Discussion Papers In Economics
And Business

Managerial Reputation, Risk-Taking, and Imperfect
Capital Markets
Koji Asano
Discussion Paper 16-12

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANManagerial Reputation, Risk-Taking, and Imperfect
Capital Markets
Koji Asano
Discussion Paper 16-12

May 2016

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANManagerial Reputation, Risk-Taking, and Imperfect
Capital Markets∗
Koji Asano†

Abstract
This paper presents a model of portfolio management with reputation concerns
in imperfect capital markets. Managers with financial constraints raise funds frominvestors and select a project that is characterized by the degree of risk. Managers diﬀer
in their ability to determine the probability of success. Based on past performance,
all agents revise beliefs about managers’ ability, and the beliefs aﬀect the availabilityof funds in the future. This provides motivation for managers to build reputation by
manipulating their performance through project selection. We show that the quality ofinvestor protection changes fund flows, thereby influencing managers’ project selection.
Our model predicts that strong investor protection causes risk-taking behavior, whereas
weak investor protection leads to risk-averse behavior.
JEL Classification: G31, G32.
Keywords: reputation, investment decision, risk-taking, investor protection, pledgeability.

∗

I am especially grateful to Katsuya Takii for the valuable discussions and suggestions. I am also gratefulto three anonymous referees and the Editor-in-Chief for many insightful comments and detailed suggestions.
I would also like to thank Shingo Ishiguro, Junichiro Ishida, Ryosuke Okazawa, and the participants of the2013 Spring Meeting of the Japanese Economic Association, the 2014 Asian Meeting of the EconometricSociety, the 2014 Australian Meeting of the Econometric Society, PET 15, and Singapore Economic Review
Conference 2015. I gratefully acknowledge financial support from the Japan Society for the Promotion of
Science through a Grant-in-Aid for JSPS Fellows No.13J06362. All remaining errors are my own.
†
Graduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka, Osaka 560-0043,
Japan. E-mail: nge002ak@student.econ.osaka-u.ac.jp1

1

Introduction

Financial intermediaries have had a significant presence in capital markets worldwide. These
intermediaries, such as mutual funds, pension funds, and banks, collect a large fraction ofmoney from investors and make investments on their behalf. 1 Based on the strong influenceof portfolio managers on investors’ wealth and capital markets as a whole, academics andpolicy makers have devoted much attention to managers’ investment strategies.
One factor of investment strategies widely debated in the literature is the degree ofrisk. Evidence suggests that managers’ incentive for risk taking diﬀers across countries withvarying levels of investor protection, which plays a major roll in explaining the diﬀerencesin financial systems (e.g., La Porta et al., 1997, 1998). In countries with strong investor
protection such as the US, Chevalier and Ellison (1997) show that mutual funds engage
in risk-taking behavior. Bartram, Brown, and Stulz (2012) also indicate that because the
US has superior investor protection compared to other countries, US firms take greaterrisk, which creates more volatile financial markets. However, firms in countries with weak
investor protection exhibit conservatism even if this implies the rejection of value-enhancing
investments (John, Litov, and Yeung, 2008).
In this paper, we develop a model to explain the cross-country diﬀerences; strong investor
protection encourages managers’ risk-taking behavior and weak investor protection leads
them to behave conservatively. The key observation that links the quality of investor protection and managers’ risk-taking is that their incentives are driven by reputation concerns
through fund flows. Considerable literature argues that because the relationship between
fund flows and the fund managers’ past performance is positive and convex when there is nofear of bankruptcy, fund managers have incentive to increase the riskiness of their portfolio(e.g., Chevalier and Ellison, 1997). 2 Other literature notes that when fund managers with1

Gillan and Starks (2007) provide data to show that institutional investors held over 70% of US equities
in 2006. Although data in developing countries is limited, according to Demirgüç-Kunt et al. (2015), in
developing economies, 54% of adults reported having an account at a financial institution or through amobile money provider in 2014.
2
The amount of funds managers have is linked to their benefits. In mutual fund companies, managers

2bad past performance are likely to go bankrupt, the fear distorts the managers’ investment
decisions to avoid risk (Dasgupta and Prat, 2006 and Guerrieri and Kondor, 2012). We
argue that because strong investor protection restricts managers’ opportunities to divert
corporate resources for personal use and thereby enhances the managers’ ability to attract
funds, the level of investor protection changes the possibility of fund flows, which influences
the possibility of bankruptcy and managers’ risk-taking behavior through their reputation
concerns.
Let us explicitly describe the model and explain the main logic of the mechanism. This
paper presents a three-period model with a manager and investors. At date 0, the manager
raises funds from investors and chooses between three investment strategies: gambling (highrisk), middle (middle risk), or safety (no risk), where the middle strategy has the highest
net present value (NPV). At date 1, all agents observe the strategy selected and its outcome(success or failure) and, then, investors decide how much money they will pour into the manager. Again, the manager has access to investment opportunities for which the investment
technology is subject to a minimum level of investment, which can be interpreted as a fixedstart-up cost, as in Acemoglu and Zilibotti (1997). At date 2, the manager may misbehave
to enjoy private benefits and thereby reduce the probability that the investment succeeds,
as in Holmström and Tirole (1998).
Because a manager has limited liability, investors cannot penalize when the investment
fails at date 2. Therefore, the manager must receive suﬃcient income when the investment
succeeds to avoid misbehavior. This means that the manager has limited income that canbe pledged to investors, which constrains the amount of funds the manager can attract at
date 1. We interpret the small private benefits generated by misbehavior as the eﬀect ofstrong investor protection because it limits opportunities for the manager to divert funds
from the firm. Thus, strong investor protection decreases income that the manager mustreceive rewards through a management fee structure that depends on the amount of funds under management.
Moreover, fund inflows can be beneficial for the managers because they can utilize the new funds for next
investment opportunities.

3

keep to behave and increases the pledgeable income and the available funds.
Managers have some ability to determine their performance, and managerial ability is
unknown for the investors and managers themselves, as in Holmström (1999). The talented
manager is more likely to succeed with investments. Because we assume that the successprobability of a riskier strategy is more sensitive to talent, the results of a riskier strategy
provide more accurate information on the manager’s ability. Therefore, the manager who
succeeded with previous investments is more likely to be talented and attracts more funds
at date 1 than the manager who failed, and if the success is the result of riskier investments,
the manager’s ability to attract funds increases further.
As a benchmark case, we consider that moral hazard is absent: a manager necessarily
behaves at date 2. In this setting, because the full returns of investments can be pledged
to investors, the manager’s ability to raise funds is not limited and is irrelevant to both thequality of investor protection and the manager’s past performance. Hence, the risk-neutral
manager is concerned only with the NPV of the investment strategy and prefers the middle
strategy with the highest NPV.
However, when moral hazard is present, the manager’s ability to raise funds at date 1
depends on the level of investor protection and the outcome with previous investments, whichleads to reputation concerns. When investor protections are strong, a manager has suﬃcientpledgeable income to attract funds that satisfy a minimum investment level regardless ofthe manager’s established reputation through past performance. This implies that strong
investor protections function in a similar manner to insurance against a bad reputation.
Consequently, the manager can choose the gambling strategy to obtain significant inflows offunds by showing great performance. When investor protections are weak, a manager withpoor past performance must go bankrupt. This fear causes the manager to choose the safety
strategy to avoid bad performance even if it fails to produce positive profits.
In the extension, we show that excessive conservatism in the manager’s investment decisions is due to investors’ limited commitment to refinance the manager at date 1. If they have4commitment power, the manager can access long-term and state-contingent contracts, whichallows the manager to hedge the risk of bankruptcy by transferring funds across states. This
option-like nature of the contract encourages the manager to choose the gambling strategy,
regardless of the quality of investor protections. However, because the commitment problem
prevents such contracts, when investor protections are weak, the only way that the manager
can avoid the possibility of bankruptcy is to reduce the riskiness of the investment strategy.
This paper is related to the literature on career concerns, such as Gibbons and Murphy(1992), Meyer and Vickers (1997), Dewatripont, Jewitt, and Tirole (1999), and Holmström(1999). In particular, our paper studies explicit contracts in the presence of career concerns,
as in Gibbons and Murphy (1992) and Meyer and Vickers (1997). All the papers focus
on managers’ choices in an eﬀort to improve their reputation without an examination of
institutional quality. In contrast, our current paper focuses on project choices to improve
managers’ reputation and investigates how the quality of the institutional environment aﬀects
their incentives.
Our paper is closely related to the literature on the relationship between managerial
reputation and investment decisions. 3 Holmström and Ricart i Costa (1986) and Hirshleifer
and Thakor (1992) show that managers are tempted to behave prudently in their bid toconceal information on their abilities, which aﬀects their labor market condition in the future.
The reason for the conservatism is that managers are risk averse (Holmström and Ricart i
Costa, 1986), and early investment failure severely stains a manager’s career (Hirshleifer andThakor, 1992). 4 While these mechanisms are independent of the quality of the institutional
environment, our results show that managerial conservatism can be a result of weak investor
protection. When investor protection is weak, the fear of losing access to suﬃcient funds for
management continuity incentivizes managers to adopt a risk-averse strategy to maintain3

See Hirshleifer (1993) for an extensive literature survey on the eﬀect of managers’ reputation concernson their investment decisions.
4
Hermalin (1993) and Tirole (2006, Ch.7) find the result that a manager driven by reputation building
prefers risky investments. However, these models assume that riskier investments supply more noisy information concerning managerial ability. Thus, the manager driven by career concerns prefers a “conservative”
strategy with regard to reputational risk not project risk.

