how to revise a risk based contribution: an application of ... saltelli, de cesare, de lisa... · 3...

How to revise a risk based contribution:

an application of Sensitivity Analysis’ importance measures to the Italian

Banking System

C. Galliani*, A. Saltelli*, A. Veccia**, M. De Cesare**, R. De Lisa**

*: Joint Research Centre, EC

**: Fondo Interbancario di tutela dei Depositi (FITD)

Draft [01]: march 2011

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How to revise a risk based contribution: an application of Sensitivity Analysis ’ importance measures to the Italian Banking System – Galliani, Saltelli, Veccia, De Cesare, De Lisa

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Abstract

Deposit Guarantee Schemes (DGS) aim to protect depositors of all credit institutions against bank failures. One of the most critical issues about DGS concerns the criteria to be used to assess the risk‐based contribution that each member bank should pay to the Scheme. As a starting point, is it possible to evaluate models developed in European DGS? In this paper we propose an approach based on Sensitivity Analysis tools applied to the Italian Banking System. In particular, we analyze methods used by the Italian DGS (Fondo Interbancario di Tutela dei Depositi – FITD) through variance-based importance measure (sensitivity Index) performed using a recursive algorithm. Sensitivity index is applied initially to the current Italian DGS model and then to an alternative model obtained by partially revising criteria currently used at FITD.

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Index

1. Introduction .............................................................................................................................................. 4

2. Methodology ............................................................................................................................................ 5

2.1 Sensitivity Analysis and Importance Measures ....................................................................................... 5

2.2 The Italian DGS ........................................................................................................................................ 7

2.3 Data ....................................................................................................................................................... 10

3. Results ..................................................................................................................................................... 13

3.1 Applying the Sensivity Analysis to the current Italian camel model ..................................................... 13

3.2 Revising haircuts and risk classes .......................................................................................................... 16

3.2 Revising aggregation criteria of data .................................................................................................... 18

4. Some conclusions ................................................................................................................................... 22

5. Bibliografia .............................................................................................................................................. 24

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1. Introduction

CAMELS are rating models born in US to classify members of Deposit Guarantee Schemes (DGS) according to their financial soundness. US DGS have an ex-ante risk-based mechanism applied by the Federal Deposit Insurance Corporation (FDIC), that is an independent Federal Agency that classifies DGS members into risk categories according to both capital levels and supervisory ratings. Capital levels are investigated through 3 capital ratios whereas supervisory ratings are assigned through a system of 6 financial indicators named CAMELS. The name in an acronym of the following indicators: Capital adequacy, Asset quality, Management capability, Earnings quantity and quality, Liquidity adequacy and Sensitivity to market risk. They contribute to build a composite indicator that, together with the capital evaluation, assign each member bank to a specific risk class.

The Italian DGS (Fondo Interbancario di Tutela dei Depositi) is an ex-post funded scheme in EU1 and it constantly monitors the financial situation of its members using a balance sheet indicators system composed by 4 ratios referred to three risk profiles: risk, solvency and profitability. The contribution base is defined through the definition of proportional and regressive quotas, that are obtained respectively using the amount of covered deposits and the size of the member banks. Regressive quotas are then adjusted through a risk correction based on the system of 4 ratios mentioned above. We can easily interpret the Italian model as a CAMEL system without Liquidity and Management profiles. In fact CAMEL models are widely spread, but procedures vary from country to country. They are generally used to construct a composite indicator that is able to provide a complete picture of banks’ risk profiles and therefore they suffer from subjective choices that compose sources of uncertainty typical of composite indicators. Choice and definition of balance-sheet variables used as crisis indicators and aggregation and weighting procedures applied to such variables represent just some of the possible rooms of arbitrariness that can occur in the construction of a composite indicator. Sensitivity Analysis is a necessary tool for the evaluation of assumptions made in the construction of the composite indicator. In particular, it allows us to explore the relationship between the output of the model (banks’ ranking according to riskiness) and its inputs, represented by the different sources of variations that flow into the model. Uncertainty and Sensitivity Analysis are then strictly linked to each other and their combination would increase the robustness of the analyzed model.

Choices made by Italian DGS regarding aggregation of information provided by the four ratios are investigated through Sensitivity Analysis tools. Scatter plots and a variance based sensitivity index will suggest a partial revision of the construction of the composite indicator. For this reason, in the last part of this work, a new Aggregate Indicator is proposed and it will be compared to the actual one. Robustness of the new Indicator is tested by introducing different weighting and aggregating procedures, in the way suggested by Uncertainty Analysis.

