Institutional ownership, analyst following, and share prices

Journal of Banking & Finance 36 (2012) 2175–2189

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Institutional ownership, analyst following, and share prices Chitru S. Fernando a,⇑, Vladimir A. Gatchev b, Paul A. Spindt c a

Michael F. Price College of Business, University of Oklahoma, Norman, OK 73019, United States College of Business Administration, University of Central Florida, Orlando, FL 32816, United States c A.B. Freeman School of Business, Tulane University, New Orleans, LA 70118, United States b

a r t i c l e

i n f o

Article history: Received 5 September 2011 Accepted 26 March 2012 Available online 4 April 2012 JEL classification: C24 G12 G30

a b s t r a c t We study the mutual relationships between institutional ownership, analyst following and share prices. We show that the pressure on firms to set lower share prices to attract analysts is attenuated by institutional monitoring. Our theory refutes the assumed causal relation between share price and institutional ownership, attributed to the share price–liquidity relation, and we show empirically that share prices and institutional ownership are positively related after controlling for liquidity. Our study provides a rationale for why better firms generally maintain higher share price levels, and offers new insights into the puzzling empirical linkages observed between nominal share price levels and firm fundamentals. Ó 2012 Elsevier B.V. All rights reserved.

Keywords: Institutional ownership Monitoring Analysts Financial intermediation Share price level Firm value

1. Introduction Institutional investors dominate US equity markets and have the ability to monitor the firms whose shares they own and increase information availability about these firms.1 However, the effect of institutional monitoring and information generation on the determination of share price levels by firms has not been previously examined. We bring together three distinct strands of the literature that study the bilateral links between (a) analyst following and share price levels; (b) institutional ownership and share price levels; and

(c) analyst following and institutional ownership.2 Our analysis offers new insights into (a) the choice of share price levels by firms when they go public or split their shares and (b) the relation between share price level, institutional ownership, and firm value. We also provide a rationale for the puzzling empirical linkages documented in the literature between nominal share price level and fundamental firm characteristics such as the probability of bankruptcy, performance, size, liquidity, and trading volume.3 Brennan and Hughes (1991) and Angel (1997) provide the first critical insights into how stock price levels are linked to information generation by financial intermediaries. They study the relation between analyst following and share price levels, and argue that lower stock price levels will increase the incentive for analysts to generate information about a firm and promote its shares. Schultz

⇑ Corresponding author. Tel.: +1 405 325 2906; fax: +1 405 325 5491. E-mail addresses: [email protected] (C.S. Fernando), [email protected] (V.A. Gatchev), [email protected] (P.A. Spindt). 1 As noted by Gompers and Metrick (2001), institutional ownership of US stocks has grown dramatically since the 1980s. Brancato and Rabimov (2008) report that by the end of 2007, institutional investors accounted for 76.4% of the ownership in the largest 1000 US firms. For a discussion of the benefits to a firm brought about by institutional ownership, see Shleifer and Vishny (1986), McConnell and Servaes (1990), Smith (1996), Carleton et al. (1998), Gillan and Starks (2000), Allen et al. (2000), Hartzell and Starks (2003), Grinstein and Michaely (2005) and Boehmer and Kelley (2009). 0378-4266/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jbankfin.2012.03.026

2 For the relation between share prices and analyst coverage, see Brennan and Hughes (1991) and Angel (1997). For the relation between institutional ownership and share price levels, see Falkenstein (1996), Gompers and Metrick (2001) and Fernando et al. (2004). For the relation between institutional ownership and analyst coverage see Bhushan (1989), Rock et al. (2001), Frankel et al. (2006) and Ljungqvist et al. (2007). 3 See, for example, Maloney and Mulherin (1992), Muscarella and Vetsuypens (1996), Falkenstein (1996), Angel (1997), Seguin and Smoller (1997), Schultz (2000), Gompers and Metrick (2001), Fernando et al. (2004), Bradley et al., 2004, and Dyl and Elliott (2006).

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(2000) and Kadapakkam et al. (2005) provide empirical evidence consistent with the notion that analysts promote stocks following stock splits and confirm that splits cause stockholders to incur higher costs of trading that translate into higher revenues for market intermediaries, as surmised by Brennan and Hughes (1991) and Angel (1997).4 While providing valuable new insights into corporate decisions that determine nominal share price levels, these studies disregard the possibility that entities other than market intermediaries, specifically institutional investors, can also generate valuable information about firms. Apart from the institutional monitoring benefits noted earlier, there is considerable evidence that institutional investors have valuable private information about firms.5 Indeed, Chen et al. (2011) provide important new evidence in this regard by showing (a) that firms do not always lower their stock prices through splits to disseminate favorable information and (b) that institutions are able to differentiate between informationally motivated splits and splits that aim to make stocks more attractive to uninformed investors. Therefore, extending the work of Brennan and Hughes (1991) and Angel (1997) to incorporate the information gathering role of institutional investors offers the prospect of providing new insights into two well-documented findings in the literature: (a) the preference of institutional investors for higher-priced stocks and (b) the positive association between share price levels and the value of the firm.6 We develop a model of nominal share price determination by firms that explicitly embodies the monitoring and informational benefits of institutional investment. Our model incorporates two types of investors: institutional and retail. Retail investors are unsophisticated and rely on outside sources, such as brokers and analysts, to provide them with information about stocks. In contrast, institutions monitor the firms whose stocks they own and help increase information availability about these firms by improving the effectiveness of analysts that cover the firm (Frankel et al., 2006; James and Karceski, 2006; Cornett et al., 2007; Ljungqvist et al., 2007; and Ruiz-Mallorquí and Santana-Martín, 2011). In our model, firms select share prices by trading off the relative costs and benefits of institutional monitoring and analyst following. As suggested by Parrino et al. (2003), there is considerable variation across firms in their perceived benefits from institutional ownership. Firms anticipating smaller benefits from institutional ownership set lower share prices to increase the relative spreads associated with trading their shares and thereby induce more information generation by market intermediaries.7 Firms anticipating larger benefits from institutional ownership set higher share prices to decrease the all-in cost to investors of owning their shares. Firms with higher price levels have higher institutional ownership than firms with lower price levels, and higher priced firms will also have a higher value than lower priced firms. 4 Conroy et al. (1990), McInish and Wood (1992), and Stoll (2000) also provide evidence that stock splits are followed by an increase in trading costs and a reduction in market liquidity. Kadapakkam et al. (2005) document that lower-priced stocks have higher relative spreads even after decimalization, although the differences are lower in absolute terms. Moreover, the discussion and findings in Weld et al. (2009) and Goldstein et al. (2009) suggest that despite the growth of discount brokerages, many brokers still charge fixed per-share commissions. 5 See, for example, Krigman et al. (1999), Wermers (2000), Cohen et al. (2002), Gibson et al. (2004), and Chen et al. (2011). 6 For the preference of institutions for higher priced stocks, see, for example, Falkenstein (1996), Gompers and Metrick (2001), and Fernando et al. (2004). For the relation between share price levels and firm value, see, for example, Seguin and Smoller (1997) and Fernando et al. (2004). 7 The benefits of institutional investment will vary widely across firms, depending on the extent and proprietary nature of firms’ private information and the moral hazard problems associated with disclosing it (Brennan and Hughes, 1991), the cost of obtaining information through other channels (Diamond, 1985), the governance of the firm and the extent to which managerial behavior can be positively influenced by institutional investors (Denis and Serrano, 1996), and the costs incurred by firms due to institutional monitoring (Bushee, 1998).

