Bank size

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Among bank size means the operation quantity of a financial institution , for the scale as the total assets , the volume of business , the number of employees or branch banks , the number of branches can be used.

General

The company size as a business code is also available for non-bank - companies in industry , trade or transport of great importance. The business economist Walther Busse von Colbe understands the size of the company as "the extent of the efficiency of a company", i.e. its capacity . The main measure of company size at non-banks is turnover , with total assets or the number of employees also playing a role. On the one hand, companies from the same branch of industry measure themselves with this within the framework of a company comparison ; on the other hand, company size also plays an important role in competition , market power and company concentration . In addition, the scope of accounting and disclosure obligations , tax breaks , subsidies and support programs depends on the size of the company and the legal form . The formation of size classes is also necessary for statistical purposes. The largest company size in the non-banking sector is found in large companies , followed by small and medium-sized companies and micro-enterprises .

These factors also apply to banking , which also recognizes the systemic importance associated with the size of the bank as an additional criterion. Because of the economic importance of the banking sector and thus of the financial system , the size of the bank plays an even more important role than the size of a non-bank company. The banking crises of the past have even led to national and international financial crises , as the financial crisis from 2007 onwards showed. The larger a bank is, the more the question of its systemic relevance arises.

Bank size in banking management

The size of the bank is discussed in banking business theory primarily under the criteria of measurement , cost and earnings position , competition and system relevance .

Measurand

A suitable measurement variable for the bank size must take into account the bank-specific division into business sphere and value sphere developed in banking management . It should be noted that the bank size cannot be determined by measuring the performance of a single production factor. Most representative measure of the sphere of operation is the number of a fiscal year incurred accounting statements . The much more important sphere of values ​​at credit institutions is represented by the deposit business . Overall, the business volume is suitable as a size indicator for bank size across all spheres .

Cost and earnings situation

An operating variable, in which the cost-cutting measures have been exhausted and the economy of scale has reached its lower limit is, as minimum optimum size ( English minimum optimal scale called). If this company size is not reached, the bank produces too expensive in relation to its competitors in order to be able to survive in the market over the long term . A company size is cost-optimal if it allows profit maximization to be achieved. The optimal company size is to be understood as the bank size at which bank production takes place at the lowest unit costs under the given economic conditions . Graphically, the unit cost curve must pass through its lowest point at the intersection of the marginal cost curve (the operating optimum ) .

According to the law of mass production , the share of fixed costs - which is particularly high in credit institutions - decreases with increasing capacity utilization per unit, resulting in economies of scale . If the increase in capacity leads to a reduction in costs , one speaks of economies of scale (static economies of scale). Degression in size occurs when the unit costs decrease with growing company sizes ( cost advantages ) until the optimum company size is reached.

The size of the business of the largest credit institutions is only partly due to internal growth (increase in customer business), but mostly due to mergers . Growing bank sizes can improve the economies of scale and profitability , because the law of mass production has a positive effect on the earnings position and rating of a bank and synergy potential can be used. The growing size of banks is accompanied by increased market power ; horizontal mergers between banks that operate at least partially in the same geographic markets also lead to an increase in market share .

competition

The competition in the banking industry constantly confronts the credit institutions - especially in view of the numerous mergers - with the problem of company size. In banking competition, the size-dependent cost advantages in the bank calculation play a decisive role for the price and fee policy , because customers can be won through low bank prices ( credit business ) or high bank prices ( deposit business ) and, if the prices of the competition are cheaper, bank customers show a tendency to churn. As customers grow, the fixed costs ( utility costs ) can be better used and additional profit-increasing margins can be achieved through improved capacity utilization .

The largest credit institutions in the German banking system are the major banks and major savings banks. Medium and small banks follow. The 2,400 smallest institutes in Germany have a market share of 20%, 1,800 of which have a business volume of less than 1 billion euros. The four largest banks have a market share of just under 17%. In Great Britain , France , Spain and the Netherlands , the three to five largest institutions have a market share of up to 80%. In Germany there is therefore more intense banking competition, while oligopolies exist in the countries mentioned . According to bank groups, the savings bank sector led in Germany in 2016 with a market share of 26.3% ( savings banks 14.4% and Landesbanken 11.9%), followed by the big banks (24.9%), and cooperative banks with 14.2% ( Credit unions 10.4%, cooperative central banks 3.8%) and regional banks / other commercial banks (11.6%).