The following paragraphs are structured in this way: the second paragraph is dedicated to the description of Sensitivity Analysis tools, Italian DGS and available data. In the third paragraph some results about the analysis of the Italian current system are presented and a possible revision of the model is proposed. Some conclusions are presented in the fourth section.

1 European Commission, Joint Research Centre, Econometrics and Applied Statistics Unit, Risk-Based

Contributions in EU DGS: Current Practices, June 2008

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2. Methodology

2.1 Sensitivity Analysis and Importance Measures

The Italian CAMEL model used at FITD develops a composite indicator (The Aggregate Indicator) using an aggregation of the four individual ratios presented above. The mathematical model underlying the indicator is made of all choices applied to the single variables aggregated. FITD is currently composing the Aggregate Indicator using an arithmetic average average of involved variables, in other words, the composite indicator Y is derived from

k

i

jiij xy1

,

Where

j=1,…,n is the single bank being measured by the composite indicator,

n is the number of involved banks,

jkj xx ,...1 are the coefficients associated to bank j over the k ratios iX ,

i is the weight associated to iX .

In the specific FITD case, weights associated to ratios’ coefficients imply a difference between A1, who benefits from a double importance, and the other 3 ratios that are equally weighted.

The developer of a composite indicator assigns weights as measures of importance of the various indicators or pillars. Thus one would expect that a measure of correlation (Pearson or

Spearman) between Y and iX will give a value which, while not identical to i , would at least

not contradict it openly. For example, we would call a contradiction a pillar weighting 0.5, i.e. corresponding to 50% of the total weight, and correlating (either Pearson or Spearman) below the 0.01 level with Y . Can we do more than that? Can we develop or adopt a measure informing the developer of the error made in assuming weights equal to importance in linear aggregation?

Here we are going to use the variance-based measure iS proposed by Paruolo et al. (2011)

named, alternatively, measure of importance, Pearson’s correlation ratio or first order

sensitivity index. iS is defined as follows:

)(

))((

YV

XYEVS

iiXX

ii

(1)

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iS is based on global sensitivity analysis theory where these concepts are ordinarily traded.

One might ask the question `What happens to the variance of Y if one variable is fixed? The point is that we do not know where to fix a variable, and furthermore we would like to get rid of the dependency from the fixing point. To do this we could modify our question as follows `what is the reduction in the variance of Y that we would get on average by fixing a variable to all its possible values?'

It is evident that the reduced variance obtained on average by fixing a variable can be written as:

))(( iiXX XYVEi

Due to the known identity

)())(())(( YVXYVEXYEV iiXXiiXX ii

then we can call ))(( iiXX XYEVi the reduction in variance of the composite indicator to be

expected by fixing a variable. Note that so far we did not assume variables' independence. In sensitivity analysis one uses - also for the case of correlated variables - a first order sensitivity

measure (also termed main effect) that is defined as the ratio between ))(( iiXX XYEVi and

the unconditional variance, as expressed in (1).

The main difference between the uncorrelated and the correlated case is that in the former

the sum of the iS must be less than or equal to one, (with 1 iS when no interactions exist

between variables), while for the correlated variables this sum might well exceed one.

In order to compute iS we can make use of the following equation:

))(())(( iiiiXX XfVXYEVi

,2

The equation above says that all what is needed to compute ))(( iiXX XYEVi is a good

estimate of function fi. This latter can be derived by an appropriate interpolation and smoothing algorithm applied to a simple scatter plot of the composite indicator Y 's scores

versus any variable iX .

Following Paruolo et al. (2011) we have estimated the iS ’s using a non-parametric

multivariate smoothing approach called State Dependant Regression that is equivalent to smoothing splines and kernel regression but is performed using a recursive algorithm to

identify relevant ANOVA terms3 . In the simple case when fi is a linear function, iS reduces to

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iR , the square of Pearson's correlation between Y and iX . Note that this smoothing

approach is but one of many possible strategies to estimate the iS 's.

