Governance Through Exit and Voice: A Theory ofMultiple Blockholders�

Alex Edmansy

University of PennsylvaniaThe Wharton School

Gustavo Mansoz

Massachusetts Institute of TechnologySloan School of Management

October 29, 2007

Abstract

Most �rms have multiple blockholders. This dilution of ownership generates�free-rider�problems and is therefore di¢ cult to explain with traditional theories.In such models, blockholders add value through direct intervention (�voice�) anda concentrated stake is optimal to encourage them to incur the associated costs.This paper rationalizes the presence of multiple blockholders by showing that co-ordination di¢ culties improve their e¤ectiveness in adding value through a secondchannel: disciplining the manager through �exit�. Since informed blockholderscannot co-ordinate to limit their trades and maximize combined trading pro�ts,competition among them impounds more information into prices. This makesthe threat of disciplinary exit more credible, thus inducing higher manageriale¤ort. The model�s comparative statics derive empirical predictions on the factorsa¤ecting optimal blockholder structure.

Keywords: Multiple blockholders, corporate governance, market e¢ ciency,exit, voice, insider trading, free-rider problem, Wall Street Rule

JEL Classification: D82, G14, G32

�We thank Rich Mathews, Holger Mueller (a discussant), Jun Qian and seminar partici-pants at the Conference on Financial Economics and Accounting at NYU, MIT, and NotreDame for helpful comments.

yaedmans@wharton.upenn.edu, 2428 SH-DH, 3620 Locust Walk, Philadelphia, PA 19104.zmanso@mit.edu, 50 Memorial Drive E52-446, Cambridge, MA 02142.

1 Introduction

Corporate governance can have substantial e¤ects on �rm value. Through ensuringthat managers act in shareholders�interest, it can minimize the agency costs arisingfrom the separation of ownership and control (Berle and Means (1932)). In turn, largeshareholders are believed to be an important component of e¤ective governance. Ablockholder�s concentrated stake gives her substantial incentives to monitor the man-ager and, if necessary, intervene to correct value-destructive actions.However, most �rms in reality have multiple small blockholders (see, e.g., Zwiebel

(1995), Barca and Becht (2001), Faccio and Lang (2002), Maury and Pajuste (2005),and Holderness (2007)). Such a structure appears to be suboptimal, as splitting equitybetween numerous shareholders leads to a free-rider problem: each investor individuallyhas insu¢ cient incentives to bear the cost of monitoring, and shareholders cannot co-ordinate to share this cost.This paper provides a potential justi�cation for multiple blockholders as an optimal

shareholding structure. While splitting a block reduces the e¤ectiveness of blockholderintervention (�voice�), we show that it increases the power of a second governancemechanism: �exit�.1 By trading on private information, blockholders cause the stockprice to more closely re�ect fundamental value, thus rewarding the manager ex postfor improving �rm value. However, such a reward mechanism only elicits e¤ort exante if it is dynamically consistent. Once e¤ort has been exerted, blockholders are onlyconcerned with maximizing their trading pro�ts. A single blockholder will strategicallylimit her order to reduce the revelation of her private information, maximizing hertrading pro�t but lowering price informativeness. By contrast, multiple blockholderstrade aggressively to compete for pro�ts, as in a Cournot oligopoly. Total quantities(here, trading volumes) are higher than under monopoly, leading to more informationbeing impounded in prices. Multiple blockholders thus serve as a commitment deviceto reward the manager ex post for his actions.The co-ordination problems and externalities created by splitting a block play op-

posing roles in �voice�and �exit.�For �voice�, the externalities are positive: interven-tion improves the value of other shareholders�stakes, but this e¤ect is not internalized

1Prior papers on blockholder trading focus on the �Wall Street Rule�(the possibility of blockholderexit), rather than additional purchases. For example, Hirshman�s (1970) book is titled �Exit, Voice,and Loyalty�, and the models of Edmans (2007) and Admati and P�eiderer (2006) only analyze blockdisposal, not enhancement. Although the blockholder can buy as well as sell in this paper, we use theterm �exit�to describe the blockholder�s value added through her trading (in either direction), to beconsistent with prior literature.

