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22 

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E€ects of the aliation of banking and

commerce on the ®rm

Õ

s investment and the

bank

Õ

s risk

Sangkyun Park

*,1

Federal Reserve Bank of New York, 33 Liberty Street, New York, NY 10045, USA

Received 23 April 1998; accepted 9 August 1999

Abstract

This paper examines how the aliation of banking and commerce a€ects the ®rmÕs investment eciency and the bankÕs risk exposure. The bankÕs holding of a borrowing

®rmÕs equity reduces the agency con¯ict between the ®rm and the bank, but increases the

monitoring need of uninformed debtholders. Thus, the ®rmÕs investment eciency is

maximized when the bankÕs equity share is between zero and its debt share. The bankÕs

risk exposure can increase in two ways. With a large equity share, the bank has more incentives to allow the ®rm to undertake risky projects. The ®rm, when it has control

over the bank, may force the bank to ®nance its risky projects.Ó2000 Elsevier Science

B.V. All rights reserved.

JEL classi®cation:G21; G28

Keywords:Glass±Steagall act; Universal banking; Investment eciency; Bank risk www.elsevier.com/locate/econbase

*

Tel.: +1-212-720-6317; fax: +1-212-720-1773. E-mail address:sangkyun.park@ny.frb.org (S. Park).

1The views expressed are those of the author and do not necessarily re¯ect those of the Federal

Reserve Bank of New York or the Federal Reserve System.

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1. Introduction

Mutual ownership between banks and ®rms is a common practice in many countries such as Germany and Japan. In the United States, lawmakers are considering repealing the Glass±Steagall Act of 1933, which separates banking from other industries. Many studies recognize the bene®ts of the aliation of banking and commerce. The agency con¯ict between shareholders and debt-holders in a commercial ®rm is reduced when a bank holds both the equity and debt of the ®rm (Prowse, 1990; Calomiris, 1993). Other bene®ts include economies of scope and product diversi®cation (Benston, 1994; Saunders, 1994). The main fear, raised mainly by political interest groups, is that the aliation of banking and commerce may undermine the stability of the banking system. Banks may make improper transactions with their aliates that increase the riskiness of bank assets rather than improve economic e-ciency. Increased bank risk, of course, is an economic and political concern because of the diculty of pricing deposit insurance and possible externalities of bank failures.

To help assess the bene®ts and costs, I present a theoretical model analyzing how the tie between the bank and the ®rm through equity ownership a€ects the ®rmÕs investment eciency and the bankÕs risk exposure. There are three agents in the model: managers acting in the interest of shareholders (®rm), a bank that is informed about the ®rmÕs pro®tability, and uninformed (nonbank) debt-holders. The bank can potentially serve as a delegated monitor for uninformed debtholders, a critical role of the bank recognized in the banking literature (e.g., Chan, 1983; Diamond, 1984). In the model, the con¯ict between the ®rm and the bank results in inecient investment choices, namely, undertaking negative net present value (NPV) projects and passing up positive NPV pro-jects. This ineciency is minimized when the bank holds the equal shares of the ®rmÕs equity and debt. The optimum share of the bankÕs equity holding, however, is likely to be smaller than its debt share because the monitoring need of other debtholders increases with the bankÕs equity holding. The model suggests an additional cost of the bankÕs equity holding. The bankÕs incentives to allow riskier projects may increase the riskiness of both the debt and equity of the ®rm, thereby increasing the riskiness of the bankÕs investment in the ®rm. In the cases where the ®rm controls the bank, the bankÕs risk exposure may increase without any eciency gain.

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produce strikingly di€erent optimal equity holdings of the bank (either very small or very large in Berlin et al.). John et al. examine how bank±commerce interrelationships a€ect the risk exposure of banks under the assumption that the ®rmÕs capital structure is determined by the bankÕs choice between equity and debt. In contrast, this study assumes that the ®rmÕs capital structure is exogenously determined. While the analyses of John et al. seem appropriate for small ®rms started by entrepreneurs, my analyses are better suited for cases that banks invest in stocks of established ®rms.

The next section presents a model showing how the interaction among the ®rm, the bank, and uninformed debtholders a€ects the ®rmÕs investment choices. Section 3 considers alternative modeling assumptions that may a€ect the paperÕs results. Section 4 discusses policy implications of the paperÕs results. Lastly, the paperÕs ®ndings are summarized.

