Large shareholder trading and the complexity of corporate investments

J. Finan. Intermediation 22 (2013) 106–122

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J. Finan. Intermediation j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j fi

Large shareholder trading and the complexity of corporate investments q Eitan Goldman a, Günter Strobl b,⇑ a b

Kelley School of Business, Indiana University, Room 356A, 1309 East 10th Street, Bloomington, IN 47405, USA Kenan-Flagler Business School, University of North Carolina at Chapel Hill, McColl Building, C.B. 3490, Chapel Hill, NC 27599, USA

a r t i c l e

i n f o

Article history: Available online 28 April 2011 Keywords: Blockholder trading Investment complexity Managerial myopia

a b s t r a c t This paper investigates how the presence of a large institutional shareholder affects the complexity of corporate investments. Our analysis is based on the observation that the blockholder’s planning horizon does not necessarily coincide with the time it takes for the market to correctly evaluate these investments. It demonstrates that this horizon mismatch creates an incentive for the large shareholder to manipulate the firm’s stock price. In equilibrium, corporate managers respond to these manipulation attempts by increasing the complexity of their investments. This in turn lowers the large shareholder’s incentive to collect costly information, which reduces price informativeness and exacerbates managerial myopia. Thus, our analysis identifies a new cost of block ownership resulting from an increased complexity of corporate investments. Ó 2011 Elsevier Inc. All rights reserved.

1. Introduction Market observers attribute the recent financial crises in part to the popularity of new asset classes whose risks were difficult to evaluate. According to experts testifying in front of the Financial Crisis Inquiry Commission in February 2010, the complicated cash flow structure of mortgage-backed securities, collateralized debt obligations, and a variety of other structured credit instruments contributed significantly to the market’s inability to price these new complex financial products and led to a

q We thank seminar participants at Indiana University as well as participants at the 2010 FIRS conference and the 2010 Summer Finance Conference at IDC for helpful comments and suggestions. The paper also benefited from comments by S. ‘‘Vish’’ Viswanathan (the editor), Alex Edmans, Francesco Sangiorgi, and an anonymous referee. ⇑ Corresponding author. Fax: +1 919 962 2068. E-mail addresses: [email protected] (E. Goldman), [email protected] (G. Strobl).

1042-9573/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.jfi.2011.04.001

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decline in liquidity. In a similar vein, US Federal Reserve Chairman Ben Bernanke argued that financial innovation may have resulted in a decline in transparency. In a speech given in April 2009, he noted that ‘‘we should be wary of complexity whose principal effect is to make the product or service more difficult to understand by its intended audience.’’1 In this paper, we investigate the broader question of why complex assets may emerge as part of a firm’s optimal investment strategy. In particular, we analyze how the incentive of corporate managers to invest in such assets is affected by the presence of a large institutional shareholder (mutual fund, pension fund, etc.) who has the ability to collect information about these investments and profits from trading on that information. By incorporating the agency problem at the fund management level (albeit in a simplistic way), we demonstrate that a larger block ownership can lead to an increased focus on complex investments. Our analysis questions the belief that blockholder trading alleviates agency problems caused by the short horizon of corporate managers. We find that, in many cases, the presence of a large shareholder who is herself an agent exacerbates managerial myopia: it makes short-term stock prices less informative about the manager’s performance, which reduces managerial effort and, hence, lowers firm value in the long term. Thus, we identify a new cost of block ownership resulting from an increased complexity of the firm’s investments. Our model considers a manager who can influence a firm’s investment policy through her effort choice as well as her choice of asset complexity. We define the complexity of an asset as the amount of time that it takes the market to correctly assess its value. Thus, our notion of complexity is closely related to the horizon of an investment: investments in research and development or in innovative financial instruments are considered complex as their value is not known to shareholders in the short-term. The manager makes her investment decisions to maximize her expected compensation net of the cost of effort, which increases in the firm’s short-term stock price. This stock price is informative about the manager’s performance to the extent that the large shareholder acquires information about the firm’s profit and trades on it. A key ingredient of our model—and our departing point from much of the existing literature—is the assumption that the large shareholder is an institutional investor whose fund manager’s tenure may be shorter than the time it takes for the value of complex assets to become public.2 This assumption is empirically motivated. In a recent study, Cronqvist and Fahlenbrach (2009) report that about three quarters of blockholders in S&P 1500 firms are institutional investors. The large shareholder’s objective is to maximize the value of her portfolio at the end of her finite employment horizon. Further, we focus on ‘‘passive monitoring’’ activities and assume that the large shareholder influences the firm’s investment behavior only through trading. This is consistent with the behavior of the vast majority of blockholders in the US who are typically small and rarely intervene in a firm’s operations.3 Our analysis leads to several interesting results. First, we find that the large shareholder’s demand for shares increases in the complexity of the firm’s investments and in her block size. The intuition for this result stems from the fact that, in contrast to the standard model with a long-lived informed trader, the large shareholder in our model has two motives for trade: on the one hand, she wants to maximize her trading profits; on the other hand, she is also concerned about the value of her initial position. Clearly, the former objective may adversely affect the latter: while selling shares following negative information increases the large shareholder’s trading profits, it also lowers the stock price and hence the value of her initial position in case her tenure ends before the value of the firm’s assets becomes public. This creates an incentive for the large shareholder to inflate her trade in order to manipulate the price upward. The magnitude of this effect is larger, the more complex the firm’s assets are (i.e., the less likely it is that their value becomes public during the shareholder’s tenure) and the larger the shareholder’s ownership stake is.

1

See the Wall Street Journal from April 17, 2009. In this respect, our paper is similar to Goldman and Slezak (2003) who examine the asset pricing implications of this assumption in a model of delegated portfolio management. See also Bhattacharyya and Nanda (2009), who study the role of shortterm performance measurement in causing fund managers to engage in ‘‘portfolio pumping.’’ 3 When blockholders are defined as 5% shareholders, Cronqvist and Fahlenbrach (2009) find that the median ownership stake of blockholders in S&P 1500 firms is only 7.8% and that blockholders rarely have board representation. 2

