跨業經營環境下的金融中介競爭與金融脆弱性(II)

行政院國家科學委員會專題研究計畫 成果報告

跨業經營環境下的金融中介競爭與金融脆弱性(第 2 年)

研究成果報告(完整版)

中 華 民 國 97 年 10 月 17 日

行政院國家科學委員會補助專題研究計畫

跨業經營環境下的金融中介競爭與金融脆弱性

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計畫編號：NSC 95－2415－H－004－007－MY2

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中 華 民 國 97年 10 月 10日

Extended Financial Services,

Banking Competition and Financial Fragility:

A Partial Equilibrium Framework

Yeong-Yuh Chiang

Department of Money and Banking National Chengchi University

NSC 95-2415-H-004-007-MY2 - Year 1

Abstract

We introduce heterogeneous borrowers and underwriting business into a framework similar to that of Boyd and DeNicol´o(2005), and find out that (1) more capable firms will tolerate higher risk; however this does not nec-essarily lead to a higher default risk than those less capable firms have; (2) when direct lending does not lead to higher default risks, no arbitrage results in higher loan rates and lower direct lending costs; (3) the availability of di-rect finance alleviates the undesired effect of the risk-incentive mechanisms discovered by Boyd and de Nicol´o (2005).

Keywords: Extended financial services, Banking competition, Risk-taking,

As more financial innovations arise and the financial sector evolves into the one with more market-oriented transaction, commercial banks get involved into more securities business than before. However their roles as intermediation are still active but in different forms of financial business (see Boyd and Gertrler (1994), Berger et al. (1999), Allen (2001), and Allen and Santomero (2001)). Dif-ferent forms of business change the way how intermediaries and their customers interact. Rajan (2005) argues that financial innovation promotes the convenience of, but at the same time also increases the complexity of, financial transaction. As markets become more complicated, it is more difficult for market participants to get information and agency problems become worse when agents make financial transactions through intermediation.

In discussing banking competition and banks’ risk-taking behaviors, it is quite often that authors assume away securities-underwriting business. Examples in-clude Allen and Gale (2004), Boyd and de Nicol´o (2005), Koskela and Stenbacka (2000), Matutes and Vives (2000), Parlour and Rajan (2001), and Shaffer (1998). Another thread of research, such as Kroszner and Rajan (1994), Kanatas and Qi (1998), Kanatas and Qi (2003), and Puri (1999), studies the underwriting behav-iors of financial intermediaries. Their discussions show the complexity of banking behaviors when involving underwriting activities.

This paper introduces securities transaction into a banking model of Boyd and De Nicol´o. The extended services enlarge the strategy space of firms, com-plicating interactions between players. This makes our analysis different from the

existing literature.

Boyd and de Nicol´o (2005) argue that there exists a fundamental risk-incentive mechanism that operates in exactly opposite direction, causing banks to become more risky as their market become more concentrated. The availability of finance through issuing securities provides an alternative for firms raise their external funds. Our purpose is to show that this alternative mitigates the unpopular effects of the risk-incentive mechanisms a l´a Boyd and de Nicol´o. To serve this purpose and make the analysis tractable, we model underwriting activities to a minimum level by assuming that the underwriter charges an exogenous underwriting fee for its service and an entrepreneur has to rely on a underwriter to issue its securities.

The remainder of the paper is organized as follows: In Section 1 we specify our model environment. In Section 2 we analyze how entrepreneurs’ choices of projects and the sources of external finance are affected by borrowing costs. Sec-tion 3 presents the analysis of competitive banking markets by using no arbitrage arguments. In Section 4 we analyze the decision problems of financial interme-diaries (commercial banks) when they have monopoly power. Banks decide loan rates by taking into account loan applicants’ reactions to loan rates. In addition we also analyze how entrepreneurs choose their production projects when they decide to issue securities through a underwriter. In Section 5 we examine how the availability of securities-finance affects the risk exposure of the economy. Section 6 summarizes what we have found and offers some concluding remarks.

1

The Environment

Heterogeneous Firms

There are heterogeneous entrepreneurs indexed by their management ability (or levels of management skill) e∈ [e, ¯e]. The distribution of e over [e, ¯e] has a con-tinuous density function f(e). Assume the population of entrepreneurs is one; i.e.,R

[e, ¯e] f(e) = 1. The type of an entrepreneur is private information and can be

observed by commercial banks when they applying the costly screening technol-ogy. A firm has access to risky constant return production projects, indexed by S. Each project requires an investment of one unit of the input to produce S units of the output with probability P(S, e), and zero otherwise. The probability function P(S, e) satisfies:

Assumption 1 Ps< 0, Pss ≤ 0, Pe> 0, and Pse> 0.

The probability of success decreases as the output increases at a non-increasing rate. For the same S-project a firm with a higher e succeeds more likely than one with a lower e. An example of P(S, e) is P(S, e) = 1 − A(S/e). One can appropri-ately choose A such that 0≤ P(S, e) ≤ 1 for all S and e.

Bank-Financed and Market-Financed Funds

A firm has no resources and has to rely on external funds to make its investment. There are two alternatives to finance a production project: applying for a loan which is financed by a commercial bank or issuing bonds which is underwritten

by an investment house. For bank-financed funds, an entrepreneur goes to a com-mercial bank and apply for a loan. We assume a firm can apply for only one loan from one bank. The loan application is subject to the bank’s approval and the bank decides the (gross) interest rate RL (called loan rates). If an entrepreneur wants to issue bonds to raise funds for its production project, it needs find an investment house to underwrite the bonds. The (gross) interest rate of bonds (RU, called secu-rity rates) is determined by the market and the performance of investment houses. We assume that an entrepreneur can have only one investment house to underwrite its bonds if he chooses to issue bonds. For simplicity, we also assume that a firm can choose to apply for a loan or to issue bonds, but not both.

Financial Institutions

There are two types of financial institutions, commercial banks (hereafter called them banks) and investment banks (hereafter called underwriters). Banks obtain funds by taking in deposits from the markets and paying depositors interests at a gross rate RD. When receiving a firm’s application for a loan, a bank utilizes its screening technology at a cost c to uncover the type of the firm and to sort out the type of its proposed production project. The screening outcome is only observable to the bank, not to other financial institutes and the public. The bank may and may not approve the loan application. When approving the application, the bank also decides the (gross) interest rate (RL) it will charge for the loan. Since the screening technology yields concrete information for the type of the applicant, the loan rates

is contingent only on the type of firms e.

