1

Universal Banking and Equity Investment:

Consequences on Bank Risk and Investment

March 2002

Laetitia LEPETIT*

Centre de Recherche en Macroeconomie Monetaire, University of Limoges, France. Department of Economics, University of Birmingham, Edgbaston, B15 2T, UK

Abstract

This paper analyses the effects of bank equity stakes in firms on bank risk and on welfare. The first purpose of this research is to determine the likelihood that financing a firm simultaneously with both equity investment and loans increases the risk of a bank’s asset portfolio under conditions of imperfect information. We show that there is a negative relationship between the risk of a universal bank’s asset portfolio and its level of equity investment as long as the latter does not exceed a critical threshold. Its second purpose is to compare bank risk and the value of the investment associated with stylized universal and specialized banking systems. We show that each system has advantages and disadvantages in terms of bank risk and investment, which are formally outlined.

Keywords: Universal banking, Specialized banking, Equity investment, Risk-taking, Investment efficiency, Social welfare.

JEL classification: G21, G24, G28.

I would like to thank Professors Andy Mullineux (University of Birmingham), Alain Sauviat (University of Limoges) and Amine Tarazi (University of Limoges) for their precious comments and support. * E-mail address: laetitia.lepetit@drec.unilim.fr, Tel: +33 (0) 555 43 56 98; Fax: +33 (0) 555 43 56 95, 4 place du Presidial, 870311 Limoges Cedex, France.

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1. Introduction

Bank ownership in commercial firms has been a common practice in Europe and Japan

for many years. In the United States, the Gramm-Leach-Biley Act of 1999 repealed the Glass-

Steagall Act of 1933, which separated commercial banking from other industries. Many

studies recognize the benefits of the affiliation of banking and commerce. The agency conflict

between shareholders and debtholders in a commercial firm is reduced when a bank holds

both the equity and debt of the firm (Prowse [1990], Calomiris [1993]). Other benefits include

economies of scope and product diversification (Benston [1994], Saunders and Walter

[1994]). The main fear, raised mainly by political interest groups, is that the affiliation of

banking and commerce may undermine the stability of the banking system (Boyd, Chang &

Smith [1998], Park [2000]). Firstly, as a creditor, a bank prefers lower risk projects, whereas

as a shareholder it prefers the riskier ones (Jensen and Meckling [1976]). The bank’s interests

are then the same as those of shareholders/managers, leading to the choice of a more risky

investment strategy. Secondly, the universal-type institutions, which combine commercial

banks with securities activity, may extend the safety net because commercial banks typically

receive much more protection than the other types of institutions. It is often argued that the

safety net provides moral hazard incentives to take more risk than would otherwise be the

case. Increased bank risk, of course, is an economic and political concern because of the

difficulty of pricing deposit insurance and possible externalities of bank failures.

To help assess the benefits and costs, I present a theoretical model analyzing how the

link between the bank and the firm through equity ownership affects the firm's investment

efficiency and the bank's risk exposure. This paper is related to John, John & Saunders [1994]

and Santos ([1997] and [1999]). We consider the objectives and incentives of a bank

regulator, a firm and a bank. The bank can take three distinct types: (i) a universal bank which

can grant loans, take equity positions and collect deposits ; (ii) a commercial bank which is

restricted to entering into a debt contract with the firm ; (iii) an investment bank which is

authorized to grant loans and take equity positions but which is not allowed to collect

deposits. The regulator has the choice to allow a universal banking system or a specialized

banking system (commercial bank and investment bank). The objective function of the

regulator is increasing with the liquidity service provided by banks as well as with the

efficiency of investment undertaken by firms, but it is decreasing with the variance (risk) of

bank asset portfolio. Such an objective function allows for potential increases in investment

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efficiency (in an environment of moral hazard) due to enhanced and more direct bank-

commerce links. However, the direct bank-commerce links (i.e. banks holding explicit equity

stakes in firms) may imply a cost in the form of an increase in banks’ risk. Optimally, the

regulator should compare the level of bank risk with the value of investment for both

universal and specialized banks.

Our paper proceeds as follows. Section 2 briefly surveys the previous literature on the

potential costs and benefits of bank equity holding in commercial firms. Section 3 describes

the model. Section 4 studies the choice of the regulator between a universal banking system

and a specialized system. Finally, section 5 summarizes and concludes.

2. The previous literature

When a bank finances a firm with a loan and an equity stake, the bank's risk exposure

may increase. Firstly, the bank has a fixed repayment for the loan fixed at the beginning of the

period whereas the expected return for the equity holding depends on the residual profit of the

firm. Secondly, with an equity position, the bank has more incentive to allow the firm to

undertake risky projects, which leads to an increase of the riskiness of both debt and equity of

the firm and hence a higher risk for the bank's investment in the firm.

However, Pozdena [1991] and Kim [1992] show that the debt-equity contract may

encourage the firm to implement a less risky investment policy than a pure debt contract. In

fact, the more the face value of the debt is high the more the firm is incited to undertake a

risky project with a high expected-return in order to repay the loan. By substituting equity to

some of this debt, the required face value of the debt needed by the firm will be lower and the

implemented policy will be less risky than in the "100% debt" case.

Park [2000], who considers only the first effect of the equity ownership, that is the

increase in the riskiness of the bank's portfolio, examines how the affiliation of banking and

commerce affects the firm's investment efficiency and the bank's risk exposure. There are

three agents in the model: managers acting in the interest of shareholders (firm), a bank that is

informed about the firm's profitability, and uninformed (nonbank) debtholders. The bank can

potentially serve as a delegated monitor for uninformed debtholders. Park shows that the

investment is likely to be maximised when the bank's equity share is greater than zero but less

than its debt share. Concerning banking stability, banks with a larger equity holding have

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more incentive to allow the firm to undertake risky projects, which results in increased

riskiness of the bank’s investment in the firm.

Boyd, Chang and Smith [1998] find a similar relationship using a model in which

there is a moral hazard problem between banks and borrowers, moral hazard between banks

and the deposit insurance system and a costly state verification problem. Their main points are

that: (i) the ability to take equity positions aligns the incentives of banks and borrowers,

potentially at the expense of the insurance system; (ii) that when funds are scarce, the ability

to take equity positions enables banks to extract additional surplus from borrowers and (iii)

banks may be able to extract maximum surplus by distorting resource allocations1. Boyd,

Chang and Smith conclude that a universal banking system that allows banks to take equity

ownership exacerbates problems of moral hazard.

John, John & Saunders [1994] and Santos ([1997] and [1999]) consider the two

features of a loan-equity financing: the increase of the riskiness of the bank’s portfolio; the

implementation of a less risky investment policy by the firm. They consider three risk neutral

agents: (i) an entrepreneur who has an investment project (a risky project in Santos, a risky or

a safe project in John, John & Saunders) but does not have the necessary funds to finance it;

(ii) a bank that is the sole source of external funding and that can finance the firm with a loan

and equity investment; (iii) a regulator who has to decide whether or not to eliminate the

universal banking with equity ownership. Santos demonstrates that that the optimal contract is

a combination of debt and equity. John, John & Saunders show that although the banks’

holding of equity suggests a riskier bank portfolio, this effect may be offset by the reduced

riskiness of the firm’s implemented investment policy. Then they find that the relationship

between bank risk and bank equity ownership is a decreasing one and the relationship

between investment efficiency and bank equity ownership is an increasing one.