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Second, we show that a larger ownership stake by the blockholder leads to more complex investments. The reason is that by investing in more complex assets, the manager reinforces the large shareholder’s incentive to manipulate the firm’s stock price upward by acquiring more shares. This implies that, ceteris paribus, more complex investments are associated with higher stock prices, which benefits the manager in form of an increased compensation. Of course, in equilibrium the market is not fooled by this ‘‘signal-jamming’’ strategy: market participants correctly anticipate the extent to which the blockholder’s demand is inflated and take this into account when pricing the firm’s stock. However, despite being unable to mislead the market, the manager continues to invest in complex assets and the blockholder continues to inflate her demand, because any deviation would reduce the firm’s stock price and thus cannot be sustained in equilibrium. Third, we demonstrate that price informativeness decreases with the complexity of the firm’s assets and the block size of the large shareholder. The intuition for this result is as follows. Since the large shareholder can only profit from trading on private information when this information gets reflected in the stock price during her tenure, her incentive to collect costly information is inversely related to asset complexity: the less complex the firm’s assets are, the more likely it is that their value becomes public before her tenure ends, and thus the more she benefits from acquiring information about them. Further, since block ownership increases asset complexity (as argued above), a larger block size also leads to less informative prices. Our fourth result relates block ownership to firm value. We demonstrate that the presence of an informed blockholder can have a negative effect on firm value. This follows from the above observation that, compared to informed traders who have no ownership stake in the firm, a blockholder has less incentive to collect costly information. Her presence thus makes the stock price less informative about the manager’s performance, which reduces the amount of effort exerted by the manager and, as a consequence, lowers firm value. We want to point out, however, that this result should not be interpreted in a cross-sectional sense: since the ownership stake of the blockholder is taken as exogenous in our analysis, the predicted negative relationship between firm value and block size does not mean that, in the cross section, firms with a more concentrated ownership have lower valuations. In fact, since block size may be related to various characteristics of the firm that also affect its value (e.g., its productivity or its growth opportunities), a cross-sectional analysis may very well find a positive relationship between these two quantities. We further address this issue when we discuss the empirical implications of our analysis in Section 4. Our paper is related to several strands of the literature. First, it is related to the literature on shareholder activism. A number of theoretical papers have studied the role of large shareholders in corporate governance.4 The role of blockholders in these papers differs from ours in that they affect the value of the firm through direct intervention, such as forcing a restructuring or vetoing an investment project. While some of these papers consider the possibility that the large shareholder trades in the secondary market, they generally focus on her incentive to engage in costly monitoring and on the firm’s optimal ownership structure. In contrast, our paper analyzes how blockholders can affect corporate behavior even if they lack control rights and are unable to intervene in the firm’s operations. Our paper is also related to the literature that studies the effect of stock-based compensation contracts on managerial investment decisions. Early contributions to this literature include Narayanan (1985), Stein (1989), Bebchuk and Stole (1993), and Bizjak et al. (1993), who show that excessive concern over short-term stock prices can lead to myopic investment choices that, depending on the type of agency problem considered, can result in either overinvestment or underinvestment. However, in contrast to our analysis, these papers take the market’s information structure as exogenous and do not consider the effect of the firm’s investment policy on price informativeness. In this respect, our approach is closer in spirit to the work of Holmström and Tirole (1993), Dow and Gorton (1997), Admati and Pfleiderer (2009), and Dow et al. (2010), who study the role of stock markets in guiding corporate investments in a world, where investors must be given incentives to collect costly information. These papers demonstrate that informed shareholders can play a part in

4 A partial list includes Shleifer and Vishny (1986), Admati et al. (1994), Burkart et al. (1997), Bolton and von Thadden (1998), Kahn and Winton (1998), Maug (1998), Aghion et al. (2004), and Faure-Grimaud and Gromb (2004).

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monitoring managerial performance even without intervening in a firm’s operations. They differ from our model in that the ownership stake of investors has no impact on their behavior: it neither affects their choice of information quality nor their trading strategy. Hence, there is no explicit role for blockholders in these models. A notable exception is Edmans (2009) who shows that a larger block size can strengthen the shareholder’s incentive to collect information by mitigating the adverse effect of short-sale constraints. This in turn improves price informativeness and increases investment efficiency. Our paper complements Edmans (2009) by identifying a new channel through which block ownership affects the quality of information acquired by outside shareholders. In our model, the ownership stake of the blockholder influences her incentive to gather information because of its effect on the complexity of the firm’s investments. Finally, our paper contributes to the growing literature on complexity in financial markets. Brunnermeier and Oehmke (2009) argue that asset complexity may have pricing implications when agents are boundedly rational. Arora et al. (2009) show that once computational complexity is taken into consideration, financial derivatives can actually amplify asymmetric information costs instead of reducing them. Carlin (2009) studies the effect of competition on complexity in retail financial markets and demonstrates that as the number of firms increases, each firm raises the complexity of its price structure in order to prevent some consumers from becoming knowledgable about prices in the market. In an experimental study, Carlin and Kogan (2010) find that complexity affects subjects’ trading behavior in a way that reduces liquidity and increases price volatility. Our paper expands on this literature by showing that complex assets can emerge rather naturally as a consequence of blockholder trading when managers are compensated based on short-term stock prices. The remainder of the paper is organized as follows. Section 2 introduces the model. Section 3 describes the equilibrium strategies of the different agents and examines the interaction between block ownership, investment complexity, and firm value. Section 4 discusses empirical implications and relates our results to the literature on the role of institutional shareholders in corporate governance. Section 5 summarizes our contribution and concludes. All proofs are contained in the Appendix. 2. The model We consider an economy with a single firm that takes place over times 0, 1, and 2. The firm is allequity financed and has a single, perfectly divisible share outstanding. It is run by a manager and owned by three different types of risk neutral agents: (i) a large shareholder who can produce information about the future value of the firm and profits from trading on that information; (ii) small shareholders who hold shares for long-term capital appreciation and do not trade in the secondary market; and (iii) liquidity traders who trade shares for reasons exogenous to the model. Besides the firm’s shares, market participants can also invest in a riskless bond. The bond is in perfectly elastic supply and its interest rate is normalized to zero. The structure of the economy is common knowledge. 2.1. Firm and manager At time 0, the firm invests in a new project whose payoff v depends on the unobservable effort e exerted by the manager: v = he + , where the coefficient h > 0 reflects the firm’s productivity and  is a normally distributed random variable with mean zero and variance s1 v . The assumption that v increases in e captures the idea that managerial effort enhances the value of the firm’s investment project. Exerting effort is costly to the manager. In particular, we assume that the manager’s private utility cost associated with an effort level of e is equal to ce2/2. In addition to her effort choice, the manager influences the firm’s investment policy through her choice of project type, parameterized by d. Specifically, d 2 [dL, dH] denotes the probability that the payoff v is publicly revealed before time 2, where 0 < dL < dH 6 1.5 With probability 1  d, the payoff 5 As will become clear in Section 3, the assumption that dL > 0 is necessary for the large shareholder’s trading strategy to be well defined.