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by the individual blockholder. Since co-ordination problems lead to positive external-ities being ignored, there is �too little� intervention with multiple blockholders. For�exit�, the externalities are negative. Higher trading volumes reveal more informationto the market maker, leading to a less attractive price for other informed traders. Ifblockholders could co-ordinate, they would form a cartel to internalize this e¤ect, lim-iting their trades to replicate the single blockholder case and achieve monopoly pro�tsin aggregate. Since they cannot co-ordinate, they act competitively, maximizing theirindividual trading pro�ts and ignoring these negative externalities. They thus trade�too much�from the viewpoint of maximizing total pro�ts. However, �rm value doesnot depend on trading pro�ts, as these are a mere transfer from atomistic sharehold-ers to blockholders. Instead, �too much� trading is bene�cial as it increases priceinformativeness and induces e¤ort ex ante.We derive an interior solution for the optimal number of blockholders that maxi-

mizes �rm value. This optimum depends on a trade-o¤ between the intervention andtrading e¤ects. Therefore, the e¢ cient number of blockholders is increasing in the e¤ec-tiveness of managerial e¤ort and decreasing in the value created by direct blockholderintervention. We show that this optimum may di¤er from the socially optimal numberof blockholders that maximizes total surplus (�rm value net of e¤ort costs), and theprivate optimum that would be chosen by the blockholders to maximize their combinednet payo¤s. In ongoing work, we are deriving further comparative statics with regardsto variables such as the level of information asymmetry and the precision of block-holders� information. In addition, while the current draft considers identically-sizedblockholders and focuses on the optimal number, we are also relaxing this symmetryassumption to investigate the e¢ cient distribution of block sizes.This paper is organized as follows. Section 2 is a brief literature review. Section 3

presents the model and analyzes the e¤ect of blockholder structure on both �voice�and�exit�. Section 4 derives the optimal number of blockholders and generates comparativestatic predictions, and Section 5 concludes.

2 Literature Review

The vast majority of blockholder models involve the large shareholder adding valuethrough direct intervention, or �voice� as termed by Hirshman (1970). This can in-volve proposing pro�table investment projects and business strategies, or overturningan ine¢ cient managerial action. In Shleifer and Vishny (1986), Maug (1998) and Kahnand Winton (1998), a larger block is unambiguously more desirable as it addresses the

2

free-rider problem and maximizes the blockholder�s incentives to intervene. Burkart,Gromb and Panunzi (1997) note that, although bene�cial ex post, blockholder inter-vention may be undesirable ex ante as it discourages managerial initiative. The optimalblock size is therefore �nite. While Burkart et al. consider a single blockholder, Paganoand Roell (1998) point out that if this �nite optimum is lower than the total amount ofexternal �nancing required, the entrepreneur will need to raise funds from additionalshareholders. Although this leads to a multiple blockholder structure, the extra block-holders play an entirely passive role: they are merely a �budget-breaker� to providethe remaining funds. Replacing the additional blockholders by creditors or dispersedshareholders would have the same e¤ect. In this paper, all blockholders play an activerole. Bolton and von Thadden (1998) and Faure-Grimaud and Gromb (2004) achievea �nite optimum through a di¤erent channel, as too large a block reduces stock marketliquidity. Again, they only advocate one blockholder.2 In addition, the present paperholds the total equity held by blockholders (and thus the free �oat) �xed, and focuseson the division of this block between one or multiple blockholders. Liquidity is thusuna¤ected by the splitting of a block.Two recent papers by Admati and P�eiderer (2006) and Edmans (2007) analyze

blockholders adding value through an alternative mechanism, �exit�. Informed tradingcauses prices to more accurately re�ect fundamental value, in turn inducing the man-ager to undertake actions that enhance value. Both models consider a single blockholderand do not feature �voice�. To our knowledge, this is the �rst theory that analyzesboth governance mechanisms of exit and voice, and the tradeo¤s between them.3

There are relatively few existing theories of multiple large shareholders. A notableexception is Zwiebel (1995), who shows that multiple blockholdings can arise whenshareholders compete for the private bene�ts of control by forming coalitions. The�nal shareholding structure represents the outcome of a power struggle rather thane¢ ciency, whereas in our paper the number of blockholders is optimally chosen tomaximize �rm value. Bennedsen and Wolfenzon (2000) show that a founding entrepre-neur may choose to distribute control among many outside shareholders, to commit toconsuming few private bene�ts in the future. Multiple blockholdings can be optimal,

2Bolton and von Thadden (1998) do raise the possibility of having more than one non-atomisticshareholder, but suspect that it is �dominated either by full dispersion or by a [single blockholder]structure.�Hence they do not derive multiple blockholders as being optimal.