This study is related to John, John & Saunders [1994] and Santos ([1997] and [1999]),

in that we consider the effect of the bank’s equity positions on the riskiness of the bank’s

portfolio and on the firm’s investment policy. Although the bank can only be a universal one

in their models, in our model three different banks statuses are compared in order to

distinguish the universal banking system and the specialized one. By specialized banking

1 A crucial aspect of Boyd, Chang and Smith’s model is the assumption that banks can share in "perks" consumption if they hold an equity position in a firm. For the authors, "perks" consumption represents broadly an ability to benefit at the expense of other claimants by taking hidden actions.

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systems, we mean the banking systems that operating in the USA before 1999 and in the

European countries before the eighties2. There was a separation between commercial banking

and commerce. Commercial banks could make loan and collect deposits, but could not take

equity positions. Conversely, investment banks3 could take equity positions, underwrite

securities and make loan, but not collect deposits. In our model we thus consider three banks:

(i) a commercial bank which can grant loans and collect deposits; (ii) an investment bank

which is allowed to take equity positions and make loans and (iii) a universal bank which can

grant loans, take equity investment and collect deposits. We assume that the regulator has to

decide to allow a universal banking system or a specialized banking system. To do that, the

regulator compares the level of bank risk and the value of the investment for both systems.

2. The model

2.1 The agents

We consider three risk-neutral agents: a borrowing firm, a bank which can be one of three

distinct types (a universal bank, an investment bank and a commercial bank) and a social planner

(the regulator).

The firm

The firm is supervised by corporate insiders (shareholders/managers). At the

beginning of the first period (t = 0), they wish to undertake an investment project which

requires two periods to be completed and an initial investment . The investment opportunity

set, available to the firm consists, of two types of projects. The first is a safe project producing

a return .

T , with t = 1, 2. The second is a risky project indexed by a parameter q which

generates a “high” return, (

T , with a probability q and a “low” return, ,

T , with a probability

(1 – q), with L N Ht t tI < I < I .

We make the assumption that only the managers of the firm observe the quality of the

risky project, q, at t = 0. However, all interested parties know that q is distributed uniformly

over the interval [0, 1]. In what follows, risk choices made by the managers (or corporate

insiders) of the firm are modeled as “private action”. That is, the managers decision of

2 Only German, Austria, Switzerland and Japan maintained the universal banking principle after the 1929 crisis. 3 We use the common terminology "investment bank" to designate the French "banque d’affaire", the English "merchant bank", the American "investment bank"…

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choosing between the risky project and the riskless project is based on their private

observation of q at t = 0.

We assume that the firm communicates the intermediate and final returns ( j j1 2I et I ,

j = L,N,H) to the bank and the regulator4. This information allows them to know the type of

the project, risky or not risky, at t = 1. Moreover, the probabilities associated with

intermediate and final returns are assumed to be identical. This implies that the realization of

the final return is independent of the realization of the intermediate return, with H H2 1I I> and

L L2 1I I< .

The managers have an initial wealth endowment of m0K , with m

0 0K I< . Thus, to

undertake the investment, the firm must obtain external funding for an amount of ( 0I - m0K ).

We assume that the bank is the only source of funding.

The bank

The bank can be a commercial one, an investment one or a universal one. Only the two

latter are allowed to take equity positions. The asset of the bank is b b b0 0 0A C K= + , with b

0C

the nominal value of the loan and b0K the equity investment ( b

0K = 0 for the commercial

bank). ( )1−β stand for the proportion of loan funding and β the proportion of equity

investment5.

Banks can be distinguished also on the basis of the information they collect about the

quality of the project chooses by the firm. Both the universal and commercial banks are

assumed to set-up checking accounts that enable them to obtain information about the

borrower after the loan is made. Fama [1985] and Nakamura [1990] show that access to the

borrower’s checking account may offer the banker the opportunity to detect liquidity

problems, to identify the major suppliers of the firm, to detect reliance on float, last minute

deposits, overdrafts…This information allows the bank to know the value of q at t = 1. The

cost of gathering this information is assumed to be equal to zero6.

4 The firm publishes the investment’s returns at the end of each period.

5 b

0

b

0

C(1 )

A−β = et

b

0

b

0

K

Aβ= .

6 No criterion of cost is retained to differentiate the three types of banks. The operational costs of banks are assumed to be normalized to zero, that is the cost of financing (deposits or loans on financial markets) or the cost of management of the information. Our objective is to compare the banking risk and the value of the investment which results from the relation

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The investment bank is not allowed to collect deposits. Thus, it cannot observe the quality

value of the risky project at t = 1. It is assumed that it is able to classify projects according to their

quality at t = 0 due to its knowledge of the productive sector. The same assumption is introduced by

Rajan [ 1991 ], Puri [ 1996 ] and Kanatas and Qi [ 1998 ]7. We assume for simplicity that the

investment bank is able to classify risky projects into two quality intervals8: those of relatively low

quality for which q ∈ [0, 2

1], and those of relatively high quality for which q ∈ [

2

1, 1].

The regulator

The regulator’s objective is to maximize the social welfare, S. The social objective S is an

increasing function of the total present value resulting from the investment policy, denoted V,

and a decreasing function of the variance of the bank’s asset, denoted Ω . V and Ω are

defined as follows:

( ) ( ) ( ) ( )b m b m0 0 0 0 0V = E I = E A + E K = E A +K (1)

( ) ( ) 22b b0 0E A E A (2) Ω = −

where E0 denotes expectations, conditional on the information set available at t = 0.

The regulator has the choice to allow a universal banking system or a specialized one. For

this purpose, it compares the level of bank risk and the present value of investment according to the

bank's type, universal or specialized. The bank risk and the present value of investment depend on

the contract, which has been established between the firm and the bank.

of financing established between the firm and the bank according to its status, without trying to discriminate the banks on the costs associate to this contract. 7 This hypothesis is based on the work of Chemmanur & Fulghieri [1994]. They show that the investment bank is an information producer in the sense of Campbell & Kracaw [1980]. The investment bank evaluates the project on the basis of private information obtained from its experience, from its knowledge of the productive sector and from the relations developed in financial markets. 8 We denote n the degree of specialization of the investment bank. We suppose that n = 2. Thus, the bank can classify the

risky projects into two quality intervals. If n = 3, the bank can classify these projects into three quality intervals: 1

]3

q [0,∈ ,

or 1 2

, ]3 3

q [∈ , or 2

,1]3

q [∈ .

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2.2 The financing contract

The contract stipulates that the bank provides the funding required for the project over

both periods. There is no intermediate repayment at t = 1. The repayment takes place at t = 2,

when the project is completed. However, a special clause in the contract allows the bank to

call for an early repayment at t = 1 if the firm is in financial distress9.

The bank will be repaid F for its loan. F is fixed at t = 0. Its determination depends on

the firm’s choice between risky and safe projects and on the potential application of the

liquidation clause.

The firm’s investment policy

The firm’s choice between the risky and the riskless projects depends on the expected value

of its assets. The managers decide to invest in the risky project only if it yields a higher present value

than the riskless project:

)N(K)L(K)q1()H(Kq m2

m2

m2 ≥−+ (3)

where: j2

m

2K (j) (1 ) max 0, I - F= − α ; j = L, N, H ; H

2F I< and ( )1−α is the proportion of

the firm’s capital held by the managers10.

