1

THE INFORMATIVE CONTENTS OF BANK DEBT

CONCENTRATION.

Fréderic Lobez

Professor

University of Lille2, E.S.A

1 place Déliot BP 381

59020 Lille Cedex

Email : lobez@hp-sc.univ-lille2.fr

Tel : (33) 3 20 90 74 77

Jean-Christophe Statnik

(Corresponding Author)

Maître de Conférences

University of Lille2, E.S.A

1 place Déliot BP 381

59020 Lille Cedex

Email: jean-christophe.statnik@wanadoo.fr

Tel (33) 6 86 83 89 42

Abstract

This paper deals with the concentration of corporate bank debt. In an economy with asymmetric information, we

show that the bank debt concentration with a main bank possessing informational monopoly is a reliable signal

of the firm’s quality for the secondary banks. Precisely, the firm’s choice of the parts lent by the main bank and

the secondary banks allows use of the main bank’s market power to signal its quality to the secondary banks.

We establish a positive relationship between the amount lent by the main bank and the firm’s quality.

JEL: G21, G32

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1. Introduction

New questions dealing with firms’ debt structure have strongly improved the understanding of

this financial field: is bank debt an unambiguous concept? How to structure the firm’s pool of

banks? What are the effects of banks-SME relationships on credit cost and availability? Is the

main banks’ monopoly power really effective?

Upstream to these questions, the literature on security design tries to endogenize credit

contracts by integrating credit market imperfections, while, downstream, empirical studies

show that financial behaviours vary according to firms and countries. For example, the work

by Ongena and Smith (1999) brings to light the different choices of firms throughout European

countries concerning the number of bank relationships; firms in Northern Europe seem to

choose a small number of bank relationships, whereas firms in Southern Europe prefer to opt

for greater diversification.

In this work, we study the question of corporate debt concentration. In perfect markets, an

enterprise should be able to raise all necessary capital to finance its projects with positive

N.P.V. On the contrary, the existence of financial intermediaries is validated by the hypothesis

of an imperfect market. However, a recent research1 discussing the dichotomy between

“relationship” lending and “transaction-based” lending induces new theoretical questions.

What differences exist between "relational banks” and "transactional banks”2? Is it necessary

to concentrate bank debt or, on the contrary, to diversify it? What information is conveyed by

either the choice of a "relational" bank or debt concentration? Is there information transfer

between different types of banks?

In this paper, we will answer these questions in the framework of contract theory. We

consider the case of firms which can obtain money from two types of lenders: a loan from a

“relational” bank (main bank) or borrowing from several “transactional” banks (secondary

1 See notably Herdsman, Klapper, and Udell ( 2001 ), Herdsman and Udell ( 2002 ), Herdsman,

Miller, Petersen, Rajan, and Stein ( 2001 ).2 In this work, a bank making mainly relationship lending is named relational bank and a bank

making mainly transaction lending is named transactional bank or secondary bank.

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banks). Hence, a firm having a large share of main bank loans compared to secondary bank’s

loans has concentrated debt. By contrast an enterprise with a weak ratio has diversified debt.

Moreover, we suppose that the “relational” bank has perfect information about the firm’s

quality (Petersen and Rajan, 1994). This bank can partly benefit from the firm’s project. On

the other hand, secondary banks do not have this private information: there is asymmetrical

information between firms and secondary banks. We show then that debt concentration can

reveal the firm’s quality. It follows that a firm can use this parameter to signal its risk level to

secondary banks. Such a signal permits it either to obtain better loan conditions or to limit the

market power of the "relational" bank.

From this general result, we can derive an original conclusion. It may be optimal for a firm to

have a main bank as a partner. The optimal debt structure will comprise a loan granted by the

“relational” bank and loans from several “transactional” banks. In particular, the debt

concentration increases according to the firm’s quality.

The rest of this paper is organized as follows. Section two situates this contribution with

regard to the existing literature. Section three presents the general model of signaling dealing

with the choice between both types of bank financing. In the conclusion, we recall the main

findings and we sketch out future research work.

2. Place of this work in the literature

2.1. The reference literature

Two trends in the literature have inspired this work, one dealing more explicitly with the

firm-creditor relationships, the other directly tackling the question of the signalcharacterised by the choice of one type of bank financing.Customer relationships with banks are characterized by long-term relationships which are

more or less concentrated. Both lenders and borrowers benefit from these relationships since

they reduce the informational problem. As Sharpe first described in 1990, these relationships

are implicit contracts. Even at that time, Sharpe stressed the informational monopoly inherent

to these relations. Following this idea Rajan (1992) then Petersen and Rajan (1994) opened the

