
where = 1, … . , 36 ሺmaturitiesሻ, t = 1, … . , T ሺtimeሻ, ߙ and ߜ are respectively individual and time effects.

Among the seven Pedroni's tests, four are based on the within dimension (panel cointegration tests) and three on the between dimension (group mean panel cointegration tests). The heterogeneity is introduced under the alternative hypothesis through the group mean dimension by considering ρ ୧ < 1 ∀ ୧ (ߩ is obtained from the regression ߝ̂ ௧ = ߩ ߝ̂ ௧ିଵ + ݑ ௧ ). In the within dimension, the homogeneity of the cointegration relation is only considered

(ρ ୧ = ρ < 1 ∀ ୧ ሻ.
For the Kao's test, the following relationship is considered:

݂݈݊݀ ௧ = ߙ + ݐ݊݁ݎܾ݈ߚ ௧ + ߝ ௧ wherei = 1, … .
, 36 ሺmaturitiesሻ, t = 1, … . , T ሺtimeሻ and α ୧ denote the individual effects.

Tables 4 and5 display our results. The null hypothesis is rejected for all tests at the 5% significance level, showing that the series are cointegrated. It is thus possible to estimate the cointegration relationship. In a panel data setting, three main approaches exist to estimate the cointegrating relationship: (i) the Fully Modified OLS (FM-OLS, [START_REF] Phillips | Statistical inference in instrumental variables regressionwith I(1) processes[END_REF], [START_REF] Pedroni | Critical Values for Cointegration Tests in Heterogeneous Panels with MultipleRegressors[END_REF] and [START_REF] Pedroni | Fully modified OLS for heterogeneous cointegrated panel[END_REF]) accounting for error autocorrelation and heteroskedasticity; (ii) the Dynamic OLS (DOLS, [START_REF] Kao | On the estimation and inference of a cointegrated regression in panel data[END_REF] and [START_REF] Mark | Cointegration Vector Estimation by Panel DOLS and Long-Run Money Demand[END_REF]) that consist in augmenting the cointegration relationship with lead and lagged differences of the regressors to control for the endogenous feedback effect; and (iii) the Pooled Mean Group estimator (PMG, [START_REF] Pesaran | Pooled Mean Group Estimation of Dynamic Heterogeneous Panels[END_REF]). Given that we have concluded in favor of the homogenous hypothesis with the application of the [START_REF] Hsiao | Analysis of Panel Data[END_REF]'s test, we rely on the PMG estimator proposed by [START_REF] Pesaran | Pooled Mean Group Estimation of Dynamic Heterogeneous Panels[END_REF], which is the appropriate methodology in this case. This procedure consists in estimating a panel error correction model where homogeneity across individuals is imposed for the long-run relationship, while heterogeneity is allowed in the short-run dynamics. It combines two procedures commonly used in panel data: (i) the "mean group estimate", (totally heterogeneous) that consists in estimating separately N individuals regressions and averaging the group specific coefficients; and (ii) the pooled estimator (homogeneous), in which only the intercept is authorized to differ freely across maturities. The PMG estimator is then an "intermediate" estimator since it combines both pooling and averaging. In this sense, the main advantage of the PMG procedure is, while imposing long-run homogeneity, that it allows for short-run and error variance heterogeneity for each group of the panel. The results of the estimation of the cointegrating relationship are reported in Table 5. The error correction term is significant and negative, and the speed of the error correction mechanism is different for the various maturities. This error correction mechanism allows short-term deviations between Brent and FOD prices to be compensated in the long-run, meaning that both series share similar long-term evolutions. The long-run and short-run elasticities (respectively 0.909 and 0.541) reveal that oil prices have more contributed to FOD prices in the long-term than in the short-term.

Conclusion

In this paper, we have investigated the long-term relationship between forward prices of crude oil and domestic fuel for a panel of 36 maturities. Relying on recent panel data methods, we have shown that there exists a homogenous cointegrating relationship between the two series, for all the maturities. The estimation of the corresponding panel error correction model shows however a heterogeneous error correction speed, and indicates that causality runs from oil prices to domestic fuel prices at both short and long run. On the whole, our results put forward that a unique model is sufficient to describe the relationship between the two series for all maturities. We think that these results should have important implications regarding the financial long-term arbitrage strategies based on energy price relations.

This paper may be extended to the analysis of other energy prices, such as the relationships between oil and gas, gas and electricity, etc. From a methodological viewpoint, it would also be interesting to account for potential structural breaks and cross-sectional dependence among individuals.

Fig. 1 .

 1 Fig.1. 12 month forward prices of Brent and FOD, August 2003-April 2010.

Table 1 .

 1 Panel Unit root tests

Table 2 .

 2 Hsiao's homogeneity tests

Table 3 .

 3 Hurlin's no causality test

	lags

Table 4 .