System relevance

For bank managers, another drive for growing bank sizes is the expected systemic relevance . What systemically relevant means specifically is defined by banking supervisory law for Germany. According to this, institutions are of systemic importance if their “going concern due to their size, the intensity of their interbank relationships and their close ties with other countries could trigger significant negative consequences for other credit institutions and lead to instability of the financial system”. The size of the bank is thus explicitly mentioned as a criterion of systemic importance. The Directive 2013/36 / EU (Capital Adequacy Directive) (CRD IV) of June 26, 2013, which applies in all EU member states , provides for size as one of the systemic relevance criteria in Article 131 (3) CRD IV.

Ultimately, can commercial banks assume that their with increasing database size insolvency can be hazardous reduced because larger banks with state aid (see more bank bailout law and bailout can count) (English word too big to fail ) and small banks with only a local market presence. The goal of increasing bank size in order to make a bank bailout more likely means a moral risk arising from false incentives . This can lead to an undesirable distortion of competition in favor of systemically important banks.

Mathematical modeling

The aggregated balance sheet total or business volume of the credit institutions in a country can be used as a measure . The aggregate allotted to the individual institute is the bank size of an institute:

The following models are based on the aggregate of the money supply instead of the aggregated balance sheet total. For the mathematical modeling of the bank size, consider the amount of money that is in the possession of the k-th bank at a certain point in time from the central bank money supply and the sight deposits (the so-called money supply M1) . The share of the money supply of a bank in the total money supply is given by:

The bank size depends on how much the share grows over time. The growth is determined by two processes: on the one hand by the inflow and outflow of money and on the other hand by the increase in the total amount of money.

The inflow and outflow of money from one bank to another can be viewed as a random process. The probability of an inflow or outflow of money is proportional to its size as a first approximation. The growth of the money supply of the k th bank can therefore be called

where the rate of growth of the money supply is the k th bank. It is characterized by the success of getting more money in than out.

The total amount of money increases on the one hand through the inflow of central bank money and on the other hand through lending . When it comes to lending, banks take advantage of the fact that, despite inflows and outflows of money, a certain part of the existing deposits does not change. Banks therefore put a minimum amount of capital as a reserve for the expected cash flows and lend the rest of the existing cash deposits. The more money a bank has, the greater the volume of credit it can provide. With the provision of a loan payments are made, which lead to the fact that the deposits of the other banks increase, from which these in turn can grant additional loans ( money creation ). The total amount of money grows with it

where is the mean growth rate of the total amount of money . It is given by the level of lending by all banks and the increase in central bank money. If one calculates the time derivative of the share of a bank in the total amount of money (first equation), the result is:

Substituting the above equations for and we get:

This is what is known as a replicator equation . It determines the development of bank size over time and states that banks are in competition for the amount of money available. The growth rate (so-called fitness) determines the success of tying money to a bank. In order to keep this rate as high as possible, banks offer attractive conditions for bank customers, for example, and try to grant advantageous loans. For a time constant , a stationary solution would arise after a sufficiently long time in which one and all of the others are. In this case a monopoly bank would be formed.

The size distribution of banks

The size of a bank depends on many factors that change rapidly over time. For example, successful loan agreements, marketing campaigns, new management or changing economic conditions can result in the growth rate varying greatly over time. However, the replicator equation states that disadvantages for one bank can mean advantages for other banks. The size of a bank changes due to the rate of growth that changes over time, but the size distribution of the banks remains relatively stable. To determine this, the difference is formed from the replicator equations of the bank with the highest mean growth rate and the market share , and any bank with the index :

with . In order to take into account the temporal changes in the growth rates one can use a fluctuating size of the shape

write. In this equation, the mean difference between the growth rates of the banks in relation to the greatest growth rate over the period under consideration and a fluctuating variable that is negligible on average and is determined by random, independent events. With this, the above equation can be transformed to:

The index is omitted to simplify the notation. It should be taken into account that the difference is usually very small, i.e. with . The characteristic growth of a bank therefore depends largely on the size of the bank. For small banks with a market share , the first term in the above equation can be neglected because it is very small on the order of magnitude . The replicator equation is reduced to for small banks

.

