Capital requirements and deposit rate ceilings as regulatory instruments in a dynamic model of imperfect competition in banking

Essay, 2011

19 Pages, Grade: 1,7



1. Introduction

2. The Model According to Repullo (2004)
2.1. Short Description of the Model
2.2. Prudent Asset Equilibrium
2.3. Gambling Asset Equilibrium
2.4. The General Description of Prudent and Gambling Equilibrium with Capital Requirements

3. Instruments of Regulation
3.1. Risk-based Capital Requirements as Instrument of Regulation
3.2. Deposit Rate Ceilings as Instrument of Regulation

4. Extensions
4.1. Discussing the Optimal Capital Requirements
4.2. Capital Requirement under the Basel III

5. Conclusion


List of Figures

Figure 1. Critical values for the prudent and gambling equilibrium with capital requirements

Figure 2. Critical values for the prudent and gambling equilibrium with risk-based capital requirements

Figure 3. Critical values for the prudent and gambling equilibrium with deposit rate ceilings

1. Introduction

An increase in financial liberalization in the banking sector leads to a growth in competition that destroys the future profits of the banks and therefore their franchise value, - a present value of the future gains. The probability of good loans decreases and involves a moral hazard problem. It leads to bigger incentives for the banks to invest in the gamble assets.

Competition has always been regarded to be an environment of extreme risk- taking and as a result, it takes a lot of measures to control the amount invested in the risky assets, and motivation of the prudent behavior of the banks. The regula- tion of deposit rate, the restrictions and barriers for entry of a new bank into the market, and the limitations of the bank activities and capital requirements are con- sidered to be the most important measures to limit the incentive for risk-taking by the banks.

It is also not clear whether competition leads to a higher stability in banking sector. On one hand, it is obvious that an increase in competition among banks drives them to lower the loan rates that diminishes the risk of borrowers and hence increases stability in banking. But on the other hand, one of the key instruments of risk-taking regulation, mainly, capital requirements can push banks to increase loan rates and therefore, creates a burden of a risky portfolio for the borrowers: the risk of insolvency of banks increases.1

The most important instruments of regulation that will be taken into account in the paper are capital regulations and deposit rate ceilings in the context of dynam- ic model of imperfect competition according to Repullo (2004). In this model, banks can invest either into the prudent asset (riskless) or gambling asset (risky). Without any regulations there are two potential types of equilibrium, which are, prudent equilibrium, where the banks invest into the riskless assets and gambling equilibrium, in which the banks invest into the risky assets. The expected payoff of the prudent asset is higher than the expected payoff of the gambling asset, but the latter gives a higher return if the gamble turns out well. The intermediation margin of the banks in prudent and gambling equilibrium is equal to the relation- ship between the transportation costs and the number of banks. This represents the so called market power of the banks.2

The purpose is also to show that for high level of intermediation margin, there would only be a prudent equilibrium on the market and for low level there would be a gambling equilibrium. If there is a middle level of intermediation margin, then both types of equilibrium are possible.

It was also unclear how the franchise value changes with an increase of capital requirements for the banks. As it was shown by Hellmann, Murdock and Stiglitz (2000), with a higher capital requirements for the banks, their franchise value may also decrease and therefore, the payments within the prudent equilibrium decrease as well. On the other hand, Repullo (2004) reveals that with increase of capital requirements for the banks, their encouragement investment into the risky assets decreases, and the deposit rate in equilibrium will decrease. This leaves the fran- chise value of the banks unchanged.

As an extension, it will be analyzed whether risk-based capital requirements are the best mechanism for regulation of the risky incentives of the banks or there should be also another mechanism of regulation to be provided by the regulator.

The paper is structured as follows: Section 2 provides a description of the mod- el and both types of equilibrium - prudent and gambling without regulation; Sec- tion 3 presents the analyses of capital requirements and deposit rate ceilings as instruments of regulations; Section 4 gives an extension of the analyses of appro- priate capital requirements regulation and Section 5 provides conclusion to the paper.