2. Agency con¯icts and investment choices

The model mimics a situation where a ®rm with long-term debt faces changed investment opportunities. Since the terms of debt are based on the return distribution of the initial project, switching to a project with a di€erent return distribution transfers wealth between shareholders and debtholders. When the ®rmÕs managers, who act in the interest of shareholders, are better informed about new investment opportunities, debtholders do not know the motive behind the ®rmÕs project choice. The ®rm may choose an opaque project either because it is expected to yield a high return or because it is of high risk, which transfers wealth from debtholders to shareholders (moral hazard). This moral hazard problem results in con¯icts between shareholders and debtholders and lowers investment eciency. The bank, which is better informed than other debtholders, can improve the situation by serving as a delegated monitor.

2.1. Structure of the economy

The economy has two periods. At the beginning of the ®rst period (t1), a ®rm ®nances a risky project (initial project) with equity and two-period debt, which are held by a bank and nonbank investors.2The ®rmÕs capital structure

2

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(ratio of debt to equity) is exogenously determined. The bankÕs choice between equity and debt thus a€ects its shares of equity and debt, but not the capital of the ®rm. In other words, a large equity holding by the bank is o€set by a small holding by other investors, and vice versa. All agents are risk neutral, and the opportunity costs of both debt and equity are the risk-free rate of return (Rf). Att1, all agents know the ®rmÕs ®nancial structure and the distribution of the

return on the initial project.

At the beginning of the second period (t2), an exogenous shock can change

the ®rmÕs investment opportunities. The shock makes the initial project un-available and presents two new investment opportunities; one is transparent and safe (transparent project) and the other is opaque and risky (opaque project). While the return distribution of the transparent project is public in-formation, that of the opaque project is private information that is available to managers of the ®rm and the bank, which has access to inside information and an expertise in processing information.

Debtholders are protected against the shock by a covenant giving them an option to redeem debt early in the event of the shock. Early redemption of debt forces the ®rm to choose the transparent project, which can be easily ®nanced at fair terms re¯ecting the return distribution of the project. The ®rm also repays or renegotiates the long-term debt when it voluntarily chooses the transparent project. On the other hand, re®nancing the opaque project is not possible because it is prohibitively costly to verify the quality of the project. Thus, the ®rm can choose the opaque project only if it is acceptable to both shareholders and debtholders.

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®rm, the bank, and nonbank debtholders when the bank does not have a controlling share of equity. The selection of the opaque project requires an agreement between the bank and nonbank debtholders if the bank has a controlling share of equity.

Att1, the return on debt per unit and per period (RD) is contracted based on

the capital ratio of the ®rm and the distribution of the return on the initial project such that the expected return on debt (E(D)) equals its opportunity cost (RfD). For simplicity, the risk-free rate of return is assumed to be 0…Rf ˆ1†.

Given thatE(D) isD, the expected per-unit return on equity (E(RK)) is greater

than or equal to 1 when the expected per-unit return on investment (x) is greater than or equal to 1.3Thus, the ®rm undertakes the initial project att1if xis greater than or equal to 1. If the shock occurs att2,E(D) and the expected return on equity (E(K)) depend on the return distributions of new projects and the project choice. The ®rm, the bank, and nonbank debtholders choose be-tween the transparent and the opaque project based on the revised estimates of

E(D) andE(K).

2.2. Expected wealth of shareholders and debtholders

The per-unit return on the initial investment can be eitherRH with

proba-bility p (high-return state) or hRH with probability 1)p (low-return state). Thus, the expected per-unit return on the investment in the ®rst period,

xˆpRH ‡ …1ÿp†hRH: …1†

To model the con¯icts between shareholders and debtholders, we need to as-sume that debt is risky initially; the ®rmÕs asset falls short of the debt payment in the low-return state and is enough to repay debt in the high-return state. This assumption implies that p and h of the initial project …h1† are strictly

greater than 0 and less than 1.

In the absence of the shock, the same project is available in the second period. If the shock occurs att2, the initial project must be replaced by either a transparent project or an opaque project, of which return distributions di€er from that of the initial project. The transparent project yields the risk-free return with certainty. The opaque project is either riskier or safer than the initial project. For simplicity, I holdp of the opaque project the same as that of the initial project and let h of the opaque project …h2† be either 0 (riskier

3When

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than the initial project) or 1 (safer than the initial project) with the equal probability. The expected return on the opaque project (x2) is drawn from a distribution f(x2), which is assumed to be independent of h. In other words, the outcome of h a€ects only the variance, not the expected return on the project.

Under the above assumptions, the expected return on the ®rmÕs equity at t1, Equityholders keep the di€erence between the asset and the liability in the high-return state and receive nothing in the low-high-return state.

