Granularity (credit)

from Wikipedia, the free encyclopedia

Under granularity ( latin "granum" , as translated "graininess") is understood in the banking system , the more or less large scattering of the credit risk of the loan amount. The complementary term is the cluster risk (concentration risk ), an unsystematic risk that differentiates the credit risk according to borrowers , foreign currencies , rating classes , industries and regions . The granularity only measures according to size classes.


All natural persons and companies , not just credit institutions , must observe the principle of risk diversification. The general aim of risk diversification is to diversify investment or asset risks as much as possible , i.e. to distribute the total amount over various amounts, terms, forms, foreign currencies and debtors. In this way, excessive individual risks are avoided. So must investment companies and investment companies means only on the principle of risk diversification invest (so u. A. § 110 , § 214 , § 243 KAGB ).

In banking, there is granularity and the additional cluster risk for measuring risk diversification. Both are related to the statistical terms of frequency distribution and probability distribution . The individual loan of a credit institution is not considered , but the entire loan portfolio to which it belongs. Both examine the composition of this loan portfolio. If certain risks accumulate in a loan portfolio, there is a cluster or granularity risk that can threaten the very existence of a bank. If several borrowers default due to bankruptcy within a short period of time , these loans must be written off , which leads to a reduction in profit or an increase in losses and can thus endanger a bank's equity .

Within the framework of the granularity principle, banks try to spread the distribution of their loan portfolio across their borrowers. A granularity between 2 and 5% of the liable equity is considered optimal, so that a borrower can account for a maximum of 2-5% of the liable equity of a bank. If an individual borrower becomes insolvent, this granularity means that no major impact on the equity of a credit institution is to be expected.

Failure probabilities

It is beyond chance to ask why several borrowers can default at a bank within a short period of time. There are two reasons for banking operations , on the one hand the systematic (general) credit risk as a change in the value of a loan portfolio as a result of changed economic conditions, verified by fundamental economic data ( e.g. interest rate level , unemployment , sales crisis , recession ). On the other hand, a piecemeal (special or idiosyncratic) credit risk at individual borrowers entering excellent credit ratings related changes ( debtor - or issuer credit rating) to the cause. While the systematic risk depends on the correlation between the individual risks, the unsystematic risk depends on the granularity. This improves the granularity by reducing the unsystematic risk and vice versa. The systematic credit risk, on the other hand, can not be eliminated even with optimal risk diversification .

Criteria and manifestations of granularity

The granularity is related to the size structure of the loans, i.e. the ratio of small and large loans within an entire loan portfolio. There is a low level of granularity in the case of a few large loans and loans in the millions if their percentage of the total loan portfolio of a bank is high and vice versa. The German Banking Act (KWG) and the Capital Adequacy Ordinance (English abbreviation CRR) have identified both types of credit, which depend on the amount of credit, as granular risk and made them subject to an upper limit or reporting requirement. The large loan and million dollar loan regulations disclose borrowers, loan amount and number of large and million loans. Stochastic dependencies between the borrowers affected by this are achieved by bank-internal borrower aggregations.

Forms of granularity are the large loan and million dollar loan as well as on the borrower side the borrower unit and the group of connected customers . Do two or more borrowers form a unit insofar as one of them has direct or indirect control over the other, or are there dependencies between these borrowers that make it appear likely that in the event of financial difficulties one of these customers will also have other customers in financing or financial difficulties? If repayment difficulties arise, a group of connected customers must be formed within the bank (Art. 4 Para. 1 CRR). This combination of loans previously seen as individual risks results in higher loan amounts from the addition of the individual risks, which worsen the granularity.


These stochastic dependencies play an essential role in granularity. Granularity is not the sum of all individual risks, but the overall risk from the specific interaction of the individual loans with one another. This interaction between the individual risks is measured using the statistical size of the correlation . Default correlations are determined according to the degree of real economic dependence. The correlation describes a linear relationship between the default rates of two or more borrowers. If there is a positive correlation , the default rates of the borrowers deviate in the same way from their expected value; if there is a negative correlation , the default rates behave in the opposite way. If the positive correlation is sufficiently high, the granularity worsens. The greater the correlation (> 0), the less favorable the granularity and vice versa.

According to Art. 291 (1a) CRR, a “general correlation risk ” arises if there is a positive correlation between the default probability of borrowers (“ counterparties ”) and general market risk factors. The “special correlation risk” arises if, due to the nature of the transactions with a counterparty, the counterparty's probability of default correlates positively with the future replacement value from the transactions with this existing counterparty (Art. 291 (1b) CRR).