5their reputation. 5
Our study is also related to the growing literature on career concerns of experts with anability to understand the state of the world (e.g., Scharfstein and Stein, 1990 and Ottavianiand Sørensen, 2006). These papers focus on the herding mechanism, which does not examine
underlying financial market conditions. In contrast, reputation concerns in our paper can be
influenced by financial friction that causes investors to be sensitive to managerial reputation.
Dasgupta and Prat (2006) show that experts driven by career concerns engage in risktaking behavior because asymmetric information concerning their ability allows uninformedexperts to mimic informed experts’ behavior. Prendergast and Stole (1996) show that young
managers behave aggressively and, through a learning process, old managers become conservative. In contrast to these papers, our mechanism does not rely on asymmetric information.
The aggressive investment behavior in our study stems from financial friction that allows
managers to exploit investment opportunities to expand their pledgeability. Also, unlike
Prendergast and Stole (1996), we focus on cross-country diﬀerences, not changes in behavior
through the learning process.
To the authors’ knowledge, Guerrieri and Kondor (2012) is the only paper that addresses
how reputation eﬀects change depending on underlying economic conditions. In this paper,
the informativeness of the investment strategies changes; managers who adopt safe investments in times of economic boom are likely to be recognized as uninformed and to be fired,resulting in risk-taking behavior, whereas managers who adopt risky investments during recessions are also likely to be similarly viewed, resulting in conservatism. In our paper, while
the informativeness does not change, the ease of access to financial markets changes depending on the quality of investor protection. We can view our model, which places cross-country
diﬀerences as the central focus, as a complement to the model of Guerrieri and Kondor(2012), who focus on asset price volatility in time series.
5

While this literature and our paper focus on the distortion caused by reputation concerns, anotherstrand of research focuses on how reputation concerns discipline opportunistic behavior. See Diamond(1989), Ordoñez (2013), and Asano (2016).

6

Finally, our paper reflects on the agency problem on the managers’ side and on theinvestors’ side. The problem that stems from a lack of investor commitment has beenemphasized in Holmström and Tirole (1998) and Lorenzoni (2008).
This paper is organized as follows. Section 2 provides the basic framework of the model.
Section 3 analyzes the equilibrium. First, we describe the benchmark scenario without
reputation concerns. Then, in the model with reputation concerns, we derive the equilibrium
strategy based on the quality of investor protection. Section 4 discusses several assumptions
and develops some extensions. Section 5 concludes.

2

The Framework

This section introduces the structure of our model. Section 2.1 describes agents, projects, andthe moral hazard problem that is the source of borrowing constraints. Section 2.2 describes
financial contracts and the model timeline. Section 2.3 introduces parametric assumptions
about the moral hazard problem and explains the incentive compatibility condition. Section 2.4 defines the equilibrium concept.

2.1

Description

The model has three periods, t = 0, 1, 2 and a single good. There are two types of agents:a manager and a continuum of investors. The manager receives nothing at t = 0 and nonverifiable capital A > 0 at the beginning of t = 1. All investors receive one unit of the goodat t = 0 and K units of the good at t = 1. All agents are risk-neutral with the following
utility function over consumption streams: c0 + c1 + c2 . All agents have access to storage
technology with a return of one.
The manager’s ability denoted by i takes two values: high (H) and low (L). This ability
denotes the manager’s skill level in generating good performance with a high probability
and is unknown to both investors and the manager, as in Holmström (1999). A manager’s

7

reputation is defined as a belief concerning the probability of being type H. All agents share
the prior beliefs π = Pr(i = H).
The manager has two opportunities at t = 0, 1 to invest. The following three strategies
are options at t = 0: investment in a risky asset (Gambling, G-strategy, or G), investmentin the most value-enhancing asset (Middle, M-strategy, or M ), or investment in storage
technology (Safety, S-strategy, or S). To focus on a pure strategy equilibrium, the manager
chooses the investment strategy x ∈ {G, M, S}. The G-strategy and the M-strategy either
succeed or fail. The G-strategy selected by a manager of type i whose investment level is
I0 yields good returns RG I0 with probability pi , whereas the M-strategy yields RM I0 (where
RG > RM > 0) with probability qi . In the case of failure, the returns from the investment
are 0, regardless of whether the G-strategy or the M-strategy is selected. The S-strategy
involves storage technology that yields a payoﬀ of one regardless of the manager’s ability
and the amount of investment. Our analysis introduces the notation R(x) that represents
the return per unit of investment when the date-0 investment strategy x succeeds; that is,R(G) = RG , R(M ) = RM , and R(S) = 1.
At t = 1, the manager has access to a new investment opportunity.6 The investment
technology is linear in investment level I1 but requires a minimum investment size Iˆ withˆ the investment managed by the manager of type i generatesIˆ ∈ [A, K + A]. 7 If I1 ≥ I,
the return RN I1 with probability δi with 1 > δH > δL > 0 and nothing with probability
1 − δi ; otherwise, it also produces nothing. Most previous papers on reputation concernswith project choices (e.g., Hirshleifer and Thakor (1992) and Guerrieri and Kondor (2012))
represent indivisibilities in investments (or start-up costs) as fixed size investments, but ourmodel represents it in the form of a minimum investment requirement as in Acemoglu andZilibotti (1997). Our approach has an advantage over the assumption of fixed size investment
because we can clarify diﬀerent implications of fixed investments and variable investments for6

If we assume that there is a project choice at t = 1, the date-0 investment selected by the manager might
be aﬀected. This point is discussed in Section 4.2.
7
We consider that only the date-1 investment is subject to the minimum size requirement for simplicity.
However, even if there is the requirement at date-0 investment, our result remains the same (see Section 4.3).

8

project choices. Managerial incentives to behave conservatively are based on indivisibilities
in investments, whereas the incentive to take risks is based on variable investments.
We make three assumptions concerning investments.
Assumption 1
1 > pH > qH > qL > pL > 0.

This implies that the project managed by an H-type manager succeeds with a higher
probability than a project managed by an L-type manager (qH > qL and pH > pL ). This
reflects the intuition that a manager’s skill is associated with productivity. Additionally,
under an H-type manager, the risky investment is more likely to succeed than the relatively
safe investment (pH > qH ), while under an L-type manager, the risky investment is lesslikely to succeed (qL > pL ). This assumption captures the idea that outcomes of riskier
investments depend more heavily on managerial skill. A manager with a high level of ability
can more eﬀectively manage riskier assets while a manager with a low level of ability cannot
eﬀectively manage risky assets, as in Hirshleifer and Thakor (1992).
Assumption 2
qRM > pRG > 1,
where q = πqH + (1 − π)qL and p = πpH + (1 − π)pL .
This means that among the three strategies at t = 0, the M-strategy yields the highest expected return and the G-strategy yields the second highest expected return. This
assumption implies q > p, which makes the G-strategy more risky than the M-strategy.
Assumption 3
δL RN > 1.

9

This means that even if an L-type manager makes the new investment at t = 1, it has apositive NPV. This assumption ensures that the date-1 investment is eﬃcient regardless of
reputation.
A manager confronts financial constraints because of a moral hazard problem where,
after date-1 investment, the manager chooses to behave without receiving private benefits
or to misbehave and take private benefits, as in Holmström and Tirole (1998, 2011).8 If the
manager behaves without receiving private benefits, the investment will continue as describedabove. If the manager misbehaves, the probability of success decreases by ∆π ∈ (0, δL ),where we assume that ∆π is independent of managerial ability. Instead, the manager enjoys
benefits BI1 that are inalienable to investors.
We can interpret the reduction in B as the manifestation of an improvement in investor
protection or corporate governance, as argued in Tirole (2006, p. 359), Antràs, Desai, andFoley (2009), and Holmström and Tirole (2011, p. 86). The idea behind this interpretationis that a better regulatory system that protects investors is likely to prevent managers fromtaking private benefits or limit their ability to divert funds from the firm for personal use.
For example, regulatory changes to improve the firm’s reporting and increase transparency
can limit opportunities for insiders to tunnel resources out of the firm and increase investor
protection.

2.2

Financial Contracts and Sequence of Events

A manager can make a take-it-or-leave-it oﬀer to investors with the storage technology as
an outside option. Both agents are protected by limited liability. The investment strategy
selection x, its returns R(x)I0 , and the date-1 return RN I1 are publicly observable andverifiable. For simplicity, R(x)I0 cannot be used for subsequent investments; therefore,
capital accumulation is removed from the model. We assume that the contract structure is
as follows.
8

If the date-0 investment is subject to the manager’s moral hazard, our result is not aﬀected (see Section 4.3).

10

First-bestGambling

Gambling

MiddleSafetyMiddleSafetyt=0

Safety

t=0

t=1

t=0

t=1

t=2

t=1

t=2

t=2

Managers offer financial
contracts
Managers invest in one ofthree investment strategies

All agents observe outcomes and Moral hazard: managers
update managerial reputation
choose to behave or
misbehaveManagers offer new contracts
Profits are realized

Figure 1: Timeline structure(i) The manager has access only to short-term contracts, that is, the manager oﬀers thecontract at t = 0, 1 because investors do not have the ability to commit to futurefinancing. We discuss the lack of commitment in Section 4.1.
(ii) At t = 0, the investors contribute their funds I0 , and the manager invests them in an
investment strategy x. When the strategy succeeds, the investors will receive d0 , andthe manager will receive R(x)I0 − d0 . When the investment fails, both parties receivenothing. Because the contract is contingent on the investment strategy x, the contract

1

specifies the tuple (I0 (x), d0 (x)).