An investment house underwrites bonds for firms in exchange of fee incomes. An investment bank delivers to the public investors the information they find out in the process of underwriting. Due to information asymmetry the public investor is not sure that the delivered information is complete and perfect. In reality, how convincing the information is depends upon many factors such as in-vestment projects, the reputation of the firm that raises funds, and the efforts of underwriters. In particular, the more efforts an underwriter put in collecting and analyzing data, the more convincing the information is. However, the information processing is costly. The efficiency of information processing technology used by underwriters also matters. How much profit an investment bank can obtain for a underwriting case depends upon all these factors. In this paper we do not get into the details of this aspect.1

Instead, we assume that underwriting business is quite competitive and, thus, the underwriting fee (φ) an investment bank can collect from its clients is deter-mined by market competition. We model the performance of underwriting pro-cess by a parameter of convincing power (denoted by θ). More specifically, we assume that the public investor understands that the probability of success P(S, e) depends on who runs what kind of production technology; however they just do

1_{In this study we did try to incorporate the details of underwriting technology (its cost and}

outcomes) into the underwriting optimization problems. However P(S, e) appears recursively in one equation. We still do not know how to solve the problem. Thus we decide put that complexity aside and move forward.

not know what (S, e) is. They make their investment decisions basing upon their belief ˜P(S, e). We useθ to describe how close the belief of the public to the real P(S, e): ˜P(S, e) =θP(S, e), 0 <θ < 1.

Nowadays it is quite common to observe the mixture of direct and indirect lending for an investment project. As shown in Bolton and Freixas (2000) an equilibrium model with a mixture of bonds- and loans-financed capital structure can be very fruitful but paying a cost of analysis complexity. The purpose of this paper is to show that how competition from markets affects the risk structure dis-cussed in banking literature. It is natural to start with a simple analytical structure and get a clear-cut picture. Only after this step we can go with more confidence to set up a more complicated framework to tackle more difficult issues.

The Gramm-Leach-Bliley Act lifted the ban of securities operation for com-mercial banks. Like universal banks in Europe, comcom-mercial banks in the US started to integrate both loans and securities business under the Act. In many economies, for example Taiwan, Korea and Japan, the integration of financial sector is also under way. Financial holding companies (or universal banks) be-come a popular form of financial organization. Economies of scale are the driving force behind this trend. The border line between banks-financed and markets-financed funds become burring. Both loans and securities issuing are substitutes and complements of each other. Obviously, universal banks and financial holding companies play an important role in such a financial environment. However. for simplicity, we do not include financial holding companies and universal banks in

our analysis. We concentrate on the substitution role of both direct and indirect lending and leave the complement role as our future research topic.

2

Firm’s Optimization

Firms use external funds to acquire inputs for their technologies. Let R denote the gross interest rate for obtaining one unit of external funds. One unit of input costs one unit the output. The firm’s optimization problem can be written as

max

S P(S, e)[S − R] (1)

The first order necessary condition is Ps(S, e) · S + P(S, e) = Ps(S, e) · R, which can

be rewritten as

H(S, e) ≡ S +P(S, e) Ps(S, e)

= R, (2)

where HS(S, e) > 1 and He(S, e) < 0. H(S, e) is the risk(Ps)-adjusted marginal

contribution of an additional unit of output to expected outputs, and the right hand side of (2) is the risk-adjusted marginal cost of increasing outputs. One can easily show that the left hand side of (2) is increasing in S, while the right hand side is constant over S. When the risk-adjusted marginal cost (R) increases, the firm should respond by increasing the scale of outputs (S). Let S∗(R, e) be the solution.

Figure 1describes how a change in R affect S∗. As S increases, the probability of

success decreases while the expected outputs increases due to the output increase. Thus the optimal response to an increase in R is to increase S. A higher costs of

R

H(S, e)

S∗(R, e) R′

S∗(R′, e) S Figure 1: Loan Rates and the Choice of S

funds (higher R) results in the choice of more risky project (a higher S and a lower probability of success).

The Ps-adjusted marginal contribution of additional output H(S, e) is

decreas-ing in e, He(S, e) < 0. Given the cost of funding R, firms with different e choose

different levels of production. A firm with a higher e indicates that his technology more likely succeed and leads him to choose a higher S for a higher return. In

Figure 2a greater e′corresponds to a lower curve of H and results in the optimal

choice of a higher S. This shows that how heterogeneity of firms affects the choice of risky technologies. In sum, S∗(R, e) has properties of S∗_R> 0 and S∗_e > 0.

Next we define the value function of the firm’s optimization (1), denoted by V(R, e), as

R H(S, e) S∗(R, e) H(S, e′) S∗(R, e′) e′> e S

Figure 2: The Choice of S and Heterogeneity of Firms

Note that R is affordable only if S∗(R, e) ≥ R. The value function V (R, e) is in-creasing in e [Ve(R, e) = Pe(S∗(R, e), e) ·[S∗(R, e) − R] > 0] and decreasing in R

(VR(R, e) = −P(S∗(R, e), e) < 0). Moreover VeR(R, e) < 0 if and only if S∗e(R, e) <

−Pe(S∗(R, e), e)/Ps(S∗(R, e), e).2 From this point on we assume this condition

holds:

Assumption 2 S∗_e(R, e) ≤ −Pe(S∗(R, e), e)/Ps(S∗(R, e), e).

An increase in e has two opposite effects. One the one hand, a firm with greater ability of managing production projects leads to a greater probability of success (Pe(S, e) > 0). On the other hand, greater ability induces an entrepreneur to choose

a higher return project (S∗_e(R, e) > 0) and results in an decrease in the probability of success(Ps(S∗(R, e), e) < 0. Assumption 2 states that the direct effect of an

2_V

eR= −Pe+ {[S − R]Pes+ Pe}S∗R= −[PsS∗e(R, e) + Pe] < 0. Hence VeR< 0 if and only if

increase in e on the probability of success dominates the indirect effect through the choice of risk projects. This assumption plays an important role in the following analysis.

Two forms of external funds

Firms have two alternatives to raise their funds, borrowing loans from banks or issuing securities to the market. Let RL denote the (gross) loan rate and RU the rate in the direct lending market. In addition to RU, a firm has to pay an amount

φ of upfront underwriting fees for issuing securities. This upfront cost can be thought of as underwriting expenses.3 The firm’s optimization problems of ob-taining funds in these two alternatives are

max S P(S, e) · [S − R L_], and max S P(S, e) · [S − R U_{] −φ,}

respectively.4 The decision of funds-raising is transformed into the following

3_{For simplicity, we assume that a firm has some resources to pay upfront costs, but they do}

not use them to finance their inputs. The results of our analysis is insensitive to this innocuous assumption. This upfront cost setup follows from Kanatas and Qi (1998, 2003). Puri (1999) has a similar setup.