3Maug (1998), Kahn and Winton (1998), and Brav and Mathews (2007) allow the blockholder tosell her stake instead of exercising voice. However, exit does not exert governance on the manager inthese models, as there is no feedback from the stock price to real decisions: governance is only throughvoice. Duan (2007) empirically studies the choice between exit and voice (through voting).

3

but for quite di¤erent reasons from the present paper. In Bennedsen and Wolfenzon,blockholders merely seek to divert cash �ows and add value indirectly by competingwith the manager in such activities, reducing the amount of stealing the manager iseventually able to undertake. Our paper features no private bene�ts or control con-tests; blockholders add value positively through exerting e¤ort or increasing stock priceinformativeness. Maury and Pajuste (2005) consider blockholders who can either di-vert steal or monitor; again, multiple blocks arise out of a desire to form a controllingcoalition and divert cash �ows.4

In this paper, �nancial market e¢ ciency increases real e¢ ciency since it impoundsthe e¤ects of managerial e¤ort into the stock price. Other papers have documentedalternative links between �nancial and real e¢ ciency. In Holmstrom and Tirole (1993),increased market e¢ ciency means that the stock price is a less noisy signal of �rmvalue, thus allowing a risk-averse manager to be tied more closely to the stock priceand ultimately leading to greater managerial e¤ort. In their model, market e¢ ciency isachieved through informed trading by arbitrageurs with no initial stake. Concentratedownership is undesirable as it reduces liquidity and thus market e¢ ciency; they donot consider the possibility that the concentrated shareholders themselves may be theinformed traders. This extension is particularly important if a large stake is requiredto become informed in the �rst place.A second channel arises if managers learn from prices to guide their investment

decisions, as in Dow and Gorton (1997), Subrahmanyam and Titman (1999), Goldsteinand Guembel (2007) and Dow, Goldstein and Guembel (2007). Third, in Stein (1996),Baker, Stein and Wurgler (2003), and Jensen (2004), managers exploit misvaluationby raising overvalued equity and investing ine¢ ciently ex post.A �nal strand of related literature concerns insider trading by managers. Propo-

nents argue that it can increase the e¢ ciency of stock prices, with consequent realbene�ts (e.g. Manne (1966)). Blockholders are likely to be signi�cantly more e¤ectivein this role than the manager, for several reasons. First, unlike blockholders who cantrade freely based on her information, the manager is con�icted since the stock priceis used to evaluate him. If he has negative private information, he is unlikely to reveal

4An alternative explanation is that, while a single concentrated block would be �rst-best in anunconstrained world, multiple small blockholders are a second-best optimum in the presence of block-holder wealth constraints and risk aversion (e.g. Winton (1993)). While these frictions are plausibleexplanations for small managerial stakes, they are likely weaker for outside shareholders. In particu-lar, institutional investors can hold sizable stakes since they have substantial capital and are held bythousands of individual shareholders, who can diversify away any idiosyncratic risk associated withhigh exposure to one particular corporation.

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it by selling stock as the low share price may lead to him being �red. By contrast,blockholders are objective monitors. Second, con�icts may also arise because the man-ager has control over the information �ow and investment decisions (Bernhardt et al.(1995)). He may release false negative (positive) information and subsequently buy(sell) shares, or sell his shares and take the incorrect investment decision. Third, themanager�s trading may be hindered by insider trading laws, wealth constraints (limitingpurchases) or lock-ups of stock as part of incentive packages (limiting sales).

3 Model and Analysis

In this section, we introduce a model in which blockholders can add value to the�rm either by direct intervention or by trading shares. The model consists of a gamebetween the manager, market maker and the I blockholders of the �rm. The game hastwo stages.In the �rst stage, the manager and blockholders take actions that a¤ect the value

of the �rm. Firm value is given by

~v = �a log a+ �b logXi

bi + e�; (1)

where a represents the action taken by the manager, bi represent the action taken byblockholder i, and ~� is normally distributed with mean zero and variance �2�. Themanager incurs personal cost a when taking action a, while each blockholder i incurspersonal cost bi when taking action bi.5 The manager�s action is broadly de�ned toencompass any decision that bene�ts �rm value but is personally costly to the man-ager, such as exerting e¤ort or forgoing private bene�ts and pet projects. Similarly, theblockholder�s action can involve e¤ort that directly helps the �rm (advising the man-ager), e¤ort that indirectly helps the �rm (deterring managerial shirking) or choosingnot to extract private bene�ts.6 �a (�b) measures the productivity of manager (block-holder) e¤ort per unit cost.