1(iii) At t = 1, the investors contribute their funds I1 − A and the manager contributes

personal capital A. When the project in which I1 has been invested succeeds, theinvestors will receive d1 , and the manager will receive RN I1 − d1 . When the project
fails, both parties receive nothing. Thus, the contract specifies the tuple (I1 , d1 ).
We outline the timeline structure (see Figure 1). At the beginning of t = 0, a manager
oﬀers the contract that specifies (I0 (x), d0 (x)), and the investors who receive the oﬀer decide
whether to accept. If the investors reject the oﬀer, the manager is terminated, and investors
must use storage technology. If the investors accept the oﬀer, the manager borrows andchooses the investment strategy x with investment level I0 (x) and the repayment d0 (x). At
t = 1, all the agents observe the subsequent outcome sx ∈ {0, 1} where 0 indicates failure and1 indicates success. Both parties infer the manager’s true ability based on sx and update11managerial reputation from π to π ′ according to Bayes’ rule. Then, the manager oﬀers
the new contract that specifies (I1 , d1 ). After receiving the new contract, investors decide
whether to roll over their funds. At t = 2, the manager decides whether to behave. Then, all
the agents observe the outcomes of the investment made at t = 1 and are paid as contracted.

2.3

The Incentive Compatibility Condition and Parametric Assumptions

We will describe the incentive compatibility condition and some assumptions concerning themoral hazard problem.
First, we assume that the investment is worthless without eﬀort:
Assumption 4(δH − ∆π)RN + B < 1.

This condition means that the project managed by even the H-type manager has negative
NPV even if the private benefit is included, if the manager misbehaves. Under Assumption 4,
the manager with any posterior reputation π ′ cannot raise any funds if misbehaving and,thus, behaves if raising funds on the equilibrium. To behave, the manager has to obtaincertain rents that satisfy the following incentive compatibility condition:!
"
δ(π ′ )(RN I1 − d1 ) ≥ δ(π ′ ) − ∆π (RN I1 − d1 ) + BI1 ,where δ(π ′ ) = π ′ δH + (1 − π ′ )δL . The left-hand side is the manager’s expected gross utility
in the case of behavior at t = 1: when the investment succeeds with probability δ(π ′ ), themanager is paid RN I1 − d1 . The right-hand side is the manager’s expected gross utility inthe case of misbehaving at t = 1, that is, the sum of the expected amount the manager ispaid (δ(π ′ ) − ∆π)(RN I1 − d1 ) and the private benefits BI1 . The condition can be rewritten12asδ(π ′ )(RN I1 − d1 ) ≥ δ(π ′ )

B
I1 ,
∆π

(1)

implying that δ(π ′ )B/∆π is the minimum expected rent for the manager per unit of investment necessary to ensure that the manager behaves. Therefore, at most, δ(π ′ )(RN −B/∆π)I1
are expected to be paid to investors without inducing the manager to misbehave; thus, wecall it expected pledgeable income, as in Tirole (2006). It is decreasing in B/∆π, that is, it iseasier for managers to pledge more income in countries with better investor protection.
We make two other parametric assumptions regarding the moral hazard problem. First,
the following assumption guarantees that the equilibrium investment at t = 1 is finite:
Assumption 5
δH

#

B
R −
∆π
N

$

< 1.

This means that the expected pledgeable income per unit of investment for the H-typemanager (the left-hand side) is lower than the unit cost of investment (the right-hand side).
If this assumption is violated, a manager can promise to pay to investors without down
payments A and collect funds without limits. This condition assures that even the Htype manager faces the financial constraint problem, implying that the manager with any
reputation π ′ also faces financial constraints. Assumption 4 and Assumption 5 are similar
to the assumptions made in Holmström and Tirole (1998, 2011).
The next assumption insures that a manager with reputation π is expected to collectfunds up to the minimum investment level Iˆ at t = 1:
Assumption 6#

Bδ(π) R −
∆π
N

13

$

Iˆ ≥ Iˆ − A.

ˆ the left-hand side is the expected pledgeable income
Given that the investment level is I,
with an ex ante reputation, whereas the right-hand side represents the funds supplied byinvestors. The condition assures that when the managerial reputation does not change,
investors contribute their funds to such a manager. This assumption captures the ideathat investors believe that the manager to whom they lend their funds has the ability to
produce enough returns in the future. Therefore, maintaining a reputation is valuable forthe manager. Unless the manager’s reputation is damaged, the opportunity to continue tomanage should persist.

2.4

Equilibrium Concept

In our paper as a whole, the appropriate equilibrium concept is the perfect Bayesian equilibrium.
Definition 1 A perfect Bayesian equilibrium is given by the investment strategy x, the eﬀort
choice, the investment levels I0 (x) and I1 , the payments for the investors d0 (x) and d1 , theinvestors’ decision for financing, and all agents’ beliefs about the probability of being an
H-type π ′ such that the following conditions are satisfied:• The investment strategy, the eﬀort choice, and the contract that specifies the investment
levels and the payments for investors maximize the manager’s expected utility where
beliefs and the investors’ financing strategies are taken as given;• The financing decision of the investors maximize its expected utility, where beliefs, themanager’s investment strategy, the eﬀort choice, and the contract the manager oﬀers
are taken as given;• Agents’ beliefs are consistent with Bayes’ rule given equilibrium strategies, wheneverpossible.

14

3

Analysis

This section characterizes the pure strategy equilibrium. Section 3.1 derives the reputation π ′on the equilibrium path. 9 Section 3.2 analyzes the benchmark for which there is no moral
hazard. In this case, because there is no relationship between a manager’s performanceand inflows of funds, the manager does not have incentive to build reputation. Section 3.3
analyzes the model with moral hazard. The problem creates borrowing constraints and thepositive flow-performance relationship, which leads to reputation concerns. We show thatthe quality of investor protection influences the relationship and the manager’s investment
decision. Section 3.4 examines comparative statics.

3.1

Reputation Updates

Observing the investment strategy x and the subsequent outcome sx , all parties update
managerial reputation from π to π ′ along the equilibrium path. Managers who implement
the S-strategy can conceal information about their ability and maintain their reputation π
because the return structure of this strategy is independent of the manager’s ability. The
reputation π ′ along the equilibrium path of the G-strategy conditional on 0 and 1 successes,
denoted by π G,0 and π G,1 , respectively, are as follows:9

π G,0 = Pr(i = H | sG = 0) =π(1 − pH ),π(1 − pH ) + (1 − π)(1 − pL )(2)

π G,1 = Pr(i = H | sG = 1) =πpH.
πpH + (1 − π)pL(3)

We ignore the posterior reputation at t = 2 because it is irrelevant for the interests of all parties.

15

For the M-strategy, the reputation π ′ conditional on 0 and 1 successes, denoted by π M,0 and
π M,1 , respectively, are as follows:
π M,0 = Pr(i = H | sM = 0) =π(1 − qH ),π(1 − qH ) + (1 − π)(1 − qL )π M,1 = Pr(i = H | sM = 1) =πqH.
πqH + (1 − π)qL

From Assumption 1, we obtain the following relationship between the reputation π ′ :π G,0 < π M,0 < π < π M,1 < π G,1 .

(4)

All the agents perceive the manager to possess a high ability after a success and to possess
low ability after a failure (π x,0 < π < π x,1 ). The diﬀerence between the G-strategy andthe M-strategy is the quantum of information: the former reveals more information about
managerial ability. The G-strategy selected by an H-type (L-type) manager is more (less)likely to succeed than the M-strategy. Consequently, both parties consider the manager
who succeeds using the G-strategy more capable than the manager who succeeds using theM-strategy (π M,1 < π G,1 ), whereas both parties consider the manager who fails using theG-strategy less capable than the manager who fails using the M-strategy (π G,0 < π M,0 ).
The investment strategies in our model feature the relationship between returns and reputation; that is, the G-strategy is more volatile concerning both returns and reputation thanthe M-strategy. The observation that investment risks and reputational risks are positively
correlated is central to our results.

3.2

Benchmark Model

As a benchmark, suppose that a manager can commit to future eﬀort although both agents
do not know managerial ability. We solve the equilibrium by using backward induction. At
t = 1, because the manager oﬀers the contract that specifies a tuple (I1 , d1 ) after observing
16the date-0 investment outcome sx , the optimal contract depends on reputation π ′ . The
optimal contract problem at t = 1 is characterized as follows:
V (π ′ ) = max δ(π ′ )(RN I1 − d1 ) − A,
I1 ,d1(5)subject toδ(π ′ )d1 ≥ I1 − A(6)

I1 ≤ K + A(7)ˆ
I1 ≥ I.

(8)The objective function (5) is the manager’s net expected payoﬀ at t = 1. The constraint (6) is
the participation constraint for investors at t = 1. The left-hand side represents the expected
payoﬀ to investors, whereas the right-hand side represents the lending amount given so thatthe storage technology that produces zero profit is the outside option. The constraint (7) is
the resource constraint at t = 1 in which all resources are split into the manager’s capital A
and the investors’ capital K. The constraint (8) is the minimum investment requirement.
Because any manager produces positive expected profits from Assumption 3, the manager
increases the investment level I1 and decreases the payment d1 as much as possible. Thismeans that (6) and (7) are binding, and (8) is not binding. A manager invests all resources
regardless of her reputation π ′ . The value function of this optimal contract problem is givenbyV (π ′ ) = (δ(π ′ )RN − 1)(K + A),(9)where the manager receives the entire social surplus because the investors have zero profit.
Given the result, we characterize the date-0 optimal contract that chooses (x, I0 (x), d0 (x))
in two steps. First, given the investment strategy x, the manager chooses (I0 (x), d0 (x)) to17

solve the following problem:!
"
U0 (x) = max Pr(sx = 1) R(x)I0 (x) − d0 (x) + V (π x,1 ) + Pr(sx = 0)V (π x,0 ),(10)subject toPr(sx = 1)d0 (x) ≥ I0 (x).