The main effect iS is an appealing measure of importance of a variable for several reasons:

2 See Paruolo et al. (2011)

3 See M. Ratto, A. Pagano (2010)

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it offers a precise definition of importance, that means `the expected reduction in variance of the composite indicator that would be obtained if a variable could be fixed';

it is always positive which makes it interpretable in all cases;

it can be used regardless of the degree of correlation between variables;

it is “model-free”, that means it can be applied in principle also in non-linear aggregations unlike the effective weights or the Pearson correlation coefficient that are constrained by the linear assumption; and finally

it is not invasive, that means no changes are made to the composite indicator or to the correlation structure of the indicators. We contrast this with the technique of eliminating one indicator at a time in order to assess its impact on the final ranking.

2.2 The Italian DGS

The Interbank Deposit Protection Fund (FITD or Fund) was established in 1987 on a voluntary membership basis as a private-law mandatory Consortium, recognised by the Bank of Italy. Its activities are regulated by the Statutes and By-Laws.

Deposit guarantee is regulated at the EU level by Directive 94/19/EC on Deposit Guarantee Schemes of the European Parliament and of the Council of May 30th 1994, later implemented by each Member State in the national regulatory framework. The Directive, focused on the principle of minimum harmonisation, has aimed at achieving the target of guaranteeing depositors of all credit institutions, while safeguarding and enhancing stability in the banking system as a whole. Currently the entire framework is under decision and a legislative proposal of the European Commission has been under discussion in the European Parliament and the Council since July 2010.

Directive 94/19/EC4 on deposit guarantee schemes was implemented in the Italian legislative system by the Legislative Decree 659/96 (published in the Official Journal of the Italian Republic on December 27, 1996 and entered into force on January 11, 1997). As a result, membership in a DGS became mandatory for all Italian banks and the level of coverage was set at 103.291,38 euro (as the equivalent of the original limit of 200 million lire).

All Italian banks (291 as of 30 June 2010) adhere to the Fund. Credit cooperative banks, however, join the other mandatory DGS established in Italy, the “Deposit Guarantee Fund of Cooperative Banks”. This latter, along with the “Bond Holders Guarantee Fund of Cooperative Credit Banks” (voluntary scheme for credit cooperative banks only) and the “National Guarantee Fund” (for investors) are the other guarantee schemes active in the Italian safety net.

FITD mandate aims at guaranteeing depositors of member banks. The financial resources for the pursuit of this aim are provided by the Consortium members in case of need, i.e. on an ex-post basis.

4 Directive 94/19/CE was amended by Directive 2009/14/EC of 11 March 2009 with regard to the

coverage level and the payout delay. The new Directive has been recently implemented by the Italian legislator, but the relevant legislation is awaiting publication in the Official Journal to enter into force.

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According to the Statutes, the Fund can intervene in favour of banks placed in Compulsory Administrative Liquidation5 either reimbursing depositors or participating in a transfer of assets and liabilities to an acquiring bank (Articles 27-28). Moreover, FITD can perform support interventions (pursuant to Article 29) in favour of member banks in Special Administration. The choice between the different types of interventions is made applying the least cost principle. Any intervention of the Fund is subject to the authorisation of the Bank of Italy.

Since when the Fund was established in 1987, the contribution system has been set up according to an insurance logic, where member banks are required to pay depending on their level of risk.

To this purpose, banks are required to send to the Fund data on their Contribution Base and on Balance-Sheet Ratios, according to the Statutory Report System provided for in FITD Statutes. A distinction is drawn among the sources of data used for the Statutory Reports System: the Fund receives data for the Contribution Base directly from member banks, while the Supervisory Authority provides data needed for calculating the balance-sheet ratios.

The Contribution Base is the key variable used for calculating the amount of member banks’ contributions both to operating expenses and interventions (Article 25 Statutes). The contribution quota is based on the portion of each bank’s deposits covered by the Fund and it is calculated in three steps. First, the proportional quota of the contribution base, expressed in thousandths, is given by the individual contribution base over the Total Reimbursable Funds. Second, The “regressive correction method” (Article 14 of the Appendix to the Statutes) modifies the proportional quota using an increasing/decreasing percentage inversely linked to the size of the bank, which is expressed by the amount of its contribution base. The incrising or reduction of the proportional quota may vary between +7,5% and – 7,5%. Third, a correction method linked to the bank riskiness in Balance-Sheet ratios is applied; this is based on the value of the “Weighted Average Aggregate Indicator” (Article 5 of the Appendix to the Statutes), calculated for each bank as the average of the value of its Aggregate Indicators (AI) on the previous three six-monthly Balance-Sheet ratios reports that the bank has submitted to the Fund. The impact of the WAAI on the regressive quota is of +20% and -20%.