Let us denote q~ the lowest (cut-off) value of q which satisfies (3) such that the risky

investment dominates the riskless one. The investment policy in (3), denoted [ q~ ], is equivalent to

investing in the risky project for all values of q such that q > q~ . It should be apparent that the cut-off

level q~ determines the riskiness of the distribution of intermediate and final returns realized at t = 1

and t = 2. The lower the value of q~ : (i) the greater the possibility that the risky investment is

undertaken and (ii) the riskier the distribution of return.11

The investment policy depends on the required face value of the debt F (see appendix A). If

the bank provides funding partly through equity claims, then the face value of debt F will be lower

and the implemented investment policy will be less risky than in the all-debt case. Although the

9 This hypothesis is common to Boyd, Chang & Smith [1998] and Park [2000]. The bank has the possibility to stop the firm’s project and to liquidate the asset of a distressed firm. This liquidation clause concerns only the project financed by the bank. For example, it’s a credit line granted by bank and stopped after one period. Therefore, the firm is unable to continue the project.

10 m

0

m b

0 0

K(1 )

K +K−α = .

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bank’s equity position suggests a riskier bank asset, this effect may be offseted by the reduced

riskiness of the firm’s implemented investment policy. In other words, the risk of the bank’s

portfolio is affected by the structure of claims it holds in borrowing firms not only through the

nature of the claims (debt vs. equity) but also through the riskiness of the investment choices made

by the firm12.

The cut-off value kq~ is observable by all agents. Thus, the bank deduces that the riskless

project is chosen with probability kq~ and the risky project with probability (1− kq~ ). This cut-off

value is decisive in the determination of the repayment F, as the cut-off value that pushes the bank to

exercise the liquidation clause.

Conditions for the liquidation clause

Funding at t = 0 is provided by the bank for two periods. The contract allows the bank

to exercise a liquidation clause when the expected value of its asset at t = 2 is lower than its

initial value:

1b b

2 0E A (j) A <

(4)

where b

2A (j) = j j

2 2min I , F + max 0 , I - Fα ; α is the proportion of the firm’s capital held by

the bank and j = H, L13.

The cut-off value of q the inequality (4) represents the legal threshold of liquidation. This

critical value depends on the information obtained by the bank at t = 1 about the quality of the risky

project. Since the universal and commercial banks observe the true value of q at t = 1, then

(4) ⇔ x x x2 2 0q A (H) + (1- q ) A (L) A< (4’)

where x = UB for the universal bank and CB for the commercial bank. The universal and

commercial banks can exercise the liquidation clause when the quality of the risky project q is

smaller than the cut-off value determined by the inequality (4’).

The investment bank cannot observe the quality of the risky project at t = 1, but it can

estimate its value at t = 014, denoted IBkq (see appendix B its computation). Then, we have:

11 For x y

q q< , the investment policy [x

q ] gives rise to a returns distribution which is than that of the investment policy

[ yq ]. The investment policy [x

q ] is thus riskier than investment policy [ yq ]. 12 This result is consistent with that of John, John & Saunders [1994] and Santos ([1997], [1999]). 13 The firm’s asset equals to b

0I at t = 2 when the riskless project is chosen. Therefore, the firm can repay the bank. In this

case, the bank can’t apply the liquidation clause.

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(4) ⇔ IB IB IB IB IBk 2 k 2 0q A (H) + (1 - q ) A (L) A< (4’’)

The investment bank can exercise the liquidation clause when the estimated quality of

the risky project IBkq is lower than the legal threshold of liquidation calculates with inequality

(4’’).

The legal threshold of liquidation depends on the face value of the debt F. This

threshold which takes different values according to F is greater or less than j2I , with j=H, L, N

(see appendix C).

However, the bank does not always decide to liquidate the project. In order to decide

whether to continue or to liquidate the project, the bank compares the expected value of its

asset if the project is liquidated at t = 1, with the expected value if it maintains its partnership

with the firm until t = 2. The bank applies the liquidation clause when the expected value of

its asset at t = 2 is lower than its expected liquidation value:

b b1 2 1E A (j) A (i) < (5)

where b

1A (i) = i b i b

1 0 1 0min I , C max 0, I -C+ α ; i = H, L and j = H, L and b = UB, CB,

IB.

The implicit cut-off value in the inequality (5) represents the effective threshold of

liquidation. The bank may decide to carry on its partnership with the firm even if the expected

value of its asset is lower than its initial value b0A . The effective liquidation threshold takes

different values depending on whether F is greater or less than j2I , with j=H, L, N (see

appendix D).

The choice of the bank whether to exercise or not the liquidation clause is decisive in

the determination of the repayment F.

The determination of the debt face value

The debt face value F is determined by the bank at t = 0. Given a competitive banking

environment, the expected profit of the bank must be equal to zero. Thus, the face value of the debt

is calculated as follow:

14 Firstly, the investment bank knows that the riskless project is chosen with probability k

q and the risky project with

probability ( )k1 q− . Secondly, it is able to classify risky projects into two quality intervals.

11

b b0 0E (A ) = A (6)

The expected value of the bank’s asset b0E (A ) depends on its decision whether to

liquidate or to continue the project at t = 1. This expected value can be split into two parts: the

expected value if the project is continued and the expected value if the project is liquidated.

Then,

(6) ⇔ b b b0 1 0 2 0.E ( A (i) ) + (1 ).E ( A (j) ) = Aλ λ− (6’)

where λ is the probability, evaluated at t = 0, that the bank exercises the liquidation clause at

t = 1 ; (1- λ ) the probability, evaluated at t = 0, that the bank doesn’t exercise the liquidation

clause at t = 1; i=H, L ; j=H, L, N (see appendix E for the calculation of λ ).

The debt face value is a function of (see appendix E): (i) the cut-off value kq~ which

determines whether the firm chooses the risky project or the riskless project ; (ii) the actual

value of q for the universal and commercials banks, and the estimated value of q for the

investment bank ; (iii) the legal and effective thresholds of liquidation.

Equation (6) and (6') may be a second, third or fourth order polynomial. Thus it is

difficult to determine the direction of change in F, in the bank risk Ω and in the present value

of investment V when the other variables decrease or increase15. In order to study the choice

of the regulator between a universal banking system and a specialized one, we carry out a

simulation to calculate Ω and V for various level of equity investment.

3. The social welfare trade-off between bank risk and the present value of investment

The following values are assigned to the exogenous variables to carry out simulations

for various levels of equity investment16 (β is maximum when F = 0, see appendix E):

0I = 60 ; m0K = 20 ; 70IH

1 = ; 10IL1 = ; b

0A = 40 ; 150IH2 = ; 8IL

2 = ; 60III 0N2

N1 === .

Firstly, we analyze the results of the simulation for the three types of banks. Secondly,

we compare the level of bank risk Ω and investment present value V for both universal and

specialized banks, and we analyze the regulator's choice.

15 No explicit solution appears. Moreover, the study of the function with implicit derivatives does not allow us to determine the direction of change in F. Thus, we conduct a series of simulations in order to interpret the results obtained in our model. The determination of the face value of debt F for the various alternatives is not presented here. A version more detailed of these calculations is available from the author. 16 There are 4 constraints to respect: (i) b m

0 0 0I =A +K ; (ii) H L

t 0 tI >I >I (t =1,2) ; (iii) H H

1 2I < I et L L

1 2I > I ; (iv) L b

1 0I <A . We

carry out several simulations with different parameter values. The results are similar for all these simulations. Therefore, in order to simplify the presentation, we present here only one simulation. Other simulations are available from the author.

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3.1 Bank risk and investment value for the universal and the commercial banks

Chart 1 presents the evolution of Ω and V for various levels of equity investment17.