By explicitly incorporating the role of institutional investors, we reconcile the notion in Brennan and Hughes (1991) that firms with favorable private information should lower their share prices to disseminate this information through analysts, with the observed positive relation between institutional ownership and share price levels. Similarly, we also reconcile the argument in Angel (1997), that firms can increase their value by lowering share prices, with empirical evidence of a positive association between share price levels and the value of the firm. What we show is that while the relations in both Brennan and Hughes (1991) and Angel (1997) continue to persist when holding constant the influence of institutional investment on the firm, in the cross-section high-value firms will maintain higher share price levels, have more institutional investors and fewer analysts than similar sized low-value firms. In addition to providing new insights into the relations among and endogeneity associated with several key firm-specific variables such as institutional ownership, analyst coverage, share price levels, stock market liquidity, and the value of the firm, our model also yields additional new empirical implications. First, while establishing a theoretical basis for the empirically observed positive relation between share prices and institutional ownership, we show that this relation exists independently of liquidity considerations, thus contradicting the widely-held notion that higher liquidity is what drives institutions to hold higher-priced stocks. Second, our model implies that the share price level will be an indicator of a firm’s value. Therefore, we would expect to find a greater propensity for institutions to invest in higher priced stocks even in the absence of ‘‘prudent-man’’ rules that constrain them to do so.8 Third, firms with higher levels of institutional ownership and higher values will choose higher split prices when they split their shares. Interestingly, though, our model further predicts that analyst coverage of such firms will be lower than analyst coverage of similar-sized firms with lower institutional ownership. This is because institutional investors reduce the need for firms to rely on costly information generation by analysts. We find strong empirical support for our theoretical predictions. We conduct some of our empirical analysis using split prices to measure firms’ preferred share price levels. In particular, while confirming prior findings that analyst coverage increases with market capitalization and declines with the share price level, we show that the number of analysts following a firm will decrease with the firm’s information quality and with institutional ownership. This result contradicts Bhushan’s (1989) finding of a positive correlation between analyst following and institutional ownership in his empirical analysis of the determinants of analyst following.9 Our theory adds new insights into this issue by employing a structural model to delineate both the relationships and the endogeneity associated with these variables (see, for example, Coles et al., 2007), and also by highlighting the importance of the share price level, which is absent in the aforementioned studies. We find that a firm’s share price level rises with institutional ownership even after controlling for differences in stock market liquidity. The relation persists when we (a) exclude low-priced stocks to allow for the possibility that some institutions may be prevented from investing in them and (b) control for recent stock price run-ups. We also find that firms with higher values of Tobin’s Q will target higher price levels when they split their shares. Tobin’s Q is also positively related to both firm information quality and the precision of analyst forecasts. Furthermore, the values of 8 See, for example, Badrinath et al. (1989) and Del Guercio (1996). Our argument here is similar to the ‘‘ownership clientele’’ effect discussed by Allen et al. (2000), where higher quality firms attract relatively less-taxed institutional investors. As noted by Allen et al. (2000), such investors have a relative advantage in ensuring that the firms they invest in are well managed. 9 Rock et al. (2001) replicate Bhushan’s (1989) study using several alternative econometric models and also cast some doubt about Bhushan’s original findings by arguing that they are not robust to the use of different empirical specifications.

C.S. Fernando et al. / Journal of Banking & Finance 36 (2012) 2175–2189

firms with higher information quality are less sensitive to analyst information precision and vice versa. The rest of the paper is organized as follows. We develop our model in Section 2 and also discuss its empirical implications. Section 3 describes our sample and methodology. Section 4 presents the empirical results. Section 5 concludes. 2. The model and empirical implications In this section, we develop a simple model of share price level selection by firms that maximize firm value, taking into account the costs and benefits of both institutional ownership and the generation of information by market intermediaries. We conclude the section by developing several empirical implications of our model. 2.1. The economy We consider a multi-stage economy with J risky assets (firms), a riskless asset, and two types of risk-averse investors: institutional and retail. Within each investor type, there is a continuum of homogeneous investors. We assume that due to participation constraints all investors do not invest in all available stocks, so that for each firm j, a proportion aj of all investors are institutional investors and the remaining proportion (1  aj) are retail investors, where aj e (0, 1). The aj parameter is exogenous to our model and is motivated by existing literature that documents the effect of imperfect information and institutional constraints on investor participation. Merton (1987), for example, presents a model of asset prices in which each investor knows only about a subset of all available securities and therefore invests only in those securities.10 In addition, existing literature presents significant evidence that prudent-man laws (see Del Guercio, 1996) and ‘‘safety-net’’ considerations (see Badrinath et al., 1989) affect the decision of institutional investors to invest in some stocks but not invest in others. To incorporate the above-mentioned insights in our model, we allow the mix of institutional and retail investors to vary across firms. The equilibrium share ownership by each investor group will be determined endogenously as discussed below. Risky asset payoffs are independently distributed, with each rise j that is normally ky asset j having a random terminal payoff of V distributed with mean lj and precision hj, where hj measures the firm’s information quality and equals to the inverse of the payoff variance. The riskless asset’s return is normalized at zero. All investors in the economy have identical constant absolute risk aversion (CARA) preferences with CARA parameter c.11 We examine the investment decision of a representative investor of each type, assuming for convenience that both investor types are endowed only with the riskless asset prior to trading in the risky asset. Investment in the risky assets is facilitated by market intermediaries, who we refer to collectively as ‘‘analysts.’’12 Analysts can produce signals of the final payoff of each firm with precision hB. Conditional on the number of analysts producing information, Nj,

10 There is abundant evidence that investors invest only in a subset of all stocks. See, for example, Blume and Friend (1975), Kelly (1995), Barber and Odean (2000), Grinblatt and Keloharju (2001), and Goetzmann and Kumar (2008). 11 Our model can be extended to the case where institutional and retail investors have different risk preferences without qualitatively altering its main predictions. In the most plausible such extension – retail investors being more risk averse than institutional investors – the incentive for institutional investors to pay for analyst information will be further reduced since institutional investors’ utility will not increase as much as the utility of retail investors from the reduction in risk ensuing from the information generated by analysts. 12 To avoid confusion and for brevity, we use the term ‘‘analyst’’ to also include the ‘‘broker’’ function, reflecting their dual (broker/analyst) role in the paper and elsewhere – generating information and intermediating trades.

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the precision of final payoff for each firm j becomes hj + NjhB. This specification assumes that analyst reports are independent of each other. We assume that all analysts are risk neutral, have identical abilities, have the same number of clients, and are perfectly competitive. For analytical tractability, we also assume a trading cost structure, where trading spreads are fixed at c per share. In our model, institutions can both substitute for analysts by monitoring the firms they own and complement analysts by enhancing the quality of the information about firms that analysts generate. These benefits of having institutional shareholders will increase in proportion to their ownership in the firm. Therefore, for each firm j, institutional investment modifies the precision of firm payoffs by the multiplicative factor, (1 + mjhI), where mj > 0 is a parameter that captures the maximum extent to which institutions are able to positively affect a firm and hI is the fraction of the firm held by institutions, resulting in a final payoff precision of (hj + NjhB)(1 + mjhI).13 This formulation directly captures potential institutional monitoring benefits as well as the idea advanced by Frankel et al. (2006) and Ljungqvist et al. (2007) that institutional investors induce analysts to generate more precise information about the firm. The firm’s overall information quality will depend on both analyst coverage and institutional investment. The aggregate benefit of institutional investment, (hj + NjhB)(mjhI), will increase with institutional ownership hI, reflecting the fact that the influence of institutional investors on both firms and analysts will rise in proportion to their ownership in the firm. In determining their optimal ownership in the firm, institutional investors effectively trade off the benefits of increased monitoring and analyst information quality against the cost of decreased risk sharing.

2.2. Stages The model consists of four stages. In the first stage firms determine the number of shares outstanding to maximize the market value of the firm, which also determines the price per share. Lower share prices (and a higher number of shares outstanding) provide greater incentive for analysts to promote the firm’s shares since the returns to analysts increase with lower share prices under prevailing transactions cost structures. Therefore, a higher number of shares (and lower share price) will increase the information generated by analysts about a firm but also the cost to shareholders of investing in the firm due to the higher trading spreads they will be required to pay. In the second stage, analysts produce information about each firm’s terminal payoff. In the third stage, investors make their investment decisions regarding each firm, which in turn determines the spreads earned by analysts and each firm’s market-clearing valuation. In the final stage, firms’ payoffs are realized and firms liquidate. The four stages are summarized below. We solve the model recursively.

13

See Parrino et al. (2003) and the discussion in Footnote 8.

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2.3. Optimal investor holdings and equilibrium valuations The representative investor of type i e {I, R} has an initial endowment of the riskless asset denoted by W0,i. The investor of type i e {I, R} solves:

h i ~ max E ecW i ;

ð1Þ

hij

~ i ¼ W 0;i þ PJ X ij V ~ j  PJ X ij ðQ j þ cSj Þ. In the expression where W j¼1 j¼1 for investor wealth, Xij measures how much each investor of type i invests in firm j and is the choice variable with respect to which each investor maximizes wealth. Given our previous assumptions of atomistic investors and two investor types, the aggregate ownership of investors of type I in firm j is hIj = 2ajXIj and the aggregate ownership of investors of type R is hRj = 2(1  aj)XRj. The corresponding market clearing condition is that hIj + hRj = 1. In addition, Qj is the market valuation of firm j at the trading stage and c is the per-share trading cost for investors. In a perfectly competitive market for analyst services, analysts will use all their trading revenues to produce information. The total revenues earned by analysts from trading the shares of firm j are equal to (hIj + hRj)cSj = cSj, and each analyst incurs a cost of f per firm to produce information with precision hB about that firm. Before proceeding to the main findings of our model, we can therefore confirm that the Brennan and Hughes (1991) result for the relation between the number of analysts and the firm’s number of shares outstanding also holds in our setting, although only as a partial equilibrium result: Lemma 1. Under perfect competition, the number of analysts producing information about firm j, Nj, is given by:

Nj ¼

cSj : f

~ iÞ  max cEðW X ij

c2 2

~ i Þ; VarðW

ð3Þ

where

~ iÞ ¼ VarðW

J P

X 2ij

j¼1

1 : ðhj þ Nj hB Þð1 þ mj 2aj X Ij Þ

ð4Þ

The expression in (4) indicates that all else equal, firms with higher information quality (hj), higher analyst coverage (Nj), more precise information produced by analysts (hB), and a higher benefit from institutional ownership (mj) have a lower variance of future values. Solving for the optimal ownership weights and the equilibrium valuation of the firm, subject to market clearing, we can state our results for the equilibrium ownership structure of the firm as follows:14 Proposition 1. The equilibrium ownership structure for each firm j is given by