Similar or identical positive correlation values ​​lead to a cumulative accumulation of risks. The members of groups , the borrower unit ( Section 19 (2) sentences 1-5 KWG) and the group of affiliated customers (Article 4 (1) no. 39b CRR) show a typical high positive correlation . They all have in common that several borrowers are linked either legally (group) or economically (borrower unit and group of connected customers). If a borrower of these groups experiences financial difficulties, there is a high probability that other borrowers from the same group, the same borrower unit and the same group of connected customers will also experience financing or repayment difficulties. One-sided dependencies are sufficient when forming risk groups. “Dependency” in this context means that a source of financing cannot be easily replaced and that in this case the borrowers cannot overcome their financial dependency on the company in question by accepting specific disadvantages or higher costs. Economic dependency is an idiosyncratic risk that represents an additional risk to sectoral and geographic risk. An idiosyncratic risk exists when, in a bilateral relationship, the financial difficulties of a company are transferred to another company that would otherwise not be affected by this relationship. The group of connected customers is to be understood as a borrower unit or a risk unit, depending on the context.

Summary based on risk exposure

According to Art. 4 Para. 1 No. 39b CRR, a group of related customers (“risk group”) must be formed if economic difficulties of one company lead to economic difficulties for another company (so-called “ contagion effect ”). Regarding the scope of the risk group, there are, in particular, provisions in the guidelines on the implementation of the revised large exposures regime , which were published in 2009 by the CEBS (which has since been incorporated into the European Banking Authority). These regulations were adopted in Germany in BaFin circular 8/2011 and in Austria in the directive on large exposures registration of September 2011 . According to the latter, a risk group is usually presumed if someone renders deliveries or services to or receives from another company that exceed 30% of their own total output or has receivables or liabilities towards the other company that exceed 20% of their own balance sheet total Has made loss coverage commitments , liabilities , guarantees , letters of comfort or similar statements of assistance to the other company in the amount of more than 30% of its own equity .


In a first step, the risk-weighted assets that require backing are determined and in a second step they are merged into clusters according to the amount of default credit (EaD) and probability of default (PD). During the assignment (English mapping ) in the third step, a hypothetical homogeneous portfolio is compared in order to determine the granularity in the last step through adjustment (English adjustment ). This can lead to different backing requirements from the banking supervisory authority . According to Art. 284 (11) CRR, alpha estimates according to Art. 284 (9) CRR of the institute take into account the granularity of credit portfolios. A high granularity leads to capital relief and vice versa. This is intended to force the banks to ensure broader credit risk diversification.

The extent to which capital is backed for risks is measured by the granularity factor. This is an economic key figure that determines risk concentrations in individual rating classes.

Improvement of the granularity

The theoretically most favorable borderline case of “infinite granularity” (concentration-free credit portfolio) arises when the portfolio weights of the rating classes are kept constant and at the same time a fictitious, infinite number of borrowers is assumed in each rating class. The assumption of infinite granularity means that unsystematic risks have been completely eliminated through diversification. The aim of risk diversification must be to distribute the total credit volume of a portfolio over as many smaller loans as possible and to avoid mutual dependencies between individual borrowers.

Instruments for this are

Individual evidence

  1. ^ "Lump risk" , "Zeit online", article from May 24, 2006.
  2. Bernd Rudolph / Bernd Hofmann / Albert Schaber / Klaus Schäfer, Credit Risk Transfer , 2012, p. 31
  3. a b Hanspeter Gondring / Edgar Zoller / Josef Dinauer, Real Estate Investment Banking , 2013, p. 24.
  4. Hanspeter Gondring / Edgar Zoller / Josef Dinauer, Real Estate Investment Banking ], 2013, p. 27.
  5. Thomas Söhlke, Regulatory Recording of Credit Risk , 2002, p. 18 FN 3
  6. BT-Drucksache 17/1720 of May 17, 2010, draft of a law for the implementation of the amended banking directive and the amended capital adequacy directive , p. 27
  7. Implementation of the CEBS large exposure guidelines of December 11, 2009 as well as further interpretative decisions on large exposure regulations , BaFin circular 8/2011 (BA) of July 15, 2011.
  8. Austrian National Bank, Guideline on Large Loans Registration from September 2011 , p. 35.
  9. Hans Tietmeyer / Bernd Rolfes, Basel II - The new supervisory law and its consequences , 2003, p. 30.
  10. Stefanie Breidenbach, Basel III and the risk management of banks , 2011, p. 71.
  11. Henner Schierenbeck, Earnings-Oriented Bank Management , Volume 2, 2001, p. 304.