The Fund evaluates the riskiness of its member banks through a system of four ratios referred to three profiles: Risk, Solvency, and Profitability (Article 6 of the Appendix to the Statutes). Ratios are calculated semi annually or quarterly, depending on the level of risk of the single member bank.

Ratio are as follows:

Risk profile:

A1 = Bad Loans / Supervisory Capital

Solvency profile:

B1 = Supervisory Capital, including Tier 3 / Supervisory Capital Requirements

Profitability profile:

D1 = Operating Expenses / Gross income

D2 = : Loan Losses, net of recoveries / Profit before tax

5 Compulsory Administrative Liquidation and Special Administration are the special bankruptcy regime

provided for by the Italian banking law for banks.

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Three thresholds are set for each ratio (Table 1) using the “Method of Percentiles” which consist in dividing at 75%, 85% and 95% the distribution of each indicator. Appling this method, the ratios are divided in four classes called “Normal”, “Attention”, “Warning” and “Violation”, into which member banks are rated.

TABLE 1 - Ratios and thresholds

Ratios and Thresholds

Ratios Normal Attention Warning Violation

A1: Bad Loans / Supervisory Capital

Up to 20%

(Coefficent 0)

from 20% to 30%

(Coefficent 2)

from 30% to 50%

(Coefficent 4)

More than 50%

(Coefficent 8)

B1: Supervisory Capital, incl.Tier 3

/Supervisory Capital Requirements

More than 110%

(Coefficent 0)

between 100% and 110%

(Coefficent 1)


(Coefficent 2)

Less than 90%

(Coefficent 4)

D1: Operating Expenses/ Gross

income

Up to 70 %

(Coefficent 0)

Up to 80 %

(Coefficent 1)

Up to 90 %

(Coefficent 2)

More than 90 %

(Coefficent 4)

D2: Loan Losses /Profit before tax

Up to 40 % or

Loan losses <=0

(Coefficent 0)

Up to 50 %

(Coefficent 1)

Up to 60 %

(Coefficent 2)

More than 60 % or Profit before Tax < 0

(Coefficent 4)

The sum of the coefficients of each ratio defines the Aggregate Indicator, which can vary from 0 up to 20. According to the value of the AI, the bank is assigned a rating class defined as “Statutory Position” (Table 2).

Table 2 - AI and Statutory Position

Banks rated in the first two Statutory Position (Normal and Attention) are considered in “Low Risk”; Banks in Warning and Penalty are in “Medium Risk”, while banks in Severe Imbalance and in the Expulsion class are in “High Risk”.

A) AI from 0 to 3, the bank is In Normal.

B) AI from 4 to 5, the bank is In Attention.

C) AI from 6 to 7 the bank is In Warning.

D) AI from 8 to 10, the bank is In Penalty.

E) AI from 11 to 12, the bank is In Severe Imbalance.

F) AI from 12 to 20, the bank is in Expulsion.

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2.3 Data

FITD’s database is composed of data received on a semi-annual base from the “Data Matrix of the Central Bank of Italy”.

Data used in the analysis refer to the period 2006-2008. The introduction of International Account Standards at the end of year 2005 forces us to use data starting from January 2006 in order to have fully comparable balance sheet extractions. The analysis involved all the FITD’s member banks (around 300), represent over 90% of total eligible deposits as of June 2010 (693,5 billion euro). This means that the dataset draws a complete picture of the Italian banking system.

More specifically, the dataset contains 290 banks in 2006, 296 in 2007 and 293 in 2008. We are interested in balance sheet variables composing the 4 ratios presented above that are used to compute risk based contributions. Table XXX provides related descriptive statistics:

TABLE 3 – Descriptive Statistics, 2008

DESCRIPTIVE STATS A1 B1 D1 D2

Mean 8,879 311,401 73,321 12,137

Median 5,858 192,033 64,955 18,930

Standard Deviation 11,289 399,684 63,210 341,211

Min 0,000 -35,051 -209,829 -4637,103

Max 87,056 3891,012 611,774 1640,828

Tot 293,000 293,000 293,000 293,000

TABLE 4 – Correlation Coefficients, 2006-2008

A1 B1 D1 D2

A1 100% -20% -5% 6%

B1 -20% 100% 12% -2%

D1 -5% 12% 100% 0%

D2 6% -2% 0% 100%

The four ratios are slightly correlated to each other, except for a negative correlation of about 20% between A1 and B1. Low correlations confirm that indicators are capturing different banks’ expositions, and their aggregation could offer a spread picture of banks expositions. As we can see from standard deviations, indicators have really disperse values among banks. Moreover, if we look at the following Tables, we can see that there are significant differences between the 3 considered years. In particular, there is a clear deterioration of ratios, which is also confirmed by Tables 5 and 6 summarizing banks’ distributions in the risk classes.