(11)

I0 (x) ≤ 1,

(12)

The objective function (10) is the manager’s net expected payoﬀ at t = 0, where the firstterm is the manager’s payoﬀ in the case of success and the second term is the manager’s
payoﬀ in the case of failure. The constraint (11) is the participation constraint for investors
at t = 0 given that the storage technology is the outside option. The constraint (12) is theresource constraint at t = 0. As with the date-1 contract problem, Assumption 2 implies
that the manager decreases the payments d0 and increases the investment level I0 as muchas possible, making (11) and (12) binding. Thus, the manager’s value function at t = 0 with
the investment strategy x is given by
U0 (x) = Pr(sx = 1)R(x) − 1 + V (π),(13)

where V (π ′ ) is given by (9).
Second, the manager chooses the strategy x that produces the highest payoﬀ to solve

W = max{U0 (G), U0 (M ), U0 (S)}.

(14)

The important point is that the investment strategy x does not aﬀect the expected payoﬀ at
date 1, that is, E [V (π ′ ) | x] = V (π). This means that the manager is concerned only withexpected return Pr(sx = 1)R(x), not reputation. Figure 2 explains the point intuitively. The

18

V (⇡ 0 )⇡0Figure 2: Benchmark casehorizontal line represents reputation π ′ , and the vertical line represents V (π ′ ) given by (9).
Here, superior reputation does not aﬀect the investment level but increases the probabilityof the success and the NPV, which generates a linear relationship between π ′ and V (π). Thisimplies that there is no distortion caused by the inflow of funds in response to the manager’s
past performance and no bias concerning the risk preference. Thus, the manager adopts theM-strategy, which yields the highest expected returns from Assumption 2. 10
Lemma 1 Under Assumptions 1–3, the benchmark strategy is the M-strategy, and the investment levels at t = 1 are all resources in the economy.

3.3

Model with Moral Hazard

This section introduces the moral hazard problem and shows how the investment decision
is distorted depending on the level of investor protection. On the equilibrium, the manager
must behave to obtain financing because investors do not lend to a manager who jeopardizes
10

The result may be counterintuitive based on Blackwell’s theorem, which states that the more informative
strategy in the sense of Blackwell (i.e., the G-strategy in our model) provides a higher expected payoﬀ. We
can reconcile our result with the theorem by Assumption 3 that implies δ(π G,0 )RN > 1. This allows investors
to contribute all their funds to a manager with any reputation and eliminates the benefits of informativeness.
Although the assumption may lead us to focus on a limited situation, this benchmark highlights the eﬀectof borrowing constraints.

19

their funds from Assumption 4. Given a posterior reputation π ′ , the optimal contract problem at t = 1 is characterized as follows: choosing (I1 , d1 ) to solve the problem (5)–(8) plus
the incentive compatibility condition (1). As with the benchmark problem, the manager
increases the investment level I1 and decreases the payment d1 as much as possible from
Assumption 3, making (6) binding. Then, combining (1) and (6), we obtain#

Bδ(π ) R −
∆π
′

N

$

I1 ≥ I1 − A,

where the left-hand side represents expected pledgeable income. As long as it is greater thanthe lending amount, the manager can borrow money; that is, the manager raises funds up
to the binding condition:
I1 = k(π ′ )A
wherek(π ′ ) =1
1 − δ(π ′ ) (RN − B/∆π)>1from Assumption 5, which represents the leverage per unit of personal capital. This implies
that I1 is increasing in π ′ ; that is, a manager with a superior reputation is perceived more
likely to succeed in the investment and collects more funds. If K is suﬃciently large, thecondition (7) is not binding.
However, the manager obtains refinancing only when the amount she can invest satisfies the minimum investment level (8) or, equivalently, managerial reputation exceeds thethreshold denoted by π̂:
%
&
ˆ− A
1
I
π ′ ≥ π̂ =− δL ,
δH − δL (RN − B/∆π) Iˆ

(15)where π̂ < π from Assumption 6. If π ′ ≥ π̂, the manager will obtain financing; otherwise, themanager will not obtain financing and will just invest personal capital in storage technology.
The relationship between reputation π ′ and level of investment I1 is depicted in Fig20

I1

k(⇡ 0 )A

Iˆ

⇡0
⇡
ˆ
Figure 3: Investment levelure 3. In contrast with the benchmark, there is a positive and non-linear flow-performance
relationship, which leads to reputation concerns and bias about risk preference. The essential point is the eﬀect of investor protection on the necessary reputation that assuresmanagement continuity. (15) implies that π̂ is increasing in B/∆π, that is, the stronger theinvestor protection, the more tolerant investors are towards managers’ failures. Thus, wheninvestor protection is strong, the manager is likely to continue to invest even after showing
an investment failure and obtaining a poor reputation.
The value function of the date-1 optimal contract problem is given by

V (π ′ ) =

⎧
!
"
⎪
⎪
⎨ δ(π ′ )RN − 1 k(π ′ )A if π ′ ≥ π̂,
⎪
⎪
⎩0

(16)

′

if π < π̂.

When π ′ ≥ π̂, V (π ′ ) represents the benefits of informativeness because V (π ′ ) is convex
in π ′ . A better reputation increases the probability of success and pledgeability, leading
to the convexity. Given the function, the manager can take advantage of the information
by managing funds. However, when π ′ < π̂, V (π ′ ) goes to 0, which represents the costof informativeness. If the investment failure reveals the manager’s incompetence and the21V (⇡ 0 )E[V (⇡ 0 ) | G]
E[V (⇡ 0 ) | M ]E[V (⇡ 0 ) | S]

⇡ G,0

⇡ M,0

⇡

⇡ M,1 ⇡

G,1

⇡0

Figure 4: The manager’s expected utility in the case of π̂ ≤ π G,0reputation becomes lower than the threshold, the manager must simply save the endowment
A.
Given the result, we solve the date-0 optimal contract problem. First, we choose (I0 (x), d0 (x))
to solve the problem (10)–(12) given the strategy x. Because there is no moral hazard at
t = 0, the problem is the same as the benchmark model, except for the value function V (π ′ ),which is given by (16) but not (9). The manager decreases the repayments d0 (x) and increases the investment level I0 (x) as much as possible, making (11) and (12) binding. Thus,
the manager’s value function at t = 0 with the investment strategy x is given by
U0 (x) = Pr(sx = 1)R(x) − 1 + E [V (π ′ ) | x](17)

where V (π ′ ) is given by (16). In contrast with the benchmark given by (13), (17) implies thatthe investment strategy x aﬀects the date-1 payoﬀ E [V (π ′ ) | x]. This is because the superior
reputation increases both NPV and pledgeability as shown in Figure 3. The investors’
responses to reputation motivate managers to build their reputation through project risk.
22

Then, consider the date-0 strategy x to solve the problem (14) as a function of the levelof investor protection B/∆π. First, we suppose the situation where the quality of investor
protection is high (B/∆π is small) such that π̂ ≤ π G,0 , as depicted in Figure 4. Strong
investor protection encourages tolerance among investors with respect to failures and leads
them to roll over their funds regardless of the manager’s reputation. Thus, the manager
is willing to reveal information about managerial competence to exploit an opportunity
to adjust funds. Because the G-strategy is the most informative strategy in the sense ofBlackwell and produces the highest benefit, as Figure 4 shows, the manager chooses theG-strategy if the diﬀerence of expected returns between the M-strategy and the G-strategy
qRM − pRG is suﬃciently small.
Next, we suppose the quality of investor protection is intermediate (B/∆π is intermediate) such that π G,0 < π̂ ≤ π M,0 . This case is illustrated in Figure 5. The diﬀerence comparedto the previous case is that a failure of the G-strategy results in bankruptcy, which is the costof informativeness. If the cost is suﬃciently large, the manager has strong disincentives toadopt the G-strategy to avoid disclosing information about managerial incompetence. Consequently, to mitigate reputational risk, an opaque strategy that is less informative becomesa more attractive option, leading the manager to engage in the M-strategy.
Finally, consider that the quality of investor protection is poor (B/∆π is large) such thata failure by either strategy does not assure management continuity corresponding to the casewhere π M,0 < π̂ ≤ π (see Figure 6). The decrease in the quality of investor protection reduces
the benefits of the M-strategy because the failure leads to the cost of losing investment
opportunity. The cost renders the manager reluctant to reveal information. If the valueof investment opportunity at t = 1 is suﬃciently high, the manager adopts the S-strategy,
although it is the least profitable, to conceal managerial ability and continue management.
This entire discussion is summarized as a proposition.
Proposition 1 Suppose that Assumptions 1–6 hold, K is suﬃciently large, and pRG is
suﬃciently close to qRM .
23

V (⇡ 0 )E[V (⇡ 0 ) | M ]E[V (⇡ 0 ) | G]
E[V (⇡ 0 ) | S]

⇡

G,0

⇡
ˆ ⇡

M,0

⇡

⇡ M,1 ⇡

G,1

⇡0

Figure 5: The manager’s expected utility in the case of π G,0 < π̂ < π M,0V (⇡ 0 )E[V (⇡ 0 ) | S]
E[V (⇡ 0 ) | G]
E[V (⇡ 0 ) | M ]⇡ G,0⇡ M,0 ⇡
ˆ ⇡⇡ M,1 ⇡ G,1