4

way for a whole stream of empirical research. They sought to locate the shared benefits of the

customer relationship and of the information transfer that it induces. Concerning the

borrowing firms, these profits can take three forms. Firstly the credit cost is lower, secondly

credit availability is greater, and finally guarantee requirement are lower. The second form

seems to be close to reality. Indeed, Cole (1998) and Petersen and Rajan (1994) on the

American market and Elsas and Krahnen (1998) as well as Harhoff and Körting (1998) on the

German market show that the borrowing firm benefits from customer relationship by means of

a weaker credit rationing. Harhoff and Körting (1998) point out a second positive effect to this

relationship, which is the lower guarantees required by the main bank.Concerning the effect of the customer relationships on interest rates the results are more

ambiguous. On the Italian market, D’auria, Foglia and Marullo Reedtz (1999) show that the

interest rates are mainly fixed by the relationship intensity and that one cannot observe use of

the monopoly power by the banks. However, this finding can be explained by diversification

of the credit supply, since it permits disciplining of the lenders. Moreover Petersen and Rajan

(1994) observe that an increase in the number of banks has a negative effect on credit cost.

Detragiache, Garella and Guiso (1997) propose a theory of the optimal number of banks for a

firm. This optimal choice results from a trade-off between the advantages of enlarged credit

availability and increased transaction costs. However their paper emphasises the strength of

the banking system3 in the determination of the optimal policy of the firm, which will not be

our concern.

The second trend in the literature with which this contribution is connected concerns the

informative contents of a bank financing decision.

Certain studies have underlined the fact that the choice of a financing mode depends on the

will of the firm not to reveal some information. Market financing imposes the necessity of

periodically revealing some private information which, therefore, becomes public. It follows

that this information loses all value for the firm concerned. On the contrary, the choice of bank

3 A firm, whose main bank has liquidity problems, will be likely to negotiate with another banks. I t

will be exposed to a “misleading” risk: these banks can suspect that the firm is risky. A solution

could be to negotiate multiple relationships.

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financing limits the disclosure of the firm’s information to the contracting bank. Thus, the

confidentiality of the information is confirmed to be a key parameter in the value of the firm’s

project, all the more so if we consider that this information, once made public, could be used

by the firm’s competitors, to its expense (Bhattacharya and Chiesa, 1995). Adopting a similar

perspective, the works of Yosha (1995) share with the former idea that bank financing

guarantees confidentiality of information. Nevertheless, Yosha goes further considering that

the choice of the financing mode itself represents information likely to inform competitors

about its perspectives and could be used by them. Finally Yosha concludes that the best firms

will avoid market financing and will opt for bank financing. This conclusion strongly depends

on the supposedly considerable production costs of information on financial markets, without

which the competitors would identify perfectly firms opting for bank financing. Yosha's paper

is certainly the closest to our work. Like Yosha, we envisage the informative contents of a

decision of bank financing. However, our framework is nevertheless different as we envisage

the information transfers between the “relational” bank and the “transactional” bank. The

distinction between these two types of banks is based on the information obtained by each

(Stein, 1997 and 2002). The "relational" bank is by definition the firm’s main bank. This bank

has, over time, gathered specific information about the firm from the relationship. This

information, of a qualitative nature, is very rich6. It takes into account elements complex and

different such as the knowledge of the manager of the firm and his managerial skill, the assets

of the firm and their value, etc. … This information updates the objective observation of the

traditional financial indicators7, ratios, scoring, etc.... Conversely, the "transactional" bank is

concerned with purely transactional lending. Such a contract is only based of quantitative and

objective information.

It follows that this "transactional" bank is in situation of asymmetric information or, more

exactly, deficit of information with regard to the "relational" bank. In this work, we envisage

explicitly that the firms can use the density of its relationship with a “relational” bank as a

signal of its quality.

6 In this respect, Stein evokes the concept of " soft information ".7 Stein uses the concept of " hard information ".

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2.2. Positioning of the research

In this work, we analyse the structure of a firm’s bank debt and consider that it can choose

between three types of financing:

- Exclusive relational bank financing with a main bank.

- Exclusive transactional bank financing with secondary banks.

- Partial relational financing with the main bank, completed by transactional financing with

secondary banks8.

• Exclusive "relational" bank financing with a main bank

This type of financing is obtained when the firm has a long-standing relationship with its

bank. This privileged relationship is will allow the bank to gradually get to know the firm’s

quality and confer on it the status of main bank. With such a status the lender is in situation of

informational monopoly. Hence, it can try to extract the surplus generated by the project9.

Such an eventuality is difficult to accept for the firm, and it is realistic to think that if the bank

can extract a fraction of the surplus, the firm will not accept the bank taking the entire surplus.