5Firm value depends on the sum of blockholder actions, and the action has a linear cost. This is toensure that adding blockholders does not change the available technology. The common assumptionof a quadratic cost (and a linear e¤ect of blockholder e¤ort on �rm value) would be inappropriatehere: for a �xed convex cost function, the blockholders�technology would improve if there are multiplesmall blockholders. A single blockholder would be able to reduce monitoring costs by dividing herselfup into multiple small �units�.

6See Barclay and Holderness (1991) for a description of the private bene�ts that blockholders canextract.

5

Action a is privately observed by the manager, while actions bi are publicly ob-served. The assumption that a is privately observable is necessary for stock priceinformativeness to have real e¤ects. If actions were not hidden, the moral hazard prob-lem disappears. By contrast, the assumption that bi is observable is made purely fortractability; results are unchanged if bi is unobserved.We normalize the number of shares outstanding to 1. The manager holds � shares

of the �rm, and each blockholder holds �=I shares. The free-�oat is thus �xed at1����, separating our paper from previous literature that has analyzed the liquiditye¤ects of concentrated ownership. In our model, a �xed fraction � is held by outsideblockholders and we focus on its optimal distribution.In the second stage of the game, the blockholders, noise traders, and a market maker

trade the �rm�s equity. The noise traders are the �rm�s atomistic shareholders. As inAdmati and P�eiderer (2006), each blockholder is assumed to observe �rm value ~vperfectly, while noise traders are uninformed. The blockholder�s superior informationcan be motivated by a number of underlying assumptions, which are not explicitlymodeled since this paper�s focus is on blockholder structure. The blockholder mayhave greater access to information than atomistic outsiders by virtue of her large stake:given her voting power, management will be more willing to meet with her; in theextreme, she may have a board seat. Alternatively, even if her cost of acquiring privateinformation is no lower than other market participants, she has stronger incentives topay this cost if there are short-sales constraints (or any non-zero short-sales costs).Information is more useful to her, since she can sell more if it turns out to be negative�hence she has a greater incentive to acquire it in the �rst place (Edmans (2007)).The results are qualitatively unchanged if each blockholder obtains an imperfect signalof ~v.7

After observing ~v, each blockholder submits a market order xi(~v). Noise traderssubmit market orders with a normally distributed net quantity ~�, with mean zeroand variance �2" . After observing total order �ow ~y =

Pi exi + ~�, the market maker

determines the price ~p and trades the quantity necessary to clear the market. Due toperfect competition, the market maker sets ~p so that he earns zero pro�ts, i.e. theprice equals expected �rm value given the order �ow.The manager is risk-neutral and his objective is to maximize the market value of his

shares less the cost of e¤ort, i.e. �~p � a. Each blockholder�s objective is to maximize7Indeed, if blockholders�imperfect signals are less than perfectly correlated, introducing additional

blockholders increases the amount of information in the economy, and it becomes easier to justify amultiple blockholder structure.

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her trading pro�ts, plus the fundamental value of her shares, less her cost of e¤ort.8

We solve for the equilibrium of the game by backward induction.

3.1 The Trading Stage

To proceed by backward induction, we take the decisions a of the manager and bi ofthe blockholders as given. The trading stage of the game is similar to the model ofspeculative trading of Kyle (1985) and its extensions to multiple informed investors.9

Proposition 1 The unique linear equilibrium of the trading stage is symmetric andhas the form:

xi(~v) = (~v � �a log a� �b logP

i bi) 8i (2)

p(~y) = �a log a+ �b logP

i bi + �~y; (3)

where

� =

pI

I + 1

����

(4)

=1pI

����: (5)

Proof If the market maker uses a linear pricing rule of the form p(y) = � + �y thenthe ith blockholder maximizes:

E[(~v � �� �y)xi j ~v = v] = (v � �� �Xj 6=i

xj)xi � �x2i .

This maximization problem yields,

xi(v) =1

�[v � �� �

Xj

xj(v)] 8i.

8The results are unchanged if the blockholder�s objective function includes the market value, ratherthan fundamental value of her shares, and are available from the authors upon request.