Figure 6: The manager’s expected utility in the case of π M,0 < π̂ < π24⇡0(i). Suppose π̂ ≤ π G,0 . The date-0 equilibrium strategy is the G-strategy and the date-1
investment levels are k(π G,1 )A after a success and k(π G,0 )A after a failure.
(ii). Suppose π G,0 < π̂ ≤ π M,0 . If
!
"
!+
,
"
pRG + p δ(π G,1 )RN − 1 k(π G,1 )A < qRM + E δ(π ′ )RN − 1 k(π ′ )A | M ,(18)

the date-0 equilibrium strategy is the M-strategy and the date-1 investment levels arek(π M,1 )A after a success and k(π M,0 )A after a failure.
(iii). Suppose π M,0 < π̂ ≤ π. If!
"!
"
pRG − 1 + p δ(π G,1 )RN − 1 k(π G,1 )A < δ(π)RN − 1 k(π)A,(19)

the date-0 equilibrium strategy is the S-strategy and the date-1 investment level isk(π)A.
Proof. See Appendix A.
Finally, we note the welfare implications. Given utilitarian social welfare and the zeroprofit condition for the investors, the manager receives all of the social surplus. Thus, social
welfare is equivalent to the manager’s value function W , which is given by
⎧
!
"
⎪
⎪
⎪
W G = pRG − 1 + E (δ(π ′ )RN − 1)k(π ′ )A | G
if π̂ ≤ π G,0 ,
⎪
⎪
⎪
⎨
!
"
W = W M = qRM − 1 + E (δ(π ′ )RN − 1)k(π ′ )A | M
if π G,0 < π̂ ≤ π M,0 ,
⎪
⎪
⎪
⎪
⎪
⎪
⎩W S = (δ(π)RN − 1)k(π)Aif π M,0 < π̂ ≤ π.

(20)

As the investor protection improves, the social welfare (20) increases through two channels. First, given that the equilibrium strategy x is constant, the manager can increase theinvestment level k(π ′ )A and the social surplus the investment produces. Second, since thecutoﬀ reputation π̂ decreases from (15), the equilibrium strategy becomes more risky. The
25

more informative investment increases the value of the option to invest and social welfare
improves (i.e., W G > W M > W S ). Therefore, the volatility in our model is beneficial to theeconomy, as in Bartram, Brown, and Stulz (2012). Compared to the benchmark solution, in
which social welfare is given by qRM − 1 + (δ(π)RN − 1)(K + A), the above two channels
decrease social welfare.

3.4

Comparative Statics

This section examines comparative statics to derive more empirical predictions and welfare
implications from our model. To clarify the explanation, before conducting comparative
statics, suppose π̂ ≤ π G,0 and the equilibrium strategy is the G-strategy, which leads tosocial welfare W G .
First, we study the comparative statics with respect to the minimum investment levelˆ (15) implies that an increase in Iˆ leads to an increase in the cut-oﬀ reputation π̂. BeI.
cause more funds must be invested, the manager who will borrow funds requires a higher
reputation. Figure 7a shows the eﬀect. When π̂ < π G,0 , a marginal increase in Iˆ does notchange the equilibrium strategy and social welfare. When π̂ = π G,0 , a marginal increase inˆ combined with Figure 4 and Figure 5, implies that increased fear of missing an investI,
ment opportunity makes the G-strategy less attractive. Therefore, the manager chooses theM-strategy, which reduces the value of the option to invest and social welfare by W G − W M .
Next, we consider the eﬀect of a decrease in the manager’s capital A (Figure 7b). A
decrease in A aﬀects the manager’s date-1 payoﬀ V (π ′ ) from (16), which is a similar prediction
as the increase in agency costs B/∆π. When π̂ < π G,0 , a marginal decrease in A induces
a fall in the investment level k(π ′ )A. This makes the expected date-1 payoﬀ with the Gstrategy E [V (π ′ ) | G] smaller than the payoﬀ with other strategies. If pRG is suﬃciently
close to qRM , the equilibrium strategy remains the G-strategy, but social welfare W G islower. When π̂ = π G,0 , a marginal decrease in A induces an increase in π̂ from (15), whichleads to the inequality π̂ > π G,0 . Thus, the manager is induced to invest in the M-strategy,26

V (⇡ 0 )

Iˆ "

⇡
ˆ
0

⇡0

⇡

(a) On minimum investment level IˆV (⇡ )B", A #
⇡

⇡
ˆ

⇡0

⇡

(b) On agency costs B/∆π and a manager’s capital A

V (⇡ 0 )pH ", pL #E[V (⇡ 0 ) | G]

⇡
ˆ

⇡

⇡0

(c) On informativeness of the G-strategy pH andpL
Figure 7: Comparative statics

27

which lowers social welfare by W G − W M . Therefore, our model predicts that capital-poor
firms have a tendency to make less risky investments to control reputational risk.
Finally, we perform comparative statics with respect to the informativeness of the investment strategy. In particular, we consider a marginal increase in the probability of successfor the H-type manager, pH , aﬀecting the manager’s payoﬀ (20) through two channels.11
First, the expected return of the G-strategy pRG increases. Second, the G-strategy becomes
more informative in the sense of Blackwell, leading to a lower posterior reputation in thecase of failure π G,0 from (2) and a higher posterior reputation in the case of success π G,1from (3). When π̂ < π G,0 , the second eﬀect makes the expected date-1 payoﬀ with the Gstrategy E [V (π ′ ) | G] greater because the more informative investment renders the option
to invest more valuable, thereby improving social welfare W G . However, when π̂ = π G,0 ,as Figure 7c shows, the second eﬀect leads to the inequality π̂ > π G,0 , and the manager
with reputation π G,0 misses the investment opportunity. This reduces the expected value ofthe date-1 investment E [V (π ′ ) | G] dramatically. Figure 5 implies that the risk created byincreased informativeness leads the manager to prefer the M-strategy, which lowers social
welfare. Thus, the welfare eﬀect of the increase in pH is not monotonous.

4

Extensions

In this section, we discuss three extensions of our model. In Section 4.1 we analyze the modelin which investors can commit future financing, which allows a manager to have access tolong-term and state-contingent contracts. The contract allows the manager to hedge thereputation risks of bankruptcy and encourages risk-taking. In Section 4.2, the manager canmake the project choice again at t = 1. In Section 4.3, the moral hazard problem and theminimum investment level are present in both t = 0 and t = 1. Although we have assumed
that the manager faces diﬀerent investment environments at t = 0 and at t = 1, the analyses
11

A decrease in the probability of success for the L-type manager, pL , has a similar eﬀect on the investment
strategy.

28

in Section 4.2 and Section 4.3 make the situation in both periods similar and show that our
result remains unchanged.

4.1

Long-term Contracts

In this section, investors do not have a commitment problem, which allows a manager to oﬀer
long-term and state-contingent contracts. The manager oﬀers contracts only at t = 0 thatspecify (I0 (x), I1 (sx ), d0 (x), d1 (sx )). We have to consider two optimal contract problems. The
first contract is one from which the manager obtains refinancing regardless of the outcome
sx , and the second contract is one from which the manager obtains refinancing in the caseof success sx = 1 but gives up refinancing and invests the capital A into storage technology
in the case of failure sx = 0. Comparing both contract problems, the manager chooses thecontract that yields higher expected utility.
First, the optimal contract problem is set to assure financing necessarily. We characterize
the optimal contract that chooses (x, I0 (x), I1 (sx ), d0 (x), d1 (sx )) and solves the following
problem:max Pr(sx = 1) [R(x)I0 (x) − d0 (x)] + Pr(sx = 1)δ(π x,1 )(RN I1 (sx = 1) − d1 (sx = 1))+ Pr(sx = 0)δ(π x,0 )(RN I1 (sx = 0) − d1 (sx = 0)) − A,

29

(21)

subject to for each x (12),Pr(sx = 1)d0 (x) + Pr(sx = 1)δ(π x,1 )d1 (sx = 1) + Pr(sx = 0)δ(π x,0 )d1 (sx = 0)
≥ I0 (x) + Pr(sx = 1)[I1 (sx = 1) − A] + Pr(sx = 0)[I1 (sx = 0) − A], (22)d0 (x) ≤ R(x)I0 (x),(23)

I1 (sx = 1) ≤ A + K,

(24)

I1 (sx = 0) ≤ A + K,

(25)

ˆ
I1 (sx = 1) ≥ I,(26)

ˆ
I1 (sx = 0) ≥ I,
#
$
B
x
N
d1 (s = 1) ≤ R −I1 (sx = 1),
∆π
#
$
B
x
N
d1 (s = 0) ≤ R −I1 (sx = 0).
∆π

(27)
(28)
(29)

The objective function (21) is the manager’s net expected payoﬀ. The first term is the
expected payoﬀ at t = 0, the second and the third terms are the expected payoﬀ at t = 1
in the case of success of the date-0 investment and in the case of failure of the date-0
investment, respectively. The fourth term is the self-investment. The constraint (22) is theparticipation constraint of the investors given their outside option that yields zero profit.
The left-hand side is the expected payments for investors, and the right-hand side is the
expected cost of the investment. The constraint (23) is the limited liability condition. 12
The constraints (24) and (25) are resource constraints at t = 1 in which all resources are split
into the manager’s capital A and the investors’ capital K. The constraints (26) and (27)are the minimum investment requirement. The constraints (28) and (29) are the incentive
compatibility conditions, which mean that financing requires that the manager can promise
investors, at most, income (RN − B/∆π)I1 (sx = 1) and (RN − B/∆π)I1 (sx = 0) without
misbehavior in case of success and failure, respectively.
12

Although the limited liability constraint is present in Section 3, we do not refer to the constraint because
it is not binding.