So, in this work we suppose that both main bank and firm share the project’s benefit between

8 From the point of view of the company, the bank with whom it negotiates relational financing becomes a main

bank, whereas the banks from whom this company obtains the additional transactional financing then have the

status of secondary banks. In reality, studies show that it is rare for a SMALL OR MEDIUM-SIZED FIRM to

have several main banks simultaneously even if this eventuality is not excluded. In our case, we shall envisage

the most frequent case of a firm having a single main bank and several secondary banks.

4 Thakor ( 2000 ), Rajan ( 1992 ) Boot and, Sharpe ( 1990 ), Von Thadden ( 1995 ).

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them. We base the model of this sharing on the supposition that the rate offered by the main

bank is between the break-even point for its loan rates and that proposed by an uninformed

bank. The positioning of the rate which is really offered and accepted thus only depends on

the negotiation power of the firm which we consider to be exogenous in the model.

• Exclusive "transactional" bank financing with secondary banks

The firm can also prefer not to build up a particular relationship with a bank. Indeed, the

construction of such a relationship can induce a greater cost than the gains made. Furthermore,

by the application of a simple financial logic, a bank can refuse to become the main bank of a

given firm. In this case, the firm will obtain the necessary capital in a market where all the

lenders compete. Therefore, banks cannot build up a relationship with the firm: it will be

impossible for them to charge the cost of the creation of such a relationship. The lenders, not

having particular information about the firm’s quality, will base their loan price on the average

quality of borrowers opting for such a mode of financing.

• Partial "relational" bank financing completed by "transactional" financing

To decrease the cost of relational financing, the firm may negotiate only a part of this debt

with its main bank, the other then being obtained from the secondary banks. Such a financing

structure has two advantages. Firstly, the amount negotiated with the main bank can be used

as a signal of the borrower’s quality. Hence, a given financing structure allows the secondary

banks to be informed of the risk level of the firm. This signalling activity avoids the drawback

and the cost of a single type of contract with a rate is based on the average firm’s quality,

obtained with pooling5 equilibrium. Secondly, that financing structure limits the cost inherent

in relational financing.

We will now consider the possible modalities of information transfer between the main bank

and the secondary banks considering the fact that the loan granted by the main bank is

5 Stiglitz and Weiss (1981)

8

negotiated before those with the secondary banks.

The informational problem concerns the firm’s project quality, knowledge of which is

asymmetrically allocated among the economic agents: the firm and the main bank have this

information while the secondary banks do not.

At the beginning of period, the firm having opted for relational financing is confronted with the

following alternatives. Either it borrows a substantial amount from its main bank to obtain a

price for this loan which corresponds to its quality, but in this case, the bank is in a monopoly

situation and hence can charge a high rate (monopoly income). Indeed it diversifies its debt,

but then the loan price obtained from the secondary banks is inaccurate and potentially

expensive, this misquoting stemming from the asymmetry of information existing between the

parties.

To resolve this informational problem, the firm uses the fact that the secondary banks operate

after the main bank and can thus observe the characteristics of loan provided by this bank.

Although freely observable, the rate charged by the main bank is of no value for the secondary

banks: the latter cannot deduce reliable information from its observation. Indeed, the amount

that the main bank can extract is dependent on its “bargaining power”. Such a characteristic is

private information between both lender and borrower. Therefore, the secondary banks cannot

deduce the firm’s quality from observation of the rate offered by the main bank.

Hence, if the secondary banks want deduce the quality level of the firm, the only reliable

feature is the size of the debt financed by the main bank.

3. A model of choice between "relational" bank and "transactional" banks

We consider an economy at two dates and over one period with two types of risk-neutral

agents: firms and banks.

The borrowers have no financial resources and want to implement a risky project. The project

starts at the beginning of the period with investment cost 1. It yields a return k (k>1) at the

9

end of the period with the probability x6, and a zero return with the complementary

probability, 1-x. This process of production can thus be expressed in the following way:

The profit expected k.x from the project is supposed higher than the risk-free asset : kx > r,

where r is equal to one plus the risk-free rate.

With such technology, every project has a different expected utility and is also characterized

by a different quality, represented by the variable x. Because this variable is specific to each

firm, we will merge the borrower and his quality x in the rest of this work.

At the beginning of the period, firms are confronted with a dual choice. Firstly, they have to

determine their type of financing: relational and\or transactional. Then, if they have opted for

relational financing, they must choose the percentage financed by the main bank.

To solve this problem, we shall proceed in two stages and by backward induction: for a given

financing structure, we shall firstly deal with the optimal concentration of the debt with the

main bank; then we shall cover the question of the choice of type of financing.

Before this resolution, we will clarify the notations used during the article:

- RP(x) represents the principal and the interest requested and paid by borrower x for one euro

loaned by the main bank if the project is a success.