9See, for example, Foster and Viswanathan (1993) and Holden and Subrahmanyam (1992). Notethat the competition e¤ect that we illustrate is not speci�c to the Kyle (1985) model and its variants,but will also hold in other microstructure models.

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The strategies of the blockholders are then symmetric and we thus have

xi(v) =1

(I + 1)�(v � �) 8i.

The market maker takes the blockholders�strategy as given and sets:

p(y) = E[~vjy].

Using the normality of ~v and ~y yields:

� =

pI

I + 1

����,

� = �a log a+ �b logP

i bi.

From this we obtain:

xi(v) =1pI

����(v � �a log a� �b log

Pi bi) 8i,

p(y) = �a log a+ �b logP

i bi +

pI

I + 1

����y.

From Proposition 1, each blockholder�s trading pro�ts are

1pI(I + 1)

����: (6)

The trading pro�ts are increasing in �� and ��, as �� re�ects the blockholders�informa-tional advantage and �� represents their ability to pro�t from information by tradingwith liquidity investors. Also, aggregate blockholder trading pro�ts are decreasing inthe number I of blockholders. This is because multiple blockholders compete as ina Cournot oligopoly. Each blockholder chooses her trading volume to maximize in-dividual pro�ts. A higher volume reveals more information and makes the price lessattractive to all informed traders, but she does not internalize the e¤ect on the otherblockholders and so trades in excess of the level that would maximize total pro�ts.While greater trading volumes reduce aggregate pro�ts, they also impound more

information into prices. Indeed, de�ne �1 � Var(~vj~p)=Var(~v), a measure of price in-formativeness. A lower �1 means that a greater proportion of the variance of ~v isexplained by prices, i.e. prices are more informative. Using the formula for the condi-tional variance of bivariate normal distributions, we obtain that �1 = 1

I+1. This implies

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that price informativeness is increasing in the number of blockholders. In the extreme,as the number of blockholders approaches in�nity, prices become fully informative. Onthe other hand, in the monopolistic Kyle model (I = 1), the blockholder fully internal-izes the e¤ect of a higher trading volume on pro�ts. She limits her order, thus leadingto �1 = 1

2: prices reveal only one-half of the insider�s private information.

Therefore, the positive link between the number of blockholders and price infor-mativeness does not arise because a greater number of informed agents mechanicallyleads to an increase in the amount of information re�ected in prices. Indeed, a singleblockholder already has a perfect signal of fundamental value; since she faces no tradingconstraints, she could theoretically impound this entire information into prices. Theresult arises instead from competition between blockholders.10

We also note that the volatility of noise trading has no e¤ect on the informativenessof prices. From equation (5), greater noise allows blockholders to trade more aggres-sively. This increased informed trading exactly counterbalances the e¤ect of increasednoise and leaves price informativeness unchanged.

3.2 The Action Stage

We now solve for the optimal actions of the manager and the blockholders in the �rststage.

Proposition 2 The optimal action of the manager is

a = �a�

�I

I + 1

�(7)

and the optimal action of each blockholder is

bi = �b�

�1

I

�2: (8)

10While we have modeled Cournot competition, all of our results would continue to hold if we allowedblockholders to collude if the the likelihood of deviation (i.e. a breakdown in collusion) is increasingin the number of parties. This is a standard result from game theory. Moreover, the incentives todeviate may be particularly strong in our setting, since institutional investor blockholders are oftenbenchmarked against each other. Indeed, there is limited real-life evidence for such collusion: in�nancial crises, investors rush to sell stocks before their rivals have sold and driven down the price.See, e.g., Stewart (1991).

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Proof From Proposition 1, if the market maker and blockholders believe that themanager took action a, then

~p = �a log a+ �b logP

i bi + �~y

= �a log a+ �b logP

i bi + �(P

i ~xi + ~�) (9)

= �a log a+ �b logP

i bi +I

I + 1(�a log a+ ~� � �a log a) +

pI

I + 1

����~�:

The manager maximizes the market value of his shares, less the cost of e¤ort:

E [�~p� a] : (10)

Therefore, the optimal action of the manager is

a = �a�

�I

I + 1

�:

Each blockholder maximizes her trading pro�ts, plus the fundamental value of hershares, less her cost of e¤ort. From (6), we know that the blockholder�s trading pro�tsdo not depend on the action she has taken in the �rst stage.11 Therefore, blockholderi simply chooses bi to maximize the fundamental value of her shares, less her cost ofe¤ort:

E

���

I

�~v � bi

�: (11)

Therefore, the optimal action of blockholder i is

bi = �b�

�1

I

�2: (12)

The manager�s action a is increasing in the number I of blockholders. The intuitionis as follows. The higher the number of blockholders, the closer the stock price is tothe �rm�s fundamental value � i.e. the greater the extent to which the stock pricere�ects the manager�s e¤ort. Therefore, the manager is more willing to bear the costof working. In e¤ect, blockholder trading rewards managerial e¤ort ex post, thereforeinducing it ex ante. The dynamic consistency of this reward mechanism depends on

11This is because the blockholder�s action is publicly observable. Informed trading pro�ts dependon the blockholder�s relative information advantage, and this is una¤ected by a publicly observablevariable. See Kahn and Winton (1998) for a model where the blockholder�s action is unobservable.

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the number of blockholders. Critically, trading occurs after the manager has taken hisaction, at which point shareholders are concerned only with maximizing their tradingpro�ts. A single blockholder optimizes her pro�ts by limiting her order. Therefore, thepromise of rewarding e¤ort by bidding up the price to fundamental value is not credible.By contrast, multiple blockholders act aggressively and thus constitute a commitmentdevice to reward the manager ex post for his actions. While such aggressive trading ismotivated purely by the private desire to maximize individual pro�ts in the presenceof competition, it has a social bene�t by eliciting e¤ort ex ante.12

In sum, multiple blockholders lead to greater trading volumes. This both reducesaggregate pro�ts and impounds more information into prices. Since �rm value is in-creasing in price informativeness (as it induces e¤ort ex ante) and independent oftrading pro�ts (which are a pure transfer from atomistic shareholders to blockholders),higher trading volumes lead overall to an increase in �rm value.In the present model, the trading mechanism works despite the fact that the man-

ager�s contract is exogenous. It is even more powerful if the manager is risk-averseand the contract is endogenous, as in Holmstrom and Tirole (1993) and Calcagno andHeider (2007). A more informative (less noisy) stock price means that an incentivecontract based on ~p imposes less risk on the manager. Hence the manager can be givena more highly-powered contract, which induces greater e¤ort.As in earlier models, the sum of the actions bi of the blockholders is decreasing

in the number of blockholders, owing to the free-rider problem. Therefore, there is atrade-o¤ between the intervention and trading e¤ects.

4 The Optimal Number of Blockholders

In this section we derive the optimal number of blockholders. We start by derivingthe optimal number that maximizes �rm value, and later discuss the social optimum(that maximizes total surplus, taking into account the costs borne by the manager andblockholder) and the private optimum (that maximizes the total payo¤ to blockhold-ers).

12Fishman and Hagerty (1995) also show that introducing additional informed traders is a commit-ment to trading more aggressively. They use this result to show that, if there are multiple informedagents, a speci�c informed agent will sell her information to other traders, rather than only exploitingit herself.

11

Proposition 3 The number I� of blockholders that maximizes �rm value is:

I� = max

�1;�a � �b�b

�: (13)

Proof Using the results of Proposition 2, we can write the expected value of the �rmas

E[~v] = �a log

��a�

�I

I + 1

��+ �b log

��b�

�1

I

��: (14)

We need to maximize the above expression with respect to I. The �rst order conditionis given by:

�a � �b � �bII + I2

= 0: (15)

I = (�a � �b)=�b satis�es the �rst order condition. To verify that I� is indeed amaximum, it is su¢ cient to note that the left hand side of (15) is positive for I < Iand negative for I > I.The optimal number of blockholders solves the trade-o¤ between the positive e¤ect

of more blockholders on managerial e¤ort, and the negative e¤ect on blockholder inter-vention. The optimum is therefore increasing in �a, the productivity of the manager�se¤ort, and declining in �b, the productivity of blockholder intervention.The magnitude of �b depends on the nature of blockholders�expertise. Using the

terminology of Dow and Gorton (1997), if blockholders have forward-looking (�prospec-tive�) information about optimal future investment decisions or strategic choices, directintervention is particularly valuable and �b is high. For example, venture capital �-nanciers are typically expert in managing start-up businesses and their e¤ort directlya¤ects the �rm�s prospects; indeed, venture capital typically features a small numberof highly concentrated shareholders. On the other hand, if blockholders do not havespecialist expertise in how to manage the company but instead are skilled at gather-ing backward-looking (�retrospective�) information on to evaluate the e¤ect of pastdecisions on �rm value, their primary contribution is to impound the e¤ects of priormanagerial e¤ort into the stock price. In such a case, �b is low and a large number ofblockholders is optimal. As �rms mature, active venture capitalist investors are typ-ically replaced by passive institutional shareholders, and the number of blockholdersusually increases.