This is a Langevin equation that describes a multiplicative growth (Gibrat's law). Assuming that it can be described by white noise, the size distribution of small banks is given by a lognormal distribution :

with the free parameters and . For large banks, however, you have to take the term into account. In order to determine the resulting change in the size distribution, new variables are introduced. Let it be:

and

By inserting you get:

This form of a Langevin equation is known from the diffusion of Brownian particles . It describes a fluctuating quantity in a potential . The distribution function is described over a longer period of time by a Maxwell-Boltzmann distribution :

It is the noise amplitude of the stochastic function and

Substituting in the original variables one obtains:

Finally, the integration provides a Pareto (power-law) distribution of the form

with . The distribution of large banks with is thus described by a power law after a long enough time . The size distribution of banks is therefore given by a log-normal distribution for small banks and a Pareto distribution for large banks, as is also found empirically. Large banks benefit significantly from their size. This so-called scale effect does not come about through successful economic activity, but because large banks can benefit more from monetary growth than small banks. This advantage can, however, be negated by mismanagement, so that even large banks can go bankrupt (see Lehman Brothers ). The growth rate of the total amount of money is, however, largely determined by the contribution of large banks, because the following applies:

If a large bank goes bankrupt, the growth rate of the money supply decreases or even becomes negative. Is , money is being destroyed on a large scale. While large banks benefit from monetary growth, a reduction in the supply of money becomes a problem for them in particular and they can be dragged into bankruptcy. Due to the networking of cash flows, the insolvency of a large bank affects all other banks as well. It can lead to a financial crisis with all its negative consequences for the economy. In order to prevent this, it may be necessary for the central bank and politicians to intervene in order to save large banks, see also: Too big to fail .

List of banks by size

For different national lists of banks by size, see the category: List (banks) . For Germany see the list of the largest banks in Germany . For the largest banks see also large bank .

literature

  • Enrique Benito: Empirical size distribution of banks. On-line.
  • Joachim Kaldasch: Evolutionary Model of the Bank Size Distribution. Economics: The Open-Access, Open-Assessment E-Journal, 8 (2014-10): 1–16., 2014, doi : 10.5018 / economics-ejournal.ja.2014-10

Individual evidence

  1. Walther Busse von Colbe, The planning of the company size , 1964, p. 13
  2. Henning Osthues-Albrecht, The Influence of Company Size on the Costs and Revenues of Credit Institutions , 1974, p. 19
  3. ^ Hans Günther, The determination of capacity at credit banks , in: Zeitschrift für Betriebswirtschaft, 1959, p. 545
  4. Eckehard Butz, The adaptation of the technical-organizational area of ​​credit institutions , 1969, p. 51
  5. ^ Lyle E. Gramley, A Study of Scale Economies in Banking , Federal Reserve Bank of Kansas City, 1965, p. 9
  6. Roland Bosch, Networks of Multinational Banks , 2000, pp. 98 ff.
  7. ^ Joe S. Bain, Barriers to new Competition , 1956, p. 53
  8. Andreas Hahn, Oligopolistic Market Dominance in European Merger Control , 2003, p. 290
  9. ^ Ernst Eisendrath, Fixed Assets and Decapitalization of German Industry , 1950, p. 31
  10. ^ Ernst Eisendrath, Fixed Assets and Decapitalization of German Industry , 1950, p. 32
  11. Michael Kutschker / Stefan Schmid, Internationales Management , 2010, p. 435
  12. ^ Robin A. Prager / Timothy H. Hannan, Do Substantial Horizontal Mergers Generate significant Price Effects? , in: Journal of Industrial Economics, vol. 46. ​​No. 4, 1998, p. 433 ff.
  13. Lothar Faißt, Concentration in the savings bank sector , in: Betriebswirtschaftliche Blätter, 1970, p. 109 ff.
  14. Deutsche Bundesbank, Banks and International Competition , October 2003, p. 4
  15. Deutsche Bundesbank, Banks and International Competition , October 2003, p. 4
  16. Statista The statistics portal, market shares of the banking groups in the total assets of the banking industry in Germany in June 2016
  17. Art. 6 para. 1 of the guideline for the implementation and quality assurance of the ongoing monitoring of credit and financial services institutions by the Deutsche Bundesbank (supervision guideline) of February 28, 2008
  18. ^ Gregor Kirchhof / Stefan Korte / Stefan Magen, Public Competition Law: New Measurement of a Legal Area , 2014, p. 227