The expected return on debt att1,

E…D1† ˆpRDD‡ …1ÿp†h1RH1AˆpRDD‡

…1ÿp†h1x1A p‡ …1ÿp†h1

: …3†

Debtholders receive the contracted amount in the high-return state and take the total asset in the low-return state.

Att1,RDis determined such thatE(D1) equals the opportunity cost of debt

(D). Setting Eq. (3) equal toDand solving forRD,

HoldingRD constant, changes in h,x, andA/D at t2 transfer wealth between

shareholders and debtholders.

The ®rm fails at the end of the ®rst period if the ®rst-period return turns out to be low…h1RH1†. In the high-return state (RH1), the ®rm pays…RDÿ1†Dto

debtholders and distributes the rest of the income among shareholders such that its capital structure (A/D) remains the same at t2. In the absence of the shock, therefore, the expected returns on equity and debt in the second period are the same as those in the ®rst period, and no wealth transfer occurs in the second period.

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Provided that the opaque project is chosen, the expected return on equity,

E…K2R† ˆpMinf…RHRAÿRDD†;0g ˆpMin x2

pA

ÿRDD

;0

and

E…K2S† ˆMinf…RHSAÿRDD†;0g ˆMinf…x2AÿRDD†;0g;

…5†

where subscript 2 denotes conditions where the shock has occurred and the opaque project is chosen, subscript R stands for the case where the opaque project is riskier than the initial project…hˆ0†, and subscriptSstands for the case where the opaque project is safer than the initial project…hˆ1†. Com-paring Eqs. (2) and (5), E…K2R†>E…K1†>E…K2S† when x1ˆx2. That is,

holding the expected return on the project constant, the expected return on equity is larger when the opaque project is riskier (wealth transfer from debtholders) and smaller when the opaque project is safer than the initial project (wealth transfer to debtholders). Thus, when the opaque project is safer than the initial project, shareholders want to choose the transparent project over the opaque project unless the expected return on the opaque project is high enough (higher thanx1) to compensate for the wealth transfer.

The expected return on debt when the opaque project is chosen,

E…D2R† ˆpMax x2

p A;RDD

and

E…D2S† ˆMaxfx2A;RDDg:

…6†

Comparing Eqs. (3) and (6),E…D2R†<E…D1†<E…D2S†whenx1ˆx2. Thus, the

opaque project o€ering an expected return that is the same or higher thanx1

may not be acceptable to debtholders when it is riskier than the initial project. In sum, the shock favors shareholders when the opaque project is riskier

…hˆ0†and favors debtholders when the opaque project is safer…hˆ1†than the initial project.

2.3. Project choice

The ®rm, the bank, and nonbank debtholders choose between the trans-parent and the opaque project based on the expected return on the two projects att2. While the expected return on the transparent project is the opportunity cost of capital (both equity and debt) for all agents, the expected return on the opaque project di€ers across agents because of potential wealth transfer.

The ®rm wants to choose the transparent project over the opaque one if

E…K2†<K: …7†

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The bank maximizes the expected return on its investment in the ®rm.4 Thus, the bank chooses the transparent project if the expected return on the opaque project for the bank,

E…B2† ˆaE…K2† ‡bE…D2†<aK‡bD; …8†

whereais the bankÕs share of the ®rmÕs equity, and bthe bankÕs share of the ®rmÕs debt. The return on the bankÕs investment is the average of returns on equity and debt weighted by the respective share.

Nonbank debtholders do not observe the outcomes of h2 and x2 that

de-termine the return distribution of the opaque project. When the bank holds both debt and equity…a>0†, nonbank debtholders estimate the expected re-turn on debt conditional on the selection of the opaque project based on the bankÕs incentives to serve debtholdersÕinterest and the distribution ofx2. They

force the ®rm to choose the transparent project if the estimated net return on debt conditional on the selection of the opaque project,

E…D2E† ˆ Z 1

x R

fE…D2R† ÿDgf…x2†dx‡ Z 1

x S

fE…D2S† ÿDgf…x2†dx‡u

Y‡u<0; …9†

wherexRandxS are the lowest levels ofx2acceptable to the ®rm and the bank

to choose the opaque project, respectively, whenhˆ0 and whenhˆ1,f(x2) is

the probability density function ofx2, anduis a random variable with mean 0.

The estimated net return on debt increases (decreases) when the ®rm and the bank are more likely to choose the opaque project whenE(D2) is greater (less)

thanD. The random variableudeviates from 0 if nonbank debtholders are not accurately informed aboutf(x2).