- RS(x) represents the principal and the interest requested and paid by borrower x for one euro

loaned to the secondary banks if the project is a success

6 The variable x is distributed in [a, b] (0 < a < b < 1) with a function of density f (x).

Beginning of the period

Investment of 1

End of the period

k with probability x

0 with probability 1-x

10

- µ represents the bargaining power of the main bank with the company.

- W (x) is the final wealth expected at the end of period by entrepreneur x.

- a (x) represents the fraction of the investment of firm x financed by the main bank.

- I represents the original information cost borne by a bank necessary for the building up of

the relationships. This cost permits the bank to become a main bank.

3.1. The concentration of the debt

Firstly, we can notice that between two firms of different qualities, greater than the average12,

the less risky borrower is the one who has opted more willingly for relational financing.

Indeed, as the rate of the transactional loan is based on the average quality of the borrowers

opting for this financing, the greater the probability of the project’s success, the higher the

cost for firm, due to a prohibitive interest rate. So, if a firm indifferent to both types of

financing exists, it is such that all the firms of greater quality opt for relational financing and

the others choose transactional financing. Moreover, such an individual is not certain to obtain

relational financing. Indeed, its level of risk can be such, the main bank would not finance it. In

the following, we name x* the firm of a lower quality obtaining relational financing.

As we specified, in the case of relational financing, the firm will try to signal its quality to the

secondary banks in using the amount a financed by the main bank. So, the choice of a level of

debt concentration a must bear out two conditions:

- the contract (a , RP(x)) is optimal for a firm of quality x.

- the choice by firm x of a pair (a , RP(x)) has to reveal its quality to the secondary banks. The

latter will offer this firm a contract (1-a , RS(x(a_)).

7 Quality firms lower than the average will always take transactional financing.

11

Before determining the concentration of the debt necessary for the signal of the quality of

individual x, we are going to characterize the rates offered by each type of bank.

3.1.1. Determination of the rates offered by each type of bank

The resolution of the problem of the choice of debt concentration requires determination of the

rates offered by the main bank and the secondary bank.

Rate offered by the main bank

As we indicated, the rate offered by the main bank depends on its bargaining power with the

borrowing firm. In fact, this rate will be situated between both boundaries formed by the

break-even point of the main bank’s loan rate and that offered by the banks providing

transactional financing13.

Let us determine first of all the rate obtained by a company requesting transactional financing.

All the individuals opting for such financing are represented, with our previous notations, by

the interval [a, x*]. So, the average quality of the firms opting for this kind of credit is:

†

x = t. f (t )dta

x*

Ú

The transactional rate RT is then defined by the following relation:

†

RT =r

x

8 In our model, we suppose that the main banks are chronologically the first ones to act and that

they do not anticipate the intention of the companies to use debt concentration as the signal of their

quality. So, the maximum rate which they can charge is the “pooling” rate offered by transactional

financing.

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We will now determine the break-even rate of the main bank. Such a rate RMIN is defined by

the equation:

†

xaRMIN = I + ar

The first part of the equation represents the expected gain of the project financed and the

second one characterizes the financing cost of the project. Such a cost includes the

implementation of the relationship and the price of the bank refinancing.

In reorganizing the previous equation, us find:

†

RMIN =1x

Ia

+ rÊ

Ë Á

ˆ

¯ ˜

The rate offered by the main bank, and accepted by the company, fits the following interval:

†

1x

Ia

+ rÊ

Ë Á

ˆ

¯ ˜ ;

rx

È

Î Í

˘

˚ ˙

This interval is not empty if the following relation is confirmed:

†

r xx

≥Ia

+ r (0)

Such a relation provides a condition for the existence of relational financing. Thus, according to

the values of the parameters I, r, and of the function of density f, relational financing cannot be

possible. For example, if the cost of the setting up of the relationship by the main bank is

greater than the value IMAX14 , then no bank will propose relational financing.

Moreover, we supposed that the bank has a bargaining power represented by m.

Consequently, the rate RP offered and accepted by the firm is given by the following

expression.

†

RP = 1- m( ) 1x

Ia

+ rÈ Î Í

˘ ˚ ˙ + m

rx (1)

As the maximum rate that the main bank can propose is independent from the borrower’s

quality, then the interval size of possible rates

†

RMIN ;rx

È

Î Í

˘

˚ ˙ increases with this quality. It follows

that the monopoly income is an increasing function of the quality of firms choosing relational

financing.