4_{Here we assume that firms are price-takers in the borrowing markets. In a seller’s market}

firms do not have any influence over the price he pays. Later on when we analyze the underwriting activities, we will relax this assumption. When a firm chooses the type of project, it affects what he pays through the riskiness he chooses.

problem:

max {V (RL, e),V (RU, e) −φ}. Recall that the value function V(R, e) has properties:

Ve(R, e) > 0, VR(R, e) < 0, VeR(R, e) < 0.

Consistent with empirical findings, we assume for the moment that the direct lend-ing is less costly than loan-finance (not considerlend-ing upfront costs); i.e., RU < RL_.

(Later on we will show that when the screening cost of loan business (c) is large enough, the equilibrium in our model economy does have this property.) Then the property of VR(R, e) < 0 implies V (RU, e) > V (RL, e) for all e. The property

of VeR(R, e) < 0 indicates the slope of V (RU, e) with respect to e is steeper than

V(RL_{, e) for any e. Thus we can useFigure 3to help us understand the differences}

between two alternatives of raising funds.

As long as the underwriting fee φ is large enough, a critical value e∗ exists such that firms with e > e∗ will choose issuing securities to raise funds, while firms with e< e∗ choose loans as the sources of funds. From the properties of S∗(R, e) we know that a lower rate RU _{leads to a choice of lower S while a firm}

with greater e chooses a higher S. As a result, one cannot infer that the S∗chosen by firms with e> e∗is greater or smaller than those with e< e∗. One interesting question is whether the probability of success for e> e∗ is greater than that for e< e∗; that is whether

V(RL_{, e)} V(RU_{, e)} V(RU_{, e) −}φ e∗ e V(R, e) e _e¯ securities loans

Figure 3: The cut-off level of e

holds for all relevant e and e′? Assumption 2 guarantees (3) holds.

Proposition 1 When RU< RL_{, markets-financed projects succeed with a greater}

probability than banks-financed projects; that is (3) holds.

[Proof] For e> e∗and e′< e∗, we have

P(S∗(RU_{, e), e) > P(S}∗_(RL_{, e), e)}

(∵ S∗_R(R, e) > 0 and Ps(S, e) < 0)

> P(S∗(RL_{, e}′_{), e}′_{) (∵ Assumption 2)}

3

A Competitive Financial Sector

So far the focus of our analysis is on the properties of firm’s optimal behaviors. Loan rates(RL), security rates(RU) and underwriting fee (φ) are given. In a highly competitive financial environment, individuals do not have much impact on the prices of financial products and services. On either side of the supply and demand of funds, every individual takes prices as given and makes her own decisions. The prices are determined through market mechanisms. If there is any opportunity of arbitrage for profits, people flock into the opportunity and soon the opportunity is gone. Thus no arbitrage becomes an important feature of equilibrium in a highly competitive financial environment. The implication of no arbitrage is that loan rates and security rates cannot give room of profitability to individuals.

Assume there is a risk free investment technology which yields RF as its re-turns. Then no arbitrage implies that all investment opportunities can provide expected returns no more than RF.

In this section we show that no arbitrage conditions lead to high loan rates and low security rates. We discuss two scenarios: when the types of firms and projects are public information and when both of them are private information.

Public Information

In a competitive financial market with abundant funds, all profitable investment opportunities are utilized and no arbitrage implies that the expected returns to a risky contract equals the risk-free rate (denoted by RF). When the type of firms

are known to the public, the rates of borrowing are type-dependent and, thus, firm-specific and project-firm-specific. They are determined by the following no arbitrage conditions:

P(S∗(RL, e(e)), e) · RU= RF, for e∈ [e∗, ¯e]

P(S∗(RU, e(e)), e) · RL= RF, for e∈ [e, e∗].

The expected return from a loan contract cannot exceed the the risk-free rate and the expected return from a security cannot exceed to the risk-free rate. By (3), RU(e) < RL_{(e) for e ∈ [e}∗_{, ¯e] and e}′_{∈ [e, e}∗_].

Private Information

When the lender cannot tell one type from another of borrowers, the rate of bor-rowing is independent of types. Notice that in a competitive market, a fund owner can fully diversify its portfolio in the financial market. Although an investor can-not identify firms and projects, they know the overall distribution of firms and the probabilistic properties of different production projects. A fully diversified portfo-lio of securities has an expected return: R

e∈[e∗_{, ¯e]F( ¯e)−F(e}f(e) ∗₎· P(S∗(RU, e), e) · RUde, where F(e) is the cumulative distribution of e over [e, ¯e]. Notice that there is noθ when calculating the expected return of a fully diversified portfolio.

Consequently, the no arbitrage condition for security investment is written as

Z e∈[e∗_{, ¯e]} f(e) F( ¯e) − F(e∗₎· P(S ∗_(RU_{, e), e) · R}U de= RF (4)

A similar argument applies to the bank loan market. The depositors expect receive RF as its deposit rates. A bank utilizes the screening technology to uncover

the types of its loan applicants and the types of their projects. Thus a bank is able to charge firm-specific and project-specific loan rates, RL(e). No arbitrage condition for loan rates is:

P(S∗(RL, e), e) · RL= c + RF, for all e< e∗. (5)

From the determination of RL(e) we can further discuss properties of RL_{(e) and}

its relation to RU.

Proposition 2 Entrepreneurs with higher e receive lower loan rates; i.e., RL(e) is decreasing in e for e< e∗;

[Proof] When markets are highly competitive, market forces pre-vent banks from exercising too much monopoly power such that pursuing revenue-maximizing stops at zero profit conditions (5) holds at inequal-ity. One can immediately find out that RL is decreasing in e by totally differentiating (5) and applying Assumption 2. entrepreneurs with higher

capability receive lower loan rates. 

Moreover bank optimization implies RL is chosen such that its marginal con-tribution to the revenue cannot be negative; i.e.,

P(S, e) + R · Ps(S, e) · S∗R(R, e) ≥ 0. (6)

This condition helps us to derive the result of RL(e) > RU _{for all e< e}∗_.

[Proof] For e< e′, P(S∗(R, e), e) ≤ P(S∗(R, e′), e′) due to Assump-tion 2. Thus P(S∗(RU_{, e), e) ≤}R

e∈[e∗_{, ¯e]F( ¯e)−F(e}f(e) ∗₎· P(S∗(RU, e), e)de, for all e< e∗. Multiplying both sides of inequality by RU, one gets, for e> e∗,

P(S∗(RU, e), e) · RU ≤ Z e¯ e∗ f(e) F( ¯e) − F(e∗₎· P(S ∗_(RU , e), e) · RUde= RF.