 4 Pedroni's panel cointegration tests

	ݏݐݏ݁ܶ	ݏܿ݅ݐݏ݅ݐܽݐܵ	ܾܽݎܲ
	H : ݊ ݊݅ݐܽݎ݃݁ݐ݊݅ܿ ሺݐ݅ݓℎ݅݊ ݊ሻ݅ݏ݊݁݉݅݀
	݈ܲܽ݊݁ ݒ -ܿ݅ݐݏ݅ݐܽݐܵ	17.41	0.0 *
	݈ܲܽ݊݁ ℎݎ -ܿ݅ݐݏ݅ݐܽݐܵ	-13.84	0.0 *
	݈ܲܽ݊݁ ܲܲ -ܿ݅ݐݏ݅ݐܽݐܵ	-10.57	0.0 *
	݈ܲܽ݊݁ ܨܦܣ -ܿ݅ݐݏ݅ݐܽݐܵ	-12.09	0.0 *
	H : ݊ ݊݅ݐܽݎ݃݁ݐ݊݅ܿ ݊݁݁ݓݐܾ݁ሺ ݊ሻ݅ݏ݊݁݉݅݀
	ݑݎܩ ℎݎ -ܿ݅ݐݏ݅ݐܽݐܵ	-9.63	0.0 *
	ݑݎܩ ܲܲ -ܿ݅ݐݏ݅ݐܽݐܵ	-9.60	0.0 *
	ݑݎܩ -ܨܦܣ ܿ݅ݐݏ݅ݐܽݐܵ	-11.15	0.0 *
	* rejection of the null hypothesis at the 5% significance level.
	.Regressions include individuals intercept and trend.

Table 5 .

 5 Kao panel cointegration test

	ݐݏ݁ܶ

Table 5

 5

	. PMG estimates
	ݐ݊ܽ݀݊݁݁ܦ ݈ܾ݁ܽ݅ݎܽݒ ∶ ݂݈݊݀ ௧	ܩܯܲ
	ݎݎݎܧ ݊݅ݐܿ݁ݎݎܿ ݉ݎ݁ݐ	-0.413 ሺ0.0 * ሻ
	݃݊ܮ -݊ݑݎ ݐ݂݂݊݁݅ܿ݅݁ܿ
	ݐ݊݁ݎܾ݈ ௧	0.909 ሺ0.0 * ሻ
	ݐݎܵℎ -݊ݑݎ ݐ݂݂݊݁݅ܿ݅݁ܿ
	ݐ݊݁ݎܾ݈∆ ௧	0.541 ሺ0.0 * ሻ
	ݐ݁ܿݎ݁ݐ݊ܫ	1.063 ሺ0.0 * ሻ
	ሺܽݐ ݐݎℎݏ -݊ሻݑݎ
	ݎܾ݁݉ݑܰ ݂ ݏݏݎܿ -ݏ݊݅ݐܿ݁ݏ	36
	ݎܾ݁݉ݑܰ ݂ ݏ݊݅ݐܽݒݎ݁ݏܾ	2844
	݃ܮ -݈݈݀݅݇݁݅ℎ	3285

* Significant at the 5% level.

2003 2004 2005 2006 2007 2008 2009 2010 FOD forward prices at 12 month Brent forward prices at 12 month


Peixin Zhang

Laurence Scialom

Michel Boutiller

Vincent Bouvatiller

Mariane Verdier

Case Study of Three German Banks Stuck in the Subprime Crisis ¤

Keywords: Systemic crisis, Leverage, Maturity mismatch, Banking regulation Classification: G01, G14, G21, G28

This paper is aimed at finding banks' destabilizing behaviors that explain why the impact of the crisis is so serious in the banking system. By comparing three German banks stuck in the crisis, I find that: I) the leverage is a common destabilizing factor and, ii) the banks were highly interconnected to other financial institutions and had a large maturity mismatch were more seriously affected by the crisis.

1.Introduction

This case study of three German banks stuck in the subprime crisis, IKB, Hypo Real Estate (HRE) and Dresdner Bank, is aimed at bringing out the impact of banks' destabilizing behaviors (high leverage ratio, high interconnection with other financial institutions and large maturity mismatch) on banks' difficulties. 1My work just concentrated on the German banking system for two reasons. On the one hand, the first banking system touched by the subprime crisis is the German banking system in which IKB was the first European bank completely affected by the crisis. The second one is to avoid to study the influence at a macro level (e.g. the difference in the macroeconomic policy and the banking regulation across the countries). Moreover, I chose IKB, HRE and Dresdner Bank as representative banks 2Many academics are interested in the transmission mechanism of the subprime crisis. [START_REF] Hellwig | Systemic Risk in the Financial Sector: An Analysis of the Subprime-Mortgage Financial Crisis[END_REF] emphasizes the systemic elements in this crisis. [START_REF] Brunnermeier | Deciphering the Liquidity and Credit Crunch 2007-08[END_REF] explains the economic mechanisms that caused losses in the mortgage market and described common economic threads that explain the mess in the financial system during the crisis. Moreover, several economists tried to reveal risky behaviors of banks before the crisis by studying in the special case, e.g. the case of Northern Rock studied by [START_REF] Shin | Reflections on Northern Rock: The Bank Run That Heralded the Global Financial Crisis[END_REF] and [START_REF] Yorulmazer | Liquidity, Bank Runs and Bailouts: Spillover Effects during the Northern Rock Episode[END_REF] who show that the fragile funding structure was for 2 reasons: firstly, the external intervention in these banks was significant; secondly, all of these 3 banks are private banks. In other words, the external intervention in these banks (especially in the case of public interventions) means that it was not required by the public status of the bank but driven by the seriousness of their potentially systemic problems. Note that in this case shareholders profit from the public rescue while the loss is assumed by the public. Furthermore, the data in this study is collected by myself from banks' annual reports.

a destabilizing factor for banks. Different from their case studies focused on one distressed bank, I concentrated on the comparison among three German distressed banks in the subprime crisis. Notice that the degree of difficulty of these banks is different, 3As [START_REF] Morris | Liquidity Black Holes[END_REF] indicate that the behavior of short horizon traders will form this study is aimed at finding the main factors which determine the extent of banks' difficulties.