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ a2j mj ð2 þ mj Þ  ð1 þ a2j mj Þ

hRj ¼ 1  aj 

14

Lemma 2. The market valuation of each firm j at the trading stage is given by

ð2Þ

Therefore, all else equal, firms with more shares outstanding will have a larger number of analysts producing information about them. Given the previous assumptions regarding the distribution of final firm payoffs, the portfolio optimization problem of each investor i can be stated as follows:

hIj ¼ aj þ

For any mj > 0, hIj lies in the interval (aj, 2aj/(1 + aj)) and thus is always greater than 0 but less than 1 for any aj e (0, 1). Furthermore, as can be seen from the above interval hIj covers the whole interval between 0 and 1: when aj approaches 0, hIj also approaches 0 and when aj approaches 1, hIj also approaches 1. More importantly, for any aj e (0, 1), as mj increases, institutional ownership hIj also increases while retail ownership hRj decreases. It is interesting to note that trading costs, which are the outcome of the number of shares/share price decision of the firm, do not directly affect the manner in which ownership of any given firm is shared between institutional and retail investors. Therefore, in our model, there is no causal relation between trading costs and ownership structure. This result remains unchanged when we assume that institutional and retail investors have different trading cost structures, provided the differential is applied uniformly across all firms. Nonetheless, as we will show later, since firms optimize their share price decision to maximize any potential benefit of institutional ownership, firms that have high (low) values of mj will also have high (low) share prices in equilibrium, thereby leading to a positive association between institutional ownership and share prices. These results are in stark contrast to the existing empirical literature which assumes that the higher costs of trading low priced shares causes a lower institutional ownership of these shares relative to high priced shares. We can state our result for the market valuation of each firm at the trading stage, conditional on the number of shares outstanding, as follows:

ð1 þ aj Þmj

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ a2j mj ð2 þ mj Þ  ð1 þ a2j mj Þ ð1 þ aj Þmj

All proofs are provided in Appendix A.

ð5Þ

;

:

ð6Þ

Q j ¼ lj  cSj 

cf C1 ðmj Þ; ðfhj þ cSj hB Þ

ð7aÞ

where

C1 ðmj Þ ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 þ mj Þ 1 þ a2j mj ð2 þ mj Þ  ð1 þ aj mj ð2 þ mj ÞÞ 2mj ð1  aj Þ2

:

ð7bÞ

The expression for C1(mj) reflects the effect of monitoring on the value of the firm. For aj e (0, 1) and mj > 0, C1(mj) lies in the interval between 0 and 1/2 and monotonically declines with mj. As the institutional monitoring benefit (mj) approaches 0, C1(mj) approaches 1/2 and the equilibrium price approaches a value with no monitoring benefits. As mj increases, C1(mj) decreases and the market value of the firm increases. It can be shown that lim C1 ðmj Þ ¼ 0 so that in the limit uncertainty is resolved and risk

mj !1

does not affect the value of the firm. Conditional on the choice of number of shares outstanding, firm value increases with the benefit of institutional ownership (mj), with the firm’s information quality (hj), and the precision of analyst information (hB), while it decreases with investor risk aversion (c). Given that institutional monitoring is positive, the proportion of institutional investors, aj, has a positive effect on the value of the firm. 2.4. The choice of shares outstanding In the first stage, firms choose the number of shares outstanding so as to maximize their value at the trading stage.15 In doing so, firms have to balance offsetting effects. On the one hand, setting a low number of shares outstanding (leading to high share prices) 15 Because the mechanism by which firms select a share price is setting the number of shares outstanding, we pose the firm’s optimization problem as one of selecting the number of shares rather than the share price, noting that share price equals the firm’s value divided by the number of shares outstanding.

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reduces the cost of trading and increases the net returns to shareholders. On the other hand, a lower number of shares outstanding induces less information production by analysts, which results in higher uncertainty and lower valuations for the firm. Proposition 2 states the equilibrium result for the optimal number of shares that arises from these tradeoffs.

ma 2, we obtain the expression for the equilibrium value of the firm, which we state in Proposition 4: Proposition 4. The equilibrium value of the firm is given by

Q j

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi fhj cf ¼ lj þ 2 C1 ðmj Þ; hB hB

Proposition 2. The optimal number of shares outstanding, Sj , for each firm j, is given by

or equivalently

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cfhB C1 ðmj Þ  fhj  Sj ¼ : chB

Q j

ð8Þ

As firm information quality (hj) and institutional benefits (mj) increase, the optimal number of shares outstanding decreases. Additionally, for a high precision of analyst information, the number of shares outstanding decreases as the precision of analyst information (hB) increases. For low precision of analyst information, however, as hB increases the optimal number of shares outstanding increases.16 We analyze the relation between equilibrium share prices and these variables in Proposition 4 below. Solving the expression in (5) for mj we obtain that

mj ¼ 2ðhIj  aj Þ=ðhIj ð2aj  ð1 þ aj ÞhIj ÞÞ:

ð9Þ

Replacing for mj in the expression for Proposition 2, we find that

Sj

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cfhB C2 ðhIj Þ  fhj ¼ ; chB

ð10aÞ

where

C2 ðhIj Þ ¼

ð1  hIj Þð2aj  ð1 þ aj ÞhIj Þ 2ð1  aj Þ2 hIj

:

ð10bÞ

Proposition 3. The number of analysts producing information is equal to:

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c h C1 ðmj Þ  j fhB hB

ð11aÞ

or equivalently

Nj ¼

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c h C2 ðhIj Þ  j : fhB hB

ð11bÞ

The number of analysts producing information is a decreasing function of the firm’s information quality (hj) and of institutional ownership (hIj). Institutional ownership, however, should not be viewed as causing analyst coverage. Expression (11b) simply shows that firms with higher institutional benefits will have higher institutional ownership and fewer analysts producing information as the equilibrium outcome. The model also relates institutional ownership and firm characteristics to equilibrium firm value. By substituting the optimal number of shares in (8) for the value of the firm expressed in Lem16

The point at which the relation changes is given by the expression hB = (2fhj)2/

cfC1(mj).

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi fhj cf ¼ lj þ 2 C2 ðhIj Þ: hB hB

ð12aÞ

ð12bÞ

It is evident from (12b) that the maximized firm value is an increasing function of firm information quality (hj) and of institutional ownership (hIj). Furthermore, for Sj > 0, the value of the firm increases with the quality of analyst coverage (hB). Note that (12b) does not imply that firms can increase their values by increasing institutional ownership. What it shows is that firms with higher institutional benefits will have higher institutional ownership and higher values as the equilibrium outcome. From Proposition 4 we can also see that the effect of analyst precision (hB) on value, while positive, declines for high firm information quality (hj). Our model also allows us to examine the relation between a firm’s share price and its expected cash flows, institutional benefits, and information quality. Proposition 5 provides the expression for a firm’s equilibrium share price (expression (12b) divided by expression (10a)). Proposition 5. The equilibrium share price of the firm is given by

Equilibrium values of institutional ownership (hIj), as we have already shown, lie in the interval (aj, 2aj/(1 + aj)). For values of hIj in this interval, C2(hIj), and thus the optimal number of shares outstanding, monotonically decreases with institutional ownership. As we prove later, this result gives rise to a positive association between share prices and institutional ownership. We should note, however, that this association is not causal. We can now extend the predictions of Lemma 1 to include the effect of institutional ownership benefits. We use expression (8) to substitute for the shares outstanding in Lemma 1, which gives the equilibrium number of analysts producing information.

Nj ¼

2179

0

1 l  f ðh =h Þ j B B C j  2A: Pj ¼ c@qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cf C ðh Þ  f ðhj =hB Þ hB 2 Ij

ð13Þ

The equilibrium share price increases with the expected cash flows of the firm (lj), institutional ownership (hIj, which proxies for institutional benefits), and the firm’s information quality (hj).17 Furthermore, a firm’s equilibrium value will increase with the precision of analyst information (hB) but the relation between the precision of analyst information (hB) and share price is not necessarily monotonic. For high precision of analyst information, as precision of analyst information (hB) increases shares outstanding will decrease and share prices will increase. For low precision of analyst information, however, as the precision of analyst information (hB) increases the value of the firm increases but the number of shares outstanding also increases and no clear relation exists unless one makes further assumptions about the remaining parameters. Further examination, however, reveals that for sufficiently high lj the effect of analyst information precision (hB) on share price declines as the firm’s information quality (hj) increases. Putting together the comparative statics results for the value of the firm and its share price, we can conclude that if the parameters in the model are not perfectly measured in practice (as we expect) there will be a positive association between the value of the firm and its share price level. This is not because share price levels directly affect firm value but because the factors that lead to a higher firm value also lead to a higher price per share. 2.5. Empirical implications Our theoretical framework gives rise to several empirical implications. Consistent with prior studies, we expect the number of analysts (the dependent variable) to decrease as share price (the independent variable) increases, and keeping share price fixed, 17 These relations hold for positive firm value (Q j ) and positive number of shares outstanding ðSj ).