Clearly we can have P(S∗(RU_{, e), e)·R}U_{< c+R}F_{. As long as P(S}∗_{(R, e), e)·}

R is increasing in R, RL(e) > RU _{for all e< e}∗_{. As argued above, (6) holds}

at inequality. Consequently, RL(e) > RU _{for all e< e}∗_{. }

When the financial sector is highly competitive, loan rates are greater than security rates (Proposition 3), and loan-financed projects is riskier than security-financed projects (Proposition 1).

In order to complete the analysis of this section, we need to figure out what e∗ is. Given e∗ and RF, from (4) we can solve RU as a function of e∗ and RF, denoted by ˆRU(e∗, RF_{). From (5) we can solve all R}L_{(e) as functions of R}F _{and c}

for all e< e∗, denoted by ˆRL(e, e∗, RF_{, c). By the definition of e}∗_{, the entrepreneur}

of type e∗is indifferent between security-finance and loan-finance:

V( ˆRU(e∗, RF), e∗) −φ = V ( ˆRL(e∗), e∗, RF, c) (7) (7) is used to solve for e∗as a function of RF and c.

4

The Model with a Monopolistic Loan market

In this section we discuss the optimization problems of financial institutes. Both banks and underwriters maximizes their profits by providing financial services.

Commercial Banks

Banks take in deposits as the source of funds and lend funds to firms through loan contracts. We assume that banks are price-takers in deposit markets. This assumption deviates from Boyd and de Nicol´o (2005)’s set up. They assume that banks have monopoly power in both loan transactions and deposit business. This assumption allow them to analyze strategic behaviors of financial firms in both markets of their outputs(loans) and inputs(deposits).

In our setup of banking optimization we only allow banks have monopoly power in loan markets, but not in deposit markets (or more precisely funds mar-kets). When a firm comes to a bank and applies for a loan, the bank applies its screening technology at a cost of c to identify the type of the firm and its pro-duction project. After identifying the type, the bank determines a loan rate RL to charge for its loan provision. Since the bank can identify loan applicants and the types of their projects, loan rates are firm- and project-specific, denoted by RL(e). We assume that the bank has monopoly power in loan markets. When a bank chooses a loan rate, it takes into account the borrower’s reaction to the loan rate - the first order condition of the loan applicant’s optimization problem. Banks take in deposits at a given deposit rate RD and the cost side of a loan business

only has two terms: the screening cost c and the deposit rate RD. Thus the bank’s optimization problem for a loan application is written as

max RL P(S, e) · R L_{− (c + R}D₎ s.t. S+_PP(S,e) s(S,e)= R L_(e) (8)

Since c and RDare exogenous to the optimization, one can solve this problem by maximizing the expected revenue. The necessary condition is written as

P(S∗(RL, e), e) + RL· Ps(S∗(RL, e), e) · SR∗(RL, e) = 0,

where S∗(RL_{, e) is the solution of the constraint. Let R}L∗_{(e) denote the solution of}

(8). The bank will approve the loan application if

P(S∗(RL∗(e), e), e) · RL∗(e) ≥ c + RD. (9)

By applying the envelope theorem one can easily show that the bank’s revenue (the right hand side of (9)) is increasing in e. The bank will welcome high cable firms. For large enough c and/or RD, firms with low e might not be able to get loans from banks. We can summarize these interesting findings from bank optimization in the following proposition:

Proposition 4

[1] The loan rate is increasing in loan applicants’ capability (e).

[2] The bank’s profit from loan business is increasing in loan applicants’

[3] Firms with higher e choose higher S with a greater probability of success.

[4] For sufficiently large c and/or RD firms with low e cannot obtain loans from banks.

[Proof] The second order sufficient condition for the maximization problem is

2PsSR∗(R, e) + RL[Pss(S∗R(R, e))2+ PsS∗RR] < 0.

[1] Totally differentiating the first order necessary condition and rearrang-ing terms, one can get

dRL

de = −

(PsS∗e(R, e) + Pe) + RL[PsS∗_Re+ S∗_R(R, e)(PsS∗e(R, e) + Pe)]

2PsS∗_R(R, e) + RL[Pss(S_R∗(R, e))2+ PsS∗_RR]

The denominator is negative by the sufficient condition. The numerator is negative when the term involving third derivatives of P(S, e), S∗_Re, is insignificant.5 Thus we have dR_deL > 0.

[2] DefineΠB as ΠB(e) = P(S∗(RL∗_{(e), e), e) · R}L∗_{(e) − (c + R}D_{). Then}

by the envelope theorem, one can easily obtain: dΠB

de = (Ps· S

∗

e+ Pe)RL∗(e)

which is positive due to Assumption 2.

[3] Plugging RL∗(e) into S∗(R, e) and differentiating the resultant, one gets: d deS ∗_(RL∗_{(e), e) = S}∗ R· RLe∗+ S∗e(RL∗(e), e) > 0. 5_{When P= 1 − AS/e, S}∗ Re= 0.

Substituting S∗(RL∗_{(e), e) into P(S, e) and taking total differentiation, one} can get: d deP(S ∗_(RL∗_{(e), e), e) = P} s· (S∗RRL∗+ S∗e) + Pe,

which is positive as long as the direct effect dominates the indirect effect (Assumption 2).

[4] Obviously, given an e, the bank profit can be negative for for suffi-ciently large c and/or RD; i.e.,

P(S∗(RL∗(e), e), e) · RL∗(e) − c + RD< 0.

In these cases banks do not approve loan application. 

At first glance, it looks odd that more capable firms pay higher loan rates for loans. However in our setup, as we analyze in the previous section, the direct effect of a change in e on the probability of success dominates the indirect effect. Although a more capable firm picks a project which is riskier than the one picked by a firm with smaller e, the dominant direct effect of e allows him to run the project more safely. In addition, as analyzed in the previous section, a higher loan rate induces firms to pick a higher S project. Thus it is optimal for a bank to respond by raising its loan rates for higher e firms to induce them to pick a higher S project and run them more safely.

Comparing to the competitive loan market, the risk structure of projects taken by entrepreneurs have greater likelihood of failure. When commercial banks have

monopoly power in determining loan rates, they naturally charge loan rates higher than those are charged in a competitive market. A higher price leads to a choice of higher S and greater failure probability.

Proposition 5 Other things being equal, when loan markets change from being highly competitive to being concentrated, loan-financed entrepreneurs will choose projects with higher output and also higher failure likelihood.