TABLE 5 – Distribution of banks in the four risk classes (%)

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TABLE 6 – Distribution of banks in the four risk classes

The number of banks in the last Tables has been reduced by the number of existing exceptions valid for banks in specific situations. As we explained before, according to the value taken by ratios each bank is located in a specific risk class. This is not valid for 3 categories of banks: start-up banks, extra-UE banks belonging to G10 and banks with no reimbursable funds. The first category benefits from a reduction of the coefficient assigned to indicators D1 and D2, the second one has a similar reduction applied to B1. The Third one reduce to 0 the coefficient of ratios A1, D1 and D2. As a result, the final dataset contains 780 observations: 263 banks in 2006, 265 in 2007 and 252 in 2008.

As we can see from Tables 5 and 6 and from the following histograms, A1 and B1 ratios rate the large majority of banks in the Normality risk class (more than 90% of banks). This is a direct consequences of how thresholds for the identification of risk classes are fixed. D1 and D2 on the contrary rate a smaller portion of banks as normal, and this is particularly clear in 2008, when the state of health of analyzed banks seems deteriorated. The same conclusion applies also for A1, even if it is not so marked graphically. Regarding this aspect, B1 is not suggesting

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any difference between 2006, 2007 and 2008, as demonstrated by the growth portion of banks classified as normal.

FIGURE 1 – Distribution of banks in the four risk classes

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Table 7 shows what happens at the Aggregate Indicator (AI) level.

TABLE 7 – Aggregate Indicator

The reduction of banks rated in the Normal class is due to the financial turmoil during 2008. Looking at individual ratios it’s clear that A1 and B1 lead to more optimistic conclusions compared to D1 and D2. Their different behavior may indicate their insufficient importance in the construction of the Aggregate Indicator. In the next paragraph we’re going to verify ratios’ contributions to the Aggregate Indicator variance using sensitivity indices and scatter plots.

3. Results

3.1 Applying Sensitivity Analysis to the current Italian camel model

The previous paragraph highlights differences in the behavior of the four ratios involved. Specifically, A1 and B1 seem to have more optimistic views on the financial soundness of

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Italian banks. Moreover, B1 is not perceiving any change in banking riskiness during the period 2006-2008 (Table XXX: portion of less risky banks remains almost unchanged). On the contrary, the other ratios indicate that both risk and profitability profiles are worsening during the considered years. The percentage of banks considered in the less risky class is passing from 94% to 88% according to A1, from 77% to 64% according to D1 and from 87% to 67% according to D2. These differences may originate from a real and deep difference in the four ratios considered in the sense that solvency profile of Italian banks, measured by B1, could have not been interested by the recent financial crisis. Alternatively, the construction of the Aggregate Indicator may suffer from some misspecification linked either to identification of thresholds for risk classes or to weighting and aggregating procedures.

As a starting point, we are interested in addressing the importance of single ratios for the composition of the Aggregate Index. For this reason, Sensitivity Analysis techniques are here applied in a double perspective. The graphical point of view is explored using scatter plots in order to verify the existence of graphical patterns in the relationship between our composite indicator (AI) and our sources of uncertainty (ratios and their aggregation). From a numerical point of view, first order sensitivity indices for the four ratios are computed in order to understand if employed ratios are significantly influencing the construction of the Aggregate Indicator.

Figure XXX is composed by scatter plots: values of Aggregate Indicator are represented on the vertical axis, while the horizontal one puts up values taken by single ratios. The analysis is conducted over the entire period 2006-2008. In order the plots not to be influenced by extreme values, a winsoring procedure has been applied to ratios in a way that extreme values both in the left and in the right part of the distributions have been replaced by the first available value considered as “not extreme”.