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Another determinant of �b is blockholders�control rights and thus ability to inter-vene (holding constant the size of their individual stakes).13 Black (1990) and Bechtet al. (2007) note that U.S. shareholders face substantial and institutional hurdles tointervention, compared to their foreign counterparts. This reduces �b, thus increasingI�, and is consistent with the fact that �rms in the U.S. typically have smaller andmore numerous blockholders compared to overseas.Given our broad de�nition of managerial e¤ort (to encompass any action that in-

creases �rm value but is personally costly to the manager), a high �a can result from anumber of underlying factors. Under the most literal de�nition of �working�, �a will behigh if managerial e¤ort is particularly productive; this is more likely to be the case ingrowing and unregulated industries. Additionally, under the interpretation of �avoid-ing private bene�ts,��a will be high if the manager is able to extract substantial rents,as the �rm value gains from the �rst-best action (forgoing private bene�ts) are high.This will occur if there are weak alternative governance mechanisms (e.g. capturedboards). However, poor governance also raises the scope for blockholder value addedthrough direct intervention, measured by �b. For example, it may lead to the managerundertaking some negative-NPV projects, which the blockholder can overturn to addvalue.14 In sum, the potency of other governance mechanisms a¤ects the scope forblockholders to add value through both �voice�and �exit�, rather than the trade-o¤between them, and so has an ambiguous e¤ect on I�.While Proposition 3 is concerned with maximizing �rm value, the social optimum

maximizes total surplus, which takes into account the costs of the manager�s andblockholders�actions. Informed trading pro�ts do not a¤ect total surplus, since theyare a transfer from liquidity traders to the blockholders. In practice, the social optimumwill be reached if there is an initial owner choosing shareholder structure when takingthe �rm public, since his IPO proceeds will equal total surplus. The owner will haveto compensate the blockholders (in the form of a lower issue price) for their expectedintervention costs, and the manager for his e¤ort in the form of a higher wage.

Proposition 4 Let eI represent the unique positive solution to�a

I (I + 1)� �bI� �a�

(I + 1)2+�b�

I2= 0: (16)

13In reality, control rights will also be increasing in the size of each blockholder�s individual stake.This will reinforce the negative e¤ect of I on intervention currently in this paper.14This can be more directly shown by allowing �b to be a decreasing function of e, at the cost of

complicating the analysis.

13

The number I�soc of blockholders that maximizes total surplus is

I�soc = maxh1; eIi : (17)

I�soc may be higher or lower than I�:

Proof Total surplus is given by:

�a log

��a�

�I

I + 1

��+ �b log

��b�

�1

I

��� �a�

�I

I + 1

�� �b�

1

I: (18)

Taking �rst-order conditions yields equation (16). The Appendix proves that there isa unique positive solution and that it is a maximum.Compared to equation (15), equation (16) contains two additional terms. Increas-

ing the number of blockholders raises the cost of managerial e¤ort, but reduces thecombined cost of blockholder monitoring. The social optimum may thus be higher orlower than the number that maximizes �rm value. Since the manager�s (blockholders�)e¤ort is multiplicative in � (�), I�soc rises relative to I

� if � is higher and � is lower.Finally, we analyze the privately optimal division of � that would maximize block-

holders� combined payo¤s. In other words, we ask the question: if blockholders inaggregate hold �% of the �rm, do they have incentives to split or combine stakes toachieve the number that maximizes either �rm value or total surplus?

Proposition 5 Let bI represent the unique positive solution to�

��a

I (I + 1)� �bI

�+�b�

I2� (I � 1)2pI(I + 1)2

���" = 0: (19)

The number I�soc of blockholders that maximizes total blockholders�payo¤ is

I�priv = maxh1; bIi : (20)

I�priv may be higher or lower than I�, and it may be higher or lower than I�soc:

Proof Total blockholders�payo¤ is given by:

�

��a log

��a�

�I

I + 1

��+ �b log

��b�

1

I

��� �b�

1

I+

pI

I + 1���": (21)

Taking �rst-order conditions yields equation (19). The Appendix proves that there isa unique positive solution and that it is a maximum.