2.4. Investment eciency

Given that all agents are risk neutral, the socially optimal solution is to maximize the expected output. Provided that the shock occurs, the expected output gain (output net of the opportunity cost of capital) in the second period

4

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E…X† ˆA 1 2…1

2

6

4 ÿZ† Z 1

x R

…x2ÿ1†f…x2†dx‡

1 2…1ÿZ†

Z 1

x S

…x2ÿ1†f…x2†dx 3

7 5

1

2…1ÿZ†A…XR‡XS†;

xRˆgR…a;b;C†;

xS ˆgS…a;b;C†;

Zˆh…a;b;C†; …10†

where Z is the probability that nonbank debtholders force the ®rm to choose the transparent project by demanding early redemption, and C is a binary variable indicating whether the bank has a controlling share of equity.

Clearly, the expected output is maximized whenxRˆxSˆ1 andZˆ0. The con¯ict between the ®rm and the bank results in two types of ineciency by causingxto deviate from 1: type 1 ineciency, which is to undertake negative net present value (NPV) projects…x<1†, and type 2 ineciency, which is to pass up positive NPV projects…x>1†. The possibility of each type of ine-ciency depends on the bankÕs shares of equity and debt (aandb) and whether the bank has a controlling equity share. If nonbank debtholders believe that the bank is not reliable as a delegated monitor …Z >0†and demand debt re-demption, the ®rmÕs asset yields the risk-free return, which is 1 per unit. In this economy, therefore, the optimal regulation on the ®rm±bank aliation is the one that minimizes type 1 and type 2 ineciencies, while preserving the bankÕs reliability as a delegated monitor.

To maximize Eq. (10) with respect toaandb, we need explicit expressions of

gR,gS, andh, which involve probability density functions. Since the solutions

involve many complicated terms even when a relatively simple probability density function is assumed, it is dicult to interpret them. Furthermore, using speci®c probability density functions can result in loss of generality. Thus, I derive key results from general properties ofgR, gS, and h without explicitly

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Proposition 1.Ataˆb6ˆ0,the expected eciency loss arising from the con¯ict between the ®rm and the bank(deviations of xRand xSfrom their maxima)is zero when the bank has a controlling share of equity, and is minimized when the bank has a noncontrolling share of equity.

A formal proof is provided in Appendix A. When a equals b, the bank equally weights the interests of shareholders and debtholders. Thus, no inef-®ciency results from agency con¯icts if the investment decision is solely up to the bank (controlling share). Without a controlling share, the bank cannot block the ®rmÕs attempt to serve the interest of shareholders, which results in an eciency loss. The eciency loss is still minimized at aˆb because no ineciency arises when the return distribution of the opaque project favors shareholders, i.e., when the ®rmÕs decision is not binding.

Lemma 1. An increase in a holdingb constant reduces both type 1 and type 2 ineciency arising from the con¯ict between the ®rm and the bank whena<b,

and a decrease inaholdingbconstant reduces both type 1 and type 2 ineciency whena>b.

It is intuitive that the eciency loss decreases as the bankÕs interest becomes more balanced (see Appendix A for a formal proof).

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Proposition 2. Holding b constant, the probability that nonbank debtholders demand redemption(Z)increases witha.

Appendix A provides a formal proof. With largera, the bank has a stronger incentive to choose the opaque project when it is riskier. Thus, largerainduces nonbank debtholders to estimate larger wealth transfer to shareholders and hence a lower expected return on debt, which increases the probability that they demand the redemption of debt. Early redemption would force the ®rm to pass up all positive NPV projects. This result leads to the following proposi-tion.

Proposition 3.The total eciency loss resulting from the con¯ict between the ®rm and the bank and that between the ®rm and nonbank debtholders is minimized at

a2 ‰0;bŠ.

Proof.By Proposition 1 and Lemma 1, bothXR and XS in Eq. (10)

continu-ously decrease as a deviates from b in either direction. Thus, for every a2 ‰b;1Š, there existsa2 ‰0;bŠat whichXR‡XS is no smaller. By Proposition

2, Z at a2 …b;1Š is greater than that at a2 ‰0;b†. Therefore, the combined eciency loss is minimized ata2 ‰0;bŠ:

It is rather intuitive that 06a6bbecause the reliability of the bank as a delegated monitor decreases witha. The exact value ofa depends on the re-sponsiveness of X and Z to a. In the case that even a small a relative to b induces nonbank debtholders to estimate a low expected return on debt and to demand debt redemption (large magnitude ofoZ=oaeven at a low level ofa),a may be close to 0. If nonbank debtholders believe that the bank is fairly reliable as a delegated monitor until a reaches b (small magnitude of oZ=oa for all

a2 …0;bŠ),a can beb. A more plausible case is that largera makes nonbank debtholders increasingly more skeptical about the bankÕs reliability as a dele-gated monitor…o2Z=oa2 >0†. In this case,ais likely to be substantially greater

than 0 but less thanb.