[Proof] Every loan applicant face a higher loan rate when loan markets

become more concentrated. It is sufficient to show that the probability of success decreases as loan rates decrease.

dP(S∗(R, e), e)

dR = Ps(S

∗

R(R, e), e) · S∗R(R, e) < 0,

which is negative because Ps< 0 and S∗_R(R, e) > 0. 

We follow Boyd and de Nicol´o (2005) to include the risk-incentive mecha-nism in the asset side of balance sheet for commercial banks. Ceteris paribus, as market competition declines banks earn more rents in their loan markets by charging higher loan rates. In themselves, higher loan rates would imply (weakly) higher bankruptcy risk for bank borrowers who, when confronted with higher in-terest rates, optimally increase their own risk of failure. (from: Boyd and de Nicol´o (2005), pp. 1329-1330).

Investment banks provide firms with underwriting services. When a firm decides to raise funds directly from markets, it needs an investment bank to underwrite its securities for public offerings. Investment banks underwrite firms’ securities in exchange of service fees. Unlike commercial banks, investment banks do not face default risks when they underwrite securities. Investors who buy the securities face default risks. However, investment banks earn profits by providing convinc-ing information to investors such that the performance of underwritconvinc-ing activities depend upon how well the information perceived by investors. The performance of underwriting affects how much an investment bank can charge firms who ask for underwriting services. A underwriter needs put efforts in order to make infor-mation convincing to investors, those efforts are costly.

How much a firm is willing to pay for underwriting services depends upon the performance of underwriting, more specifically, the interest rate required by investors. There are a number of factors affect prices of securities (and the inter-est rates firms are required to pay), including macroeconomic conditions, issuers’ reputation, tightness of funds in markets, ..., and so on. How an investment bank helps firms to obtain funds is certainly one of these factors. This paper focuses on the analysis of how market-oriented finance affects the risk exposure of the entire economy. For simplicity we abstract from all factors which cannot con-trolled by investment banks and to focus on only the performance of underwriting technology (θ).

contract, completely under the control of banks and firms. When raising funds through issuing bonds, the cost of funds faced by firms differs to those raised through loan contracts. Both the buyer and the seller of underwriting services have no “complete” control over the cost of funds. Market investors’ belief plays an important role. The contingency on investors’ belief makes the analysis of underwriting activities different from that of loan activities. We will elaborate what are differences before we analyze the strategic behaviors of both firms and underwriters.

(a) Investors’ belief and the costs of funds An investor decides to buy a se-curity mainly because he expects the returns from the investment on the sese-curity is worthwhile, and the information an investor receives determine how he expects the returns. Investors know that the type of production projects (S) and the en-trepreneur’s ability (e) are two of main factors determining the real returns of the investment. More specifically, investors know what P(S, e) is, but do not really know what S and e are. Their information about S and e is limited, and therefore, investors are conservative about the probability of success and believe that the probability of success to be smaller than its true probability. Instead of perceiving P(S, e) · RU _{as the expected returns, an investor uses a smaller probability, ˜P(S, e),}

to predict his expected returns. This implies that an investor asks for higher returns to justify his investment and, thus, increases the costs of funds.

(b) Convincing power Delivering convincing information to investors is one of main functions investment banks serve. Investment banks collect and

ana-lyze information about the projects in the early stage of the underwriting pro-cess. Gathering and analyzing information make investment banks be better in-formed of the security-issuing firms than those public investors. The investment bank’s statement about the underwritten case is the main source of information public investors rely on. The more convincing the information is, public in-vestors’ belief ˜P(S, e) will be closer to the true probability P(S, e). We assume that ˜P(S, e) =θ · P(S, e) to reflect the performance of underwriting efforts, and ignore the costs of underwriting for the simplicity of analysis. Given this setup, the underwriting technology is fixed and the investment bank does not have an optimization problem to solve. It simply runs underwriting business and collect fee incomesφ.

(c) Securities-issuing firms’ best response The required payments for funds raised through markets, RU depends onφP(S, e). Appealing to arbitrage activities, RU is determined by

θ· P(S, e) · RU = RM, (10) where RM is the market rate of returns determined by the supply and demand of funds in markets. The market rate RM is beyond the firm’s control and is given to the firm; however, the choice of S will affect the probability of success. The firm’s optimization problem is written as

max S P(S, e)  S− R M θ· P(S, e) 

The first order condition is Ps(S, e) · S + P(S, e) = 0. As one can see that the

to do with underwriting performance (θ). This is different from what we have in Section 2 and in bank finance.

The optimal choice of S, SU∗, is strictly increasing in e. Furthermore the security rate RU = RM/(θ· P(SU∗(e), e)) is decreasing in e. Define VU(e, RM,θ) as VU = P(SU∗(e), e) · SU∗(e) − RM/(θ· P(SU∗(e), e)). One can easily verify that V_eU> 0, VU

RM< 0 and VθU> 0. The value function of optimization by underwriting an investment project is VU(e, RM_,θ_{) −}φ_.

We can summarize the findings about underwriting activities in the following proposition:

Proposition 6

[1] Firms with higher e choose higher S with a greater probability of success.

[2] The security rate is decreasing in firms’ capability (e).

[3] For sufficiently large RM and/or φ, firms with low e will not consider funds from markets.

[4] For sufficiently smallθ, firms with low e will not consider funds from markets.

[Proof] [1] Totally differentiating the first order condition, one can get

dSU∗

de = −

Pe+ SU∗· Pse

2Ps+ SU∗· Pss

,

The denominator is negative due to the second order sufficient condition. All three terms (Pe, SU∗ and Pse) in the numerator are positive. Thus SU∗

is increasing in e. Moreover, d

deP(S

U∗_{(e), e) = P}

s· Pse+ Pe> 0

[2] Recall that RU =_P(SU∗R_(e),e)·M _θ. We have

dRU de = RM θ · −_ded P(SU∗_{(e), e)} P(SU∗_{(e), e)} < 0

[3] and [4] Since VU is decreasing in RM and increasing in e. It is clear that when RM andφ are too large orθ is too small, the firm will have a

negative value. 

There is an interesting contrast between bank finance and market finance. The loan rate is increasing in firms’ capability (Proposition 4 [1], page 18), while the security rate is decreasing in firms’ capability (Proposition 6 [2], page 25). In market finance, a firm faces a given market rate and he can affect his security rate by choosing the type of project. More capable entrepreneurs choose higher productive projects with higher probability of success. When the probability of success is higher, public investors will require less returns. In bank finance, the loan rate is controlled by banks. Firms with higher e choose higher S with a greater probability of success. Banks take into account of firms’ best responses. Due to more capable firms have incentive to choose more productive projects and high loan rates also induce them to choose more productive projects. It is optimal for banks to charge high loan rates in order to take advantage of the capability of running productive projects with less failure rates.