The first result is the following:

Result 1:

There exists for the universal bank a decreasing relationship between asset risk UBΩ and the

level of equity investment β as long as β is lower than the threshold ∗β .

_ If 0 < β < *β , ΩUB decreases.

_ If β > *β with β < 1 and F > 0, ΩUB increases.

Banking risk

0100200300400500600700800

0 0,04 0,08 0,12 0,16 0,2 0,24 0,28 0,32 0,36

Level of equity investment β

ΩUB

Present value of the investment

78

80

82

84

86

88

90

0 0,04 0,08 0,12 0,16 0,2 0,24 0,28 0,32 0,36

Level of equity investment β

VUB

Chart 1. Bank risk and investment value for different levels of equity investment

The "U-shaped" relationship between bank risk and the level of equity investment can be

justified as following. The bank’s equity position has two effects on its risk exposure. Firstly, it

implies for the bank a riskier asset because the repayment of debt takes place before the payment of

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shareholders. Secondly, the debt face value F decreases when β increases and therefore the

investment policy implemented by the firm is less risky. As long as the level of equity investment of

the universal bank is lower than *β , the risk induced by the equity positions is more than offset by

the reduced riskiness of the firm’s implemented investment policy. If β > *β , the firm’s

implementation of a less risky investment policy when F decreases and when β increases no longer

offsets the additional risk induced by a greater level of equity investment.

Concerning the value of the investment, the simulation shows a second result:

Result 2:

The present value of the investment increases until the debt face value F is equal to the lowest

value of the firm’s return I L2 .

The higher the face value of debt, the more the firm has incentives to choose the risky

project in order to fulfill its financial commitments. Thus, a positive level of equity

investment decreases the firm's constraint. The firm may choose between the risky and the

riskless project according to the value of the risky project’s quality and the expected present

value of the investment may increase.

Summing up, if the regulator allows commercial banks to take equity positions, this

will not imply a higher banking instability as long as *β ≤ β . Moreover, the present value of

the investment is higher. The regulator should implement a regulation, which limits the

universal bank's equity position, rather than forbid the commercial bank to take equity

investment.

3.2 Bank risk and the investment’s value for the investment bank

Two cases are distinguished for the investment bank according to the quality of the

risky project.

17 These values are extracted from Table F1 in appendix F for the universal bank. The commercial bank corresponds to the particular case of the universal bank for which the le level of equity investment is equal to zero.

14

The risky project’s quality is relatively low: q ∈ [0,1

2]

The simulated values of the bank risk and the investment’s present value are presented

in Chart 218. The investment bank will not fund the firm in all cases. In our example, it

finances the firm when ≥β 0.28.

Result 3:

The bank provides the funding only if it can take a minimum βmin of equity position in the firm

when the risky project’s quality is low.

Banking risk

0

100

200

300

400

500

600

0 0,2 0,4 0,6 0,8 1

Level of equity investment β

ΩIB

Present value of the investment

61

61,5

62

62,5

63

0 0,2 0,4 0,6 0,8 1

Level of equity investment β

VIB

Chart 2. Bank risk and investment value for different levels of equity investment

The investment bank’s decision depends on its information set. We show that the cut-

off value kq~ increases when the debt face value F decreases. Then, a low value of β (i.e. a

high value of F) implies that kq~1

[0, ]2

∈ . In this case, the investment bank’s information set is

18 These values are extracted from Table F2 in appendix F.

15

D1 (1

q [0, ]2

∈ and kq~1

[ 0, ]2

∈ , see appendix B) and it ignores the firm’s choice between the

risky and the riskless projects. If the risky project’s quality is low, the investment bank

provides the financing only if the probability that the firm chooses the riskless project is

relatively high, with k1k q~2)d/q~q(P =< 19. The higher the bank’s equity position, the higher

this probability is. This is due to the increasing relationship between β and the cut-off value

kq~ (see table F2 in appendix F). Thus, the investment bank decides to finance the firm if its

equity position is relatively high, i.e. min max[ , ]β ∈ β β 2. That implies a reduction of the

probability λ that the bank exercises the liquidation clause at t = 1 when β increases.

We can see that the relationships between the bank's equity positions and ( Ω , V) are

not continuous. The discontinuity is linked to the value of the thresholds of liquidation and to

the estimated value of q (see Table F2 in appendix F). The investment bank compares these

variables to take the decision to liquidate or to pursue the project at t = 1. In the left-hand side

of the chart, these variables are such that the probability λ decreases with the bank's equity

position. In this case, there is a decreasing relationship between bank's asset risk and β , and

an increasing relationship between the present value of investment and β . In right-hand side

of the chart, the estimated value of q, IBkq , is greater than the legal threshold of liquidation.

Then, the probability that the bank exercises the liquidation clause equals to zero (in reference

to equation (4'')). In this case, there is a U-shaped relationship between the bank's asset risk

and the level of equity investment, with Ω minimum when F = L2I . The present value of

investment increases until F = L2I . Thus,

19 If the information set is D1, the bank knows thatk

1q q ,

2∈

. Schematically, we have:

1

2q

10

The probability that the firm chooses the risky project (

kq q≥ ) is the following:

( )k

k 1 k

1q

2P q q / D 1 2q1

02

−≥ = = −

−

, and therefore ( )k 1 kP q q / D 2q< = .

2 max

β is the maximum value of β reaches when F = 0.

16

Result 4:

The bank’s asset risk Ω and the present value of the investment V evolve in an opposite sense

when the risky project’s quality is relatively low. For *β β= , Ω is minimum and V is

maximum. For *>β β , Ω increases and V remains constant.

As for the universal bank, the regulator should implement a regulation that forbids

investment banks from exceeding the threshold of equity investment *β . For *β>β , the bank’s

asset risk is higher and the present value of the investment is lower.

The risky project’s quality is relatively high: q ∈ [1

2, 1]

If the risky project’s quality q ∈ [1

2, 1], the investment bank knows that the firm

chooses the risky project when kq~ is relatively low ( kq~ ∈ [0, 2

1])20. Conversely, if kq~ is

relatively high ( kq~ ∈ [2

1, 1]), the firms chooses either the risky project or the riskless projects.

We showed that the cut-off value kq~ is relatively low when the bank’s equity position is low.

Then,

Result 5:

The firm chooses the risky project if its quality is relatively high and if the bank’s equity

positions β is low. This implies a high value of the probability λ that the project is to be

liquidated at t = 1

If the risky project is chosen, the return is “high” with a probability q and “low” with

probability (1-q), with L Ht 0 tI < I < I (t = 1, 2). Thus, there exists an uncertainty concerning the

capacity of the firm to repay the bank at t = 2. In this case, the probability λ is relatively high21. In

our example, this probability is a constant equal to IBk

3.

4q = Therefore, the present value of the

investment is also a constant, equal to 81.125.

20 We have k

q q.< 21 The probability IBλ is determined by equation (E2) (see appendix E).

17

Concerning the level of bank risk, Chart 3 shows that it starts decreasing before it increases

when *β>β .

Banking risk

0

20

40

60

80

100

120

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,19

Level of equity investment β

ΩIB

Chart 3. Investment bank ownership and bank risk

Result 6:

There exists for the investment bank a decreasing relationship between asset risk IBΩ and the

level of equity investment β as long as β is lower than the threshold ∗β .

_ If 0 < β < *β , ΩIB decreases.

_ If β > *β with β < 1 and F > 0, ΩIB increases.

We find a result similar to the one previously obtained for the universal bank. As long

as the equity position of the investment bank is lower than *β , the risk induced by the holding

of equity investments is more than offset by the firm’s choice to follow a less risky

investment policy.