2.5. Riskiness of the ®rm's assets

The project choice shown above suggests that the bankÕs equity ownership also in¯uences the riskiness of the ®rmÕs assets.

Proposition 4.Holdingband Z constant, the expected variance of the ®rm's asset increases witha.

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opaque project is chosen when it is riskier (smaller xR), while decreasing the probability when it is safer (largerxS). In expected value terms, therefore, the variance of the ®rmÕs asset increases witha.

When the ®rmÕs asset becomes riskier, of course, both the equity and debt of the ®rm are riskier. With largea, therefore, the bankÕs investment in the ®rm is riskier not only because equity is riskier than debt but also because the bank may allow the ®rm to pursue riskier investments. Lacking accurate informa-tion, nonbank debtholders may not be able to completely block the ®rmÕs at-tempt to undertake riskier projects. Assuming that the social cost of bank failures is larger than the private cost because of the possibility of bank failure contagion and the diculty of pricing deposit insurance, the socially optimal level of a is lower than the one at which the ®rmÕs investment eciency is maximized.

2.6. Firm's ownership of the bank's equity

When the ®rm owns a noncontrolling share of the bankÕs equity, the ®rmÕs ownership may not signi®cantly a€ect the bankÕs lending decisions. The ®rmÕs ownership of a controlling share of the bank, however, would align the interest of the bank with that of the ®rm. In this case, the monitoring burden is entirely on nonbank debtholders who have only limited information about the distri-bution of the project return. Nonbank debtholders relying on limited infor-mation may often fail to block the ®rmÕs attempts to undertake socially inecient investments, while mistakenly forcing the ®rm to liquidate some projects that bene®t both shareholders and debtholders. The resulting e-ciency loss can be very large.

We can apply Eq. (10) to this situation by rede®ningxR andxS as the lowest levels ofx2acceptable to the ®rm respectively whenhˆ0 and whenhˆ1 and Zas the probability that nonbank debtholders demand debt redemption when the ®rm chooses the opaque project. Since the ®rm is not monitored by the bank,x

R;xS, andZdo not depend ona,b, andCanymore.

The ®rm may want to undertake an opaque project of negative NPV when its return distribution is in favor of shareholders …hˆ0† and pass up an opaque project of positive NPV when the return distribution favors debt-holders…hˆ1†. When the investment decision is left to the ®rm, therefore,xR is strictly less than 1 (large type 1 ineciency), andxS is strictly greater than 1 (large type 2 ineciency). Given thatxR<1 andxS>1, the ®rmÕs decision to choose the opaque project is a strong signal that the return distribution is in favor of shareholders. Thus, if the ®rm chooses the opaque project, nonbank debtholders estimate a low expected return on debt, which in turn increases the probability of early redemption. In sum, the ®rmÕs ownership of the bank results in smallXR and XS and largeZ, all of which contribute to increasing

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because the ®rmÕs investment decision is biased toward risky projects. In the context of this model, therefore, the ®rmÕs ownership of the bank is not desirable.

2.7. Numerical example

This section presents a numerical example to clarify the analytical results of the model. Let us assume that Kˆ2; Dˆ8; RH1ˆ1:3; h1ˆ0:5, and

pˆ0:6. Thenx1ˆ1:04 from Eq. (1), andRDˆ1:125 from Eq. (4). If the low

return is realized at the end of the ®rst period, the ®rm goes bankrupt because the ®rmÕs asset falls below its debt obligation. Debtholders receive the re-maining asset…hRH1Aˆ6:5†and su€er a net loss of 1.5 (8)6.5). Shareholders lose all of the equity (2). There is no second period in this case. In the high-return state, the ®rm pays interest …net gainˆ0:1258ˆ1† to debtholders and dividends…net gainˆ13ÿ10ÿ1ˆ2†to shareholders at the end of the ®rst period. Thus, if it does not fail in the ®rst period, the ®rm starts the second period with the same capital structure (Kˆ2 andDˆ8). In the absence of the shock, the same project continues, and the expected returns on equity and debt remain the same.