The research of these factors is conducted by observing three variables: banks' capitalization level, interconnection with other institutions and maturity mismatch. The justifications for choosing these variables is as follows.

The first investigation in the capitalization level is inspired by the idea of [START_REF] Gennote | Capital Controls and Bank Risk[END_REF] who show that a sufficient level of capital gives banks incentives to fulfill their social obligation, that is to say, screening and monitoring industrial projects. Other theoreticians were also interested in this subject, such as [START_REF] Giammarino | An Incentive Approach to Banking Regulation[END_REF], [START_REF] Rochet | Towards a Theory of Optimal Banking Regulation[END_REF], [START_REF] Bensaid | Efficient Regulation of Banks' Solvency[END_REF]. These people develop the theories on capital regulation by the incentive approach. In this study, for the purpose of investigating the capitalization level, I used both the regulatory capital level, and non-regulatory leverage level which is inspired by the study of Brunnermeier et al. (2009) and [START_REF] Adrian | Liquidity and Leverage[END_REF] who point out that leverage ratio is a better indicator for investigating the capitalization level of banks.

According to the argument of Rochet and Tirole (1996) which proves that the interbank funding is vulnerable in the systemic crisis so that the banks that largely depend on interbank funding are less stable, I examine whether these banks were highly interconnected to other banks for the second investigation in the interconnection.

Moreover, on the ground of the fact that banks can be affected by non-bank financial institutions in problem just like what happened in this crisis, I also examine whether these banks are interconnected to other non-bank financial institutions.

the liquidity black holes in the market, in my opinion it could also happen in banks. In addition, [START_REF] Brunnermeier | Market Liquidity and Funding Liquidity[END_REF] argue that market liquidity drying up the impact of maturity mismatches on the banks' problem. Then I make the last investigation in maturity mismatch for these German distressed banks.

Three results obtained from the investigation in these aspects:

1) All three banks were well capitalized in terms of regulatory requirement, but not in terms of simple leverage ratio. Then the leverage is a common factor to explain these banks' difficulties in the crisis.

2) The interconnection with other financial institutions (bank or non bank) and maturity mismatch are two main factors which can explain the difference in the extent of the difficulty of three German banks stuck in the crisis.

3) In the systemic crisis, a large maturity mismatch can amplify the impact of the interconnection on banks in problem. The reason is that the banks with a large maturity mismatch need to face the problem that both their non bank financial creditors and bank creditors want to withdraw their funding or refuse the renewal. 4As this paper is a case study, the sample size (only three banks) took in my study is limited. However, concentrating on the special cases may help us to capture the main destabilizing factors of banks. Furthermore, the different business model of these banks, which could partially explain the difference in maturity mismatch of these banks, is always used by banks as an excuse for avoiding banking regulation. 5The paper is structured as follows. Section 2 analyzes the capitalization level of these banks. Section 3 is invested in the interconnection factor. Section 4 is focused on

In my opinion, it's the same problem on the regulation perimeter as the argument that investment banks should be equally regulated like commercial banks. maturity mismatches. According to the results of previous sections, Section 5 proposes policy implications for regulatory reforms. Then section 6 concludes. The appendix highlights the panorama of the difficulties of these banks and explains how the approximate maturity mismatch is computed.

Capitalization Level

Regulatory Capitalization Level

Figure 1 illustrates 2 important results: 1) all three banks had a higher risk-based capitalization ratio than the regulatory requirement (both core capital ratio and total capital ratio, 4% and 8% respectively). 2) Dresdner Bank (DB in figure 1) was better capitalized relative to IKB and HRE. Brunnermeier et al. (2009) argue that the systemic shock has had a considerable volume effect on banks' balance sheet so that banks that were well capitalized in accordance with Basel norms could not escape the systemic risk. As the regulatory capitalization level cannot correctly reveal the potential systemic risk that could affect banks, they propose the use of the leverage ratio to measure banks' risk level. Moreover, [START_REF] Adrian | Liquidity and Leverage[END_REF] indicate that the leverage ratio has a negative impact on the credit cycle.

Leverage Ratio

According to the above-mentioned arguments, I investigate in this subsection whether the leverage ratio is a factor that explains the difficulties of these banks as well as the difference between their problems. Here I used the asset to equity ratio in order to measure the leverage ratio of these banks. As these banks didn't issue preferential actions during this period, the leverage ratio applied here can be considered as leverage on common equity as well as leverage on shareholder equity.

Before the subprime crisis breaking out, HRE, IKB and Dresdner Bank had a leverage ratio around 50, 36, 36,5 respectively. Indeed the rise of their leverage ratio during the crisis is explained by the fact that they had to use their equity to absorb losses. 30 before the crisis breaking out. As everyone knows, all of these American investment banks were gravely affected by the crisis.