2. The Model according to Repullo (2004)

2.1. Short Description of the Model

The economy with n>2 banks should be considered. In case of the bankruptcy of one bank, another bank will enter the market, so the number of banks always stays the same and equals n. The banks are located proportionally on the circle which represents market in the model. There are also a certain number of deposi- tors that are distributed equally to the banks. Depositors live for two periods. In the first period of time, they have a certain wealth (here equals to 1) that they want to allocate and in the second period of time they want to consume. The model is constrained to the assumption that depositors are unable to allocate their wealth other than bank deposits and their aggregate demand stays the same. Travelling to the banks for depositors has a cost of μ times the distance that is required to a cer- tain bank.

In the environment of competition, banks offer different deposit rates and since the wealth of depositors equals to one, the amount of deposits that can be raised by each bank in the equilibrium equals to 1/n. Banks also need to get a certain amount of capital that has the expected rate of return ρ.

Banks can invest the capital that was obtained from depositors either in prudent or gambling asset. The riskless asset has a rate of return equal to α. The risky asset has a return of λ with a probability of (1-π) if the gamble succeeds and a return of β if the gamble fails with a probability of π. The next assumption that is to be taken into account is the return of the prudent asset higher than the expected return of the gambling asset, but it is lower than the return of the gambling asset if gamble turns out well. This means: [Abbildung in dieser Leseprobe nicht enthalten].

One of the main assumptions that should be considered in the model is that the capital of the banks is expensive and it is obliged that the expected return should be higher than the return of the riskless asset.

It is required by the regulator to hold a minimum amount of capital k per a certain volume of deposits, so that the deposits can be totally insured. The problem of deposit insurance is disregarded in this model, although there was a number of works that have studied the influence of deposit insurance on the gambling incentives of the banks. The main result of these studies was that, the abolition of the formal deposit insurance in the countries with problems of regulation in banking system was not a solution to the problem.3

The choice of investment of the bank is not detected by the regulator or deposi- tors, but in a situation of bankruptcy the bank will be closed and a new competitor arises.

2.2. Prudent Asset Equilibrium

In the model with prudent asset equilibrium each bank decides on the minimum amount of capital kj to hold and invests all the funds, raised from depositors. This is done by offering a certain deposit rate rj, and investing to a prudent asset with a riskless yield α. The distance between depositors and a certain bank is z. If there is a bank j that offers a deposit rate rj, than within the assumption of the model there are some other contestant banks j-1 and j+1. The distance between them and de- positors equals to 1/n-z. A depositor will be neutral between going to a bank j or bank j+1, if the return between deposit rate of bank j and transport costs μ is iden- tical. Therefore, formally it means:

Abbildung in dieser Leseprobe nicht enthalten

The demand of the bank that is dependent on deposit rate of the bank and its competitor is a double distance of the depositor to a certain bank and equals to:

Abbildung in dieser Leseprobe nicht enthalten

The maximization problem of the bank’s shareholders is:

Abbildung in dieser Leseprobe nicht enthalten

The first part in the equation is the contribution of the capital of the bank for a certain amount of deposits at date t before investment; therefore it is stands with a minus sign. The second part is the value of the assets of the bank, represented by the return of the investment minus liabilities. This is characterized by deposits, discounted with an expected rate of return of equity capital at date t+1. The last part in the equation is the discounted value of revenues to the date t+1 from the future profits in next periods.

After differentiation of the maximization function with respect to deposit rate of the bank j, the first order condition can be obtained, from which an equilibrium deposit rate will be derived:


1 See Hakenes H., Schnabel I. (2010) and Agoraki M. K., Delis M. D., Pasiouras F. (2008).

2 Repullo R. (2004) for evidence.

3 Hellmann, T. F., Murdock, K. C. and Stiglitz, J. E. (2000).

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Capital requirements and deposit rate ceilings as regulatory instruments in a dynamic model of imperfect competition in banking
Martin Luther University  (Finance and Banking)
Seminar in Banking and Competiton
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Olga Korniienko (Author), 2011, Capital requirements and deposit rate ceilings as regulatory instruments in a dynamic model of imperfect competition in banking, Munich, GRIN Verlag,


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