If the shock occurs, the expected returns on equity, debt, and the bankÕs investment (combination of equity and debt) depend on the outcomes ofh2and x2. The ®rm, the bank, and nonbank debtholders choose between the trans-parent and the opaque project based on the expected returns. It is further assumed thatbis ®xed at 0.5 and that the expected return of the opaque project (x2) is uniformly distributed between 0.5 and 1.5.

The ®rm wants to choose the transparent project if (see Eqs. (5) and (7))

E…K2R† ˆpMin x2

p A

ÿRDD

;0

ˆMinf…10x2ÿ5:4†;0g<2 when hˆ0

and

E…K2S† ˆMinf…x2AÿRDD†;0g ˆMinf…10x2ÿ9†;0g<2 whenhˆ1:

Fully informed debtholders would want to choose the transparent project if (see Eq. (6))

E…D2R† ˆpMax x2A

p ;RDD

ˆMaxf10x2;5:4g<8 whenhˆ0;

and

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The bank wants to choose the transparent project if (see Eq. (8))

The critical levels ofx2 derived from the decision criteria of the ®rm and the

bank (see the proof of Proposition 1),

xRˆ0:74‡0:13

The net expected return on debt conditional on the selection of the opaque project (see Eq. (9)),

The maximum expected gain from the opaque project (see Eq. (10)),

MGˆ1

Type 1 and type 2 ineciency,

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share of equity (Panel A) and for the case of a noncontrolling share (Panel B). As Proposition 1 states, ataˆbˆ0:5, bothType1and Type2are zero, and

Gain is maximized in the case of a controlling share. In the case of a non-controlling share, Type2 is positive, but both Type1 and Type2 are at their minima whenaˆbˆ0:5. The table also shows thatType1andType2decrease asaapproachesbfrom either direction (Lemma 1). In both cases,Ydecreases witha which meansZincreases witha (Proposition 2). In addition,Y <0 at aˆbˆ0:5.5Thus, the bank with the equal share of equity and debt is not reliable as a delegated monitor in this example. Given that the error term (u) in Eq. (9) has mean 0, Z>0 when Y <0. Assuming for simplicity that

Table 1

Investment eciencya

a x

R xS Type1 Type2 Total Gain Y

A.Controlling share of equity

0.0 1 0.8000 0.1000 0.6250 0.7250 0.5250 0.6500 0.1 2.0400 0.8400 0.0640 0.6250 0.6890 0.5610 0.6420 0.2 1.3900 0.8800 0.0360 0.3802 0.4163 0.8338 0.3320 0.3 1.1733 0.9333 0.0111 0.0751 0.0862 1.1638 )0.2827

0.4 1.0650 0.9750 0.0016 0.0106 0.0121 1.2379 )0.6060

0.5 1.0000 1.0000 0.0000 0.0000 0.0000 1.2500 )0.8000

0.6 0.9567 1.0167 0.0047 0.0007 0.0054 1.2446 )0.9293

0.7 0.9257 1.0286 0.0138 0.0020 0.0158 1.2342 )1.0217

0.8 0.9025 1.0375 0.0238 0.0035 0.0273 1.2227 )1.0910

0.9 0.8844 1.0444 0.0334 0.0049 0.0383 1.2117 )1.1449

1.0 0.8700 1.0500 0.0422 0.0063 0.0485 1.2015 )1.1880

B.Noncontrolling share of equity

0.0 1 1.1000 0.0000 0.6500 0.6500 0.6000 0.4000 0.1 2.0400 1.1000 0.0000 0.6500 0.6500 0.6000 0.4000 0.2 1.3900 1.1000 0.0000 0.4052 0.4052 0.8448 0.1140 0.3 1.1733 1.1000 0.0000 0.1001 0.1001 1.1499 )0.4493

0.4 1.0650 1.1000 0.0000 0.0356 0.0356 1.2144 )0.7310

0.5 1.0000 1.1000 0.0000 0.0250 0.0250 1.2250 )0.9000

0.6 0.9567 1.1000 0.0047 0.0250 0.0297 1.2203 )1.0127

0.7 0.9257 1.1000 0.0138 0.0250 0.0388 1.2112 )1.0931

0.8 0.9025 1.1000 0.0238 0.0250 0.0488 1.2012 )1.1535

0.9 0.8844 1.1000 0.0334 0.0250 0.0584 1.1916 )1.2004

1.0 0.8700 1.1000 0.0422 0.0250 0.0672 1.1828 )1.2380 a

bis ®xed at 0.5. Variable de®nitions:aˆbankÕs share of the ®rmÕs equity;bˆbankÕs share of the ®rmÕs debt;x

Rˆthreshold expected return on the riskier opaque project;xSˆthreshold expected

return on the safer opaque project; Type1ˆtype 1 ineciency; Type2ˆtype 2 ineciency; TotalˆType1+Type2; Gainˆexpected total output net of opportunity costs (social gain);Y ˆ

expected net return on debt based on nonbank debtholdersÕinformation.