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is revealed after time 2 and thus does not affect the time 2 stock price. The manager’s choice of project type is only observed by the large shareholder, but not by other market participants.6 The revelation probability d captures an important characteristic of the firm’s project: it reflects the extent to which its value can be determined by outside investors in the short-term. Thus, d is inversely related to the horizon of the project. A shorter horizon makes it more likely that the payoff v becomes public before time 2 and is hence associated with higher values of d. Alternatively, d can be interpreted as a measure of the complexity of the investment project. In this case, a lower d indicates a more complex project, the idea being that the more complex a project is, the longer it takes for the market to correctly assess its value. The manager is assumed to be risk neutral. Her compensation is based on the market’s short-term beliefs about the firm’s value as indicated by the time 1 stock price P1. In particular, we assume that the manager initially receives x shares of the firm’s stock which she sells at time 1. Thus, her compensation equals xP1, where we take x > 0 as given.7 This focus on short-term performance is a standard assumption in the literature and can be motivated by a number of factors such as reputational concerns (Narayanan, 1985), takeover threats (Stein, 1988), or the manager’s ability to sell her own shares (Stein, 1989).8 2.2. Large shareholder There is a single risk neutral shareholder who can collect information on the value of the firm’s project v before the stock market opens at time 1.9 By incurring a cost js2/2, she observes the realization of a signal s = v + g, where g  N ð0; s1 s Þ is independent of  and ss = svs/(1  s). Note that ss is increasing in s. This assumption captures the idea that the large shareholder can increase the precision of her signal at a cost. In addition to obtaining the private signal s, the large shareholder’s ability to collect information about the firm’s investment project also enables her to observe the manager’s choice of project type d. Based on her private information, the large shareholder then submits a market order for x shares of the firm’s stock to the market maker. Her initial ownership stake in the firm, which we denote by b P 0, is assumed to be common knowledge. In most firms, blockholders are institutional investors (mutual funds, pension funds, etc.) whose fund managers may have a tenure that is shorter than the time it takes for their private information to become public.10 To capture this fact, we assume that the informed shareholder is herself an agent who expects to resign her position at time 2 and hence trades to maximize the expected value of her portfolio at that time. In particular, her objective function is given by:

max E½xðP2  P1 Þ þ bP2 j s: x

ð1Þ

2.3. Price formation At time 1, the firm’s shares are traded in a competitive market-making system similar to that of Kyle (1985). In addition to the large shareholder, there are liquidity traders who trade for reasons exogenous to the model. The aggregate demand of these liquidity traders is given by u  N ð0; s1 u Þ and is independent of the stock price P1 (and all other random variables in the model). As in Kyle (1985), liquidity traders serve the purpose of disguising the trades of the informed shareholder. 6

We discuss the implications of this assumption in Section 3.4. Goldman and Slezak (2006) show how x can be endogenized in a model with unobserved managerial effort. The assumption that the manager’s compensation only depends on the short-term stock price is not critical to our analysis. Introducing a long-term component based on the terminal value v would affect the manager’s choice of investment horizon, but would not alter our results qualitatively as long as the short-term component is nonzero. 9 The assumption of a single informed shareholder is not crucial to our results, as we will show in Section 3.4. 10 Cronqvist and Fahlenbrach (2009) report that about three quarters of blockholders in S&P 1500 firms are institutional investors. 7 8

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Otherwise, prices would fully reveal the large shareholder’s private information, and there would be no gains to collecting information. The large shareholder, liquidity traders, and the manager submit their demands to a risk neutral market maker who sets the price and acts as a counterpart to all trades. The market maker observes the aggregate net order flow z = x + u  x, but not its individual components. Bertrand competition among market makers leads to zero expected profits, so that P1 equals the expected value of a share, conditional on the observed order flow. Following Kyle (1985), we restrict our attention to linear equilibria. Thus, we postulate that the equilibrium price is a linear function of the net order flow z, such that:

P1 ¼ E½v jF M  þ kðz  E½zjF M Þ;

ð2Þ

where F M denotes public information (excluding z) that is available to the market maker at time 1. In the ensuing analysis, we derive a linear equilibrium in which this conjecture is confirmed to be correct. For simplicity, we assume that there is no further trading at time 2. Since the firm’s payoff v is revealed before time 2 with probability d, the above modeling framework implies that the time 2 stock price is given by:

 P2 ¼

v;

with probability d;

P1 ; with probability 1  d:

ð3Þ

3. Equilibrium In this section, we solve for the equilibrium of the economy defined above. The equilibrium concept we use is that of a Perfect Bayesian Equilibrium (PBE). Formally, a PBE of our economy is (i) an effort choice e and a choice of project type d by the firm’s manager that maximize her expected compensation, given the large shareholder’s information acquisition and trading strategy and the market maker’s price-setting rule, (ii) an information acquisition strategy s and a trading strategy x by the large shareholder that maximize her expected time 2 wealth, given all other strategies, and (iii) a pricing rule P1 by the market maker that allows her to break even in expectation, given all other strategies. Moreover, (iv) the market maker uses Bayes’ rule in order to update her beliefs about the project value v based on the observed order flow z. Finally, (v) all agents have rational expectations in the sense that each player’s beliefs about the other players’ strategies are correct in equilibrium. 3.1. Stock market equilibrium We first solve for the equilibrium in the stock market. As discussed in Section 2, the time 2 stock price, P2, is simply the project’s payoff if v is publicly revealed before time 2 (which happens with probability d) and equals P1 otherwise. The time 1 stock price, P1, depends on the precision of the large shareholder’s private signal s, which in turn depends on her expected profit and, hence, on her beliefs about the manager’s effort choice and investment strategy. We begin our analysis of the stock market equilibrium by deriving the large shareholder’s optimal trading strategy x, taking as given her signal precision s and the market maker’s pricing rule in (2). Using the above characterization of the time 2 stock price, the large shareholder’s optimization problem can be written as:

max dE½v  P1 jF L x þ ðdE½v jF L  þ ð1  dÞE½P1 jF L Þb; x

ð4Þ

where F L denotes the large shareholder’s information set which contains the signal realization s, her initial ownership stake b, as well as the project type d. Since v and s are jointly normally distributed, the conditional expectation of v follows immediately from the projection theorem:11

E½v jF L  ¼ ð1  sÞh^eL þ ss;

11

See, e.g., Anderson (1984), Chapter 2.