In order to decide whether or not to implement a functional separation of banking

activities, the regulator compares both the bank's asset risk and the present value of the

investment for: (i) universal and commercial banks; (ii) universal and investment banks.

18

3.3 Comparative study and regulator’s choice

Chart 4 presents the compared value of V and Ω 22.

Banking risk

0

100

200

300

400

500

600

700

800

0 0,2 0,4 0,6 0,8 1

Level of equity investment β

ΩUB

ΩIB

β

Present value of the investment V

0

20

40

60

80

100

0 0,08 0,16 0,22 0,3 0,38 0,5 0,64 0,78

Level of equity investment

VUB

VIB

β

The comparison of V and Ω for the universal bank and the commercial bank leads to the

two following results.

Result 6:

• The U-shaped relationship between bank risk and the equity position of the universal bank

implies that this latter presents a level of risk lower than the commercial bank as long as β ≤ *β .

22 These values are extracted from Table F1 in appendix F for the universal and commercial banks and from Table F2 for the investment bank. For the investment bank, the total value of the investment is equal to the average of the present value of the investment calculated for a low quality and the present value calculated for a strong quality. Also, the global banking risk is equal to the average of the risk associated with a project of low quality and the risk associated with a project of strong quality. The graph’s discontinuity is due to the information set. We suppose that the investment bank can

classify the risky projects into two quality intervals: 1

q [0, ]2

∈ et , 11

q [ ]2

∈ . The graph will be not discontinue if we

have choice another information’s structure (12

q [0, ]∈ ,1 23 3

q [ , ]∈ …).

19

Once the threshold *β is exceeded, the universal bank’s asset risk can become higher than the

commercial bank’s one.

• The present value of the investment associated with the universal bank is higher than the one

associated with the commercial bank.

The result concerning bank risk follows from the result 1. The present value of the

investment, the higher the face value of debt, the more the firm has incentives to choose the

risky project in order to fulfill its financial commitments. Thus, a level of equity investment

β > 0 decreases the firm’s constraint which then chooses between the risky and the riskless

project according to the value of q. This implies that V is greater for the universal bank than

for the commercial bank.

The comparison of V and Ω for the universal bank and the investment bank leads to the

following two results.

Result 7:

• The risk of the universal bank’s asset is higher than that of the investment bank, whatever the

level of equity investment considered.

• The present value of the investment associated with the universal bank is higher than the one

associated with the investment bank.

These two results depend on the information available to the bank on the quality of the

project.

The universal bank does not know the riskiness of the project chosen by the managers at the

beginning of the first period. It provides funding to the firm at t = 0. At t = 1, the universal bank

knows the risk of the project chosen by the firm. This information helps it to decide whether or not

to exercise the liquidation clause.

The investment bank cannot observe the quality of the risky project at t = 1. It relies upon

the estimated value of q to decide whether to liquidate or to pursue the project at t = 1. This

estimated value is the same at t = 0 and at t = 1. Thus, it refuses to provide the necessary funding to

the firm if it estimates at t = 0 that the probability of liquidation is equal to one. It does not want to

finance the project when it knows, on the one hand, that the quality of the risky project is low and,

on the other hand, that the probability that the project chosen by the firm is risky is high.

20

The universal bank always provides the necessary funding to the firm, whereas it is not

always the case for the investment bank. Such a behavior has consequences for the present value of

the investment, which is lower for the investment bank. Indeed, the universal bank may benefit from

a greater final asset than the investment bank when it systematically finances the project of the firm.

This will occur in the following two situations. Firstly, if the lowest return on the investment L1I is

achieved in the intermediary period (at t = 1), the universal bank may not exercise the liquidation

clause given that L b1 0I A< . It hopes that the highest return on investment H

2I will occur in the

second period, with H b2 0I A> . Secondly, if the intermediate value of the investment is H

1I and if it

has the right to exercise the liquidation clause, its final asset is greater than its initial value even if it

liquidates, given that H b1 0I A> .

Thus, the expected present value of the investment obtained in the case of the universal bank

is greater than that obtained in the case of the investment bank. However, the risk of the universal

bank’s asset is higher.

This double comparative analysis of bank risk and the present value of investment does not

allow the regulator to decide either in favor or against the implementation of a functional separation

of banking activities23. The regulator should make a trade-off between the level of bank risk and the

present value of the investment. Indeed, the universal bank presents a lower risk and a higher

economic efficiency than the commercial bank as long as its level of equity investment does not

exceed a certain threshold. However, the risk of the universal bank’s asset is greater than that of the

investment bank for the same level of equity investment, with the investment bank having a lower

present value of the investment. These results end up in favor of bank regulation which would forbid

banks from exceeding a threshold of equity investment.

4. Conclusion

Our theoretical work addressed two main objectives. The first was to determine

whether the ability to simultaneously finance a firm with equity investments and loans

23 We assume that the degree of specialization of the investment bank, n, allows it to classify the risky projects in two intervals of quality. If one deletes this the banking risk decreases as the degree of specialization of the investment bank increases and, at the same time, the present value of the investment increases. Thus, the higher the degree of specialization of the investment bank is, the more the investment bank tends to catch up the universal bank in terms of economic efficiency without presenting a more important banking instability. It is then more difficult to decide either in favor or against the implementation of a functional separation of banking activities.

21

increases the risk of bank’s assets. The second was to compare the level of bank risk and the

value of the investment associated with the two types of banking systems, universal and

specialized.

We show that there is a negative relationship between the universal bank’s asset risk

and its level of equity investment as long as the latter does not exceed a critical threshold. For

the investment bank, the conclusions are less clear-cut. The relationship between the level of

bank equity investment and bank asset risk is conditional on the quality class to which the

risky project belongs. If the quality of the risky project is relatively low, this relationship is

not continuous. If the quality of the risky project is relatively high, there exists a " U-shaped "

relationship between the investment bank’s asset risk and its level of equity investment. Thus,

these results end up favoring bank regulation which should forbid banks from exceeding a

threshold of equity investment.

The comparison of both bank risk and the value of investment associated with the

universal bank with those associated with the specialized banks does not allow the regulator

to decide either in favor or against the implementation of a functional separation of

commercial bank and investment bank activities. The universal and specialized banking

systems each display advantages and disadvantages in terms of bank risk and investment, and

there is no clear domination.

References

Allen F. and D. Gale [1995], « A welfare comparison of intermediaries and financial markets in Germany and the US », European Economic Review, 39. Black F. and M. Scholes [1973] « Bank portfolio regulation and the profitability of bank failure », Journal of Money, Credit and Banking, 10, February. Boyd J., C. Chang and Smith [1998] : « Moral hazard under commercial and universal banking » - Journal of Money, Credit and Banking – Vol. 30, n°3, August.

Campbell T. and W. Kracaw [1980], « Information production, market signaling and the theory of financial intermediation », The Journal of Finance, Vol XXXV, n°4, pp863-882. Chan Y., S. Greenbaum and A. Thakor [1992], « Is fairly priced deposit insurance possible ? », Journal of Finance, 47. Chemmanur T. and P. Fulghieri [1994], « Investment bank reputation, information production and financial intermediation », The Journal of Finance, Vol. XLIX, n°1, pp57-79.