30

The second contract can be characterized to obtain refinancing only when sx = 1. This
optimal contract problem is to choose (x, I0 (x), I1 (sx = 1), d0 (x), d1 (sx = 1)), to solve!
"
max Pr(sx = 1) R(x)I0 (x) − d0 (x) + δ(π x,1 )(RN I1 (sx = 1) − d1 (sx = 1)) − A ,(30)subject to for each x (12), (23), (24), (26), (28), and the participation constraint for investorsPr(sx = 1)d0 (x) + Pr(sx = 1)δ(π x,1 )d1 (sx = 1) ≥ I0 (x) + Pr(sx = 1)[I1 (sx = 1) − A]. (31)Proposition 2 Suppose that Assumptions 1–6 hold and K and pRG are suﬃciently large.
The equilibrium investment strategy is the G-strategy. If the inequalityˆ(δ(π G,1 )RN − 1)A ≥ (π G,1 − π G,0 )(δH − δL )IB/∆π

(32)

G,0
ˆ
is satisfied, the date-1 investment levels are k(π G,1 )[A + RG − 1/p − (1 − p){I/k(π) − A}/p]after a success and Iˆ after a failure. If (32) does not hold, the date-1 investment levels arek(π G,1 )[A + RG − 1/p] after a success and 0 after a failure.
Proof. See Appendix A.
The moral hazard problem that creates financial constraints restricts the investment levelat t = 1 and, thus, the manager cannot obtain full funding. It is optimal for the manager
to oﬀer a contract under which investment must be contingent on reputation; that is, agood reputation attracts more funds than a bad reputation. The important feature of suchstate-contingent contracts is that the manager can oﬀer an insurance-like contract in which
ˆ Theeven when sx = 0, the manager attracts funds up to the minimum investment level I.
option-like nature generates benefits to adjust funds based on the information the date-0
investment produces. The benefits of informativeness induce the manager to undertake themost informative strategy, the G-strategy.
When investor protection is weak (B/∆π is large) such that the condition (32) is violated,
31

I1
k(⇡ G,1 )[A + RG

1/p

(1

G,0
ˆ
p){I/k(⇡)

A}p]k(⇡ G,1 )Ak(⇡ M,1 )Ak(⇡ G,0 )Ak(⇡)Ak(⇡ M,0 )A

Iˆ
B
⇡

(1)

⇡
ˆ  ⇡ G,0

(3)

(2)
⇡ G,0 < ⇡ˆ  ⇡ M,0

⇡

M,0

<⇡
ˆ⇡

Figure 8: The comparison of the investment level in the equilibrium between the model in Section 3.3(depicted as the light (red) line) and the model in Section 4.1 under condition (32) (depicted as
the dark (black) line)

it becomes costly to assure the minimum investment level Iˆ when the manager obtains a bad
reputation. Thus, even though the insurance-like contract is available, the manager prefers
aggressive investments: choosing to forsake the date-1 investment opportunity when sx = 0
and selecting the G-strategy.
Comparing Proposition 1 with Proposition 2, we show that the limited commitment of investors prevents the manager from transferring funds across states and oﬀering an insurancelike contract, which induces the manager to behave conservatively to avoid the possibility of
missing investment opportunities. Figure 8 clarifies this point by comparing the equilibrium
investment level in Proposition 1, which is depicted as the light (red) line, with the equilibrium investment level in Proposition 2 under condition (32), which is depicted as the dark
(black) line, for each B/∆π.13 Figure 8 implies that the long-term contract using the transfer between states allows the manager to hedge the risks in which she loses the investment
ˆ i.e., (δ(π G,1 )RN −We can compare both cases if (32) holds for any B/∆π ≤ RN − (Iˆ − A)/δ(π)I,
G,1
G,0
N
ˆ
ˆ
ˆ
ˆ
1)A/(π − π )(δH − δL )I ≥ R − (I − A)/δ(π)I. The condition holds when I is suﬃciently small. This isbecause when Iˆ = A, the condition can be rewritten as δ(π G,0 )RN − 1 ≥ 0, and it holds from Assumption 3.
13

32

opportunities at t = 1 regardless of the level of investor protection.
In region (1) where π̂ ≤ π G,0 , although the investment strategy is the G-strategy inboth models, the investment level in Section 4.1 is more volatile than in Section 3.3. In
Section 4.1, the manager transfers available funds from the state of failure (sG = 0) to thestate of success (sG = 1). In Section 3.3, however, the limited commitment prevents suchtransfers across states and forces the manager to hedge against failure.
In region (2) where π G,0 < π̂ ≤ π M,0 , the manager with the G-strategy who faces theinvestors’ limited commitment (in Section 3.3) cannot assure the minimum investment levelˆ 14 The only way to avoid the bankruptcy is to select a
Iˆ when sG = 0 (i.e., k(π G,0 )A < I).
less risky investment strategy, the M-strategy, which results in less volatile investment levels
than Section 4.1. In region (3) where π M,0 < π̂ ≤ π, a lack of commitment prevents theˆ and induces
manager with the M-strategy from assuring Iˆ when sM = 0 (i.e., k(π M,0 )A < I)
the manager to adopt the S-strategy to avoid the risk of bankruptcy.

4.2

Date-1 Risk Choice

Suppose at t = 1 the manager chooses the investment strategy x′ among the three strategies,
not new investment technology. Accordingly, we introduce the minimum investment requireˆ the G-strategy (the M-strategy)
ment into the G-strategy and the M-strategy. If I1 ≥ I,
operated by a manager of type i yields RG (RM ) with probability pi (qi ) and nothing withprobability 1 − pi (1 − qi ); otherwise, it produces nothing. We make the following stronger
assumption concerning the investment return than Assumption 2:
Assumption 7
q(π G,1 )RM > p(π G,1 )RG and p(π G,0 )RG > 1,
where q(π ′ ) = π ′ qH + (1 − π ′ )qL and p(π ′ ) = π ′ pH + (1 − π ′ )pL .
ˆ the manager can transfer resources
Strictly speaking, when B/∆π is a little above RN −(Iˆ−A)/δ(π G,0 )I,ˆ The explanation in thisfrom the return of the date-0 investment to the state of failure to compensate for I.
section ignores such transfer for simplicity.
1433

This condition implies that the investment made by any manager is always eﬃcient and,for the manager with possible reputation on the equilibrium, the M-strategy yields higher
expected return than the G-strategy. The condition assures that under a benchmark casein which there is no moral hazard problem, the M-strategy is the equilibrium investment
strategy in both periods 0 and 1.
Then, we modify the moral hazard problem. When the manager chooses the S-strategy,
the moral hazard is irrelevant because only storage technology is used. Choosing the Gstrategy or the M-strategy, the manager faces the moral hazard problem. If the manager
behaves without receiving private benefits, the probability of success for each investment
strategy is not aﬀected. If the manager misbehaves and enjoys private benefits BI1 , theprobability of success decreases by ∆π regardless of the type and the investment strategy.
We modify three assumptions about the moral hazard problem (Assumptions 4–6) in thefollowing way:
Assumption 8 (pH − ∆π)RG + B < 1+,
Assumption 9 pH RG − B/∆π < 1

+
,
+
,.
Assumption 10 max p(π) RG − B/∆π , q(π) RM − B/∆π Iˆ ≥ Iˆ − A
The only diﬀerence from Assumptions 4–6 is that the date-1 investment is not new investment technology. The first assumption implies that even the H-type manager with the
G-strategy produces negative NPV if the manager misbehaves. The second assumptionmeans that even the H-type manager with the G-strategy cannot oﬀer suﬃcient expected
pledgeable income and must face financial constraints. Under these assumptions, managers
with any reputation and any date-1 investment strategy have to behave on the equilibrium
and face financial constraints. The third assumption means that the manager whose reputation remains unchanged can collect funds up to Iˆ by choosing either the G-strategy or theM-strategy.

34

Consider the date-1 contract problem. The manager with reputation π ′ can oﬀer the contract that is contingent on the date-1 investment strategy x′ . Under Assumption 1 and Assumptions 7–10, we solve the date-1 optimal contract problem by choosing (x′ , I1 (x′ ), d1 (x′ ))in two steps.
First, given the investment strategy x′ ∈ {G, M } and the outcome of the date-0 investment sx , we choose (I1 (x′ ), d1 (x′ )) to solve′

U1 (x′ ) = max Pr(sx = 1 | sx )(R(x′ )I1 (x′ ) − d1 (x′ )) − A,(33)

subject to′Pr(sx = 1 | sx )d1 (x′ ) ≥ I1 (x′ ) − A,

(34)

I1 (x′ ) ≤ K + A,

(35)

ˆ
I1 (x′ ) ≥ I,
#
$
B
′
′
d1 (x ) ≤ R(x ) −I1 (x′ ).
∆π

(36)
(37)

The problem is almost the same as the date-1 optimal contract problem ((1) and (5)–(8)),
except for the date-1 investment technology. The objective function (33) is the manager’s
expected payoﬀ at t = 1, the constraint (34) is the participation constraint of the investors,
the constraint (35) is resource constraints at t = 1, the constraint (36) is the minimum
investment requirement, and the constraint (37) is the incentive compatibility condition.
Because we can apply the same analysis in Section 3.3 to the problem (33)–(37), we havethe investment level and the value function with the strategy x′ ,(I1 (G), U1 (G)) =

⎧
/
⎪
⎪
⎨

′
G
A
, (p(π )R −1)A
1−p(π ′ )(RG −B/∆π) 1−p(π ′ )(RG −B/∆π)⎪⎪⎩(0, 0)

35

0

ˆ

I−A
if p(π ′ ) ≥ (RG −B/∆π),Iˆotherwise,(38)

V (⇡ 0 )V (⇡ 0 )The G-strategy
The M-strategy

The M-strategy

⇡0⇡0

I1 (G)I1

I1 (G)I1

I1 (M )I1 (M )

Iˆ

Iˆ

⇡0

⇡0

(a) Low B/∆π(b) High B/∆π

Figure 9: The manager’s expected payoﬀ and the investment at t = 1

and(I1 (M ), U1 (M )) =

⎧
/
⎪
⎪
⎨

′
M
A
, (q(π )R −1)A
1−q(π ′ )(RM −B/∆π) 1−q(π ′ )(RM −B/∆π)⎪⎪⎩(0, 0)0ˆI−A
if q(π ′ ) ≥ (RM −B/∆π)
,
Iˆ

(39)

otherwise.