9 With:

†

IMAX = Maxa

a rxx

- rÊ

Ë Á

ˆ

¯ ˜

Ê

Ë Á

ˆ

¯ ˜

13

Rate offered by the secondary banks

In the case of mixed financing, the secondary banks will price their loan in using as a source of

information the part financed by the main bank. Furthermore, these banks being in a

competitive situation, the rates that they will offer will be the same. It follows that the rate

RS(x(a)) offered by the secondary banks confirms the following relation:

†

x(a ) 1-a( )RS x(a )( ) = 1- a( )r We obtain after simplification:

†

Rs(x(a)) =r

x(a) (2)

3.1.2. Characterization of the equilibrium.

Let us consider a particular quality firm x which opts for a financing structure characterized by

both following contracts: (a , RP(x)) and ( 1-a , RS (x(a))). The expected wealth W(a,x) at the

end of the period by this firm is given by:

†

W (a, x) = x k -aRp (x) - (1- a)R s(x a( ))[ ] (3)

The entrepreneur negotiates a fraction a with the main bank and (1-a) with secondary banks.

The financial expenses that must be paid to the main bank and the secondary banks are then

respectively aRP(x) and (1-a_RS(x(a)).Where:

- RS(x(a)) is the rate charged by the secondary banks after anticipation of the quality x(a).

This anticipation is based on the observation of the fraction financed by the main bank.

- RP(x) is the rate charged by the main bank in perfect information conditions.

The objective of the firm of quality x is thus to negotiate an amount _ with its main bank in

order to reach the following three objectives:

1- To maximize its final wealth.

2- To signal its risk level to the secondary banks.

3- To allow the lenders to reach their breakeven point.

The expression of the amount a allowing a reliable signal of the firm’s quality is hence the

solution of the following optimisation problem.

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†

Maxa

x k -aRp (x) - (1- a )Rs ( x(a ))[ ] { } (3)

sc :

RP = 1- m( ) 1x

Ia

+ rÈ

Î Í

˘

˚ ˙ + m

rx

(1)

Rs (x(a )) =r

x(a ) (2)

x(a ) = x (4)

Ï

Ì

Ô Ô Ô Ô Ô

Ó

Ô Ô Ô Ô Ô

Relation (3) is the final wealth expected by the firm. Relations (1) and (2) characterize the

budget constraints of both lender types, and equality (4) allows the signal sent by the firm to

be reliable. Using constraints (1) and (2) and the objective function (3) we deduce the

following expression.

†

W(a , x) = kx - I 1- m( ) -a 1- m( )r - marxx

- 1- a( ) rxx(a )

At the optimum, the choice of a verifies:

†

∂W (a,x)

∂a = 0

Hence, we can write:

†

- 1- m( )r - mrxx

+ xr

x(a )+ 1-a( )rx ¢ x (a )

x2(a )

Ê

Ë Á

ˆ

¯ ˜ = 0

Where x’(a) is the derivative of x() with respect to the variable a.

In another way, the signal must correctly reveal the borrower’s quality, so that the following

expression is verified:

†

x(a) = x. After some calculus we obtain the following relation.

†

¢ x (a )

x (a )=

m1-a

x(a)x

-1Ê

Ë Á

ˆ

¯ ˜ (5)

Equation (5) permits the establishment of property 1.

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Property 1 : The fraction of the investment financed by the main bank is an increasing

function of the borrower’s quality.

Proof:

Since we have supposed that x and m are strictly positive numbers, that (1-a) is also strictly

positive and that x is always greater than

†

x (x > x * >

†

x ), then one deduces easily from (5)

that the derivative of x with respect to a is positive.

It is necessary to insist on the mechanism of the signal and to explain the robustness of the

equilibrium. Let us imagine a firm of quality x2 trying to be considered as a less risky firm x1.

Firm x2 thus has to duplicate the signal sent by firm x1 and thus chooses to borrow the same

amount from its main bank. This strategy will generate two effects :

- towards the secondary banks, firm x2 will indeed be viewed as having quality x1 and will

thus receive the same rate as firm x1. However it will borrow less from its secondary banks

than if it had not cheated. Here, both price and quantity effects are contrary, and the expected

profit is thus lessened.

- on the other hand, the main bank cannot be misled by this strategy because it is in a perfect

information situation. Thus, as it measures a higher risk it charges a greater rate. Firm x2

having chosen to cheat, also borrows more from this main bank. We observe that price and

quantity effects are both negative, double punishment for our firm x2.

On the contrary, firm 1, which does not cheat, obtains the same rate from the secondary banks

and the rate charged by the main bank is lower. The marginal cost of the signal is thus

effectively weaker for the good quality firms. Such a characteristic permits to ensure a

perfectly separating equilibrium.

Thus, a given firm has no advantage in copying the signal sent by a firm having a greater

quality.

Therefore, a firm can use the fraction of its debt financed by the main bank as a reliable signal

of its quality to the secondary banks.

16

The expression of the fraction financed by the main bank15 is then obtained by resolving the

differential equation ( 5 ) by the classic methods of resolution of the differential equations of

Bernouilli (Appendix 2). We hence obtain the following relation:

†

x(a ) =1x

+ K 1-a( )-mÈ

Î Í

˘

˚ ˙

-1

(6)

In this equation (6), K is a constant which we determine by using the fact that the quality of

firms having opted for relational financing belongs to the interval [x *, b]. We know (property

1) that the fraction loaned by the main bank is an increasing function of the quality of the

borrowing firm. Thus, determination of the constant K is dependent upon that of the amount

negotiated by firm x* with the main bank.