22

Fama E. [1985], « What’s different about banks ? », Journal of Monetary Economics, 15, pp29-39. Flannery M. [1989], « Capital regulation and insured banks’ choice of individual loan default risks », Journal of Monetary Economics, 24. Gale D. and M. Hellwig [1985], « Incentive-compatible debt contracts », Review of Economic Studies, Vol. 52, pp 647-663. John K., John T.A. and A. Saunders [1994] : « Universal banking and firm risk-taking » - Journal of Banking and Finance – Vol. 18 – pp307-323. Kanatas G. and J. Qi [1998] : « Underwriting by commercial banks : incentive conflicts, scope economies and project quality » - Journal of Money, Credit and Banking – August. Kareken J. and N. Wallace [1978], « Deposit insurance and bank regulation : a partial aquilibrium exposition », Journal of Business, 51(3). Kim S. B. [1992] : « Corporate financing through a shareholder bank : lessons from Japan » - Federal Reserve Bank of San Francisco – Working Paper n°PB92-03.

Lepetit L. [2001], « Banque universelle vs banque spécialisée : Conflits d'intérêt, participations et risque bancaires », unpublished dissertation, University of Limoges. Merton R. [1977], « An analytic derivation of the cost of deposit insurance and loan guaranties : an application of modern option pricing theory », Journal of Banking and Finance, Vol. 1, June. Nakamura L. [1990], « Loan workouts and prive commercial bank information : why banks are special », Economic Research, Federal Reserve Bank of Philadelphia. Park S. [2000], « Effects of the affiliation of banking and commerce on the firm’s investment and bank’s risk », Journal of Banking and Finance, 24, pp 1629-1650. Pozdena J.R. [1991] : « Why banks need commerce powers » - Federal Reserve Bank of San Francisco - Economic Review - Summer - pp 18-31. Puri M. [1996] : « Conflicts of interest, intermediation, and the pricing of underwritten securities » - Mimeo, Graduate School of Business, Stanford University – Mars.

Rajan R. [1991] : « Conflict of interest and the separation of commercial and investment banking » - Working Paper, University of Chicago. Santos J.A.C. [1999] : « Bank capital and equity investment regulations » - Journal of Banking and Finance - Vol. 23, n°7 - pp 1095-1119.

Santos J.A.C. [1997] : « Debt and equity as optimal contracts » - Journal of Corporate Finance - 3 - pp 355-366.

23

Sharpe W. [1978], « Bank capital adequacy, deposit insurance, and security values », Journal of Financial and Quantitative Analysis, 13.

Appendix A

The inequality (3) ⇔

−≥−−+

− FI 0,maxFI ,0max q)1(FIq

0

L

2

H

2. So,

the cut-off value kq takes three different values according to the value of F:1

L0 2

c H L2 2

I - Iq =

I - I

for F < L2I ;

2

0c H

2

I - Fq =

I - F for L

2 0I < F< I ; 3cq = 0 for H

0 2I F < I≤ , with

1 2 3c c cq > q > q and ( )

2

Hc 0 2

2H2

q I - I= < 0

F I - F

d

d

.

Appendix B

The investment bank can estimate four different values of q at t = 0 according to the

quality interval and the value of kq (k = c1 , c2 , c3).

Case d1 : q ∈[0,1

2] et kq ∈[0,

1

2]

1

IB kkd k

q 0.5 1q (1 2 q ).

2 4

+= = +

Case d2 : q ∈[0, 1

2] et kq ∈ ]

1

2, 1 ] In this case, q < kq~ . The investment bank

deducts from it that the riskless project is always chosen.

Case d3 : q ∈[1

2, 1]et kq ∈ ]

1

2, 1 ]

3

IBkd k

1q = ( 1 + q ).

2

Case d4 : q ∈[1

2, 1] et kq ∈[0,

1

2]

4

IBkd

0.5 + 1 3q = = .

2 4

Appendix C

We note xkq (x = UB, CB) the cut-off value of q which satisfies (4’) for the universal

bank (UB) and the deposit bank (CB): x x

x 0 2k x x

2 2

A - A (L)q =

A (H) - A (L). It takes different values

according to the three cases determined for the investment policy:

If F L H2 0 2I < I < I≤ :

1

UBUBc

L0 2

H L2 2

A - F - (I - F)q =

(I - I )

αα

and 1

CBcq = 0

24

If L2 0I < F< I < H

2I or L H2 0 2I < I F I≤ < :

3 2

UBUB UBc c

L0 2

H L2 2

A - Iˆ ˆq = q =

(1 )F I - Iα α− + and

3 2

CBCB CBc c

L0 2

L2

A - Iˆ ˆq = q =

F - I.

We note IBkq the cut-off value which determines the legal threshold of liquidation for

the investment bank (IB). It depends on the estimation of q and not on its observed value as

the universal bank. We get:

If F L H2 0 2I < I < I≤ :

1

IBIBc

L0 2

H L2 2

A - F - (I - F)q =

(I - I )

αα

IF L2 0I < F< I < H

2I OR L H2 0 2I < I F I≤ < :

3 2

IBIB IBc c

L0 2

H L2 2

A - Iˆ ˆq = q =(1 ) F I - Iα α− +

.

Appendix D

If the intermediate value of the investment is high ( H1I ), the effective threshold of

liquidation, noted respectively H/UBk

ˆq , H/CBk

ˆq and H/IBk

ˆq , for the universal bank, the commercial

bank and the investment bank, are defined by: x x

H/x 1 2k x x

2 2

A (H)-A (L)ˆqA (H)-A (L)

= and

IB IBH/IB 1 2k IB IB

2 2

A (H)-A (L)ˆqA (H)-A (L)

= . If the intermediate value of the investment is low ( L1I ), we get:

x xL/x 1 2k x x

2 2

A (L) - A (L)ˆq =A (H) - A (L)

and IB IB

L/IB 1 2k IB IB

2 2

A (L) - A (L)ˆq =A (H) - A (L)

. As the legal threshold of

liquidation, the effective threshold of liquidation takes different values if F is lower or greater

to j2I (j = N, H, L).

Appendix E

The bank exercises the liquidation clause when the three following conditions are

verified: (i) the firm chooses the risky project: q ≥ kq~ ; (ii) the expected value of the bank’s

asset at t = 2 is lower than its initial value: q < xkq , IB

kq < IBkq ; (iii) the expected value of the

bank’s asset at t= 2 is lower than its expected liquidation value : q < i/xk

ˆq , IBkq < i/IB

kˆq . Chart

E1 represents these three conditions and the expected value of the bank’s asset in each case.

25

Cha

rt E

1 : C

ondi

tions

for

the

appl

icat

ion

of th

e liq

uida

tion

clau

se a

nd e

xpec

ted

valu

e of

the

bank

’s a

sset

.

The

ban

k c

ontin

ues

the

proj

ect

If it

’s n

ot th

e

case

, i.e

: L

/xkˆ

qq

≥;

IBL

/IB

kk

qq

≥

The

ris

ky p

roje

ct

is c

hose

n.