FIGURE 2 – Scatter Plots for A1, B1, D1 and D2

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B1 reveals a flat behavior: the Aggregate Indicator seems not to be influenced by B1 movements. The other figures show a clear pattern in the relationship ratio-Aggregate Indicator, giving evidence of their relative importance in the construction of the composite indicators. All of them have a monotonic behavior, except for D2, that shows non-monotonicity caused by its peculiar construction: a bank is considered riskier either when D2 is negative or when it assumes large positive values.

Numerically, we can investigate the informative power of each ratio through the first order sensitivity index, explained in the paragraph 2.1. As we mentioned before, its construction gave us the possibility to compare the four ratios in order to see if some of them is less useful than the others in the construction of the Aggregate Indicator. The following Table presents results:

TABLE 8 – Sensitivity Indices associated to A1, B1, D1 and D2 computed over the entire period 2006-2008

IMPORTANCE MEASURE

A1 0,2466

B1 0,1016

D1 0,6222

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D2 0,5862

The analysis confirm that B1 is lacking in informative power, and also A1 has a low Sensitivity index compared to the one associated to profitability indices. Moreover, the important role given to A1 by its double weight is not confirmed here looking at associated importance measure, that is even lower to the one associated to profitability ratios.

Sensitivity Analysis conducted over the actual FITD model reveals some critical issues connected in particular to the ratios A1 and B1. In the next sections we provide possible corrections: equal weighting procedure is proposed together with different methods for the identification of risk classes associated to the four ratios. In particular, two possibilities will be explored: a revision of actual weights associated to A1 and B1 and a different system that identifies risk classes through measures of distances.

3.2 Revising haircuts and risk classes

In this section thresholds associated to A1 and B1 are re-modeled following a criterion that makes the distribution of banks in the 4 risk classes similar to what happens for D1 and D2. That is we looked for thresholds able to assign 75%, 10%, 10% and 5% of banks respectively in the Normal, Attention, Warning and Violation risk class. The new version of Table 1 is presented below:

TABLE 9 – A1 and B1 with new thresholds

Ratios and Thresholds

Ratios Normal Attention Warning Violation

A1: Bad Loans / Supervisory Capital

Up to 12%

(Coefficent 0)

from 12% to 16%

(Coefficent 2)

from 16% to 22%

(Coefficent 4)

More than 22%

(Coefficent 8)

B1: Supervisory Capital, incl.Tier 3

/Supervisory Capital Requirements

More than 136%

(Coefficent 0)


(Coefficent 1)


(Coefficent 2)

Less than 111%

(Coefficent 4)

The following tables contain summary of the distribution of banks in the 4 risk classes obtained with new thresholds:

TABLE 10 - Distribution of banks in the four risk classes (%)

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TABLE 11 - Distribution of banks in the four risk classes

B1 is goes in the opposite direction respect to the other three ratio: 2008 is represented as an year of improvements in banks solvency profiles.

Regarding the Aggregate Indicator, Table 12 gives the new population of statutory positions and Table 13 provides an example referred to 2008 about movements of banks driven by changes in A1 and B1 thresholds:

TABLE 12 – Statutory Positions associated to the new thresholds

TABLE 13 – Current FITD model vs model with different thresholds for A1 and B1, 2008

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We expect changes in thresholds having impacts on sensitivity indices: the increasing number of banks in the Warning and Violation risk classes implies a rise of the importance of A1 and B1 in the composition of the Aggregate Indicator.


IMPORTANCE MEASURES

A1 0,4840

B1 0,1463

D1 0,3279

D2 0,4082

Changes on weights and thresholds imply an increase of Sensitivity Index related to A1 and B1 and also a reduction of the index associated to profitability ratios.

3.2 Revising aggregation criteria of data

The Italian DGS is currently cutting ratios’ distributions in order to find thresholds that are used as identifiers of risk classes. This approach implies the transformation of a continue variable (the balance sheet ratio) into a discrete variable (the associated coefficient), with a consequent lack of information. We are now proposing an alternative way for analyzing banks’ performances based on distances to a reference value. More specifically, we consider the median of each ratio as an indicator of good bank performance, and a distance to such reference as an indicator of bad performance. The most penalizing coefficient associated to each ratio is maintained equal to 4, as it is in the current model. In this way, risk coefficients have a linear relationship with balance sheet ratios.

Notice that ratios have been manipulated via winsoring transformation.