Firm x* is by definition the one of the worst quality choosing relational financing. Thus, this

borrower does not need to indicate his risk level via debt concentration. It will thus opt for the

minimum loan that its main bank proposes, this amount corresponding to a fraction a0 of the

whole investment.

So, the boundary conditions of equation ( 6 ) is the following one:

†

x* =1x

+ K 1- a0( )- mÈ

Î Í

˘

˚ ˙

-1

The constant K has as its expression:

†

K =x - x *x * x

1-a0( )m

We can thus write the complete solution of the differential equation (5) in the case of our

model:

†

x(a ) =1x

+x - x *x * x

1-a0

1-a

Ê

Ë Á

ˆ

¯ ˜

mÈ

Î Í Í

˘

˚ ˙ ˙

-1

(7)

Where:

-

†

x is the average quality of the borrowers opting for transactional financing

- x* is the quality of the borrower of weaker quality negotiating relational financing

10 This expression represents the " better signal " well, because the second-class local condition is verified.

17

- a0 is the minimum fraction of the investment, which the main bank agrees to finance and

which gives this bank the status of main or relational bank

- a is the amount negotiated between the main bank and quality x firm.

From equation (7), we can determine the fraction of investment of firm x financed by the main

bank . We thus obtain:

†

a(x) =1- 1-a0( ) x *x

x - xx - x *

È

Î Í

˘

˚ ˙

-1

m

Ê

Ë Á

ˆ

¯ ˜

(7’)

This last relation allows the following property to be obtained describing the variations in debt

concentration with the bargaining power of the main bank.

Property 2: The amount negotiated with its main bank by a firm opting for relational financing

is a decreasing function of the bargaining power of the main bank.

Proof: appendix 2.

The result given in the previous property proceeds directly from the construction of the

signalling equilibrium. When the bargaining power m increases then the rate Rp charged by the

main bank is closer to the maximum boundary

†

rx

(equation 1). Hence, for a firm trying to

cheat, the marginal cost is higher. It follows that, the intensity of the signal necessary for the

separation of firms could then decrease. At the other extreme, in a world where banks had no

bargaining power, no signal would be possible and every firm would be financed completely

via its main bank. This property has important and original consequences because the Western

economy has experienced a movement of concentration in the banking system for some years

now. This concentration has as a corollary an increase in the bargaining power of banks.

Property 2 allows to us to deduce that firms should use relational financing proportionally

less. In other words, a concentrated banking system is associated with a greater use of

transactional financing, to the detriment of relational financing.

18

3.2. Determination of the choice of the type of financing

Having determined the expression of the fraction financed by the main bank in this signalling

equilibrium, we have to determine the quality of firm x*.

We know that this firm is the borrower of the worst quality obtaining relational financing.

Hence, this enterprise is that of the lowest quality respecting the two following constraints:

- relational financing is more interesting than transactional financing (a constraint necessary for

the choice of relational financing);

- the main bank agrees to finance it (budgetary constraint of the main bank).

The determination of x* is given in the following property.

Property 3: Firm x* of worse quality obtaining a relational financing strictly prefers relational

financing to transactional financing and its quality is such that for a minimum negotiated

amount with its main bank, the minimum rate ( Rmin) of the latter is identical to the rate (

Rmax) which it would obtain via transactional financing. Quality x* is thus defined by the

following equation:

†

x *x

=1+Ira0

(8)

Proof: appendix 3.

One of the important implications of our model is that there are firms which do not obtain

relational financing: these firms are rationed in relational financing. Indeed, all the enterprises

whose quality is situated between the quality of the firm indifferent to relational and

transactional financing and level x* do not obtain the expected financing: the main bank refuses

to finance them. Of these firms, the main bank sustains a net loss equal to the informational

cost. We shall suppose that these losses are anticipated and covered by the profits that the

main bank made via the monopoly income.

From property 3, we can easily deduce the different possible structures of bank financing.

19

Corollary: According to the value of the parameters fI6, r, a0, a and b, three structures of

financing are possible:

1-if I=0, then the financing is exclusively relational;

2-if

†

x >b

1+Ira0

, then the financing is exclusively transactional;

3- if

†

I ≠ 0 and x <b

1+Ira0

, then the financing is mixed.

In the case of the mixed financing, the firms whose quality is greater than x* will opt for

relational financing and will use debt concentration as a signal of their quality to the secondary

banks. On the other hand, the firms whose quality is strictly lower than x* will opt for

transactional financing. Among these companies, there is a subset of firms rationed in

relational financing: these firms prefer this type of financing but the main bank does not agree

to finance them.