14

Blockholders�objective function di¤ers from �rm value in three ways. They onlyenjoy �% of any increase in �rm value; bear the costs of intervention; and are concernedwith informed trading pro�ts. Increasing I above I� therefore has an ambiguous e¤ect:it reduces the combined costs of intervention, but also reduces combined trading pro�tsthrough exacerbating competition. Therefore, as with the social optimum, the privateoptimum may be higher or lower than the number that maximizes �rm value. I�privrises relative to I� if � is higher (as this increases the cost of e¤ort) and �� and �" arelower (as these augment informed trading pro�ts). Thus, if informed trading pro�tsare particularly important, shareholders will combine blocks to the detriment of �rmvalue.Blockholders�objective function also di¤ers from the social optimum in three ways.

In addition to being concerned with informed trading pro�ts and only �% of �rm value,they also ignore the cost of managerial e¤ort. Again, the sum of these three e¤ectsis ambiguous. Increasing I above I�soc would both reduce total blockholder costs andtotal trading pro�ts.In ongoing work, we are extending the model to analyze further determinants of

the optimal block sizes, such as the level of information asymmetry and the precisionof blockholders�retrospective information.

5 Conclusion

This paper o¤ers a rationalization for the multiple blockholder structures observed inmany �rms. The co-ordination issues resulting from splitting a block lead to free-riderproblems that hamper direct blockholder intervention. This is the e¤ect captured bymany existing papers, which lead to their advocacy of highly concentrated ownership.However, this paper shows that the same co-ordination problems can be bene�cial for�rm value: multiple small blockholders act competitively in their trading behavior,impounding a greater level of information in the stock price and thus inducing highermanagerial e¤ort. The optimal number that maximizes �rm value depends on therelative importance of managerial and blockholder e¤ort. This optimum may di¤erslightly from the social optimum that maximizes total surplus, and the private optimumthat maximizes the blockholders�combined payo¤.

15

A Proofs

Proof of Proposition 4Putting equation (16) under a common denominator yields

�aI (I + 1)� �bI (I + 1)2 � �a�I2 + �b� (I + 1)2

I2 (I + 1)2= 0: (22)

The equation is thus a cubic, and has at most three roots. The function is discontin-uous at I = �1 and approaches �1 either side of I = �1 (since the � �a�

(I+1)2term

dominates). It is also discontinuous at I = 0 and approaches +1 either side of I = 0(since the �b�

I2term dominates). It is continuous everywhere else.

As I ! �1, the ��bIterm in equation (16) dominates, and so the function as-

ymptotes the x-axis from above. Since it approaches �1 as I rises to �1, and iscontinuous between I = �1 and I = �1, there must be one root between these twopoints. Similarly, since the function tends to +1 as I rises from just above �1 tojust below 0, and is continuous between these two points, there must be a second rootwithin this interval. As I ! +1, the ��b

Iterm in equation (16) again dominates, and

so the function asymptotes the x-axis from below. Since the function tends to +1 asI approaches 0 from above, and is continuous between I = 0 and I = +1, there mustbe a third root (eI) between these two points. There can only be one positive root,since there are two negative roots and at most three roots in total. The positive rootis a local maximum, since the gradient is negative for I < eI and positive for I > eI.Proof of Proposition 5Owing to the

pI term in the denominator of the �nal term in equation (19), the

only real roots are positive. As I tends to 0 from above, the function tends to +1since the �b�

I2term dominates. As I ! +1, the ��b

Iterm dominates the function

asymptotes the x-axis from below. There is thus at least one positive root.The second derivative is given by:

�

���a(2I + 1)I2 (I + 1)2

+�bI2

��2�b�I3

�2pI(I + 1)2 � (I � 1)

h2pI(2I + 2) + 1p

I(I + 1)2

i4I(I + 1)4

���":

(23)As I approaches 0 from above, the second derivative becomes highly negative, as the�2�b�

I3term dominates. As I rises, the second derivative becomes less negative and

eventually becomes positive as the � �bI2term increasingly dominates. Since this term

16

continues to dominate as I approaches +1, the second derivative never becomes neg-ative again. Hence there is only one positive root, bI. The positive root is a localmaximum, since the gradient is negative for I < bI and positive for I > bI.

17

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