2) Another example is the Spanish banking system recognized as one of the best for resisting the crisis. Here I chose several large Spanish banks to verify their leverage ratio in the eve of the subprime crisis. Banco santander had a leverage ratio around 20. The leverage ratio of Banco Popular Espanol was 20. Banco Sabadell had 17 as leverage ratio. BBVA's leverage ratio was 19,6.9

On the one hand, it is clear that three German banks in the study even had a higher leverage than American investment banks that were the most shocked by the systemic risk. On the other hand, the good example of Spanish banks shows that a lower leverage ratio could help banks to resist to the systemic risk. Figure 2 seems to show that it's not the case of these German banks. Therefore, the leverage ratio should be considered as a common factor for explaining their difficulties.

Table 1 Test of the compatibility between leverage ratio and degree of difficulty Nevertheless, Table 1 illustrates that we can't affirm that the leverage is the reason why these banks are different in terms of the degree of difficulty. HRE had a highest leverage ratio among three banks, then it consumed a large amount of public rescue funds. It's consistent with my initial conception that is to say, the higher their leverage is, the more they have serious difficulties. However, the comparison between IKB and Dresdner Bank seems that we can't conclude this relationship between the leverage and the degree of difficulty as above. Another information brought by Figure 3 is that liabilities to banks of all three banks were more than 25% of their total liabilities. As knowing that liabilities to banks belong to the wholesale funding, this type of funding source is less stable than the retail funding such as retail deposits. Indeed, the ratio of their liabilities to banks, one part of wholesale funding, to the whole funding is higher than the ratio of Northern Rock' total wholesale funding to the whole funding (Figure 4). Recalling the last result about the net position in the interbank market, the funding structure of IKB and HRE was really unstable before the crisis. Regarding the interconnection with non-bank financial institutions, I concentrated on securitized liabilities, financial investment and off balance sheet items in order to measure whether these banks were interconnected with other financial institutions.

Interconnection

When banks profit the low cost of funding from issuing securitized liabilities, they bear the risks. The reason is that the relationship between banks and their institutional creditors is less stable than the relationship between banks and their traditional clients.

This unstable relationship is more significant in a systemic crisis like the subprime crisis, because of the contagion effect among the financial system. When the subprime crisis extended from the banking system to the whole financial system after the great difficulties of Lehman and AIG, all financial institutions feared the contagion effect so that the most of them refused to lend to others. Moreover, liquidity drying-up made the situation worse. These institutions did everything they can do to protect themselves, for instance running on their debtors. The only constrain for them is the maturity limit that is to say, when their loans will be matured. If it's a short term loan, it is clear that they will not renew this loan. Therefore, the banks that had more short term funding were more unstable in the crisis.

Figure 5 illustrates that IKB and HRE considerably relied on securitized liabilities before the crisis breaking out relative to Dresdner Bank. Moreover, 29% and 53% of this type of liabilities are short horizon for IKB and HRE respectively. As described by

13

As I mentioned above, a bank can also be affected by the institutions it financed. It happens because sometimes banks are not able to early detect the danger in their debtors, especially off balance sheet entity (e.g. SPV). Figure 6 indicates that HRE and IKB had more financial investments in comparison with Dresdner Bank. More precisely, the first had more assets that depended on the financial market performance.

Evidently, these market-relative assets are more volatile than traditional assets (loans to non financial firms). As soon as financial markets decline, these banks' portfolio value will decrease as well.

Figure 6 Financial Moreover, contingent liabilities and commitments can be considered as a good indicator that capture the impact of other financial institutions on banks. In fact, banks provide SPVs with credit facilities. If these credit lines were not used, banks will receive commissions. However, when these SPVs are attacked by the crisis, banks that signed commitments with these entities have to refinance them. Therefore, the problem of reintermediation emerges. That is the case of IKB illustrated by Figure 7 (see the appendix for details).

The analysis in this section showed that HRE and IKB were more interconnected with other financial institutions so that their difficulties were more serious than Dresdner Bank. Indeed my work illustrates an idea about the importance of interconnection between financial institutions. Several academic have concentrated on this point, for example, [START_REF] Adrian | CoVaR[END_REF] propose a method to measure the systemic risk by taking account of the interdependance between financial institutions.

Maturity Mismatch

As mentioned above, the impact of interconnection can be amplified by maturity mismatches. More precisely, banks are more fragile while they are highly interconnected to other institutions and when their liabilities' maturity is short. By contrast, a bank with a stable funding structure (less financial creditors or small By supposing a simple system, I make a example in this section in order to understand why maturity mismatches have an impact on the difficulties of banks, especially for banks which are highly interconnected to other financial institutions.

It is a two-date (0, 1, 2) and zero-interest-rate system. In this system, there are three types of agents, a continuum of firms which need funding to finance their project, only one bank (for simplicity), and a continuum of investors which are only willing to finance the bank because of risk-aversion. To simplify the analysis, I assume that at date 0 and 1 the only rational capacity for the bank of collecting deposits and then granting to firms is two units. For example, if the bank collected two units of deposits at date 0, and if its investors withdraw the deposits, one or two units, the only one thing the bank can do is to find other sources in order to keep its funding pool at two units. Moreover, for firms (and investors of the bank), there are two strategies, the long-term funding (resp. investment) that comes to maturity at date 2 and the short-term funding (resp.

investment) which comes to maturity at date 1. Furthermore, if the investors of the bank agree, the short-term funding offered by them can be renewed for a period (for instance, after being renewed, a short-term deposit matured at date 1 will mature at date 2).