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we expect the number of analysts to increase as the market capitalization of the firm increases. Extending the prior literature, the model also predicts that institutional ownership and share price will be positively correlated. From Expression (11b) of Proposition 3, the number of analysts will decrease with institutional ownership and a firm’s information quality. While the model predicts a non-monotonic relation between analyst information precision and the number of analysts following the firm, the model also predicts that such a relation would be significantly more positive for firms with high information quality. Empirically, we can also examine how the value of the firm is affected by the firm’s information quality and institutional ownership benefit. Expression (12b) of Proposition 4 predicts a positive relation between firm value and institutional ownership and between share price and institutional ownership, which also suggests a positive association between firm value and share price. It should be noted that the latter relation is not causal. It stems from the fact that both share price levels and firm value are positively affected by institutional benefits and the firm’s information quality. Proposition 4 also predicts that the value of the firm would increase with the firm’s information quality and with the accuracy of analyst forecasts. However, the positive effect of analyst forecast accuracy on firm value would be less pronounced for firms with high information quality. Proposition 5 allows us to make empirical predictions about the cross-sectional differences in share price levels of firms. A firm’s share price will increase with institutional ownership and the firm’s information quality. This relation should hold even after controlling for measures of market liquidity. Examining Expression (13), we do not find a clear relation between the share price of the firm and the precision of analyst information. While it is true that the value of the firm monotonically increases with the precision of analyst information, the optimal number of shares outstanding first increases and then decreases as the precision of analyst information increases. Empirically, we expect the relation between the precision of analyst information and the firm’s split price to be more negative for firms with high information quality. This is because as the precision of information about the firm increases, the precision of analyst information becomes less important. As a direct consequence, split prices will be less (more) sensitive to levels of analyst information precision for firms with higher (lower) information quality. We test these empirical predictions in Section 4 after describing our sample and variable definitions in the next section. 3. Sample and variables Our sample covers the years from 1985 to 2008 and includes all firms with common stock (CRSP share codes 10 or 11) listed on NYSE/AMEX/Nasdaq (CRSP exchange codes 1, 2, or 3). We also require that firms have data available in the Center for Research in Security Prices (CRSPs) daily and monthly files and the Compustat database. From the CRSP monthly files we identify firms that split their shares and we use their split price for year t as our main measure of the firm’s preferred share price. The split price is measured as in Ikenberry et al. (1996) and Conroy and Harris (1999) and is the closing price in the month before the split announcement divided by one plus the split factor. In addition, we also use the actual share price of the firm as a measure of its preferred price range. Share price levels and shares outstanding for year t are based on values at the end of June in year t and come from the CRSP monthly files.18 18 We have replicated all our results while excluding all firms with share prices below $5 per share. The coefficient estimates and their significance are not sensitive to this robustness check. Using CRSP average share prices for year t and Compustat share prices also leads to similar results. The results are available from the authors.

As measures of firm size we use firm market capitalization (June of year t closing price times shares outstanding from CRSP) and total assets (Compustat item AT for fiscal year t). In order to control for trends in firms’ market capitalizations (asset sizes) over time, we divide firm market capitalization (total assets) by median NYSE market capitalization (total assets). Following Badrinath et al. (1989) and Del Guercio (1996), we measure the firm’s information quality (hj) using the Standard & Poor’s (S&P) common stock quality ranking, which we obtain for each fiscal year from the Compustat annual files (Compustat item SPCSRM, available from 1985 onward). Each month, in its Security Owner’s Stock Guide, S&P publishes common stock ranks of firms that are listed on the NYSE/AMEX or are among the most active Nasdaq firms. Based on a firm’s history of earnings and dividends, the S&P common stock rank quantifies firm-specific uncertainty as perceived by market participants. The range of scores is aligned with the following ranks: A+ (Highest); A (High); A (Above Average); B+ (Average); B (Below Average); B (Lower); C (Lowest); D (in Reorganization).19 For the purposes of our quantitative analyses we translate the S&P ranks into the following scores: (A+: 9), (A: 8), (A: 7), (B+: 6), (B: 5), (B: 4), (C: 3), (D: 2). We measure the number of analysts producing information about the firm (Nj) by the number of analysts providing 1-year earnings forecasts from I/B/E/S. As a measure of the precision of analyst information (hB), on the other hand, we use the inverse of the mean absolute error of 1-year earnings forecasts from I/B/E/ S.20 This variable is not available for a significant part of our sample. In order to maximize sample size when estimating the coefficients for the remaining variables, in the subsequent regressions we make this measure of analyst precision equal to zero when missing while at the same time we also include a dummy variable indicating whether analyst precision is missing. This approach effectively allows us to estimate the coefficient for analyst precision only for firms with an available measure of analyst precision. We use the standard deviation of daily returns for year t from the CRSP daily files as a measure of overall firm risk. The model in the previous section shows that institutional ownership increases monotonically with institutional benefits (mj), which permits us to use institutional ownership as a direct measure of institutional benefits. We collect end-of-June percentage institutional ownership data from the CDA Spectrum database of Thomson Financial, which consists of institutional 13F filings. We use two measures of Tobin’s Q, both from the existing literature, to measure firm value (Qj). The first measure of Tobin’s Q is the ratio of the market value of assets to the book value of assets, where asset market value is the sum of the book value of assets (Compustat item AT) and the market value of common stock (Compustat item PRCC_F times item CSHO) less the book value of common stock (equity (Compustat item SEQ, or item CEQ plus item PSTK, or item AT minus item LT) minus preferred stock (Compustat item PSTKL, or item PSTKRV, or item PSTK)) and deferred taxes when available (Compustat item TXDITC) net of post-retirement benefits when available (Compustat item PRBA). Because of its ease of calculation and because it is available for a large set of firms, this measure of Q is widely used in existing literature (see, for example, Kaplan and Zingales, 1997; Gompers et al., 2003; and the references therein). Lewellen and Badrinath (1997) show that using book values of assets in the denominator of the Q ratio has shortcomings (for example, downward biased Q ratios and incorrect ordering of Q ratios across firms). They propose a different measure of Q that 19 Further information on this ranking methodology is available in the S&P Security Owner’s Stock Guide. 20 To adjust for the scale of mean absolute forecasts, we divide by the absolute value of the actual earnings-per-share.

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calculates and uses replacement costs (rather than book values) of fixed assets and inventory. For our second measure of Tobin’s Q we calculate replacement values using the approach of Lewellen and Badrinath (1997) as modified by Lee and Tompkins (1999).21 This second measure of Tobin’s Q is equal to the market value of the firm’s common stock plus the book values of preferred stock, short-term debt, and long-term debt divided by the replacement value of firm assets. Asset replacement values are calculated as book value of total assets minus book values of fixed assets and inventory plus replacement values of fixed assets and inventory minus all liabilities other than long-term and short-term debt. The replacement value of fixed assets in year t requires the estimation of historic investments in fixed assets year by year. Then the method uses specific depreciation and inflation estimates to determine the replacement value in year t of each year’s investment ‘‘vintage.’’ The replacement value of fixed assets is the sum of the replacement values of historic investments. The calculation of inventory replacement values is simpler. If firms use FIFO to account for inventory, then inventory replacement value is equal to its book value. If firms use a different method to account for inventory (such as LIFO) they usually report what adjustment to make to obtain the current (FIFO) value of inventory (Compustat item LIFR).22 Lewellen and Badrinath (1997) and Lee and Tompkins (1999) provide further details on the calculation of asset replacement values. Both measures of Q are adjusted for the median Q of the firm’s industry, where industries are defined as in Fama and French (1997). The existing literature frequently uses share price level as a proxy for stock market liquidity. To control for liquidity differences in our sample while also studying the relation of share price levels to other firm-specific variables, we employ the share turnover and the proportionate bid-ask spread of the firm. Our measure of liquidity is the natural logarithm of 0.01 plus the annualized share turnover for June of year t. To address the overstatement of trading volume on Nasdaq compared to trading volume on NYSE/AMEX and to also control for other differences between NYSE/AMEX and Nasdaq, in our regressions we also use a dummy variable equal to one if an issue is traded on NYSE/AMEX and equal to zero if it is traded on Nasdaq. We measure proportionate bid-ask spreads using June of year t average proportionate bid-ask spreads. The proportionate quoted bid-ask spread is the quoted bid-ask spread divided by the average of the bid and ask quotes. Bid and ask quotes are provided by the Trades and Quotes (TAQ) database. Our measure of the bid-ask spread is available from 1993 to 2008 so when we use this measure we use only the period of 1993–2008 in our analysis. Existing research has shown that firm value, as measured by the industry-adjusted Q ratio, is positively related to the growth opportunities of the firm and S&P 500 membership. We control for growth opportunities using the change in assets (Compustat item AT) from year t  1 to year t relative to year t assets and the R&D expenses relative to total assets (Compustat item XRD divided by item AT). Similar to our measure of the precision of analyst earnings forecasts, R&D expenses are not available for a significant part of our sample. We again make R&D expenses equal to zero when not available and at the same time we include a dummy variable indicating whether or not R&D expenses are missing. This allows us to estimate the coefficient for R&D expenses relative to assets only for firms with available R&D expenses and to estimate

21 To increase sample size, Lee and Tompkins (1999) propose an approach to calculate replacement values of fixed assets for firms for which the Lewellen and Badrinath (1997) procedure leads to missing observations. 22 Our results remain unchanged if we measure firms’ Q ratios based on Lindenberg and Ross (1981). Papers that calculate Q ratios based on Lindenberg and Ross (1981) include McConnell and Servaes (1990) and Lang and Stulz (1994).