ð5Þ

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where ^ eL denotes the large shareholder’s belief about the manager’s effort choice e. Moreover, from the price conjecture in (2), we have:

E½P1 jF L  ¼ E½h^eM þ kðx  x  E½zjF M ÞjF L ; ¼ h^eM þ kðx  x  E½zjF M Þ;

ð6Þ ð7Þ

where ^ eM denotes the manager’s effort choice expected by the market maker. The last equality follows from the fact that the market maker’s information set is a subset of the large shareholder’s information set, i.e., F M  F L . Substituting the above expression and the expression in Eq. (5) into the objective function in (4), we derive the first order condition for a maximum of the large shareholder’s expected time 2 wealth with respect to x as:12

x¼

  1 1 1d b : ðsðs  h^eL Þ þ hð^eL  ^eM ÞÞ þ x þ E½zjF M  þ 2k 2 d

ð8Þ

In equilibrium, the beliefs of the large shareholder and the market maker about the manager’s effort choice have to be correct (i.e., ^eL ¼ ^eM ¼ e). Thus, E½s  h^eL j F M  ¼ 0. Furthermore, the market maker’s expectation of the net order flow is given by:

E½zjF M  ¼ E½xjF M   x ¼

1  ^dM b  x; ^dM

ð9Þ

where ^ dM denotes the market maker’s belief about d.13 Substituting this expression into the above first order condition, we can rewrite the large shareholder’s optimal demand as follows:

! 1 1 1  d 1  ^dM ^ ^ ^ b: x¼ ðsðs  heL Þ þ hðeL  eM ÞÞ þ þ ^dM 2k 2 d

ð10Þ

The above expression decomposes the net demand into two parts: the first term reflects the trading based on the large shareholder’s private information, whereas the second term captures her concern about the value of her initial position. If the value of the firm’s project is revealed with certainty before time 2 (i.e., if d = 1), the second term vanishes and the informed trader is only concerned about maximizing her trading profits, as in Kyle (1985). However, if there is some uncertainty about whether her private information will become public before her tenure ends at time 2, such a trading strategy may adversely affect the value of her initial position. For example, if the shareholder has a positive position b > 0 and receives negative information about v, her profit-maximizing trade will lower the value of her initial position: selling shares because of a negative signal will lead to a reduction in the time 2 stock price in the event that v does not become public (i.e., when P2 = P1). The optimal trade takes this negative effect on the value of her initial position into account and thus will be less negative than if the shareholder had no initial position. Unless the signal is sufficiently negative, she may not sell any shares at all since her trading profit may not outweigh the loss in value of the initial position. Eq. (10) shows that, if the large shareholder has a positive initial position, her optimal demand always exceeds the profit-maximizing trade in the standard Kyle (1985) model, regardless of her private information. Thus, the initial position creates a ‘‘lock-in effect’’ in that it gives the shareholder an incentive to bias upwards her trade, making a sale less likely. The extent of this bias depends on her initial holdings and the complexity of the firm’s investment project. Intuitively, the shareholder is more concerned about adversely affecting the future stock price P2 through her trade when she holds a larger number of shares (i.e., when b is large) and/or when the probability that the true value will be revealed before time 2 is low (i.e., when d is small). It is important to note, however, that in equilibrium this bias in trading does not affect the stock price as the market maker correctly anticipates the upward bias in the large shareholder’s demand.14 12

The second order condition for a maximum implies that this is the unique maximum if k > 0. Recall that the market maker does not observe the manager’s choice of project type. 14 This is due to our admittedly strong assumption that the market maker perfectly observes the shareholder’s initial position b and is thus aware of her trading motives when setting the equilibrium price. 13

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Having characterized the large shareholder’s trading strategy, we now turn to the market maker’s pricing rule. In a competitive market-making system, the equilibrium price function is simply the conditional expectation of the terminal value v given the market maker’s information set, which includes information revealed by the unexpected order flow, z  E½z j F M . The following proposition characterizes the equilibrium price coefficient k as a function of the large shareholder’s information quality. Proposition 1. There exists a unique linear equilibrium at the trading stage. The equilibrium price function is as specified in (2), and the equilibrium price coefficient is given by:

1 k¼ 2

sffiffiffiffiffiffiffiffiffiffiffi su s^M

sv

;

ð11Þ

^M denotes the market maker’s belief about the large shareholder’s signal precision s. where s Proposition 1 shows that in our model market depth, which is typically defined as the order flow required to move the price by one unit (and is thus characterized by the term 1/k), is similar to that in the standard Kyle (1985) model: it decreases in the payoff uncertainty, s1 v , and increases in the amount of liquidity trading, s1 . In addition, market depth decreases in the large shareholder’s inforu mational advantage over the market maker as measured by the precision of her private information, s^M . This latter effect captures the intuition that market makers protect themselves against losses to better informed traders by making the market less liquid. 3.2. Information acquisition In this section, we investigate how the large shareholder’s incentive to collect information is affected by the market maker’s pricing rule and the manager’s choice of project type. Prior to observing her private signal s, the large shareholder’s expected time 2 portfolio value, net of the cost of acquiring information, is given by:

ds js2 þ ðdh^eL þ ð1  dÞh^eM Þb  : 4ksv 2

ð12Þ

This expression follows immediately from substituting the shareholder’s optimal demand function given by (10) into her objective function in (4) and taking expectations over all possible signal realizations s. Maximizing this quadratic function with respect to s yields:

s¼

d : 4kjsv

ð13Þ

Note that, by construction, s cannot exceed 1, which is a necessary condition for the precision of the signal noise ss to be nonnegative. In the ensuing analysis, we assume that the cost parameter j is sufficiently high so that this constraint is not binding. The above expression reveals two important properties of the shareholder’s information acquisition decision. First, it shows that the optimal signal precision increases in d. This is intuitive: the higher d is, the more likely it is that the private information of the large shareholder becomes public before her tenure ends at time 2, which is necessary for her to profit from this information. As a result, she exerts more effort collecting information by choosing a higher signal precision s. This insight is critical to our analysis and our departing point from much of the earlier literature. In fact, it has been argued that more complex, long-term projects attract more informed investors—and are therefore more beneficial to the firm—as they are more uncertain and thus provide greater opportunities for information collection. However, this argument implicitly relies on the assumption that informed shareholders have an infinite planning horizon. When their horizon is finite, such projects may actually discourage information production, as our analysis shows. The second property is that, for a fixed level of d, the equilibrium amount of information collection increases in market depth (i.e., the inverse of k). This is not surprising, since a more liquid market allows the informed investor to trade larger quantities without being spotted, which increases her trading profit. It is important to note, however, that market liquidity itself depends on the