In the competitive financial environment in which banks do not have any monopoly power over loan rates, the loan rate is determined by the zero profit condition. Just like in the competitive underwriting market, the loan rate is de-creasing in entrepreneurs’ capability (e) (Proposition 2, page 15).

Concerning project choices and their risk structure, entrepreneurs with high capability always choose higher productive projects with greater probability of success than those with low capability, in both bank-finance and market-finance, and also in both competitive and monopolistic loan markets.

In the competitive financial environment we show that loan rates are lower than security rates. When intermediation cost (c) is large enough, the profitabil-ity consideration, commercial banks would charge loan rates higher than market rates.

Proposition 7 Given e∗, RM, and RD, when c is sufficiently large, RL(e) > RU(e′) for all firm e who seeks loan finance and firm e′security finance.6

[Proof] Deposit rates and market rates have some relations due to

arbi-trage activities. Since our point is to show a sufficiently large c results in that loan rates are higher than security rates, we can assume RD= RM

6_{From the analysis of both loan finance and security finance, we find that the firm’s expected}

profit is an increasing function of e, say VL(e) and VU_{(e). If we can show that the slope of V}U_(e)

is greater than that of VL(e) and VU_{(e) has a lower vertical intercept than V}L_{(e) such that both}

curve intersects at an e∗∈ [e, ¯e]. Then e∗_{is the cut-off level of e such that for firms with e< e}∗ seek loan finance and the rest seek security finance.

without loss of generality. From the loan approval condition (9) and for no arbitrage condition for a security (10), we have

P(S∗(RL∗_{(e), e), e) · R}L∗_{(e) ≥ c + R}D

= c +θ· P(S∗(RU_{, e}′_{), e}′_{) · R}U

which implying that

RL∗(e) ≥ c P(S∗_(RL_{(e), e), e)}+θ· P(S∗(RU_(e′₎′_{, e), e}′₎ P(S∗_(RL_{(e), e), e)} · R U (e′).

When c is sufficiently large, RL(e) > RU_(e′_{). }

5

The Impact of Security Markets on Project Choices

How bank competition affects the incentive of risk taking has been an important topic in banking literature. Deposit insurance and other government interventions distorts banks’ risk incentives. When facing stiff competition, banks intend to take more risks to keep its profits or competitive status. Deposit insurance and the government’s rescue often create a payoff structure in which large gains go to bank shareholders and large loss to the tax payers. This is one popular argument for bank competition and bank risk taking.

Boyd and de Nicol´o (2005) argue that there exists a fundamental risk-incentive mechanism that operates in exactly opposite direction, causing banks to become more risky as their market become more concentrated. We modify their model by incorporating market finance into the framework and show that the presence of

market finance provides alternatives for firms to finance their projects. The market alternative substitutes expensive loans with security finance of lower rates, which in turn keep firms from choosing high risk projects.

As we analyze inFigure 3high-e firms choose markets to raise their funds. When loan market becomes more concentrated, loan rates go up and V(RL, e) goes down and the critical value of e∗changes to a smaller value. More firm will choose to go for market finance. As long as such a shift to the market does not change security rate too much, those firms switching to markets choose projects with less risk. As we point out earlier, market rates are determined competitively while banks in concentrated loan markets can set loan rates. Banks’ strategic responses result in both high loan rates and the choice of high-risk projects by loan-finance firms (Proposition 1).

Those firms which stay with banks when loan markets become more concen-trated will choose higher risk projects (i.e., higher failure probability due to the higher loan rates). Those firms which transfer into market finance face a lower rate than the rate they would face if they stay with loan finance. That is why the pres-ence of market finance can mitigate the effect of Boyd-DeNicol´o risk-incentive mechanism.

Proposition 8 The presence of market finance mitigates the undesired effect of the risk-incentive mechanism due to higher borrowing rates in the loan market.

6

Conclusion and Summary

In this paper we extend Boyd and de Nicol´o (2005)’s model by adding hetero-geneity of entrepreneurs and market finance to discuss how the availability of market finance affect risks faced by production projects . Heterogeneous en-trepreneurs make their choices of risks basing on the borrowing cost they face. Boyd and de Nicol´o (2005) shows that more concentrated banking markets lead to choosing riskier investment projects.

In our research we show that when entrepreneurs have market finance as an alternative to loans, they can shift from loan markets to securities markets and borrow in funds at lower costs and adjust their productivities and risk exposure accordingly. As a result, they will have higher probabilities of success. The intro-duction of market finance as an alternative to loans mitigates the perverse effect of risk incentive mechanisms discovered in Boyd and de Nicol´o (2005) (Proposition 8).

The setup with heterogeneous entrepreneurs allows us to have more details on firms’ behaviors. Entrepreneurs with higher levels of management skill face higher loan rates in concentrated loan markets (Proposition 2), while in highly competitive loan markets they face lower loan rates (Proposition 4 [1]). Moreover we show that the borrowing costs of loan finance are higher than those of security finance if the screening cost of the loan technology is high enough.

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Extended Financial Services,

Banking Competition and Financial Fragility:

A General Equilibrium Framework

Yeong-Yuh Chiang

Department of Money and Banking National Chengchi University

NSC 95-2415-H-004-007-MY2 - Year 2

Abstract

We develop a general equilibrium model to analyze how the presence of direct lending affects entrepreneurs’ choices of production projects. We show that the presence of direct lending alleviates the perverse effect of the risk-incentive mechanisms of Boyd and de Nicol´o (2005). The general equi-librium framework allows us to analyze not only the direct effects, but also the general-equilibrium(GE) feedback effects, of changes in intermediation technologies and the availability of funds. Although improvements in finan-cial technologies reduce the cost of obtaining funds, they also increase the demand for funds and this GE feedback effect dominates the effect of cost reduction. As a result, both deposit and market rates increase. Then en-trepreneurs who issue securities to finance their projects face higher market rates and chooses projects with lower probability of success. The economy faces a more fragile financial sector.

Keywords: Extended financial services, Banking competition, Risk-taking, Financial fragility

The project of the first year deals with an environment with exogenous risk-free interest rate, deposit rate and market rate, with a purpose of focusing on how market finance mitigates the perverse effect of the risk incentive mechanisms caused by high loan rates discussed in Boyd and de Nicol´o (2005). In the research of the second year, we incorporate the first-year experience into a general equi-librium model and study how economic primitives affects the interaction of direct and indirect finances.