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the other coefficients using all data for the remaining variables. As an additional control for Q and to also control for indexing affecting both firm value and institutional ownership, we also include a variable indicating whether the stock is in the S&P 500 index (Compustat item SPMIM). We include two additional control variables when we analyze stock prices: the gross stock returns for year t  1 (from June of year t  1 to June of year t) and for year t  2 (from June of year t  2 to June of year t  1). We take the natural logarithm of both returns, which gives us two measures of past returns. The rationale for controlling for recent stock returns is that a stock may have a high (low) price due to a recent run-up (decline) rather than a systematic preference for high (low) price levels. Stock returns data comes from the CRSP monthly files. Table 1 reports the mean, median, standard deviation, and number of observations for the variables discussed above. The average (median) firm in our sample has approximately 7 (4) 1-year analyst earnings forecasts. The median firm has a split price of around $21 per share and a share price of around $12 per share. The median firm in our sample is small relative to NYSE firms: its market capitalization is approximately 13% of median NYSE market capitalization and its asset size is approximately 12% of median NYSE asset size. Both average and median S&P common stock ranks are around 5 (or B) while institutional ownership is 30% for the average firm and 24% for the median firm. 4. Empirical findings In this section we present the results of our empirical tests of the hypotheses developed in Section 2.5. In Section 4.1 we examine how analyst coverage is related to share prices and other variables. We examine the relation between firm value and several key variables in Section 4.2. Finally, in Section 4.3 we study the determination of share price levels. In our tests we use panel data and estimate OLS regressions. Petersen (2009) presents evidence of a significant clustering of residuals across firms in finance panel data sets. Failure to control for this firm-level clustering leads to biased standard errors and therefore biased significance tests. In all our analysis, significance tests control for firm-level clustering. 4.1. Analyst coverage Table 2 reports our estimates from regressions, where the dependent variable is the number of analysts providing earnings forecasts. When the measure of share price is the split price of the firm and when we do not control for proportionate bid-ask spreads, the regression uses 3853 firm-years. The regressions in Panel A include controls for trading activity, standard deviation of returns, and historic returns. As an additional control variable, in Panel B we include the proportionate bid-ask spread. We find strong support for the predictions of our model for a firm’s analyst coverage. The number of analysts is negatively related to the split price and positively related to the firm’s market capitalization, with both relations significant at the 0.01 level.23 Using the approximate interpretation of coefficients for log explanatory variables, the coefficient on split price in Panel A implies that if a firm has a share price that is one percent higher than the share price of another firm, the firm with the higher share price would have around 0.0197 fewer analysts relative to the firm with the lower share price. The results remain very similar when we use the actual share price as our measure of the firm’s target price level despite 23 Brennan and Hughes (1991) also find a negative relation between the number of analysts following a firm and the firm’s share price.

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Table 1 Summary statistics. This table reports the mean, median, standard deviation, and number of observations for the variables used in the subsequent analyses. We use all firms from CRSP and Compustat with common stock trading on NYSE, AMEX, or Nasdaq between 1985 and 2008. The variables include the number of analysts providing 1-year earnings forecasts (from I/B/E/S), split price (the closing price of the month before the split announcement divided by one plus the split factor from CRSP monthly files), share price (June closing price from CRSP monthly files), relative market capitalization (June market capitalization divided by median NYSE market capitalization from CRSP monthly files), relative asset size (total assets divided by median NYSE assets for fiscal year t from Compustat), standard deviation of daily returns (from CRSP daily files), and an exchange dummy equal to 1 if a stock is listed on NYSE/AMEX and equal to 0 if it is listed on Nasdaq (from CRSP). We use two measures of Tobin’s Q and we adjust both for the median Q of the firm’s industry. Industries are defined as in Fama and French (1997). The first measure of Tobin’s Q is the ratio of the market value of assets to the book value of assets: the market value is calculated as the sum of the book value of assets and the market value of common stock less the book value of common stock and deferred taxes net of postretirement benefits. The second measure of Tobin’s Q is the market value of the firm’s common equity plus the book value of preferred equity, short-term debt, and long term debt divided by the replacement value of the firm’s assets. Other variables include the S&P common stock rank (from Compustat), the inverse of the mean absolute error of 1-year analyst earnings forecasts (from I/B/E/S), asset growth from year t  1 (from Compustat), R&D expenses relative to assets (from Compustat), S&P 500 membership dummy (from Compustat), institutional ownership for June of year t (from the CDA Spectrum database), annualized share turnover for June of year t (from CRSP monthly files), the proportionate bid-ask spread for June of year t (from TAQ), and returns for calendar years t  1 and t  2 (from CRSP monthly files). S&P ranks are whole numbers between two (lowest) and nine (highest). All variables are winsorized at the 1st and the 99th percentiles.

Number of analysts Log(split price) Log(share price) Log(market cap/median NYSE market cap) Log(assets/median NYSE assets) NYSE/AMEX vs. Nasdaq Indicator Standard deviation of daily returns (%) Industry adjusted Q (value-to-assets) Industry adjusted Q (market-to-replacement value of assets) S&P rank Log(1/(0.0001 + mean absolute error)) Change in assets from t  1 to t/assets in Year t (%) R&D expense relative to asset (%) S&P 500 membership dummy (%) Institutional ownership for June of year t (%) Log(0.01 + share turnover (%)) Log(0.01 + proportionate bid-ask spread (%)) Log(1 + return for year t  1) (%) Log(1 + return for year t  2) (%)

Mean

Median

Standard deviation

Number of observations

6.98 2.91 2.28 1.84 1.96 0.37 3.95 0.42 0.57 5.05 2.37 4.96 11.94 8.23 32.12 4.11 0.29 0.30 1.98

4.00 3.07 2.50 2.00 2.05 0.00 3.28 0.01 0.00 5.00 2.33 6.64 6.46 0.00 25.45 4.19 0.45 4.63 5.65

6.96 0.81 1.23 1.99 2.18 0.48 2.50 1.59 2.00 1.65 1.50 32.81 16.46 27.48 27.62 1.26 1.37 51.58 48.86

73,781 5134 116,256 116,256 116,494 116,494 116,458 107,227 58,348 58,682 41,613 115,191 45,643 116,444 116,494 116,446 79,768 105,092 95,671

Table 2 Number of analysts providing earnings forecasts. Using a sample of firms between 1985 and 2008 (Panel A) and 1993–2008 (Panel B), this table shows estimates from regressions explaining the number of analysts providing 1-year earnings forecasts as reported by I/B/E/S. We use all firms with common stock trading on NYSE, AMEX, or Nasdaq. As explanatory variables in Panel A we use firm relative market capitalization (June market capitalization divided by median NYSE market capitalization from CRSP monthly files), split price (the closing price of the month before the split announcement divided by one plus the split factor from CRSP monthly files), share price (June closing price from CRSP monthly files), institutional ownership for June of year t (from the CDA Spectrum database), S&P rank (from Compustat), high S&P rank dummy (rank of ‘‘A+’’, ‘‘A’’, or ‘‘A‘‘), the inverse of the mean absolute error of 1-year analyst earnings forecasts (when available from I/B/E/S), an interaction between the high S&P rank dummy and the inverse mean absolute analyst earnings forecast error, standard deviation of daily returns (from CRSP daily files), annualized share turnover for June of year t (from CRSP monthly files), and returns for calendar years t  1 and t  2 (from CRSP monthly files). We also include an exchange dummy equal to 1 if a stock is listed on NYSE/AMEX and equal to 0 otherwise. In each model we further include year dummies (coefficients not reported for the sake of brevity). In Panel B as an independent variable we add the proportionate bid-ask spread for June of year t (from TAQ). All variables are winsorized at the 1st and the 99th percentiles. The table reports the estimated coefficients and their p-values (in parentheses) adjusted for firm clustering as in Petersen (2009). The last row of the table reports the number of observations and the adjusted R-squared of each model. (1) Panel A: Liquidity is measured by share turnover (1985–2008 sample) Log(mkt. cap/median NYSE mkt. cap) 4.2732*** (0.0001) Log(split price) 1.9682*** (0.0001) Log(share price)