In this context, as the bank would collect two units of deposits and then grant to firms, it has to choose at date 0 its funding and investment structure among three strategies for funding (two units of long-term funding, two units of short-term funding, or one unit of each type) and three strategies for investment (the same choices as funding structure).

As a consequence, the bank has nine options (three categories according to fundingstructure choice) described as follow to construct its portfolio. It is clear that the bank's level of riskiness at date 1 will be different across these options.

A. The bank chose two units of short-term funding:

A-1. Suppose that the bank at date 0 granted two units of long-term loans to firms. In this case, the bank will be in trouble if it cannot renew the old deposits or cannot find other sources.

A-2. If the bank at date 0 granted one unit of long-term loan and one unit of short-term loan to firms, it will face the similar situation as above. The reason is that in this case it has to find one unit of funding source to refinance its long-term investment.

A-3. If the bank at date 0 chose two units of short-term investments, it will not be stuck in trouble by the withdrawal of its investors at date 1.

B. The bank chose one unit of short-term funding and one unit of long-term funding:

B-1. If the bank granted two units of long-term loans to firms at date 0, there is a risk that the bank couldn't find one unit of funding source (renewing the old one or finding another one) to refinance its long-term investments at date 1.

B-2. Assume that the bank invested at date 0 one unit of long-term loan and one unit of short-term loan. In this case, there will not be difficulties for the bank at date 1, because maturity mismatches don't exist.

B-3. If the bank granted two units of short-term loans to firms at date 0, it will be safer than the second situation.

C. The bank chose two units of long-term funding (C-1, C-2, C-3):

As all the bank's funding sources are over two periods, there is not the risk of investors withdrawing. Then whatever the bank chose the investment structure at date 0, it will be safe at date 1.

As a consequence, the last three options are not risky at date 1 for the bank, however the probability of Category B and A at date 1 is 1/3 and 2/3 respectively. Moreover, three troublesome conditions (A-1, A-2, B-1) have a common feature that is to say, the average maturity of assets (AMA) is longer than the average maturity of liabilities (AML). 12Now suppose that in each case the investors of the bank agree to renew their loans to the bank, however, only one unit of funding source. This assumption is interpreted as the amelioration of market conditions. In this case, Option A-2 and B-1 are not any more the risky option at date 1. Nevertheless Option A-1 is still risky for the bank due to the large maturity mismatch when it constructed its portfolio at date 0. Therefore, even if creditors are less jittery, the bank that has a large maturity mismatch cannot avoid the liquidity shock. From the opposed point of view, the maturity mismatch amplifies the impact of agitation of creditors on banks' funding conditions.

Regarding three German banks in my study, I checked whether they had a large maturity mismatch before the crisis breaking out. For this purpose, I calculated the approximate maturity mismatch for these banks in time of their difficulties. 13Indeed, regulatory reforms by using these factors could be implemented in two ways.

The first is the Early Warning System proposed by [START_REF] Dewatripont | The Treatment of Distressed Banks[END_REF].

Regulators and supervisors can use these factors as indicators to detect banks' risk level.

The result is very interesting: HRE had an approximate maturity mismatch of 2.84, IKB's approximate maturity mismatch is 1.79, and Dresdner Bank's maturity mismatch is only 0.7. It seems that larger maturity mismatches of HRE and IKB, coupled with higher interconnection with other financial institutions rendered them fragile in the crisis. Thus they were more seriously affected by the subprime crisis.

Regulatory Reforms

The analysis in previous sections justified the impact of capitalization level (leverage), interconnection and maturity mismatch on banks' stability. Moreover, interconnection and maturity mismatch can be considered as the discriminative factors that explain the difference in these banks' problems during the crisis. Therefore, regulatory reforms in the light of these factors found in this study are necessary and pressing in the face of what happened in this crisis.

With suitable indicators, supervisors can choose the right time for interventions in order

to reduce serious consequences of banks' difficulties. The second way is to integrate these factors in future micro and macro prudential regulations to limit individual banks' risk taking.

Several academics and central bankers propose to place importance on leverage ratio.

For example, [START_REF] Blum | Why 'Basel II' May Need a Leverage Ratio Restriction[END_REF], Brunnermeier et al. (2009) and [START_REF] Hildebrand | Is Basel II Enough? The Benefits of a Leverage Ratio[END_REF].

Moreover, Adrian and Shin indicate that leverage is procyclical with the result that there is a spill-over effect of a high leveraged institution to other institutions. Therefore, taking into account the leverage ratio is reasonable to verify whether a bank is susceptible to be affected by the systemic risk and whether it will generate externalities in the financial system.