The interpretation at individual ratio level is the following:

A1 measures risk profile in a way that implies the relationship larger ratio-larger risk. Banks with a ratio smaller than median obtains a coefficient equal to zero, the other banks gain a coefficient that lies on the line identified by points

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and . Notice that the maximum obtainable coefficient is 4. No doubling procedure has been performed.

B1 works in the opposite direction, therefore banks with B1 bigger than median obtain a coefficient equal to zero, the other banks have a coefficient that lies on the line

identified by and .

D1 has the same behavior as A1.

D2 has a difficulty derived from the existence of negative values indicating a very risky situation. In this case, we replicate what currently happens at FITD, applying a coefficient equal to 4 to those banks having a negative D2, and a coefficient identified following the procedure valid for A1 and D1 for the other banks.

For each ratio, 50% of banks have a distance coefficient equal to 0. Values gathered by the other banks are summarized in the following histograms, where frequency of banks falling into different distance intervals are presented:

FIGURE 3 – Dimension of distances

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Obviously, D2 presents the largest frequency of banks having the maximum distance to the median. This is due to the fact that all the banks with negative ratio have been forced assuming a distance coefficient equal to 4.

The Aggregate Indicator for each bank is obtained simply summing up distances that a specific bank has to reference medians. In this way AI is a continuous variable taking values in the interval [0; 16]. The following histogram represents what happens at the Aggregate Indicator level:

FIGURE 4 – Aggregate Indicator as a sum of distances to median values

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Sensitivity indices related to the four ratios are presented below. Given the peculiar behavior of D2, an imbalance in favor of that indicator is expected.


IMPORTANCE MEASURES

A1 0,2326

B1 0,2827

D1 0,2436

D2 0,5086

FIGURE 5 – Scatter Plots for A1, B1, D1 and D2

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As we can see from tables above, the alternative method proposed allows us to rebalance sensitivity indices by identification of a more rigorous way to address the riskiness in Italian banks. The large sensitivity index associated to D2 draws a direction for future research: different methods to compute distances to a specific threshold must be investigated.

4. Some conclusions

Our work represents an application of Sensitivity Analysis’ measures of importance to Italian DGS model for the identification of risk based contributions to DGS. Measures of importance are a valid instruments that can be easily applied to DGS around EU.

The proposed analysis highlights aspects that must be better addressed in the current Italian model:

The weighting method must be evaluated on the basis of results obtained with Sensitivity Analysis’ measures of importance. In particular, the double weighting for A1 seems not justified by results obtained with Sensitivity Analysis.

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The identification of thresholds in the individual ratios based on the cut of their distributions can be refined using measures of distances to risk thresholds. As a starting point, we proposed a model that maintains the same methodology in the identification of thresholds with a recalibration of risk classes associated to A1 and B1. Sensitivity Analysis applied to this approach reveals that we have still important differences between ratios. Results related to A1 reflect the double weight associated to this ratio, but B1 has an associated sensitivity index that reveals the scarce importance of the ratio in the construction of the Aggregate Indicator. As an alternative, we propose here a method that takes into consideration distances that each ratio has with its own median. Distances are designed considering peculiarities of individual indicators. Sensitivity Analysis applied to this approach reveals that it is possible to construct a model with homogeneous measures of importance. However, the high value associated to D2 implies that a alternative distance measures must be investigated.

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5. Bibliography

1) Basel Committee on Banking Supervision (2005), Studies on the Validation of Internal Rating Systems, Working Paper No. 14.

2) Basel Committee on Banking Supervision (2009), Strengthening the Resilience of the Banking Sector, December.

3) Basel Committee on Banking Supervision (2010), Basel III: International framework for liquidity risk measurement, standards and monitoring, http://www.bis.org/list/bcbs/index.htm

4) Engelmann, B., Hayden, E., Tasche, D. (2003), Testing rating accuracy, Risk, January, pp. 82-86.

5) European Central Bank (2009), Financial Stability Review, June.

6) Joint Research Centre (June 2008), Directorate General JRC, European Commission, Risk-based contribustions in EU Deposit Guarantee Schemes: current practices

7) Moody’s (2007), Bank financial strength ratings: global methodology.

8) Porath, D. (2004), Estimating probabilities of default for German savings banks and credit cooperatives, Deutsche Bundesbank Discussion Paper, Series 2, 06/2004.

9) S&P (2001a), Banks: rating methodology, Ratings Direct.

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