(2)

(3)

(4)

(5)

(6)

4.2815*** (0.0001) 2.0879*** (0.0001)

3.8665*** (0.0001)

3.8721*** (0.0001)

3.7811*** (0.0001)

3.7707*** (0.0001)

1.7190*** (0.0001)

1.7205*** (0.0001) 0.0052* (0.0790) 0.0591 (0.2238) 0.1010*** (0.0077)

0.0047 (0.1191) 0.0890* (0.0892) 0.0397 (0.2616) 0.5895*** (0.0017)

Institutional own. for June of year t (%) S&P rank Log(1/(0.0001 + mean absolute error)) High S&P rank dummy High S&P rank dummy  Log(1/(0.0001 + mean abs. error)) NYSE/AMEX vs. Nasdaq indicator

0.0699 (0.7628)

0.3509*** (0.0004)

0.5021*** (0.0001)

0.4776*** (0.0001)

Standard deviation of daily returns Log(0.01 + share turnover (%))

0.5569*** (0.0001) 0.4100*** (0.0001) 0.5802*** (0.0001)

0.3846*** (0.0001) 0.5798*** (0.0001) 0.3819*** (0.0001) 0.5842*** (0.0001)

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(2)

(3)

(4)

(5)

(6)

73,771 0.6314

2.3328*** (0.0001) 1.1004*** (0.0001) 41,127 0.6765

2.3114*** (0.0001) 1.0481*** (0.0001) 41,127 0.6778

Log(1 + return for year t  1) Log(1 + return for year t  2) Number of observations Adjusted R-squared

3853 0.6381

3853 0.6424 (1)

73,771 0.6256 (2)

Panel B: Liquidity is measured by share turnover and proportionate bid-ask spread (1993–2008 sample) Log(mkt. cap/median NYSE mkt. cap) 3.9754*** 3.4233*** (0.0001) (0.0001) Log(split price) 2.5249*** (0.0001) Log(share price) 1.7457*** (0.0001) Institutional own. for June of year t (%) S&P rank Log(1/(0.0001 + mean absolute error))

(3)

(4)

3.7199*** (0.0001)

3.7166*** (0.0001)

0.0054* (0.0549) 0.1527*** (0.0023) 0.1419*** (0.0005)

0.0056* (0.0550) 0.1115** (0.0412) 0.0447 (0.2757) 0.7705*** (0.0001) 0.3072*** (0.0001) 0.7876*** (0.0001) 0.2312*** (0.0001) 0.5815*** (0.0001) 2.2020*** (0.0001) 0.9879*** (0.0001) 0.4473*** (0.0010) 28,853 0.6678

High S&P rank dummy High S&P rank dummy  Log(1/(0.0001 + mean abs. error)) NYSE/AMEX vs. Nasdaq indicator

0.6503** (0.0428)

0.8048*** (0.0001)

0.2648** (0.0135)

0.2642*** (0.0001)

0.4202** (0.0500) 2555 0.6257

0.6013*** (0.0001) 54,199 0.6214

Standard deviation of daily returns Log(0.01 + share turnover (%)) Log(1 + return for year t  1) Log(1 + return for year t  2) Log(0.01 + prop. bid-ask spread (%)) Number of observations Adjusted R-squared

0.7745*** (0.0001) 0.2397*** (0.0001) 0.5806*** (0.0001) 2.2208*** (0.0001) 0.9939*** (0.0001) 0.4499*** (0.0010) 28,853 0.6670

*

Significance at the 0.10 levels from a two-tailed t-test. Significance at the 0.05 levels from a two-tailed t-test. *** Significance at the 0.01 levels from a two-tailed t-test. **

a significant increase in sample size.24 These findings are robust to controlling for the liquidity of a firm’s stock measured by share turnover (Panel A) as well as by share turnover and proportionate bidask spreads (Panel B). Our model also makes predictions about the relation between analyst coverage and firm information quality and ownership structure. Specifically, we expect that the number of analysts following the firm will decrease with firm information quality (as measured by S&P rank) and with institutional ownership. Consistent with these predictions, institutional ownership is negatively and significantly related to the number of analysts following the firm. The coefficient is significant at the 0.10 level for model (5) in Panel A and models (3) and (4) in Panel B. Using the coefficient estimate from Panel A, model (5), we find that an increase in institutional ownership by one percentage point is associated with a reduction in the number of analysts following the firm by around 0.07% for the average firm and by around 0.13% for the median firm. We also find that firms with higher quality of information (as measured by their S&P rank) have fewer analysts following

24 When we use annual share prices, the same firm would generally appear repeatedly in the sample, potentially violating the assumption of independent residuals. To address this concern, our tests are based on standard errors adjusted for firm-level clustering (Petersen, 2009). This concern is less relevant when we use split prices.

their stock. The coefficient estimate for S&P rank in model (3) of Panel B is significant at the 0.01 level and implies that an increase in S&P rank by 1.00 is associated with a 2.15% (3.75%) reduction in analyst coverage for the average (median) firm in our sample. The coefficient for analyst information precision (model (5) in Panel A and model (3) of Panel B) is significant at the 0.01 level and positive. Our theory does predict a positive relation between analyst information precision and analyst coverage, but only when firms’ information quality is sufficiently high. Even though our model does not predict a uniformly monotonic relation between analyst precision and the number of analysts covering the firm, the model does predict that the relation would be more positive for firms with high information quality. To test this prediction, we create an indicator variable equal to 1 for firms with rank of A, A, or A+ (that is, high S&P rank firms) and equal to 0 otherwise. We then interact the high S&P rank dummy variable with the analyst precision variable. We expect the coefficient on this interaction variable to be positive. Indeed, as predicted, we find that the effect of analyst precision on the number of analysts covering the firms is more positive for high S&P rank firms relative to low S&P rank firms. In both Panels this result is significant at the 0.01 level. All our findings remain in Panel B, where we further control for the proportionate bid-ask spread of the firm as an additional liquidity measure. In this case our sample covers the years from 1993 to 2008 and as a result the sample size is smaller. Examining

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Table 3 Value of the firm. This table uses firms between 1985 and 2008 and estimates regressions to examine the Tobin’s Q of the firm minus the median Q of the firm’s industry. Industries are defined as in Fama and French (1997). We use all firms with common stock trading on NYSE, AMEX, or Nasdaq. In Panel A, Q is the ratio of the market value of assets to the book value of assets: the market value is calculated as the sum of the book value of assets and the market value of common stock less the book value of common stock and deferred taxes net of postretirement benefits. The market value of equity and the accounting variables are measured as of the end of the current fiscal year. In Panel B, Q is measured as the market value of the firm’s common equity plus the book value of preferred equity, short-term debt, and long-term debt divided by the replacement value of the firm’s assets. As explanatory variables we use relative asset size (assets divided by median NYSE assets from Compustat), institutional ownership for June of year t (from the CDA Spectrum database), split price (the closing price of the month before the split announcement divided by one plus the split factor from CRSP monthly files), share price (June closing price from CRSP monthly files), S&P rank (from Compustat), high S&P rank dummy (rank of ‘‘A+’’, ‘‘A’’, or ‘‘A‘‘), the inverse of the mean absolute error of 1-year analyst earnings forecasts (when available from I/B/E/S), an interaction between the high S&P rank dummy and the inverse mean absolute analyst earnings forecast error, standard deviation of daily returns (from CRSP daily files), asset growth from year t  1 (from Compustat), R&D expenses relative to assets (when available from Compustat), a R&D availability dummy, and S&P500 membership dummy (from Compustat). We also include an exchange dummy equal to 1 if a stock is listed on NYSE/AMEX and equal to 0 otherwise. In each model we further include year dummies (coefficients not reported for the sake of brevity). All variables are winsorized at the 1st and the 99th percentiles. The table reports the estimated coefficients and their p-values (in parentheses) adjusted for firm clustering as in Petersen (2009). The last row of the table reports the number of observations and the adjusted R-squared of each model. (1) Panel A: Dependent variable is the industry adjusted Q (value-to-assets) of the firm Log(assets/median NYSE assets) 0.1398*** (0.0001) Institutional own. for June of year t (%) 0.0042*** (0.0001) Log(split price)

(2)

(3)

(4)

(5)

0.1393*** (0.0001) 0.0036*** (0.0001)

0.3831*** (0.0001)

0.2020*** (0.0001)

0.1443*** (0.0001) 0.0039*** (0.0001)

1.1169*** (0.0001)

0.0642*** (0.0001) 0.1208*** (0.0001)

0.0754*** (0.0001) 0.1053*** (0.0001)

0.0299 (0.2315) 0.1653*** (0.0001)

0.4454*** (0.0001) 0.0173** (0.0268) 0.1075*** (0.0001)

57,132 0.0491

0.0232 (0.3519) 0.0005 (0.9338) 0.0059*** (0.0001) 4.0387*** (0.0001) 0.1823*** (0.0001) 0.4187*** (0.0001) 57,031 0.1325