We consider a general equilibrium model with the setup of the first year as the production side of the real sector and the demand side of the financial sector. For the tractability of the analysis, we use a specific form of the probability function of success which satisfies all assumptions in the model. We endogenize the sup-ply side in the financial sector and the consumption side of the real sector to the environment to set up a general equilibrium model.

By using a general equilibrium framework we take into account of feedback effects of technological changes in the financial sector. We find out that techno-logical improvements in the financial sector tighten the supply of funds and cause deposit rates and market rates to rise. An increase in the deposit rate is offset by the decrease in the screening cost, and the loan rate remains unchanged. An increase in the market rate raises the cost of finance faced by securities-issuing firms and induces them to choose higher risky projects.

1

The Environment

Consider an economy with one consumption goods and one input. The consump-tion goods can be produced by a number of risky producconsump-tion technologies. Entrepreneurs

There are a continuum type of entrepreneurs (also called firms) with different skill levels of managing risky production technologies, denoted by e; e is distributed over the interval [e, ¯e] with a distribution function n ˙f(e) where n is the mass of entrepreneurs and R

[e, ¯e] f(e)de = 1. The type of the entrepreneur is private

infor-mation and can be observed by commercial banks when they applying the costly screening technology. A firm does not have any unit of the input, but has access to risky production projects with different levels of productivity, indexed by S. A production project with productivity S requires an investment of one unit of the input to produce S units of the output with probability P(S, e), and zero otherwise. The probability function P(S, e) satisfies the following conditions:

Assumption 1 Ps< 0, Pss ≤ 0, Pe> 0, and Pse> 0.

A higher skill level of management indicates a higher probability of success in production. For entrepreneurs there is a trade-off between productivity and risk. The choice of a higher productive project leads to a higher possibility of failure. Here is an example satisfying Assumption 1:

P(S, e) = 1 −AS

To simplify the analysis and keep the tractability, we use this example to derive our analysis.

We assume that entrepreneurs are risk neutral and maximize their expected profits by choosing where to borrow funds and what type of projects to adopt. They borrow funds either through security markets by issuing securities or through loan markets by going to a commercial bank to apply a loan. When a firm chooses to issue securities, it needs go to an investment bank to underwrite its securities. We assume that a firm can arrange its fund sources with only one financial insti-tutions to rule out the possibility of syndicate loans and mixtures of direct and indirect finance.

Agents

There are identical agents (also called households). The population of these iden-tical agents is m. Each agent has one unit of input and has access to only the risk free technology which uses one unit of input to produce RF units of output. The agents are risk averse and have a strictly concave and differentiable utility func-tion u(C). An agent chooses to allocate its endowed unit of input either to the risky free technology or lend it to entrepreneurs who have access to risky assets. We assume all lending activities have to go through either banks or financial mar-kets. We assume that private information makes it too costly for agents to have financial transaction directly with entrepreneurs. Thus there is no possibility of pairwise meetings between agents and entrepreneurs.

Financial Institutions1

Assume that there are two types of financial institutions, commercial banks and investment banks (hereafter called underwriters). Banks obtain funds by taking in deposits from agents and paying depositors interests at a gross rate RD. After receiving a firm’s application for a loan, a bank applies its screening technology to uncover the type of the firm at a cost of c units of the input goods and to verify the type of its proposed production project. The screening outcome is observable only to the bank, not to all other financial institutes and the public investors. The bank may and may not approve the loan application. If it approves the application, the bank also decides an (gross) interest rate (RL) it will charge for the loan. Since the screening technology yields exact information for the type of the applicant, the loan rates is contingent on the type of firms e.

An investment house underwrites securities for firms in exchange of fee in-comes. An investment bank delivers to the public investors the information they find out in the process of underwriting. Due to information asymmetry the pub-lic investor is not sure that the delivered information is complete and perfect. In reality, how convincing the information is depends upon many factors such as in-vestment projects, the reputation of the firm that raises funds, and the efforts of underwriters. In particular, the more efforts an underwriter put in collecting, an-alyzing and deliver data, the more convincing the information is. However, the

1_{The description of financial institutions mainly repeat what described in the report of the}

first year research with some changes to make the description relevant to this general equilibrium model.

information processing is costly. The efficiency of information processing tech-nology used by underwriters also matters. How much profit an investment bank can obtain for a underwriting case depends upon all these factors. In this paper we do not get into the details of this aspect. Instead, we assume that underwriting business is quite competitive and, thus, the underwriting fee (φ) an investment bank can collect from its clients is determined by market competition. We model the performance of underwriting process by a parameter of convincing power (de-noted by θ). More specifically, we assume that the public investor understands that the probability of success P(S, e) depends on who runs what kind of produc-tion technology; however they just do not know what (S, e) is. They make their investment decisions basing upon their belief P(S, e) on P(S, e). We use˜ θ to de-scribe how close the belief of the public to the real P(S, e): P(S, e) =˜ θP(S, e), 0<θ < 1.

Nowadays it is quite common to observe the mixture of direct and indirect lending for an investment project. As shown in Bolton and Freixas (2000) an equilibrium model with a mixture of bonds- and loans-financed capital structure can be very fruitful but paying a cost of analysis complexity. The purpose of this paper is to show that how competition from markets affects the risk structure dis-cussed in banking literature. It is natural to start with a simple analytical structure and get a clear-cut picture. Only after this step we can go with more confidence to set up a more complicated framework to tackle more difficult issue.

com-mercial banks. Like universal banks in Europe, comcom-mercial banks in the US started to integrate both loans and securities business under the Act. In many economies, for example Taiwan, Korea and Japan, the integration of financial sec-tor is also under way. Financial holding companies (or universal banks) become a popular form of financial organization. Economies of scale are the driving force behind this trend. The border line between banks-financed and markets-financed funds become burring. Both loans and securities issuing are substitutes and plements of each other and, Obviously, universal banks and financial holding com-panies play an important role in such a financial environment. However. for sim-plicity, we do not include financial holding companies and universal banks in our analysis. We concentrate on the substitution role of both direct and indirect lend-ing and leave the complement role as our future research topic.