If the manager has a suﬃciently good reputation, financing is secured for investment; otherwise, the manager cannot continue management.
Second, the manager chooses the investment strategy x′ to solve
V (π ′ ) = max{U1 (G), U1 (M )},(40)

where the S-strategy that produces zero payoﬀ is not selected at t = 1. This result issummarized in Figure 9. When B/∆π is low (Figure 9a), any manager chooses x′ = M(i.e., U1 (G) < U1 (M )) because Assumption 7 assures that the M-strategy is eﬃcient. Whenthe manager’s rents B/∆π is high (Figure 9b), the manager with the M-strategy mustreceive much larger expected rents q(π ′ )B/∆π to behave than the manager with the G36

strategy p(π ′ )B/∆π. This, in turn, leads to lower pledgeable income with the M-strategy+,+,q(π ′ ) RM − B/∆π than with the G-strategy p(π ′ ) RG − B/∆π . As reputation π ′ increases, the diﬀerence in pledgeability also increases. Consequently, when B/∆π and π ′ arehigh, the G-strategy reduces the moral hazard problem and leads to larger investments thanthe M-strategy (i.e., I1 (G) > I1 (M )). The benefit of the additional inflow of funds induces
the manager with high π ′ to choose the G-strategy (i.e., U1 (G) > U1 (M )).
Based on Figure 9, we consider the date-0 investment strategy. In the case of Figure 9a,
where investor protection is strong, because the shape of the manager’s net expected payoﬀ
at t = 1 V (π ′ ) changes minimally, we use the same logic in Section 3.3. The manager
prefers risky investments, and the conclusion is not aﬀected. In the case of Figure 9b, where
investor protection is weak, the option to select the G-strategy at t = 1 increases the benefitsof obtaining a good reputation. The additional reputation benefit can induce the manager
to take risks. Thus, when the reward for a good reputation is small, the manager still has afear of losing her reputation and behaves conservatively at t = 0.

4.3

Date-0 Moral Hazard Problem

We incorporate the minimum size requirement and the moral hazard problem at t = 0 intoˆ the G-strategy (the M-strategy) operated by a manager
the model in Section 3.3. If I1 ≥ I,of type i yields RG (RM ) with probability pi (qi ) and nothing with probability 1 − pi (1 − qi );otherwise, it produces nothing. The manager with the G-strategy or the M-strategy faces amoral hazard problem t = 0 as well as t = 1. When she behaves, the project will proceed as
described above. When the manager misbehaves, the probability of success decreases by ∆πregardless of the type and the investment strategy. We assume that the date-0 investmentin the case of misbehavior is ineﬃcient regardless of the investment strategy:
Assumption 11 (p − ∆π)RG + B < 1 and (q − ∆π)RM + B < 1.
This ensures that the manager does not misbehave on the equilibrium path. Also, we
assume that Iˆ ≤ 1 because there is only one unit of good in the economy at t = 0.
37

Suppose that Assumptions 1–6 and Assumption 11 hold. Because the date-1 contract
problem is the same as in Section 3.3, we consider the modified date-0 contract problem. In
this phase, the manager chooses the contract (x, I0 (x), d0 (x)) to maximize (10) subject tothe participation constraint for investors (11), the resource constraint (12), and the following
incentive compatibility constraint,Pr(sx = 1)(R(x)I0 (x) − d0 (x) + V (π x,1 )) + Pr(sx = 0)V (π x,0 )≥ [Pr(sx = 1) − ∆π] (R(x)I0 (x) − d0 (x) + V (π x,1 )) + [Pr(sx = 0) + ∆π] V (π x,0 )The left-hand side represents the manager’s gross expected utility at t = 0 in case of behaving,whereas the right-hand side represents the manager’s gross expected utility at t = 0 in thecase of misbehaving.
The incentive compatibility condition can be rewritten as

R(x)I0 (x) − d0 (x) ≥!
"B
I0 (x) − V (π x,1 ) − V (π x,0 ) ,
∆π

(41)

where the right-hand side is the minimum rent at t = 0 necessary for the manager tomake an eﬀort. Compared to the date-1 incentive compatibility condition (1), the manager
is more likely to behave at t = 0 because of reputation benefits, which is represented as
V (π x,1 ) − V (π x,0 ). The reward for success gives the manager the incentive to behave. Thisimplies that the manager’s expected pledgeable income at t = 0 is higher and financial
constraints are less severe than the case at t = 1. Consequently, when the reputation
benefits are suﬃciently large, the manager can collect all funds in the economy despite thepresence of moral hazard, and Proposition 1 does not change. 15

15With small reputation benefits, the financial constraints may prevent the manager from collecting funds
ˆ At that time, the manager prefers the S-strategy to avoid a moral hazard problem. However,up to I.
the case where reputation benefits are small resembles that of Proposition 1.(iii), in which severe financial
constraints already induce the manager to choose the S-strategy without the date-0 moral hazard problem.
Thus, even if the reputation benefit is small, the result may not change.

38

Managers’ expected
payoff 

Perfect capital markets (Lemma 1)
Strong investor protection (Proposition 1.1)
Weak investor protection (Proposition 1.3)


Past performance(or reputation)

Figure 10: Reputation eﬀects on managers’ expected payoﬀ for each scenario

5Conclusion

In this paper, we consider reputation concerns in capital markets as a primary motivatorfor delegated portfolio managers. By showing impressive performance, the managers raise
more funds from investors and receive greater rewards. Previous literature thoroughly documents the eﬀect of the flow-performance relationship on investment decisions while ignoring
the role of investor protection, which aﬀects the managers’ ability to raise funds and theflow-performance relationship. To fill the gap, we develop a model to study how investor
protections aﬀect fund flows and managerial risk choice.
Figure 10 summarizes the relationship between managerial reputation (or past performance) and the consequent payoﬀ. The (blue) dashed line depicts the benchmark case withperfect capital markets. In this case, better reputation increases the probability of high returns by showing the manager’s competence, but does not boost pledgeability. Because there
is no distortion caused by reputation concerns, the risk neutral manager is not concernedwith risk and selects the strategy that yields the highest expected returns.
In imperfect capital markets with strong investor protection, a manager with a better39

reputation increases the probability of high returns and also raises more funds. The inflows
of funds generate a convex utility function, illustrated by the dotted line to light (red)solid line, and causes excessive risk-taking to obtain upside benefits. However, when the
manager’s ability to borrow falls below a certain threshold, the manager is unable to invest
because management requires a certain fixed cost. Consequently, in a context of weak
investor protection, managers with a poor reputation cannot raise suﬃcient funds to invest.
The threat of missing investment opportunities creates part of a concave utility function,
depicted by the dark (block) solid line, and induces the manager to behave with excessive
conservatism.
Finally, we state policy interventions. Because we explicitly introduce investor protections
into a model for reputation, we can consider the eﬀect of policy interventions for countries
with varying levels of investor protection. For example, we can analyze the eﬀect of financial
market openness on portfolio management with reputation concerns by extending the analysis to an economy in which there are many managers and interest rates are determined in
the markets. In countries with poor investor protection, the increases in interest rates reducemanagers’ profits and mitigate the threat of lost investment opportunities. Consequently,
our model predicts that the manager may be induced to adopt value-enhancing risk-taking
behavior. A detailed prediction of the change in reputation building and the potential welfare
eﬀect of removing financial repression policies is an interesting subject for future studies.

A

Appendix

A.1

Proof of Proposition 1

ˆProof. (i) Suppose B/∆π is small such that B/∆π ∈ (RN − 1/δH , RN − (Iˆ − A)/δ(π G,0 )I].
B/∆π must be higher than RN − 1/δH from Assumption 5. First, we compare U0 (M ) toU0 (S). Because V (π ′ ) is strictly convex in π ′ , Jensen’s inequality implies that E[V (π ′ ) |M ] > V (π). Hence, from the condition Assumption 2, U0 (M ) > U0 (S).
40

Next, we compare U0 (G) to U0 (M ). sG is more informative than sM in the sense ofBlackwell, that is, there exists a non-negative function h(sM , sG ) for which the following
three conditions hold:Pr(sM | i) =11sG

h(sM , sG )Pr(sG | i) for all sM and for all i,h(sM , sG ) = 1 for all sG ,

sM

1
sG

h(sM , sG ) ∈ (0, ∞) for all sM .