The regulators and supervisors have effectively attached importance to the necessity of strengthening the existing capital requirement. According to the Basel III developed by the Basel Committee on Banking Supervision after the subprime crisis breaking out, there will be a package of reforms which are aimed at making the banking system more resilient. The most important measure of this package is to increase the equity requirement. For instance, the minimum common equity requirement will rise from 2% to 4.5% in 2015 when the Tier 1 capital requirement will have to be at least 6% against 4% at present. Moreover, even if the minimum total capital requirement will remain 8%, the capital conservation buffer which is considered as the countercyclical buffer will be phased between 2016 and 2018. 14Besides leverage, reducing banks' interconnection with other financial institutions is another way for future regulatory reforms. Nevertheless, it is hard to put into practice in comparison with leverage. In reality, interconnection between financial institutions is very complex, so it needs enormous data of all institutions in the financial system to measure the systemic risk's impact on each institution and contributions of each institution to the systemic risk. Then determining a proper level of interconnection for each bank is a very hard work.

However, since my analysis about maturity mismatch showed that the latter can amplify the impact of interconnection on the banks' problem, we should try to limit maturity mismatches so as to reduce the impact of interconnection. Then, liquidity regulations should be putted into action with the purpose of decreasing maturity mismatches. It is remarkable that the liquidity regulation is not aimed at eliminating maturity mismatches, because we all know that the maturity transformation is an important and profitable activity of banks. In my opinion, the liquidity regulation could be aimed for attenuating the negative impact of maturity mismatches.

Actually, there are three ways for liquidity regulations. The first is the liquidity minimum requirement. It forces banks to hold minimum liquid assets or cash. It is a type of liquidity regulations that is totally based on assets. However, it is less effective for two reasons. On the one hand, holding liquidity minimum, especially cash, is costly for banks and the whole real economy. On the other hand, this requirement is not sufficient to cover a systemic risk.

The second way is Core Funding Ratio, actually putted into practice by the Reserve Bank of New Zealand. This requirement asks banks to hold sufficient solid funding, for example retail funding, in comparison to total assets. It is more effective than the first one because of taking account of the funding structure. However, it neglected the impact of assets composition on the stability of banks.

The third solution of liquidity regulations is Liquid Assets to Liquid Liabilities Ratio.

The idea is that banks have to hold sufficient liquid assets to cover the risk related to unstable funding from jittery creditors. 15 BIS Press release at its 12 September 2010 meeting. 16 Assets (maturity < 1 month) / Liabilities (maturity < 1 month) must be higher than 1.

without distinguishing different assets and liabilities, its effect is very limited. That's why IKB and HRE which respected the liquidity requirement of Bundesbank were still affected by the liquidity risk.

Indeed, the third one is the best in terms of effectiveness. However, it is more complicated when regulators compute different balance sheet items' maturity. For this reason, regulators could put into practice hybrid liquidity regulations in the sequential manner. More precisely, regulators could define a threshold for each type of liquidity regulation or when each one will be applied for banks. For example, one bank perhaps is under Core Funding Ratio requirement on condition that its liquid assets are higher than the regulatory threshold. Otherwise, the Liquid Assets to Liquid Liabilities Ratio will be applied.

Conclusion

This case study highlights the high leverage is a common factor for explaining the difficulties of three German banks in the subprime crisis on the one hand; high interconnection with other financial institutions coupled with large maturity mismatches are the discriminative factors that explain the difference in the extent of difficulties of these banks on the other hand.

Moreover, the paper showed that in the light of difficulties of these German banks maturity mismatches could amplify the impact of interconnection with other financial institutions on the banks' stability. According to this result, it is necessary to reform the actual banking regulation by integrating liquidity regulations as complementarity of capital regulations. For future researches, the liquidity regulation based on assets and liabilities structure deserves the attention of economists. Like their American rivals, European banks didn't escape from the crisis, even though they didn't directly involve in American mortgage activities. Amongst European banks in trouble, the famous case is Northern Rock and UBS. Moreover, the market liquidity drying up due to the failure of Lehman jeopardized a great deal of European banks of which funding largely depended on short-term financial markets.

A) IKB Case

IKB Deutsche Industriebank is a German bank specialized in lending to small and medium-sized companies. In addition, IKB largely involved in real estate financing. On 27 th July 2007, IKB was explicitly affected by the subprime crisis. To avoid the failure of IKB, the German government's financing bank, along with Bundesbank and three the above-mentioned risky exposure which amounts to €15.17 billion is not negligible. In other words, IKB needed the external power to help itself to cover these risks. Knowing that HRE's total balance sheet in September 2008 was €392.5 billion, the amount of public rescue funds proved the gravity of its difficulties. In the case of Dresdner Bank, we should pay attention to its investment bank division.

B) HRE Case

C) Dresdner Bank Case

In fact, Dresdner Bank was affected by the crisis because its investment bank considerably involved in American mortgage activities. We can see

Figure 1 Risk

 1 Figure1

Figure 2

 2 Figure2shows the evolution of leverage of these German banks.7

I

  Figure3shows the net position of three German banks in the interbank market. Even

Figure

  Figure 3

Figure 4 Northern

 4 Figure 4 Northern Rock's wholesale funding as proportion of total liabilities, June 2006 to June 2007

Figure 5 ,

 5 Figure5, HRE had a dangerous funding structure that have destabilized this bank during the crisis. Coupling the result of Figure5with the result of the net position in the interbank market, we could obtain the interesting result about the funding structure of these banks justified the importance of retail funding. Highly depending on interbank liabilities and securitized liabilities means that HRE and IKB used little retail funding which is deemed as the most stable source of funding. As a consequence, unstable funding structure made HRE and IKB be more seriously affected by the systemic shock than Dresdner Bank of which funding structure was more solid.

