Post on 31-Jan-2023
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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 In the United States, the Gramm-Leach-Biley Act of 1999 repealed the Glass-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.
10
(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
≥;
IBL
/IB
kk
≥
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
≥
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
<
If
L/x
kˆq
<q
;
IBL
/IB
<
L 2Ib 2
A(L
)
H 2Ib 2
A(H
)
b 1A
(L)
If it
’s n
ot
the
case
, i.e
: H k
≥;
IBH
/IB
kk
≥
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
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
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
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
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
≥
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
≥
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
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