H qL pH −qH pL
H pL
When we take h(sM = 1, sG = 1) = pqHH − 1−p, h(sM = 1, sG = 0) = qL ppHH−q, h(sM =pH
pH −pL−pL
H qL pH −qH pL
H pL0, sG = 1) = 1 − pqHH + 1−p, and h(sM = 0, sG = 0) = 1 − qL ppHH−q, the abovepH
pH −pL−pL

conditions are satisfied. We exploit Theorem 2 in DeGroot (1970, p. 436): sG is more informative than sM in the sense of Blackwell if and only if sG yields a higher expected valueof V than sM , 16 that is, E[V (π ′ ) | G] > E[V (π ′ ) | M ]. Thus, if pRG is suﬃciently close toqRM , U0 (G) > U0 (M ).
ˆ RN −(ii) Consider B/∆π is intermediate such that B/∆π ∈ (RN − (Iˆ − A)/δ(π G,0 )I,ˆ The expected utility of a manager is reduced when implementing the(Iˆ − A)/δ(π M,0 )I].
G-strategy to!
"
U0 (G) = p δ(π G,1 )RN − 1 k(π G,1 )A + pRG − 1,

while the expected utilities in cases of other strategies are unchanged. Thus, the M-strategy
yields higher expected utility than the G-strategy if the condition (18) holds. Because qRM ≥!
"pRG from Assumption 2, some parameters satisfy (18) when p δ(π G,1 )RN − 1 k(π G,1 )A <!+,"E δ(π ′ )RN − 1 k(π ′ )A | M holds as shown in Figure 5.
16

Weber (2010) shows that Blackwell’s theorem is applicable to any stochastic decision problem in whicha decision maker with a continuous utility function chooses an action after observing a signal that has
two outcomes. In our model, the outcome of date-0 investment corresponds to the signal and the date-1
investment corresponds to the decision. If the manager obtains zero profit at date 0 and makes the date1 investment regardless of the signal, our model corresponds to the original decision problem. Thus, theappropriate continuous utility conditional on the signal is V .

41

ˆ RN − (Iˆ −(iii) Suppose B/∆π is large such that B/∆π ∈ (RN − (Iˆ − A)/δ(π M,0 )I,
ˆ Because E[V (π ′ ) | G] > E[V (π ′ ) | M ] from Figure 6, if pRG is suﬃciently closeA)/δ(π)I].
to qRM , we have U0 (G) > U0 (M ). Figure 6 also shows that there exist some parameters suchthat E[V (π ′ ) | G] > E[V (π ′ ) | M ] holds. Thus, the S-strategy yields the highest expectedutility of the three if pRG falls in the range that satisfies (19).

A.2

Proof of Proposition 2

Proof. Consider the first optimal contract problem. We solve the problem given the investment strategy x and, then, compare the payoﬀ for each strategy. We write the Lagrangianas
L = Pr(sx = 1) [R(x)I0 (x) − d0 (x)] − A+ Pr(sx = 1)δ(π x,1 )(RN I1 (sx = 1) − d1 (sx = 1)) + Pr(sx = 0)δ(π x,0 )(RN I1 (sx = 0) − d1 (sx = 0))+ λ1 (x)[Pr(sx = 1)d0 (x) − I0 (x) + Pr(sx = 1)(δ(π x,1 )d1 (sx = 1) − I1 (sx = 1))+ Pr(sx = 0)(δ(π x,0 )d1 (sx = 0) − I1 (sx = 1)) + A]

2#

B
R −
∆π
N

$

x

x

+ λ2 (x) [1 − I0 (x)] + λ3 (x) [R(x)I0 (x) − d0 (x)] + λ4 (x)I1 (s = 1) − d1 (s = 1)
2#
$
3
4
5
B
N
x
x
+ λ5 (x) R −I1 (s = 0) − d1 (s = 0) + λ6 (x) I1 (sx = 0) − Iˆ∆πwhere λl (l = 1, 2, 3, 4, 5, 6) is the Lagrange multipliers for each constraint. After solving the
problem, we check whether the solution satisfies the constraints (24), (25), and (26).

42

3The first order conditions for each x are as follows:Pr(sx = 1)R(x) − λ1 (x) − λ2 (x) + λ3 (x)R(x) = 0#$! x,1 N"B
xN
Pr(s = 1) δ(π )R − λ1 (x) + λ4 (x) R −
=0
∆π
#
$
!
"
B
Pr(sx = 0) δ(π x,0 )RN − λ1 (x) + λ5 (x) RN −+ λ6 (x) = 0
∆π

(A.1)

− Pr(sx = 1) + λ1 (x)Pr(sx = 1) − λ3 (x) = 0(A.4)

d1 (sx = 1) :− Pr(sx = 1)δ(π x,1 ) + λ1 (x)Pr(sx = 1)δ(π x,1 ) − λ4 (x) = 0(A.5)

d1 (sx = 0) :− Pr(sx = 0)δ(π x,0 ) + λ1 (x)Pr(sx = 0)δ(π x,0 ) − λ5 (x) = 0.

(A.6)

I0 (x) :I1 (sx = 1) :I1 (sx = 0) :d0 (x) :

(A.2)
(A.3)

Inserting (A.5 ) into (A.2 ), we have λ1 (x) = δ(π x,1 )k(π x,1 )B/∆π > 1. Plugging (A.4 ) into
(A.1 ), we have λ1 (x) (Pr(sx = 1)R(x) − 1) = λ2 (x). Because λ1 (x) > 0, we have λ2 (x) > 0
that implies I0 (x) = 1. Combining λ1 (x) > 1 with (A.4 ), (A.5 ), and (A.6 ), we get λ3 (x) > 0
that implies d0 (x) = R(x), λ4 (x) > 0 that implies d1 (sx = 1) = (RN − B/∆π)I1 (sx = 1),and λ5 (x) > 0 that implies d1 (sx = 0) = (RN − B/∆π)I1 (sx = 0). (A.3 ) and (A.6 ) leads
to λ6 (x) > 0, which implies I1 (sx = 0) = Iˆ that satisfies (25). I1 (sx = 1) is determined by(22) because K is suﬃciently large that (24) is satisfied. 17
We show that the G-strategy is the optimal for any Iˆ ∈ [A, k(π)A], where Iˆ ≤ k(π)A because of Assumption 6. Let us define as UI (x) the manager’s value function with investment
strategy x in this insurance-like contract, which is given by#

δ(π)
UI (x) = λ1 (x) [Pr(s = 1)R(x) − 1] + [λ1 (x) − 1] A − λ1 (x) 1 −δ(π x,1 )
x

$

ˆ
I.

(A.7)

Because ∂UI (G)/∂ Iˆ < ∂UI (M )/∂ Iˆ < ∂UI (S)/∂ Iˆ = 0, if UI (G) > max{UI (M ), UI (S)} forˆIˆ = k(π)A, the condition holds, that is, the G-strategy is optimal, for any I.
17

If I1 (sx = 1) which is determined by the above contract is higher than all endowments K + A, theinvestment level I1 (sx = 1) is binding at the level of K + A. Instead I1 (sx = 0) is determined such that (22)ˆ If I1 (sx = 0) is suﬃciently higher, the optimal strategy becomes the benchmark
is binding, higher than I.
strategy, i.e., the M-strategy. In this problem, we preclude this case by assuming that K is suﬃciently large.

43

Setting Iˆ = k(π)A, we can rewrite UI (x) as λ1 (x) [Pr(sx = 1)R(x) − 1]+[δ(π)k(π)B/∆π−1]A. Because λ1 (G)(pRG − 1) > 0, UI (G) > UI (S). We also get UI (G) > UI (M ) if
λ1 (G)(pRG − 1) > λ1 (M )(qRM − 1). The condition holds when pRG is suﬃciently large
because λ1 (G) > λ1 (M ). Then, because

I1 (sG = 1) = k(π G,1 )A +

G,1

%

k(π )
pRG − 1 − (1 − p)
p

6

7&
ˆ
I
−A
,
k(π G,0 )G,1ˆ (26) is
we show that when Iˆ = k(π)A, I1 (sG = 1) = k(π)A + k(πp ) (pRG − 1) > k(π)A = I,satisfied.
Next, consider the second contract problem that maximizes (30) subject to (12), (23),(24), (26), (28), and (31). Using the same logic as the previous problem, we see that theconditions (12), (23), (28), and (31) are binding, whereas the conditions (24) and (26) are
not binding. The manager’s net expected utility with investment strategy x in the second
contract, which has no insurance roll, is given by
UN I (x) = λ1 (x) (Pr(sx = 1)R(x) − 1) + Pr(sx = 1) [λ1 (x) − 1] A,(A.8)

where λ1 (x) = δ(π x,1 )k(π x,1 )B/∆π is the Lagrange multiplier of the participation constraint(31). The first-term is the highest in the case of the G-strategy if pRG is suﬃciently large
as mentioned above. Because p [λ1 (G) − 1] A > q [λ1 (M ) − 1] A from Figure 6, UN I (G) >UN I (M ). The manager chooses either the G-strategy or the S-strategy in the contract that
does not oﬀer insurance and obtains max{UN I (G), UN I (S)}. Note that the assumption thatthe manager with the S-strategy succeeds with probability one implies UI (S) = UN I (S).
Given these results, the manager chooses the first contract and the G-strategy if UI (G) ≥UN I (G), that is, (32) holds because UI (G) > UI (S) = UN I (S). Otherwise, the manager
chooses the second contract. In that case, since UN I (G) > UI (G) > UI (S) = UN I (S), theG-strategy is optimal.

44

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