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informational advantage that the large shareholder has over the market maker: the better informed the shareholder is, the more sensitive the market maker’s price is to the observed order flow (Eq. (11)). Thus, there exists a feedback loop between the signal precision s and the price coefficient k. In equilibrium, the market maker’s conjecture about the large shareholder’s signal precision has to ^M ¼ s). We can therefore use Eqs. (11) and (13) to solve for the equilibrium price coefbe correct (i.e., s ficient under endogenous information acquisition:

k¼

^dM su 16js2v

!13 ð14Þ

;

where as before ^ dM denotes the market maker’s belief about the firm’s project type d. The above expression further illustrates the effect that the firm’s (expected) project type has on the investor’s information collection activities and, hence, on the liquidity of the firm’s stock. As the revelation probability d decreases, the large shareholder acquires less information, which reduces the price impact of orders and thus improves liquidity. This reflects the idea that prices are less informative about complex projects whose value will only become public in the long run. 3.3. Managerial effort choice and investment policy Our analysis so far has focused on the strategy of the large shareholder while taking the actions of the firm’s manager as given. In this section, we examine how the manager’s investment decision as well as her effort choice are affected by the large shareholder’s strategy. The manager chooses her effort level and the type of the firm’s investment project to maximize her expected compensation payment, net of her cost of effort. Since her compensation is linear in the firm’s stock price P1, the manager faces the following optimization problem:

max

eP0;d2½dL ;dH 

xE½P1 j F MGR  

ce2 ; 2

ð15Þ

where F MGR denotes the manager’s information set at time 0. The conditional expectation of the stock price follows immediately from the market maker’s pricing rule in (2) and the large shareholder’s trading strategy in (10):

! 1 k 1  d 1  ^dM ^MGR hðe  ^eL Þ þ hð^eL  ^eM ÞÞ þ  E½P1 jF MGR  ¼ h^eM þ ðs b; ^dM 2 2 d

ð16Þ

where we have used the fact that, from the manager’s perspective, the expected signal s equals he, her effort level multiplied with the firm’s productivity factor. Note that the manager does not observe the ^MGR the signal precision that the precision of the large shareholder’s signal. We therefore denote by s manager expects the investor to choose. The above expression shows that the manager’s effort choice affects her compensation only through its effect on the expected realization of the large shareholder’s signal. Since the manager’s objective function is strictly concave in e, her optimal effort level is uniquely determined by the first order condition:

e¼

xh ^ sMGR : 2c

ð17Þ

This is a standard result: the manager exerts more effort, the more informative the stock price is about her performance and the more sensitive her compensation payment is to the stock price. The latter effect is captured by the parameter x, which defines the stock-based component of her compensation. The former effect depends on the (anticipated) information quality of the large shareholder, s^MGR : the more information the shareholder collects, the more accurately the stock price reflects the value of the firm and, hence, the manager’s choice of effort. As usual, the equilibrium level of effort decreases with the cost parameter c.

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When choosing the firm’s project type d, the manager takes into account the effect that her choice has on the trading strategy of the large shareholder. As discussed in Section 3.1, when the large shareholder has a positive initial position, her optimal demand x is a decreasing function of d: the lower the probability that the true value of the firm’s project will become public before time 2, the more likely it is that the terminal value of her initial position is based on the short-term stock price P1, and thus the stronger is her incentive to manipulate the price upward by acquiring more shares (Eq. (10)). This implies that, ceteris paribus, lower values of d are associated with higher stock prices (Eq. (16)). Since the manager also benefits from a higher stock price in form of an increased compensation, this creates an incentive for her to encourage the shareholder’s manipulation attempts by investing in more complex (or more long-term) projects. Of course, in equilibrium the market is not fooled by this ‘‘signal-jamming’’ strategy: the market maker correctly anticipates the extent to which the shareholder’s demand is inflated and takes this into account when setting the price (i.e., ^ dM ¼ d in Eq. (16)). However, despite being unable to mislead the market, the shareholder continues to inflate her demand. Any deviation would lead to a reduction in the stock price and thus cannot be sustained as an equilibrium strategy.15 In addition to this ‘‘price manipulation effect,’’ the manager’s choice of project type influences the firm’s stock price through its effect on the quality of information acquired by the large shareholder. As shown in Section 3.2, a higher d increases the shareholder’s optimal signal precision s. This motivates the manager to exert more effort (Eq. (17)), which improves firm value. Since in equilibrium the shareholder correctly anticipates this increase in managerial effort, she demands more shares (Eq. (10)), thereby boosting the firm’s stock price. Thus, the large shareholder’s ability to observe the firm’s project type ensures that the increase in firm value, due to an increase in managerial effort, is reflected in the stock price. As Eq. (16) shows, this argument relies again on the assumption that the market maker cannot observe the manager’s investment decision: her conjecture of the managerial effort level does not depend on the manager’s choice of project type. Of course, in equilibrium her conjecture has to be correct: the effort level expected by the market maker, ^ eM , must coincide with the actual effort level, e. The above discussion shows that the two channels through which the manager’s investment decision affects the firm’s stock price work in opposite directions: the price manipulation effect makes the manager favor more complex, long-term investments, whereas her interest in stimulating information production by the large shareholder gives her an incentive to invest in less complex, short-term projects. The manager’s optimal choice of project type trades off these two effects. The following proposition shows that the equilibrium value of d is uniquely determined and provides sufficient conditions for the existence of an interior solution. Proposition 2. There exists a rational expectations equilibrium in our economy. This equilibrium is unique among the class of equilibria defined by the linear price function in (2). Furthermore, if: 1

4

d2L  ð4j2 sv su Þ3 d3L < 

2cjsu b

xh

2

 1 4 < d2H  4j2 sv su 3 d3H ;

ð18Þ

the firm’s investment type is characterized by an interior solution d⁄ 2 (dL, dH). The analytical solution for the equilibrium value of d is defined by a cubic equation and is not tractable. However, we can gain several interesting insights into the manager’s choice of project type directly from the first order condition. The following proposition presents comparative static results with respect to the block size of the large shareholder and the firm’s productivity. Proposition 3. Suppose that the condition in Proposition 2 is satisfied so that the manager’s problem has an interior solution. Then, the complexity of the firm’s investment project (as measured by the inverse of the

15 This is analogous to the prisoner’s dilemma. The preferred cooperative equilibrium would involve no manipulation by the large shareholder, and no conjecture of manipulation by the market maker. Unfortunately, this cannot be sustained as an equilibrium. If the market maker conjectures no manipulation, the shareholder will have an incentive to mislead her by inflating her demand.