2

Firm’s Optimization

Firms use external funds to acquire inputs for their technologies. Let R denote the gross interest rate for obtaining one unit of external funds. One unit of input costs one unit the output. The firm’s optimization problem can be written as

max

S (1 − AS/e)[S − R] (2)

The first order necessary condition is(−A/e) · S +(1 −AS/e) = (−A/e) · R, which can be rewritten as

H(S, e) ≡ S +1− AS/e

R

H(S, e)

S∗(R, e) R′

S∗(R′, e) S Figure 1: Loan Rates and the Choice of S

H(S, e) is the risk(Ps)-adjusted marginal contribution of an additional unit of

out-put to expected outout-puts, and the right hand side of (3) is the risk-adjusted marginal cost of increasing outputs. One can easily show that the left hand side of (3) is increasing in S, (i.e., HS(S, e) > 0 for e ∈ [e, ¯e]), while the right hand side is

con-stant over S. When the risk-adjusted marginal cost (R) increases, the firm should respond by increasing the scale of outputs (S). Let S∗(R, e) be the solution. When P(S, e) = 1 − AS/e, S∗ = (e + AR)/(2A). Figure 1 describes how a change in R affect S∗. As S increases, the probability of success decreases while the expected outputs increases due to the output increase. Thus the optimal response to an in-crease in R is to choose a greater S. A higher costs of funds (higher R) results in the choice of more risky project (a higher S and a lower probability of success).

decreas-R H(S, e) S∗(R, e) H(S, e′) S∗(R, e′) e′> e S

Figure 2: The Choice of S and Heterogeneity of Firms

ing in e, He(S, e) < 0. Given the cost of funding, R, firms with different e choose

different levels of production. A firm with a higher e indicates that his technology more likely succeed and leads him to choose a higher S for a higher return. In

Figure 2a greater e (e′) corresponds to a lower curve of H and results in the opti-mal choice of a greater S. This shows that how heterogeneity of firms affects the choice of risky technologies. In sum, S∗(R, e) has properties: S∗_R> 0 and S∗e > 0.

Next we define the value function of the firm’s optimization (2), denoted by V(R, e), as

V(R, e) = P(S∗(R, e), e)[S∗(R, e) − R] =(e − AR) 2

4Ae ;

Note that R is affordable only if S∗(R, e) = (e + AR)/(2A) ≥ R, or e > AR. The value function V(R, e) is increasing in e:

Ve=

e2− A2_R2 4Ae2 > 0.

and is decreasing in R:

VR(R, e) = −

e− AR

2e < 0. (4)

Moreover VRe = −_{2 e}AR2 < 0. Some important result about the choice of projects

and the probability of success are summarized in the following proposition:

Proposition 1 Facing the same borrowing rate R,

[1] Firms with greater skill levels of management chooses more productive projects:

S∗_e(R, e) > 0.

[2] the default risk decreases as the skill level of management increases:

dP(S∗(R, e))

de =

AR 8 e2 > 0

Firms with higher e choose technologies of higher productivity than firms with lower e; however, their failure probabilities are lower. The greater productiv-ity (S) indicates a higher failure probabilproductiv-ity (Ps(S, e) < 0); however a higher skill

level of management indicates a higher success probability (P(S, e1) > P(S, e2)) for all S. Two impacts work in the opposite directions. However, the direct effect dominates the indirect effect.

Two forms of external funds

Firms have two alternatives to raise their funds, borrowing loans from banks or issuing securities to the market. Let RL denote the (gross) loan rate and RU the rate in the direct lending market. In addition to RU, a firm has to pay an amount

φ of upfront underwriting fees for issuing securities. This upfront cost can be thought of as underwriting expenses.2 The firm’s optimization problems of ob-taining funds in these two alternatives are

max S P(S, e) · [S − R L ], and max S P(S, e) · [S − R U_{] −φ,}

respectively.3 The decision of funds-raising is transformed into the following problem:

max {V (RL, e),V (RU, e) −φ}. Recall that the value function V(R, e) has properties:

Ve(R, e) > 0, VR(R, e) < 0, and VRe(R, e) < 0. (5)

Consistent with empirical findings, we will only discuss the equilibrium out-come in which the direct lending is less costly than loan-finance (not considering upfront costs); i.e., RU < RL_{. (Later on we will show that, in our parametric}

2_{For simplicity, we assume that a firm has some resources to pay upfront costs, but they do}

not use them to finance their inputs. The results of our analysis is insensitive to this innocuous assumption. This upfront cost setup follows from Kanatas and Qi (1998, 2003). Puri (1999) has a similar setup.

3_{Here we assume that firms are price-takers in the borrowing markets. In a seller’s market}

firms do not have any influence over the price he pays. Later on when we analyze the underwriting activities, we will relax this assumption. When a firm chooses the type of project, it affects what he pays through the riskiness he chooses.

e1 A e2 A V(·, e1) V(·, e2) RL V(RL_{, e} 2) RU V(RU_{, e} 2) V(RL_{, e} 1) V(RU_{, e} 1) V(RU_{, e} 1) −φ φ V(RU_{, e} 2) −φ φ R V e1> e2

Figure 3: Underwriting Fee and Fund-Raising

example, when the screening cost of loan business (c) is large enough, the equi-librium in our model economy does have this property.) Then the the property of VR(R, e) < 0 implies that V (RU, e) > V (RF, e) for all e. We will use the properties

of (5) to show that as long as the underwriting fee φ is large enough and RU and RL falls apart enough distances, high e firms will issue securities to raise their funds, while low e firms will raise their funds through loans.

We use Figure 3 to illustrate this result: when φ is large enough and e1 is greater than e2 by a significant gap, it can be the case in which V(RU, e2) −φ > V(RL_{, e2), while V (R}U_{, e1) −}φ _{< V (R}L_{, e1). This can happen because the third}

property of (5). As a result, type e1 firms choose market finance, while type e2 firms choose loan finance. Moreover, from Proposition 1, one can easily verify

that projects financed by markets have greater probabilities of success than those financed by loans. We summarize these results in the following proposition.

Proposition 2 When RL> RU _andφ _{is large enough,}

[1] a very high e firm chooses market finance and a very low e firm chooses loan

finance;

[2] markets-financed projects succeed with a greater probability than banks-financed

projects:

3

Loans and Securities

In this section we discuss the optimization problems of financial institutes. Both banks and underwriters maximizes their profits by providing financial services.

Commercial Banks

Commercial banks take in deposits as the source of funds and lend funds to firms through loan contracts. We assume that banks are price-takers in deposit markets. This assumption deviates from Boyd and de Nicol´o (2005)’s set up. They assume that banks have monopoly power in both loan transactions and deposit business. This assumption allow them to analyze strategic behaviors of financial firms in both markets of their outputs(loans) and inputs(deposits).

In our setup of banking optimization we only allow banks have monopoly power in loan markets, but not in deposit markets (or more precisely funds