3.3. Numeric simulation

Equation (8) not being easy to resolve, we preferred to make this resolution in a particular case

which will allow us to show the various properties of our model. Moreover, mixed financing

represents the richest structure because it illustrates the interactions between relational and the

transactional financing. Thus, in this section we shall limit ourselves to its study in the case of

a uniform function of density f.

11 Function f represents the density function characterizing the distribution of the firms’ quality in interval [a,b].

Informational cost : I 0,01Least fraction financed by the main bank : a0 0,5Monopoly power : m 0,5Inferior boundary ofthe quality :a 0,9Superior boundary of the quality : b 0,99Riskless rate : r 1,02

Quality of firm x* 0,9360Quality of firm 0,9180

data

Results

x

Data and results of the simulation

20

From the data in the previous table resolution of the equation (8) gives quality x* of the firm

with the greatest risk and obtaining relational financing. By using these data and the results

obtained for x* and

†

x , figure1 represents the choices of debt concentration of the firms

obtaining relational financing, knowing that these choices must be a reliable signal of their

quality to the secondary banks. Hence, the firm of quality x* (x * = 0,936) not needing to

signal its quality will opt for a minimal debt concentration with its bank ( a=a0=0,5). The

firm of just greater quality than x* will thus need to signal its quality to opt for a

concentration slightly greater than the one chosen by firm x*.

This goes on right up to the better quality firm (b=0, 99) which will have to negotiate a

considerable concentration of its debt ( a=0,965) to signal its quality to the secondary banks.

Figure 2 represents the joint evolution of three rates being at the heart of our model:

- the rate negotiated with the main bank in the case of relational financing;

- the rate obtained when the information is perfect (this rate corresponds to that proposed by

the secondary banks in the case of mixed financing).

- the global rate obtained (the financing being transactional and relational).

Evolution of the debt concentration

0,000

0,200

0,400

0,600

0,800

1,000

1,200

0,9

36

0,9

41

0,9

46

0,9

51

0,9

56

0,9

61

0,9

66

0,9

71

0,9

76

0,9

81

0,9

86

0,9

90

Firm's quality chosing a "relational" financing

Fra

ctio

n f

inan

ced

by t

he m

ain

b

an

k

Firm if quality x*

Firm of quality b

Figure 1

21

On this figure, we notice that for the firm of a lower quality than

†

x (x mean) transactional

financing is the most advantageous because the rate obtained is lower than the one that it

would obtain in perfect information conditions (discontinuous straight line on the figure2).

Such a fact is not true for the firm whose quality is located between

†

x and x*. This firm then

has to accept a higher rate than that granted a perfect information situation. Therefore, some of

these firms would strictly prefer relational financing but they cannot obtain it: the risk level is

too great for a main bank to agree to finance them. Finally, all the enterprises whose quality is

greater than x* opt for mixed financing and a signalling strategy. This strategy induces a global

rate greater than the one offered by the secondary banks (in perfect information) but lower

than the one obtained via transactional financing.

Figure 2

Evolution of different rates

1,02

1,04

1,06

1,08

1,1

1,12

0,900

0,918

0,936

0,941

0,946

0,951

0,956

0,961

0,966

0,971

0,976

0,981

0,986

0,990

quality of firms

Rat

es (i

nter

est a

nd p

rinc

ipal

)

Rate offered by the main bank Global rate obtainRate offered by the secondary banks Série2

x mean

x*

a

Transactionalfinancing Relational financing

22

Conclusion

In this work, we analyzed the question of corporate bank debt concentration. The answer

provided is based on the firm’s possibilities to send a reliable signal in an economy where the

“relational” banks supposedly know the firms’ quality whilst the “transactional” banks have

no such knowledge. We show then that the monopoly power of the “relational” bank allows

the firms to indicate their quality to the transactional banks. The signal used is the size of the

debt financed by the main bank. We also show that an increase of the concentration in the

bank sector which induces an increase in the monopoly power of the banks should end in a

development of transactional financing to the detriment of relational financing. These

conclusions should nevertheless receive an empirical validation which seems to us to establish

a decisive challenge for research on corporate bank financing.

References

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opaque small businesses", Journal of Banking and Finance, 25, 2127-2167.

Berger, A., Miller, N., Petersen, M., Rajan, R., Stein, J., (2001), "Does function follow

organizational form? Evidence from the lending practices of large and small banks", WP,

SSRN.

Berger, A., Udell, G., (2002), "Small business credit availability and relationship lending: the

importance of bank organisational structure", Economic Journal, Vol. 112,n°77.

Bhattacharya, S., et G., Chiesa, (1995), "Financial Intermediation with Proprietary

Information", Journal of Financial Intermediation, 4, 328-357.