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revelation probability d) is increasing in the ownership stake b of the large shareholder and decreasing in the firm’s productivity factor h, i.e.:

dd < 0 and db

dd > 0: dh

ð19Þ

The intuition for the relationship between the firm’s productivity and the complexity of its investment project is straightforward. A higher value of h increases the marginal value of managerial effort. This motivates the manager to exert more effort and, at the same time, to encourage information production by the large shareholder by investing in a less complex, short-term project to ensure that this increase in effort is reflected in the firm’s stock price. A key factor in the determination of the firm’s investment type is the size of the ownership stake held by the large shareholder. When the shareholder owns a larger block, she has a stronger incentive to inflate her demand in order to boost the firm’s stock price (Eq. (10)). In this case, the price manipulation effect dominates the manager’s interest in a more informative stock price and she will reinforce the shareholder’s desire to manipulate the price upward by increasing the complexity of the firm’s investment project (i.e., by choosing a lower d). Proposition 3 has several interesting implications. First, it predicts an inverse relationship between the number of shares held by passive institutional investors and the expected time it takes for the value of the firm’s investments to become public: the larger the institutional stock ownership, the more the manager delays the resolution of uncertainty by investing in complex and/or long-term projects. Second, combined with our results from Sections 3.1 and 3.2, it suggests that a larger institutional ownership share may result in less information collection by investors, which reduces price informativeness and improves market liquidity. This is in contrast to Edmans (2009) who argues that, in a setting with short-sale constraints, a larger block size typically leads to more information production. Our analysis complements Edmans’s argument by showing that this result may be reversed once the finite horizon of a blockholder who is herself an agent is taken into account. Finally, Proposition 3 implies that the size of the ownership stake held by an informed blockholder is negatively related to the manager’s effort choice: a larger ownership stake lowers the blockholder’s benefit from collecting information and hence decreases price informativeness, which reduces the amount of effort exerted by the manager. This, in fact, establishes the following result. Proposition 4. The expected value of the firm, E½v , is a decreasing function of the ownership stake of the large shareholder, b. By endogenizing the complexity of the firm’s investment project, we demonstrate that the presence of an informed blockholder can have a negative effect on firm value. The reason is that, compared to informed traders who have no ownership stake in the firm, a blockholder has less incentive to collect costly information, which leads to a reduction in managerial effort.16 The existing literature on performance monitoring shows that informed shareholders can add value even if they cannot intervene in a firm’s operations. However, in most of the earlier work, the size of their ownership stake plays no role: it has no effect on their trading strategy and hence on the manager’s behavior (e.g., Holmström and Tirole, 1993; Dow and Gorton, 1997; Admati and Pfleiderer, 2009; Dow et al., 2010). A notable exception is Edmans (2009) who shows that a larger block size mitigates the adverse effect of short-sale constraints and thus improves price informativeness. Our analysis adds a new facet to this literature by identifying an additional channel through which a firm’s ownership structure affects the quality of information acquired by outside shareholders. In our model, the size of the blockholder’s position influences her incentive to gather information because of its effect on the manager’s investment strategy. 16 We want to emphasize, however, that the presence of an informed blockholder increases firm value relative to a situation without informed traders. In the absence of informed traders, the firm’s stock price is completely uninformative about the manager’s performance, which leads to a zero effort choice by the manager.

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3.4. Discussion of information structure As in any ‘‘signal-jamming’’ model, we assume that the actions taken by an agent (the manager, in our case) are not observable to some other agent (the market maker). This assumption is crucial for any value-destroying action to be part of the equilibrium strategy. In particular, our result that the manager chooses an investment type that is suboptimal from the shareholders’ perspective relies on the fact that the large shareholder is better informed about the manager’s choice than the market maker. This assumption reflects the idea that a shareholder who has the ability to collect information about the value of the firm’s investments is also likely to know more about other aspects of the firm’s investment strategy such as its horizon.17 We want to point out, however, that if the large shareholder and the market maker shared the same information (e.g., because they both observed the manager’s choice of d), the manager would have no incentive to delay the resolution of uncertainty by choosing a revelation probability of less than dH, since any decrease in d would be perfectly undone by the market maker’s pricing rule. In other words, there would be no price manipulation effect.18 In light of the above discussion, one might argue that the manager would be better off making her choice of investment type public, thereby eliminating any informational asymmetries between the large shareholder and the market maker. However, any such announcement would not be credible: once the manager announces a d > d⁄ and the firm’s shares are priced accordingly, she will always have an incentive to deviate to the lower value d⁄ in order to boost the firm’s stock price. Finally, we discuss to what extent our results are driven by the assumption of a single informed trader. In a generalized version of our model with multiple informed traders, one might expect that the bias introduced by the institutional blockholder would be completely undone by the trades of long-term investors. In the following, we show that this is not the case. Consider a setting with N long-term investors who, like the large institutional shareholder described in Section 2.2, have the ability to produce information about the value of the firm’s project v and to observe the manager’s choice of project type d.19 Each long-term investor i = 1, . . . , N chooses her demand for the firm’s shares, which we denote by yi, to solve the optimization problem:

max E½v  P1 j F i yi ; yi

ð20Þ

where F i denotes investor i’s information set.20 As before, investors conjecture that the equilibrium price is a linear function of the net order flow, which in this generalized setting equals z = x + y1 +    + yN + ux. The optimal demand of investor i is then characterized by the first order condition:

! X 1 1 E½xjF i  þ yi ¼ ðE½v jF i   E½v jF M Þ  E½yj jF i   x  E½zjF M  : 2k 2 j–i

ð21Þ

Summing this demand function over all investors and taking expectations over all possible signal realizations yields: N X i¼1

E½yi jd; F M  ¼

  N 1 ðE½v jd; F M   E½v jF M Þ  E½xjd; F M  þ x þ E½zjF M  : Nþ1 k

ð22Þ

17 This is similar to the standard assumption that the large shareholder can observe an informative signal about the manager’s effort choice, even though the market maker cannot. Note also that the assumption that the large shareholder perfectly observes the manager’s choice of d is not critical to our results. Introducing uncertainty about the manager’s action into the model would change the shareholder’s incentive to collect information, but would not alter our basic conclusions. 18 This can be seen from the manager’s optimization problem in (15) when ^dM is set equal to d in the expected price function (Eq. (16)). 19 Our argument does not rely on a specific information structure. The correlation between the long-lived investors’ signals, the blockholder’s signal, and the firm’s payoff is irrelevant. 20 Note that the expected profit of long-term investors is independent of their initial positions, since the long-term value of these positions is not affected by the stock price P1.