The

ba

nk

has

the

righ

t to

ap

ply

the

liqui

datio

n cl

ause

if

The

ban

k li

quid

ates

th

e pr

ojec

t

The

ban

k c

ontin

ues

the

proj

ect

The

ban

k li

quid

ates

th

e pr

ojec

t

If

kq~q

<

If

kq~q

≥

The

risk

less

pro

ject

is

cho

sen

If it

’s n

ot th

e ca

se, i

.e:

qx kq

≥;

IBIB

kkˆ

qq

≥

The

ban

k ca

n’t

appl

y th

e liq

uida

tion

clau

se

b 2A

(H)

If

x kˆq

<q

; IB

IBk

kˆq

q<

If th

e ba

nk

obse

rves

L 1I

, it

liqu

idat

es w

hen

L/x

kˆq

<q

;

IBL

/IB

ˆq

q<

If th

e ba

nk

obse

rves

H 1I

, it

liqu

idat

es

whe

n H

/xkˆ

q<

q;

IBH

/IB

kkˆ

qq

<

If

L/x

kˆq

<q

;

IBL

/IB

qq

<

L 2Ib 2

A(L

)

H 2Ib 2

A(H

)

b 1A

(L)

If it

’s n

ot

the

case

, i.e

: H k

qq

≥;

IBH

/IB

kk

qq

≥

If

H kq

q<

; IB

H/I

Bk

kq

q<

L 2Ib 2

A(L

)

H 2Ib 2

A(H

)

b 1A

(H)

L 2I H 2I

b 2A

(L)

The

ban

k co

ntin

ues

the

proj

ect

b 2A

(N)

26

The probability of liquidation λ depends on the bank’s information set. λ is defined by:

For the universal and deposit banks:

( ) ( ) ( ) ( ) ( ) ( )x x L / x L / x H / x H / xk k 1 k 1 k

ˆ ˆˆ ˆ ˆP q q / D .P q q / D . P I / D .P q q / D P I / D .P q q / D λ = ≥ < < + < (E1)

⇔ ( ) ( )( ) ( )x x 2 x 2 x x x x L / x x x

k k k k k k k k k

1 1 ˆˆ ˆ ˆ ˆ ˆ(q ) (q ) q q 2 q q P q q / q q q2 2

λ = − + − − − < < < (E1)

where x = UB, CB ; k = c1, c2, c3 ;

≤<

<≤−−

=<≤<xkk

x/Lk

xk

x/Lkk

kxk

kx/L

k

xkk

x/Lk

qq~qsi0

qqq~siq~q

q~q

)qqq~/qq(P

For the investment bank :

( ) ( ) ( ) ( ) ( ) ( )IB BI IB L / IB BI L / IB H / IB BI H / IB

k k k 1 k k 1 k k

ˆ ˆˆ ˆ ˆP q q / D .P q q / D . P I / D .P q q / D P I / D .P q q / D λ = ≥ < < + < (E2)

where ; k = c1, c2, c3 ; i = H, L ; P( HtI ) = IB

kDq ; P( LtI ) = (1 - IB

kDq ) ;

IB IBk kIB IB

k k IB IBk k

ˆ1 si q < qˆP ( q < q / D )ˆ0 si q q

= ≥

; IB i/IBk kIB i/IB

k kIB i/IBk k

ˆ1 si q < qˆP ( q < q / D )ˆ0 si q q

= ≥

The probability IBλ depends on the quality interval of the risky project. We have :

Different cases D1 D2 D3 D4

and IB L/IB H/IB

k k k

ˆ ˆˆ ˆq < q <q IB IB

k k(1 2q )qλ = − IB IB

k k2(1 q )qλ = − IBλ = 0 IBλ = 1

If IB IB

k kˆq <q

and IB L/IB H/IB

k k k

ˆ ˆˆ ˆq q <q≤ IB

k(1 2q )λ = − IB

k2(1 q )λ = − IBλ = 0 IB IB

k= q λ

If IB IB

k kˆq q≥ and i/IB

k

ˆq∀ IBλ = 0 IBλ = 0 IBλ = 0 IBλ = 0

i = H, L ; k = c1, c2, c3 ; D1 : q ∈ [0,2

1] et

kq ∈ [0,

2

1] ; D2 : q ∈[0,

2

1] et

kq ∈ ]

2

1, 1] ;

D3 : q ∈[2

1, 1] et

kq ∈]

2

1, 1; D4 : q ∈[

2

1, 1] et

kq ∈[0,

2

1].

27

App

endi

x F

Tab

le F

1: R

esul

ts o

f th

e si

mul

atio

ns f

or th

e un

iver

sal a

nd d

epos

it ba

nks.

β α

b 0C

F

kq~

x kq

H

/xkˆ q

L

/xkˆ q

1−

λ

Ω

V

0 0

40

67.4

47

0 0.

538

0.53

8 0.

0336

0.

855

751.

216

82.3

83

0.02

0.

038

39.2

64

.003

0

0.53

9 0.

540

0.03

37

0.85

4 54

3.52

4 82

.386

F

≥0I

3

33

3

L/x

xH

/x

cc

cc

ˆˆ

ˆˆ

ˆq

qq

q≤

≤≤

0.04

0.

074

38.4

60

.559

0

0.54

0 0.

553

0.03

38

0.85

3 47

8.78

2 82

.388

0.

05

0.09

1 38

46

.811

0.

127

0.66

4 0.

683

0.04

1 0.

787

419.

333

86.3

75

0.06

0.

107

37.6

43

.562

0.

154

0.68

1 0.

704

0.04

2 0.

779

327.

991

86.8

85

0.08

0.

138

36.8

38

.575

0.

192

0.69

6 0.

726

0.04

3 0.

775

273.

908

87.5

88

0.10

0.

167

36

34.4

79

0.22

1 0.

699

0.73

6 0.

0437

0.

779

242.

629

88.1

78

0.12

0.

193

35.2

30

.843

0.

244

0.69

7 0.

739

0.04

35

0.78

6 23

0.41

2 88

.737

0.

14

0.21

8 34

.4

27.4

93

0.26

5 0.

691

0.73

8 0.

0432

0.

796

226.

277

89.2

75

0.15

0.

231

34

25.8

95

0.27

4 0.

687

0.73

7 0.

0429

0.

801

226.

382

89.5

36

0.16

0.

242

33.6

24

.339

0.

283

0.68

3 0.

735

0.04

27

0.80

6 22

7.63

9 89

.791

0.

18

0.26

5 32

.8

21.3

29

0.30

0 0.

675

0.73

1 0.

0422

0.

817

232.

975

90.2

84

0.2

0.28

6 32

18

.430

0.

315

0.66

6 0.

725

0.04

16

0.82

7 24

1.29

9 90

.752

0.

22

0.30

5 31

.2

15.6

19

0.33

0 0.

657

0.72

0 0.

041

0.83

8 25

1.92

8 91

.194

0.

24

0.32

4 30

.4

12.8

79

0.34

3 0.

648

0.71

4 0.

0405

0.

848

264.

364

91.6

11

0.25

0.

333

30

11.5

32

0.35

0 0.

644

0.71

1 0.

0402

0.

853

271.

138

91.8

1

L 2I

< F

<

0I

22

22

L/x

xH

/x

cc

cc

ˆˆ

ˆˆ

ˆq

qq

q<

≤≤

0.26

0.

342

29.6

10

.199

0.

356

0.63

9 0.

708

0.03

99

0.85

8 27

8.22

9 92

.002

0.

2767

0.

356

28.9

32

8 0.

366

0.63

2 0.

702

0.03

95

0.86

6 29

0.68

92

.312

0.

28

0.35

8 28

.8

7.64

6 0.

366

0.63

2 0.

702

0.04

36

0.86

7 29

6.11

9 92

.306

0.

3 0.

375

28

5.51

3 0.

366

0.63

0 0.

700

0.06

67

0.86

8 32

9.14

4 92

.251

0.

32

0.39

0 27

.2

3.40

0 0.

366

0.62

8 0.

698

0.08

67

0.86

9 36

2.11

2 92

.176

0.

34

0.40

4 26

.4

1.30

3 0.