Boot, A., et Thakor, A., (2000), "Can relationship banking survive competition ?", The

Journal of Finance, 55,679-713.

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Banking and Finance, 22, 959-977.

23

D’Auria, C., Foglia, A., Marullo-Reedtz, P., (1999), "Bank interest rates and credit

relationships in Italy", Journal of Banking and finance, 23, 1067-1093.

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Stein, J., (2002), "Information production and capital allocation: decentralized vs. Hierarchical

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Appendices

24

Appendix 1: Resolution of the differential equation ( 5 )

We must resolve the following equation:

†

x '(a)x (a)

=m

1-ax(a )

x -1Ê Ë

ˆ ¯ (5)

To resolve this equation (type of Bernouilli), we set:

†

x a( )=1

z a( )

With this change of variable, the differential equation ( 5 ) becomes:

†

-z'= -m

1-az +

mx

11-a

(5')

The equation without a second member associated to this linear equation is:

†

¢ z =m

1-az

The solutions of this equation are:

†

z = Y 1-a( )-m

By the method of the constant variation, we find:

†

Y a( )=1x

1-a( )m

+ K

The solutions of (5 ’) are thus:

†

z a( )=1x

+ K 1-a( )-m

Thus, for equation ( 5 ) we obtain:

†

x a( )=1x

+ K 1-a( )-mÈ

Î Í

˘

˚ ˙

-1

Appendix 2: proof of property 2.

The demonstration ensues directly from the derivation of equation (8’). The latter

characterises a function of class C1 (with respect to m) on ] 0,1[.

†

a x( ) =1- 1-a0( ) x *x

x - xx - x *

È

Î Í

˘

˚ ˙

-1

m

( ¢ 8 )

Thus we have:

25

†

∂a∂m

= - 1-a0( ) 1

m2

Ê

Ë Á

ˆ

¯ ˜ ln

x *x

x - xx - x *

Ê

Ë Á

ˆ

¯ ˜

x *x

x - xx - x *

È

Î Í

˘

˚ ˙

-1

m

Now, as

†

x > x* > x then:

†

lnx *x

x - xx - x *

Ê

Ë Á

ˆ

¯ ˜ > 0

Thus we obtain :

†

∂a∂m

< 0 .

Appendix 3: proof of property 3.

To determine the quality of firm x, we will determine the quality of firm x’ indifferentto the two types of financing. Subsequently, we will characterise the quality of firmx’’ which exceeds the feasibility constraint (0) of the main bank. To conclude thisproof we shall compare these two qualities.

a )Quality x’ of the firm indifferent to the two kinds of financing.

Firm x’ is indifferent to:

- Relational financing of which a fraction a012 is obtained from the main bank.

- Exclusively transactional financing.

To determine the quality of this firm we will analyse the wealth gained from eachtype of financing

• Final wealth gained with transactional financing

The final wealth WT of firm x’ generated by the kind is given by the following relation:

†

WT = ¢ x k - RT{ } Using the expression of RT defined in the section 3.1.1, we obtain:

†

WT = ¢ x k -rx

Ï Ì Ó

¸ ˝ ˛

With :

12 Such a firm does not need to signal it; hence it will opt for the minimal amount agrred by the main

bank.

26

†

x = tf (t )dta

¢ x Ú

• Final wealth gained with relational financing

The final wealth WR of firm x’ generated by the kind is given by the following relation:

†

WR = ¢ x k -a0 RP - 1- a0( )RS{ }We know (section 3.1.1) that the expressions of RP (x’) and RS (x’) are:

†

RP ¢ x ( ) = 1- m( ) 1¢ x

Ia0

+ rÈ

Î Í

˘

˚ ˙ + m

rx

(1)

and

†

Rs ( ¢ x ) =r¢ x (2)

Integrating the relations (1) and (2) in the equation giving WR we obtain:

†

WR = k ¢ x - r - 1- m( )I + a0mr 1-¢ x

x

È

Î Í

˘

˚ ˙

Now that we have characterised the final wealth induced by each kind of financing, we can deal

with the expression of the quality of firm x’ indifferent to both.

In fact, we have to seek x’ such that WR =WT.

The resolution of this equation has the following relation:

†

¢ x x

= 1+1- m

r 1- a0m( ) I (9)

b)Quality x” of the firm exceeding the feasibility constraint of the main bank.

We have shown that for firm x the feasibility constraint of the main bank is :

†

rxx

≥I

a0

+ r (0)

Thus, quality x’’ is given by the following relation.

†

x"x

=1+I

ra0

(10)

27

In conclusion, we easily note that the solution given by (9) does not verify (0). Hence, firm x*

is not indifferent to the two kind of financing: it prefers relational financing and the expression

of its quality is given by (10).