0.2916*** (0.0007) 0.0329 (0.2269) 0.0115*** (0.0001) 3.2423*** (0.0001) 0.0176 (0.8234) 0.6666*** (0.0001) 2859 0.2989

0.0821*** (0.0008) 0.0955*** (0.0001) 0.0039*** (0.0001) 3.9638*** (0.0001) 0.2427*** (0.0001) 0.4070*** (0.0001) 56,996 0.1784

0.5106*** (0.0001)

0.2688*** (0.0001)

Log(share price) S&P rank Log(1/(0.0001 + mean absolute error)) High S&P rank dummy High S&P rank dummy  Log(1/(0.0001 + mean absolute error)) NYSE/AMEX vs. Nasdaq indicator Standard deviation of daily returns Chg. in assets year t/assets in year t R&D expense relative to assets R&D expense availability dummy S&P 500 membership dummy Number of observations Adjusted R-squared

Panel B: Dependent variable is the industry adjusted Q (market value-to-replacement value of assets) of the firm Log(assets/median NYSE assets) 0.1689*** 0.1779*** (0.0001) (0.0001) Institutional own. for June of year t (%) 0.0053*** 0.0052*** (0.0001) (0.0001) Log(split price)

Log(1/(0.0001 + mean absolute error))

0.0889*** (0.0001) 0.1932*** (0.0001)

0.1164*** (0.0001) 0.1711*** (0.0001)

0.1255** (0.0144) 0.3096*** (0.0001)

0.5840*** (0.0001) 0.0398*** (0.0040) 0.1724*** (0.0001)

0.0569 (0.2069) 0.0237** (0.0131) 0.0057*** (0.0001) 6.2548*** (0.0001) 0.2014*** (0.0001) 0.6334***

0.5970*** (0.0026) 0.0460 (0.3195) 0.0153*** (0.0001) 5.9907*** (0.0001) 0.1305 (0.3588) 0.9323***

0.1476*** (0.0010) 0.1493*** (0.0001) 0.0032*** (0.0001) 6.1443*** (0.0001) 0.2675*** (0.0001) 0.6441***

High S&P rank dummy High S&P rank dummy  Log(1/(0.0001 + mean absolute error)) NYSE/AMEX vs. Nasdaq indicator Standard deviation of daily returns Chg. in assets year t/assets in year t R&D expense relative to assets R&D expense availability dummy S&P 500 membership dummy

0.1829*** (0.0001) 0.0056*** (0.0001)

1.5541*** (0.0001)

Log(share price) S&P rank

0.0413*** (0.0001) 0.1146*** (0.0001) 0.2443*** (0.0001) 0.0335*** (0.0007) 0.0231 (0.3494) 0.0031 (0.5973) 0.0059*** (0.0001) 3.9878*** (0.0001) 0.1801*** (0.0001) 0.4252*** (0.0001) 57,031 0.1344

0.0539*** (0.0010) 0.1731*** (0.0001) 0.3765*** (0.0001) 0.0216 (0.2603) 0.0478 (0.2867) 0.0165* (0.0904) 0.0058*** (0.0001) 6.1667*** (0.0001) 0.1966*** (0.0001) 0.6330***

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C.S. Fernando et al. / Journal of Banking & Finance 36 (2012) 2175–2189 Table 3 (continued)

Number of observations Adjusted R-squared * **

(1)

(2)

(3)

(4)

(5)

43,552 0.0502

(0.0001) 43,530 0.1374

(0.0001) 2082 0.2829

(0.0001) 42,512 0.1758

(0.0001) 43,530 0.1399

Significance at the 0.10 levels from a two-tailed t-test. Significance at the 0.05 levels from a two-tailed t-test. Significance at the 0.01levels from a two-tailed t-test.

***

the liquidity variables, we find that more analysts are attracted to firms with higher share turnover and firms with higher proportionate bid-ask spreads. 4.2. The value of the firm Table 3 reports our findings on the links between firm value (as measured by Tobin’s Q) and other key variables of interest, such as the firm’s information quality (measured by S&P rank), the precision of analyst forecasts, institutional ownership, size, and share price levels. In Panel A we compute Q as the ratio of the market to the book value of assets, whereas in Panel B we compute Q as the ratio of the market value of assets to the replacement value of assets. We obtain broadly consistent results across the two panels. Our findings provide strong support for our theory. Specifically, Tobin’s Q is positively related to the S&P rank. In Panel A this relation is significant at the 0.01 level in models (1) and (2), and significant at the 0.05 level in model (4) while in Panel B it is significant at the 0.01 level in models (1), (2), and (4) and significant at the 0.05 level in model (3). For example, model (2) of Panel A shows that a one unit increase in the S&P rank (for example, from C to B) is associated with a 7.54% increase in firm market value relative to book value. When the split price is included as an explanatory variable in the regressions, the relation between Tobin’s Q and S&P rank remains significant in Panel B but becomes insignificant in Panel A despite having the correct sign. The relation between S&P rank and firm value is more pronounced in Panel B, with a unit increase in S&P rank associated with a 11.64% increase in firm value. Controlling for actual share prices (model (4)) provides similar results, with S&P rank positively and significantly related to firm value in both Panel A and Panel B. When we control for share price, however, the magnitude of the coefficient on S&P rank is substantially reduced. According to our model, share price levels are related to the information quality of the firm and, therefore, it is not surprising that when share price is included as an explanatory variable the estimated effect of S&P rank on the Tobin’s Q declines. Tobin’s Q is also positively related to the precision of analyst forecasts, a finding further supporting our theory. In both panels this relation is significant at the 0.01 level for all regression specifications. For an economic interpretation of the coefficients we note that Table 1 shows that the standard deviation of the measure of analyst information precision is 1.50. Combined with the coefficient estimates in model (2) of Panel A, for example, we find that a one standard deviation increase in the precision of analyst information is associated with a 15.80% increase in firm market value relative to its book value of assets. Our model also predicts that the effect of analyst precision on firm value would be more pronounced for firms with relatively lower information quality and less pronounced for firms with relatively higher information quality.25 Consistent with this prediction, we find that the coefficient on the precision of analyst 25

We thank the referee for suggesting this test.

information is less positive for firms with relatively higher S&P rank. This finding is significant at the 0.01 level in Panel A but not significant at conventional levels in Panel B. Interpreting the coefficients from model (5) of Panel A, for firms with relatively lower S&P rank (below ‘‘A’’), a one standard deviation increase in analyst precision is associated with a 17.9% increase in the firm’s Q. In contrast, for firms with relatively higher S&P rank (‘‘A’’ and above), a one standard deviation increase in analyst precision is associated with a 11.94% increase in firm’s Q. Further support for our theory is provided by the relation between Q and institutional ownership and between Q and the share price of the firm. We find a positive and significant (at the 0.01 level) relation for all specifications in both panels.26 Using the standard deviation of institutional ownership from Table 1 and the estimated coefficient from model (2) of Panel A, we find that a one standard deviation (27.62%) increase in institutional ownership is associated with a 9.94% increase in value. Examining the share price coefficients, we find that Tobin’s Q is significantly (at the 0.01 level) and positively related to the share price using all specifications (share price or split price and in both panels). When we examine the control variables we find that, consistent with existing literature, growth opportunities (as measured by R&D expenses and asset growth) and S&P 500 membership are positively related to the value of the firm, while size is negatively related to firm value (see, for example, Lang and Stulz, 1994).

4.3. Share price levels Our last set of predictions concerns the determinants of crosssectional differences in the share price levels of firms. These predictions are tested in Tables 4 and 5. Table 4 reports our empirical findings using split prices and Table 5 repeats the analysis using share price levels. Our findings provide significant support for our theory. Regardless of which specification we use, split prices and share price levels are positively and significantly (at the 0.01 level) related to institutional ownership and the S&P rank. It is especially important to note that this relation is robust to our control for stock market liquidity as measured by share turnover and proportionate bid-ask spread. In addition, this finding is also robust to controlling for recent stock price run-ups, to rule out the possibility that high stock prices may have been induced by an influx of institutional investors. These results are also robust to controls for size, analyst forecast precision, listing exchange, and returns volatility. Examining the coefficient estimate of institutional ownership in model (3) of Table 4, for example, we find that a one standard deviation (27.62%) increase in institutional ownership is associated with an increase in the split price of the firm by 15.74%. At the median firm this implies an increase in the split price from around $21 per share to around $25 per share. The economic effect of S&P rank on split prices is also notable. For example, the estimated model (3) of Table 4 implies that a one unit increase in S&P rank 26 Gompers and Metrick (2001) find a positive relation between stock price performance and institutional ownership.