366

0.62

6 0.

104

0.10

41

0.87

1 39

4.85

4 92

.088

0.

35

0.41

1 26

0.

258

0.36

6 0.

625

0.11

2 0.

1121

0.

872

400.

102

92.0

41

F ≤

L 2I

11

11

L/x

xH

/x

cc

cc

ˆˆ

ˆˆ

ˆq

qq

q<

≤≤

0.35

25

0.41

3 25

.904

0

0.36

6 0.

624

0.69

5 0.

114

0.87

2 42

4.98

8 92

.030

β =

sha

re o

f th

e eq

uity

inve

stm

ent i

n th

e fi

nanc

ing

; α =

par

t of

the

resi

dual

pro

fit f

or th

e ba

nk ;

b 0C

= n

omin

al v

alue

of

the

debt

; F

= f

ace

valu

e of

the

debt

; k

q=

cut

-off

val

ue

of q

whi

ch d

ecid

es t

he f

irm

to

inve

st i

n th

e ri

sky

proj

ect ;

x k

q=

leg

al t

hres

hold

of

liqui

datio

n ;

i/x

kq

= e

ffec

tive

thre

shol

d of

liq

uida

tion

; (1

-λ)

= p

roba

bilit

y es

timat

ed a

t t

= 0

that

the

proj

ect i

s liq

uida

ted

at t

= 1

; V

= p

rese

nt v

alue

of

the

inve

stm

ent ;

Ω =

ban

k ri

sk.

i=H

,L ;

k =

c1,

c2,

c3

; x =

UB

, DB

.

28

Tab

le F

1: R

esul

ts o

f th

e si

mul

atio

ns f

or th

e un

iver

sal a

nd d

epos

it ba

nks.

The

ris

ky p

roje

ct’s

qua

lity

is lo

w

β α

b 0C

F

kq~

IB kdq

IB kq

H

/IB

kˆ q

L/I

Bkˆ q

1−

λ

Ω

V

0.28

0.

359

28.8

37

.052

0.

203

0.35

1 0.

469

0.51

1 0.

0287

0.

406

460.

956

61.2

88

0.3

0.37

5 28

33

.858

0.

225

0.36

2 0.

461

0.51

5 0.

0288

0.

45

415.

472

61.8

11

0.34

0.

404

26.4

29

.575

0.

252

0.37

6 0.

455

0.51

2 0.

0284

0.

504

372.

387

62.3

05

0.38

0.

432

24.8

26

.222

0.

272

0.38

6 0.

446

0.50

7 0.

0279

0.

544

348.

231

62.5

56

0.4

0.44

4 24

24

.727

0.

281

0.39

1 0.

441

0.50

3 0.

0276

0.

562

339.

281

62.6

36

0.44

0.

468

22.4

21

.973

0.

297

0.39

8 0.

433

0.49

6 0.

0270

0.

594

324.

819

62.7

38

0.48

0.

489

20.8

19

.452

0.

310

0.40

5 0.

424

0.48

9 0.

0265

0.

62

313.

103

62.7

86

21

q~0

2c≤

≤

et

22

2

L/I

BIB

IBH

/IB

ckd

cc

ˆˆ

ˆˆ

ˆq

qq

q≤

<<

0.5

0.5

20

18.2

59

0.31

6 0.

408

0.42

0 0.

486

0.02

62

0.63

2 30

7.86

1 62

.795

0.

54

0.51

9 18

.4

18

0.31

8 0.

409

0.40

6 0.

473

0.02

54

1 48

3.24

62

.197

0.

58

0.53

7 16

.8

15.5

57

0.33

0 0.

415

0.40

1 0.

468

0.02

50

1 48

1.65

8 62

.362

0.

6 0.

545

16

14.2

90

0.33

6 0.

418

0.39

8 0.

466

0.02

49

1 48

0.03

8 62

.419

0.

64

0.56

1 14

.4

11.8

81

0.34

8 0.

424

0.39

3 0.

462

0.02

45

1 47

5.20

6 62

.497

L 2I

< F

<

0I

21q~

02c

≤≤

e

t

2

IBIB

kdcˆ

qq

≥

0.68

0.

576

12.8

9.

612

0.35

9 0.

429

0.38

8 0.

457

0.02

42

1 46

8.38

5 62

.535

0.

71

0.58

7 11

.6

7.99

0.

366

0.43

3 0.

384

0.45

4 0.

0240

1

462.

783

62.5

42

0.74

0.

596

10.4

6.

637

0.36

6 0.

433

0.38

4 0.

454

0.03

01

1 47

8.13

62

.542

0.

78

0.60

9 8.

8 4.

834

0.36

6 0.

433

0.38

4 0.

454

0.03

74

1 49

8.53

5 62

.542

0.

8 0.

615

8 3.

932

0.36

6 0.

433

0.38

4 0.

454

0.03

19

1 50

8.41

6 62

.542

0.

84

0.62

6 6.

4 2.

129

0.36

6 0.

433

0.38

4 0.

454

0.03

19

1 52

7.56

4 62

.542

0.

88

0.63

7 4.

8 0.

325

0.36

6 0.

433

0.38

4 0.

454

0.03

19

1 54

5.92

6 62

.542

F ≤

L 2I

1c

10

q2

≤≤

et

1

IBIB

kdcˆ

qq

≥

0.88

72

0.63

9 4.

512

0 0.

366

0.43

3 0.

384

0.45

4 0.

0319

1

549.

15

62.5

42

The

ris

ky p

roje

ct’s

qua

lity

is st

rong

β

α b 0

C

F k

q~

IB kdq

IB kq

H/I

Bkˆ q

L

/IB

kˆ q

1-dµ

Ω

V

0 0

40

50.6

67

0.09

3 0.

75

0.75

0.

76

0.04

6 0.

25

85.3

33

81.1

25

0.02

0.

038

39.2

45

.093

0.

142

0.75

0.

778

0.78

7 0.

048

0.25

79

.734

81

.125

0.

04

0.07

4 38

.4

39.5

2 0.

185

0.75

0.

805

0.82

4 0.

050

0.25

75

.539

81

.125

0.

06

0.10

7 37

.6

33.9

46

0.22

4 0.

75

0.83

3 08

61

0.05

2 0.

25

72.4

95

81.1

25

0.08

0.

137

36.8

28

.373

0.

260

0.75

0.

861

0.89

8 0.

054

0.25

70

.398

81

.125

0.

1 0.

167

36

22.8

0.

292

0.75

0.

888

0.93

5 0.

055

0.25

69

.083

81

.125

0.

12

0.19

3 35

.2

17.2

26

0.32

2 0.

75

0.91

6 0.

971

0.05

7 0.

25

68.4

13

81.1

25

L 2I

<

F

<

H 2I

0.14

0.

218

34.4

11

.653

0.

349

0.75

0.

943

0.99

8 0.

058

0.25

68

.277

81

.125

0.

16

0.24

2 33

.6

6.56

0.

366

0.75

0.

961

1 0.

089

0.25

73

.179

81

.125

0.

18

0.26

4 32

.8

2.38

0.

366

0.75

0.

961

1 0.

163

0.25

87

.249

81

.125

F

≤

L 2I

21q~

0k

≤≤

e

t

L/I

BIB

IBH

/IB

kK

kk

ˆˆ

ˆˆ

ˆq

qq

q≤

<<

0.19

14

0.27

6 32

.344

0

0.36

6 0.

75

0.96

1 1

0.19

8 0.

25

95.4

24

81.1

25

29