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The above expression shows that long-term investors who are informed about the manager’s choice of project type exploit their knowledge by trading against the institutional blockholder: their non-informational demand (i.e., the part of their demand unrelated to their private information about v) is negatively related to the blockholder’s non-informational demand. This result is rather intuitive. The more shares the blockholder trades to boost the value of her initial position, the further the stock price deviates from the fundamental value, and thus the more profitable it is for long-term investors to take the opposite position. Strategic considerations prevent these investors, however, from completely offsetting the blockholder’s trade (as long as N is finite).21 As Eq. (22) shows, the non-informational demand of the N long-term investors only adds up to a fraction N/(N + 1) of (minus) the blockholder’s non-informational demand. Thus, although the addition of long-lived informed investors reduces the impact that the blockholder’s ownership stake has on the aggregate demand function, it does not eliminate the blockholder’s incentive to manipulate the firm’s stock price.22 This demonstrates that our results hold even if we add informed investors with a long planning horizon to the model: in this generalized setting, the manager still has an incentive to encourage the blockholder’s manipulative trades by investing in more complex projects, which discourages investors from acquiring information and ultimately lowers firm value. 4. Empirical Implications Our analysis in the previous section highlights the importance of the informed shareholder’s ownership share for the manager’s investment decision and hence the value of the firm. In this section, we discuss the empirical implications of our model and relate our results to blockholder effects documented in the literature. We first discuss the effect of blockholders on the firm’s investment behavior. Proposition 3 predicts that an increase in block size leads to more complex and/or long-term investments. It is important to keep in mind, however, that a longer investment horizon indirectly lowers firm value in our model because of its negative effect on price informativeness and, hence, on managerial effort. Thus, an increase in the firm’s investment horizon should not be confused with an increased focus on long-term value creation: a longer horizon does not mean that the manager behaves less myopically. On the contrary, the manager chooses to invest in complex, long-term projects to boost the firm’s short-term stock price, even at the expense of long-term performance. In that sense, a longer horizon should be interpreted as a more myopic investment decision. A number of recent empirical papers have studied the impact of institutional investors and their horizon on firms’ investment behavior. Bushee (1998) examines whether institutional investors encourage corporate managers to engage in myopic investment behavior. He finds that, for the subset of institutions that have high portfolio turnover, this is indeed the case: a large ownership share by these institutions makes it more likely that managers reduce investment in research and development (R&D) to reverse an earnings decline. The opposite is true for institutional investors that have a low portfolio turnover. These findings are consistent with our model: to the extent that a high turnover indicates a short investment horizon, our analysis suggests that a high turnover is associated with more short-term price manipulation by the manager. Bushee (2001) also presents evidence that a high level of ownership by institutions with short investment horizons puts pressure on managers to focus on short-term performance: he shows that these institutions invest more heavily in firms with greater expected short-term earnings and less heavily in firms with more value expected to be realized in the long run.

21 Similar results have been derived by Holden and Subrahmanyam (1992) and Foster and Viswanathan (1996) who analyze dynamic auction models with multiple privately informed traders. 22 This can also be seen from the aggregate non-informational demand of long-term investors and the institutional blockholder, which in this generalized setting is given by:

1 1d Nþ1 ðx þ E½z j F M Þ: bþ Nþ2 d Nþ2

ð23Þ

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We next turn to the relationship between block size and firm value. As shown in Section 3.3, our model predicts that firm value decreases with the ownership stake of the large shareholder. One might therefore conclude that, in the cross section, firms with a more concentrated ownership structure should have lower valuations. However, this is not necessarily the case. First, our analysis abstracts from the fact that large shareholders may be better able to influence corporate policies and to improve firm value through ‘‘active’’ (rather than ‘‘passive’’ or ‘‘trade-based’’) monitoring. Second, and more importantly, the argument ignores differences in productivity across firms: our result in Proposition 3 shows that the negative effect of the block size b on the revelation probability d and hence on firm value has to be contrasted with the positive effect of the firm’s productivity (as measured by h) on these quantities. If block size is positively related to productivity in the cross section of firms, firm value may be positively correlated, negatively correlated, or uncorrelated with the blockholder’s ownership share. While block size is taken to be exogenous in our analysis, one can easily envision a setting in which a positive relationship between block size and productivity arises endogenously from the large shareholder’s optimal choice of ownership stake. In our model, the informed shareholder does not benefit from owning shares of the firm’s stock: any block size large enough to make the manager choose a d of less than dH reduces the shareholder’s expected trading profit. Thus, the optimal size of the shareholder’s initial position is zero—or, more precisely, any number of shares that induces the lowest level of complexity (or the shortest horizon). However, a nonzero optimal block size can be obtained by incorporating a benefit for the blockholder into our analysis—for example, in the form of private benefits of control (Barclay and Holderness, 1989) or short-sale constraints (Edmans, 2009). The optimal block size then trades off this benefit against the loss in trading profits associated with a lower revelation probability d. If the magnitude of the benefit is independent of the firm’s productivity, our analysis in Section 3.3 suggests that the optimal block size is positively related to firm productivity. The above discussion shows that there are significant challenges in testing the implications of our model. Since block size may be related to various firm characteristics, a cross-sectional analysis of its correlation with firm value is problematic.23 Rather, to test the predicted relationship, one has to identify sources of exogenous variation in block size that are not motivated by private information.24 Further, one has to exclude blockholders who actively intervene in the firm’s operations (such as inside blockholders) as well as blockholders who rarely trade on information (such as index funds). An increase (decrease) in block size should then generate a negative (positive) price reaction, especially in situations where short-sales costs and other trading frictions are negligible. To the best of our knowledge, there is no systematic empirical evidence linking changes in the ownership stake of passive shareholders to changes in firm value. Our analysis also has implications for the relationship between the investment horizon of firms and that of their shareholders. The revelation probability d measures the firm’s horizon relative to that of the large shareholder. A firm’s optimal investment policy thus depends on the characteristics of its shareholders. The presence of more short-term shareholders requires more short-term investment projects in order to maximize the firm’s stock price, and vice versa. If there is little variation in the optimal d across firms, our model therefore predicts a positive correlation between the investment horizon of firms and shareholders in the cross section. This is consistent with Bøhren et al. (2005) who show that the investors’ ‘‘ownership duration,’’ which is defined as the length of time that investors hold on to their shares, appears to match the duration of the firms’ investment projects. Derrien et al. (2011) also provide evidence that investor horizon affects corporate policies. They document that, for undervalued firms, the presence of more short-term investors is associated with a reduction in long-term investment (capital expenditure and R&D expenditure). Similar results have been obtained by Polk and Sapienza (2009). Finally, our results also provide some guidance on how to construct empirical measures of investor horizon. Most studies identify short-term (long-term) investors based on their high (low) portfolio turnover (e.g., Wahal and McConnell, 2000; Gaspar et al., 2005; Yan and Zhang, 2009; Derrien et al., 23