Figure 8 TED

 8 Figure 8

Figure 9

 9 Figure 9Quarterly growth of balance sheet of Depfa, HRE & All monetary financial institutions,Dec. 2003 to Sep. 2007, Base: Dec. 2003

  The regulatory capitalization level of IKB was stable while the leverage ratio soared in the end of 2007, because IKB received in September 2007 a public rescue fund, which is included in the calculation of regulatory capitalization ratio but excluded in the computation of leverage ratio. /www.lehman.com/press/qe/docs/031808_1q08.pdf#financials the latter had a leverage ratio around 28 for two quarters before the crisis. Moreover, Lehman isn't the unique case in US, most of investment banks in US held a leverage ratio around 25 to

	Figure 2
	Leverage of HRE, IKB & Dresdner Bank, June 2006 to June 2008
	300
	270
	240
	210
	180
	150
	120
	90
	60
	30
	0
	1) According to the interim report of Lehman Bros., 8 7 8 Lehman Bros.'s interim report of the 12/06 06/07 12/07 06/08 HRE IKB Dresdner http:/06/06 Bank	first	quarter	in	2008,

  3

	Dresdner Bank, IKB & HRE's interbank position, June 2006 to June 2008
	HRE		IKB
	40,00%			40,00%
	30,00%			30,00%
	20,00%			20,00%
	10,00%			10,00%
	0,00%			0,00%
	31/12/06	31/12/07	31/12/06	31/12/07
	30/06/06	30/06/07	30/06/08	30/06/06	30/06/07	30/06/08
	Liability as	Loan as %	Liability as	Loan as %
	% of total	of total	% of total	of total
	assets	assets	assets	assets
			Dresdner Bank
		40,00%
		30,00%
		20,00%
		10,00%
		0,00%
			30/06/06 31/12/06 30/06/07 31/12/07 30/06/08
			Liability as	Loan as %
			% of total	of total
			assets	assets
	Source: Dresdner Bank, IKB & HRE, annual and interim reports, 2006-2008

  investment as proportion of total assets, June 2006 to June 2008

	Source: IKB, HRE & Dresdner Bank, annual and interim reports, 2006-2008
	Financial investment as proportion of total assets
	40,00%
	35,00%
	30,00%
	25,00%
	20,00%
	15,00%
	10,00%
	5,00%
	0,00%
	06/06	12/06	06/07	12/07	06/08
		HRE	IKB	Dresdner Bank
	Source: IKB, HRE & Dresdner Bank, annual and interim reports, 2006-2008
	Figure 7
	Ratio of contingent liabilities & commitments to assets, June 2006 to June 2008

  In the new Basel III, this type of liquidity In fact, the Deutsche Bundesbank has put into effect this type of liquidity regulation in 2007. Nevertheless, since the one applied by Bundesbank is only a simple ratio16

	address liquidity mismatch. 15
	requirement is proposed as the Liquidity Coverage Ratio (LCR) which will require
	banks to have sufficient high-quality liquid assets to withstand a 30-day stressed
	funding scenario that is specified by supervisors. Besides, it is complemented by the Net
	Stable Funding Ratio (NSFR) which is a longer-term structural ratio designed to

  BdB, BVR and DSGV) formed a rescue fund which amounted to €3.5 billion to bail out IKB. In February 2008, a new rescue package which amounted to €1.5 billion was announced by the German government.IKB was the first European bank touched by the subprime crisis. It didn't directly involved in American mortgage activities, but it had a large position in structured products related to American mortgage loans in direct or indirect ways as the below paragraph described. 17• Rhineland Funding which had €13.2 billion of investment consumed a credit facility which amounted to €8.1 billion provided by IKB. • Credit lines granted to SPVs Havenrock I and Havenrock II made that IKB is exposed to a credit risk which amounted to €1.2 billion. • IKB AG had a risky position resulting from the portfolio investment which amounted to €5 billion, and IKB International S.A. Luxembourg had a risky position of the portfolio investment which amounted to €1.3 billion • IKB held €109 million of SIV Rhinebridge plc.'s equity that was a risky position during the crisis.

	January February April 0,00% 1,00% 2,00% 3,00% 4,00% 5,00% 6,00% 3 months Libor USD bank associations (In comparison with IKB's total balance sheet (€53.17 billion) and equity (€1.38 billion) June August October December 3 months T-bill rate TED Spread
	in time of its difficulties, 18
	17 IKB's annual report of 2007/2008
	18 IKB's interim report of June 2007

Table 2

 2 in European banking system. However, this giant German bank didn't escape from the subprime crisis in the second half of 2007. For this reason, Allianz, its parent company from 2002, decided to sell this bank to others. Even though Allianz was refused by Lloyds TSB in July 2007, the former reached an agreement with the number 2 of German banks, Commerzbank in August 2008. Finally, the takeover of Dresdner Bank by Commerzbank, that put into effect in January 2009, amounted to €9.8 billion. From that date on, Dresdner becomes one part of its old rival. Net Profit Before Tax of Dresdner Bank's divisions, million €

	19 Depfa's annual report of 2007

Calculation of approximate maturity mismatches I

  Table 2 concerning the sharp decrease of Dresdner Bank's invest bank's profit between 2006 and 2007. calculated approximate maturity mismatches of these banks at different times, becausethey didn't encounter problems at the same time. Precisely, July 2007 for IKB and Dresdner Bank, and September 2008 for HRE. Because of the availability of data, I used the data at the moment of one year before their difficulties that is to say, the data in March 2007 (end of fiscal year 07/08) for IKB, the data in December 2006 for Dresdner Bank, and the data in December 2007 for HRE. Furthermore, for the same reason, I chose principal balance sheet items 20 20 Liabilities to banks, securitized liabilities, liabilities to customers, loans to banks, financial to calculate approximate maturity mismatches.