5SinceYcritically depends on the distribution ofx

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uˆ0;Zˆ1 whenY <0, andZˆ0 whenYP0. In this case, the optimal level of a at which the expected output is maximized is between 0.2 and 0.3 (Proposition 3).

Now suppose that the ®rm controls the bank. Then from the ®rmÕs decision criteria above, xRˆ0:74, and xS ˆ1:1. At these values of xR and xS; Type1

ˆ0:1690; Type2ˆ0:0250; Totalˆ0:1940; Gainˆ1:0560, and Y ˆ ÿ1:5760. In this example,Gainis larger than those in some cases of the bankÕs ownership of the ®rm (a60:2 in Table 1). The signi®cantly negativeY, however, suggests that nonbank debtholders are highly unlikely to allow the ®rm to choose the opaque project. Thus, the con¯ict between the ®rm and nonbank debtholders can eliminate all potential gains from the opaque project.

3. Alternative assumptions

This paper has adopted key assumptions mainly from two branches of the banking literature: moral hazard models focusing on con¯icts between debt-holders and sharedebt-holders and delegated monitoring models in which banks monitor borrowing ®rms on behalf of debtholders. The literature on corporate governance also emphasizes con¯icts between shareholders and managers (e.g., Hirshleifer and Thakor, 1992; Jensen, 1986). Managers may maximize their own utility instead of acting in the best interest of shareholders. In this case, shareholders need to monitor managers and may want to delegate the moni-toring to banks. Depending on the objectives of managers, incorporating the shareholder±manager con¯ict can change the optimal shareholding of the bank. The key result of this paper should hold if the shareholder±manager con¯ict is independent of the shareholder±debtholder con¯ict. For example, the shareholder±manager con¯ict may be only about the operating expense that is unrelated to the project choice. It is reasonable to assume that holding their own interest constant, managers act in the interest of shareholders who have the voting power. Then the role of the bank should remain the same. The result would be similar when the objective of managers was more closely aligned with that of shareholders than that of debtholders. On the other hand, a close alignment of the managersÕand the debtholdersÕinterest is likely to increase the optimal shareholding of the bank. In addition, introducing some uncertainties about managersÕ behavior would complicate the results. Future research modeling various objectives of managers may produce interesting results.

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the bank signals the quality of the opaque project by marginally changing its shares of equity and debt. Credible signaling can prevent inecient debt re-demption and hence reduce the eciency loss. The possibility of signaling by the bank is a potentially interesting topic for future research. Interesting issues include conditions under which signals are credible and the extent to which eciency gains can be realized.

4. Policy implications

Many policymakers and academic researchers recognize that the aliation of banking and commerce may improve economic eciency. The main policy concern is whether or not the aliation would increase the riskiness of banks and hence the liability of deposit insurance. If it does, the issue is what form of the aliation would minimize the risk while improving economic eciency.

The previous section shows that the bankÕs ownership of a commercial ®rm may increase the riskiness of the bank. Since the ®rm is allowed to undertake riskier projects, both the equity and debt of the ®rm may become riskier. This problem is more serious when the ®rm controls the bank, depriving the bank of its monitoring ability.

Currently, the US banking laws do not allow the aliation between banks and commercial ®rms. Banks can own commercial ®rmsÕ equity only in ex-ceptional circumstances (for example, as a means to recover loan losses from failing ®rms), and bank holding companies are severely restricted from investing in nonbanking organizations. The Federal Reserve Act, however, contains a few relevant provisions governing banksÕtransactions with their aliates such as the holding company, other banks controlled by the same holding company, and bank subsidiaries. For example, Section 23A limits the bankÕs lending to an aliate to 10% of the bankÕs equity. In addition, loans to aliates must be collateralized. Section 23B requires that banks make transactions including lending and asset purchases with their aliates at fair-market terms.

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ecient mix of equity and debt holdings derived above…bPaP0†. Further-more, the bank holding only collateralized debt would not have incentives to serve debtholdersÕ interest. The eciency loss, of course, is greater when nonbank debtholders cannot rely on the bank as a delegated monitor. Lending restrictions, therefore, can seriously limit the marketÕs ability to improve eco-nomic eciency.