This is often called the ‘‘unobserved heterogeneity problem’’ (see, e.g., Holderness, 2003). As our analysis in Section 3 shows, information-based trades typically move prices in the same direction as the order, regardless of the initial block size. 24

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2011). Our analysis suggests that such measures may be problematic because they ignore the effect of the shareholders’ horizon on their decision to acquire information: a longer horizon enhances an investor’s expected profit from information-based trades and, hence, increases her incentive to collect information. This induces a more aggressive trading behavior and leads to a higher turnover. In addition, turnover-based measures do not account for the reluctance of short-term investors to sell shares based on negative information (see our discussion of the ‘‘lock-in effect’’ in Section 3.1). These observations suggest that the relationship between investment horizon and turnover is less clear than previously thought: higher turnover might in fact indicate a longer horizon. 5. Conclusion This paper develops a model of blockholder trading and its impact on the complexity of corporate investments. In particular, we examine how the presence of a large shareholder who has the ability to produce information about the firm’s prospects affects the investment behavior of corporate managers that are compensated based on short-term stock prices. Our analysis shows that a larger ownership stake by the blockholder leads to more complex investments. The intuition for this result is based on the insight that a blockholder whose planning horizon may be shorter than the time it takes for the value of complex assets to become public has two motives for trade: in addition to maximizing her trading profits, she is also concerned about protecting the value of her block. The latter objective causes her to inflate her demand, relative to her profit-maximizing trade, in order to boost the firm’s short-term stock price. Since the manager also benefits from a higher stock price in form of an increased compensation, she has an incentive to reinforce the blockholder’s price manipulation attempts by investing in more complex assets. It is important to note that this argument does not rely on investor irrationality. In equilibrium, the market is not mislead by these manipulation attempts: it correctly conjectures that the blockholder’s demand is inflated and prices the firm’s stock accordingly. Nonetheless, the manager and the blockholder, who take the market’s conjecture as fixed, continue to behave myopically. This increase in investment complexity comes at a cost. It reduces the blockholder’s incentive to collect information and hence lowers the informativeness of stock prices about the manager’s performance, rendering market monitoring less effective. Thus, our analysis identifies a new channel through which block ownership influences corporate investment efficiency. Contrary to popular belief, our results suggest that the presence of a blockholder can adversely affect firm value. Appendix Proof of proposition 1. In a competitive market-making system, the equilibrium price is equal to the expected payoff v conditional on the observed order flow z. From the large shareholder’s demand function in (10), it follows that v and z are jointly normally distributed. Thus, the conditional expectation of v is given by:

P1 ¼ E½v j F M  þ

cov½v ; zjF M  ðz  E½z j F M Þ; var½zjF M 

¼ h^eM þ  2 s^M 2k

s^M 1 s 2k

v

ðz  E½z j F M Þ;

ð24Þ ð25Þ

s s þ s1 u 1 ^1 v M

where as before F M denotes public information that is available to the market maker at time 1, which includes the large shareholder’s initial position b. This confirms the conjectured price function in Eq. (2). Equating the coefficient of z in the above expression to k yields:

1 k¼ 2

sffiffiffiffiffiffiffiffiffiffiffi su s^M :

sv

ð26Þ

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Since the second order condition for the shareholder’s optimal demand requires the price coefficient k to be positive, it follows that the linear equilibrium at the trading stage is uniquely determined by the positive root given in the proposition. h Proof of proposition 2. The existence of an equilibrium follows from the continuity of the manager’s utility function specified in (15) and the fact that it is maximized over the compact set [dL, dH]. To prove uniqueness, it suffices to show that the manager’s problem has at most one interior solution d⁄ 2 (dL, dH). The unique solution is then given by this interior solution or by a corner solution (dL or dH). Letting U denote the manager’s utility function, we can express the first order condition for an interior optimum with respect to d as follows:

@U de @U de @U ds @U þ þ ¼ 0: þ ^MGR dd @d @e dd @ ^eL dd @ s

ð27Þ

From the envelope theorem, it follows that, at the optimum, the partial derivative of U with respect to ^MGR is zero as well, since ^eL ¼ e in equilibrium. e is zero. Further, the partial derivative with respect to s Using the expression for the manager’s optimal effort choice in (17), we can thus write the first order condition as:

x2 h 2 4c

 1

d



4kjsv

1 xkb  ¼ 0: 4kjsv 2d2

ð28Þ

Substituting the expression for the price coefficient k from Proposition 1 into the above equation and 2 rearranging yields the following polynomial in d3 which characterizes the equilibrium project type:

 2 3  1  2 2 2cjsu b  d3 þ 4j2 sv su 3 d3  ¼ 0: xh2

ð29Þ

2

This cubic polynomial in d3 has two changes of sign in the sequence of its coefficients. Hence, by Descartes’ rule of sign, it has at most two positive roots. Further, since the value of the polynomial in (28) is negative for values of d close to zero, it follows that only the larger root can satisfy the second order condition for a maximum of the manager’s utility function. This proves that the manager’s problem has at most one solution in the interval (dL, dH). A sufficient condition for the existence of an interior solution is that the value of the polynomial in (29) is positive for d = dL and negative for d = dH. This condition, which is stated in the proposition, ensures that Eq. (29) has a solution in the interval (dL, dH) and that it is a maximum. h Proof of proposition 3. These comparative static results follow from the Implicit Function Theorem. Let F denote the polynomial in Eq. (29) characterizing the equilibrium project type and assume that the condition in Proposition 2 holds. This condition implies that @F/@d < 0, for all d 2 (dL, dH). Further, we have that:

@F 2cjsu ¼ <0 @b xh2

and

@F 4cjsu b ¼ > 0: @h xh3

ð30Þ

Thus, the interior solution d⁄ satisfies:

 1 dd @F @F <0 ¼ @b @d db

and

 1 dd @F @F > 0:  ¼ @h @d dh

ð31Þ

Proof of proposition 4. In equilibrium, the ex ante expected value of the firm is given by E½v  ¼ he. Since the manager’s optimal effort choice e is increasing in the precision s of the large shareholder’s signal (Eq. (17)) and since s is increasing in the revelation probability d (Eq. (13)), firm value is positively related to d. Thus, it follows from the results in Proposition 3 that firm value is decreasing in the block size b of the large shareholder (assuming that an interior solution for d exists). h

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