	FI	88851	5,95	1,49
	IKB Total	353999	Total Average Maturity 5,37
		Amount (million €)	Average Maturity	Weighted Average Maturity
	Liabilities	(A)	(AM)	PAM=(AM / Total A)*AM
	Assets LiB	111241	0,69	0,22
	LoB LiC	4441,9 27106	0,68 3,07	0,05 0,23
	LoC SL	29685 218080	3,5 3,33	1,69 2,04
	FI SC	27265 5616	5,17 5,06	2,3 0,08
	Total Total	61391,9 356427	Total Average Maturity 4,04 Total Average Maturity 2,53
	Liabilities		Maturity Mismatch	2,84
	LiB Dresdner Bank 13912,5	2,91	0,7
	LiC	4277,8 Amount (million €)	4,45 Average Maturity	0,33 Pondered Average Maturity
	SL	39555,5 (A)	1,5 (AM)	1,03 PAM=(AM / Total A)*AM
	SC Assets	3026,4	5,81	0,29
	Total LoB	57745,8 138947	Total Average Maturity 2,24 0,6 0,25
	LoC	187680	Maturity Mismatch 2,2	1,79 1,22
	FI	11208	3,96	0,13
	Total	337835	Total Average Maturity 1,6
	HRE Liabilities
	LiB	Amount (million €) 162455	Average Maturity 0,75	Pondered Average Maturity 0,31
	LiC	(A) 182227	(AM) 0,71	PAM=(AM / Total A)*AM 0,33
	Assets SL	45970	1,56	0,18
	LoB SC	51975 6192	3,13 5,24	0,46 0,08
	LoC Total	213173 390652	5,68 Total Average Maturity 0,9 3,42
			Maturity Mismatch	0,7
	investments, loans to customers and subordinated liabilities.

2.

The panorama described in the first appendix can help us to understand their difficult situation.

Among the German banks in problem in the crisis, there are Deutsche Bank and Dresdner Bank as the commercial bank, Hypothekenbank and Hypo Real Estate as the Pfandbrief bank (mortgage bank), IKB as the specialized and Pfandbrief bank, SachsenLB and WestLB as the Landesbank.

See the appendix 1 for details about the difference in their difficulties.

Generally, the funding of non-bank financial creditors are more stable than it of bank creditors. Nevertheless, the first may be equally excited as the latter in time of the systemic crisis.

As IKB and HRE are Pfandbrief banks that finance their real estate loans by asset backed liabilities, their maturity mismatch is generally larger than commercial banks.

Quarterly reports in June 2007 of Banco Santander, Banco Popular Espanol, Banco Sabadell, and BBVA.

Net position means that loans to other banks minus liabilities to other banks is not equal to zero. When a bank has a negative position in the interbank market, this bank is a net borrower vis-a-vis other banks. Then, this bank could have to face the problem of withdrawal of its bank creditors. In a systemic crisis, it is more possible to happen. The more closely a bank is dependent upon other banks, the less stable its funding structure in the systemic crisis.

In contrast to the interconnection with other banks, the interconnection with non bank financial institutions affects the stability of bank in different ways. On the one hand, non bank financial institutions have a role as creditor. In this situation, as soon as these institutions are touched by the systemic risk, they will be jittery as well as banks regarding withdrawing their funding. On the other hand, some non bank financial institutions play another role as securitization entities, which are partially financed by banks' financial investment or off balance sheet commitments, and invest in structured products. When these entities are affected by the liquidity crisis, the banks that provided funding for these entities is not able to be well out of the crisis.

A-1: AMA = (2+2) / 2 = 2 > AML= (1+1) / 2 = 1; A-2: AMA = (1+2) / 2 = 1.5 > AML= (1+1) / 2 = 1; B-1: AMA = (2+2) / 2 = 2 > AML= (1+2) / 2 = 1.5This gap between assets and liabilities' maturity measures the maturity mismatch of banks.

See the appendix for some details.

BIS Press release at its 12 September 2010 meeting.

Appendix 1. Panorama of the subprime crisis and the difficulties of IKB, HRE and

Dresdner Bank

The crisis breaking out in 2007 putted many banks in trouble. Even if the first banks affected are American banks, non-American banks were next targeted by the crisis.

Serious consequences of this crisis are explained by the fact that in recent years banks have considerably involved in the securitization business which amplified the impact of the real estate bubble exploding on the financial system.

From the summer of 2007, the crisis started to spread its influence in the financial system. The shape of the crisis was manifest in time of the difficulties of Bear Stearn in March 2008. Then, the crisis reached its pike on the fifth September 2008, when Lehman Bros. failed. The failure of Lehman resulted in a series of difficulties in the financial system. From the moment, the crisis seemed to be systemic.