The model developed in this paper does not o€er direct implications about the requirements of fair market terms. In general, preventing price distortions should improve economic eciency. Aliated ®rms may make transactions at concessionary terms mainly to gain at the expense of third parties (e.g., avoiding taxes and transferring wealth from uninformed agents).

In recent years, US lawmakers introduced many ®nancial reform bills that would allow the aliation of banking and commerce, but most of them pro-posed restricted equity ownership: for example, minority shares or nonvoting shares only. These restrictions also have mixed implications. Based on the model presented above, while the ®rmÕs in¯uence over the bank results in large eciency losses, the bankÕs in¯uence over the ®rm is desirable; the agency con¯ict is minimized when the bank has a controlling share of the ®rm. Thus, although restricting equity ownership can be e€ective in preventing the ®rm from controlling the bank, it may limit the potential gain from the bankÕs control over the ®rm.

In sum, the aliation of banking and commerce in restricted forms may produce smaller eciency gains. Nevertheless, bank regulators may need to limit the bankÕs risk exposure if deposit insurance cannot price the increased risk caused by the bankÕs equity holdings. In such cases, the most ecient restriction based on the analyses of this paper is to limit the maximum share of the bankÕs equity holding to its share of the ®rmÕs debt.

5. Conclusion

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The aliation of banking and commerce can increase the bankÕs risk ex-posure in two ways. With a larger equity holding, the bank has more incen-tives to allow the ®rm to undertake risky projects, which result in increased riskiness of both debt and equity of the ®rm and hence increased riskiness of the bankÕs investment in the ®rm. When the ®rm controls the bank, the ®rm may force the bank to provide necessary funds to undertake risky projects at the expense of debtholders. Then, of course, the bankÕs investment in the ®rm becomes riskier. Increased bank risk is problematic if deposit insurance pre-miums do not fully re¯ect the increased risk or if bank failures have negative externalities.

Based on the ®ndings of this paper, allowing the aliation of banking and commerce in a restrictive manner may reduce potential eciency gains. For example, when the bank is not allowed to lend to its commercial aliate, in-vestment eciency may not improve. The bankÕs in¯uence over the ®rm may improve investment eciency, while the ®rmÕs in¯uence on the bankÕs lending decisions can worsen investment eciency.

Acknowledgements

I would like to thank two anonymous referees for helpful comments and suggestions.

Appendix A. Proofs of propositions and lemmas

Proof of Proposition 1. Only the bankÕs decision matters when it has a con-trolling share of equity. The bank prefers the opaque project to the transparent one if

E…B2† ˆaE…K2† ‡ bE…D2† P aK‡bD:

Whenhˆ0,

E…B2† ˆaE…K2R† ‡bE…D2R† ˆbx2A forx2 6 pRDD

A ;

ˆa…x2 AÿpRDD† ‡bpRDD forx2> pRDD

A :

The ®rst case is irrelevant because from Eqs. (3) and (4),E…B2†<aK‡bDat x2ˆ …pRDD†=A. Setting the second line of the above equation equal to

…aK‡bD†and solving forx2

xRˆ1ÿ 1

ÿb

a

…1ÿ

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Thus,x

where subscriptCstands for the case with a controlling share. Thus, in both cases,xSCˆ1 whenaˆb.

The opaque project must be acceptable to both the bank and the ®rm when the bank does not have a controlling share of equity. That is,

E…B2†PaK‡bD and E…K2†PK:

Whenhˆ0, the ®rmÕs decision is not binding because the return distribution is in favor of shareholders. Thus,x

Ris the same as the case of a controlling share.

Whenhˆ1, it is the ®rmÕs decision that is binding because the return dis-tribution favors debtholders. Setting E(K2S) from Eq. (5) equal to K and

solving forx2,

xSN ˆ1‡…RDÿ1†D

A ;

where subscriptNstands for the case of a noncontrolling share. In this case, x

SN is independent of a and b. Thus, the overall ineciency without a

con-trolling share is minimized whenaˆb:

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Thus, asaapproachesbfrom below, bothx

RandxSapproach 1, reducing both

types of ineciency.

Whena>b; xR<1 andxS>1. Thus, asaapproachesbfrom above, both xR andxS approach 1, reducing both types of ineciency.

Proof of Proposition 2.From Eq. (9) ZˆP…u<ÿY† ˆW…ÿY†;

whereWis the cumulative distribution of u.

oY

When hˆ0, wealth is transferred from debtholders to shareholders. Thus,

…E…D2R† ÿD†<0 atxR, where the net gain from the opaque project is 0 either

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