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Table 4 Split price levels. This table uses firms between 1985 and 2008 (1993–2008 when using bid-ask spread as an independent variable) performing stock splits and estimates regressions to examine the split price of these firms. We use all firms with common stock trading on NYSE, AMEX, or Nasdaq. The split price is the closing price for the month before the split announcement divided by one plus the split factor from the CRSP monthly files. As explanatory variables we use relative asset size (assets divided by median NYSE assets from Compustat), institutional ownership for June of year t (from the CDA Spectrum database), S&P rank (from Compustat), high S&P rank dummy (rank of ‘‘A+’’, ‘‘A’’, or ‘‘A‘‘), the inverse of the mean absolute error of 1-year analyst earnings forecasts (when available from I/B/E/S), an interaction between the high S&P rank dummy and the inverse mean absolute analyst earnings forecast error, standard deviation of daily returns (from CRSP daily files), annualized share turnover for June of year t (from CRSP monthly files), the proportionate bid-ask spread for June of year t (from TAQ), and returns for calendar years t  1 and t  2 (from CRSP monthly files). We also include an exchange dummy equal to 1 if a stock is listed on NYSE/AMEX and equal to 0 otherwise. In each model we further include year dummies (coefficients not reported for the sake of brevity). All variables are winsorized at the 1st and the 99th percentiles. The table reports the estimated coefficients and their p-values (in parentheses) adjusted for firm clustering as in Petersen (2009). The last row of the table reports the number of observations and the adjusted R-squared of each model.

Dependent variable is the split price of the firm in year t (log) Log(assets/median NYSE assets) Institutional own. for June of year t (%) S&P rank

(1)

(2)

(3)

(4)

0.1569*** (0.0001) 0.0088*** (0.0001) 0.0741*** (0.0001)

0.1553*** (0.0001) 0.0080*** (0.0001) 0.1235*** (0.0001) 0.1527** (0.0438) 0.1175*** (0.0011) 0.0478*** (0.0001) 0.0048 (0.8072)

0.1325*** (0.0001) 0.0057*** (0.0001) 0.0641*** (0.0001) 0.0048 (0.4504) 0.0052 (0.8693) 0.0213*** (0.0084) 0.0072 (0.6836) 0.0732*** (0.0001) 0.0237** (0.0428)

0.1158*** (0.0001) 0.0041*** (0.0001) 0.0533*** (0.0001) 0.0116 (0.1195) 0.0063 (0.8740) 0.0310*** (0.0015) 0.0751*** (0.0011) 0.0583*** (0.0001) 0.0043 (0.7628) 0.1454*** (0.0001) 0.3429*** (0.0001) 0.2113*** (0.0001) 1850 0.7899

Log(1/(0.0001 + mean absolute error)) High S&P rank dummy High S&P rank dummy  Log(1/(0.0001 + mean abs. error)) NYSE/AMEX vs. Nasdaq indicator Standard deviation of daily returns Log(0.01 + share turnover (%)) Log(0.01 + proportionate bid-ask spread (%)) Log(1 + return for year t  1) Log(1 + return for year t  2) Number of observations Adjusted R-squared

2917 0.6262

2917 0.6370

0.3701*** (0.0001) 0.2271*** (0.0001) 2897 0.7398

*

Significance at the 0.10 levels from a two-tailed t-test. Significance at the 0.05 levels from a two-tailed t-test. *** Significance at the 0.01 levels from a two-tailed t-test. **

(for example, from C to B) is associated with around a 7.21% increase in the split price of the firm. Consistent with our theoretical predictions, we also find that the effect of analyst precision on the share price of the firm is more negative for firms with high information quality. This result is significant at the 0.01 level and is present both for split prices as well as for actual share prices of firms. The relation between share prices and the rest of the variables are qualitatively similar when we use split prices (Table 4) and when we use actual share price levels (Table 5). Overall, the findings in this section provide strong support for our theory. Firm value is positively related to the firm’s information quality, analyst information precision, and institutional ownership while share price levels are positively related to institutional ownership and the firm’s information quality. Furthermore, share prices of higher information quality firms are less sensitive to analyst information precision and vice versa. To control for the possibility that our results may be driven by some institutional investors being prevented from investing in low-priced stocks due to prudent-man or other constraints, we have replicated all our results while excluding all firms with share prices below $5 per share. The coefficient estimates and their significance are not affected in any noteworthy way by this change. The results are not reported for brevity. In additional robustness tests we examine whether our results still hold after the decimalization of NYSE, AMEX, and Nasdaq, completed in 2001. For that purpose we re-estimate Tables 2–5 using data from 2002 (the first full year in which stocks traded

in decimal increments) to 2008. While our sample size is substantially reduced, we find similar results.27 Namely, all coefficient related to our hypotheses maintain their signs and, with minor exceptions, their statistical significance. The only notable exception is that after decimalization we find that the interaction term between the high S&P rank dummy and analysts’ information precision is insignificantly related to analyst coverage and to firm’s Q.

5. Conclusions We develop a model to examine cross sectional differences in institutional ownership, analyst following and share prices across firms. In contrast to the prior literature, our model of share price level determination explicitly incorporates the role of institutional investors in monitoring and improving analyst information quality. We show that firms select nominal share price levels by trading off the relative costs and benefits of institutional ownership and analyst following. Firms that anticipate smaller net benefits from institutional ownership set lower share prices to increase the trading revenue associated with trading their shares and thereby induce more information generation by market intermediaries. In contrast, firms that anticipate larger net benefits from institutional ownership set higher share prices to decrease the cost to investors of owning their shares. In equilibrium, higher priced firms have a higher institutional ownership and higher valuations than lower 27

These results are not reported but are available upon request.

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Table 5 Share price levels. This table uses firms between 1985 and 2008 (1993–2008 when using bid-ask spread as independent variable) and estimates regressions to examine the share price levels of firms. We use all firms with common stock trading on NYSE, AMEX, or Nasdaq. The share price is the June closing price of the firm’s common stock from the CRSP monthly files. As explanatory variables we use relative asset size (assets divided by median NYSE assets from Compustat), institutional ownership for June of year t (from the CDA Spectrum database), S&P rank (from Compustat), the inverse of the mean absolute error of 1-year analyst earnings forecasts (when available from I/B/E/S), an interaction between the S&P rank and the inverse mean absolute analyst earnings forecast error, standard deviation of daily returns (from CRSP daily files), annualized share turnover for June of year t (from CRSP monthly files), the proportionate bid-ask spread for June of year t (from TAQ), and returns for calendar years t  1 and t  2 (from CRSP monthly files). We also include an exchange dummy equal to 1 if a stock is listed on NYSE/AMEX and equal to 0 otherwise. In each model we further include year dummies (coefficients not reported for the sake of brevity). All variables are winsorized at the 1st and the 99th percentiles. The table reports the estimated coefficients and their p-values (in parentheses) adjusted for firm clustering as in Petersen (2009). The last row of the table reports the number of observations and the adjusted R-squared of each model.

Dependent variable is the share price of the firm (log) Log(assets/median NYSE assets) Institutional own. for June of year t (%) S&P rank

(1)

(2)

(3)

(4)

0.1786*** (0.0001) 0.0128*** (0.0001) 0.2271*** (0.0001)

0.1852*** (0.0001) 0.0118*** (0.0001) 0.3158*** (0.0001) 0.0441*** (0.0001) 0.3965*** (0.0001) 0.0670*** (0.0001) 0.0459*** (0.0037)

0.1373*** (0.0001) 0.0084*** (0.0001) 0.1768*** (0.0001) 0.0031 (0.3288) 0.2111*** (0.0001) 0.0213*** (0.0001) 0.0917*** (0.0001) 0.1667*** (0.0001) 0.0418*** (0.0001)

0.0814*** (0.0001) 0.0056*** (0.0001) 0.1709*** (0.0001) 0.0194*** (0.0001) 0.2334*** (0.0001) 0.0223*** (0.0001) 0.2518*** (0.0001) 0.1265*** (0.0001) 0.0565*** (0.0001) 0.3017*** (0.0001) 0.5417*** (0.0001) 0.3116*** (0.0001) 40,127 0.8072

Log(1/(0.0001 + mean absolute error)) High S&P rank dummy High S&P rank dummy  Log(1/(0.0001 + mean abs. error)) NYSE/AMEX vs. Nasdaq indicator Standard deviation of daily returns Log(0.01 + share turnover (%)) Log(0.01 + proportionate bid-ask spread (%))

0.5786*** (0.0001) 0.3560*** (0.0001) 57,966 0.7959

Log(1 + return for year t  1) Log(1 + return for year t  2) Number of observations Adjusted R-squared

58,642 0.6318

58,642 0.6449

⁄

Significance at the 0.10 levels from a two-tailed t-test. Significance at the 0.05 levels from a two-tailed t-test. *** Significance at the 0.01 levels from a two-tailed t-test. ⁄⁄

priced firms. In addition to establishing a theoretical basis for the empirically observed positive relation between share prices and institutional ownership, we show that this relation exists independently of differences in size and market liquidity, which are widely believed to be the drivers for institutions to hold higher priced stocks. Firms with higher institutional ownership will choose higher split prices when they split their shares. We show that highpriced firms with high institutional ownership and high value have a lower analyst following when size differences are controlled for. Overall, our study provides several new insights into the puzzling empirical linkages observed between nominal share price levels and firm fundamentals, and adds to the growing literature on the influence of institutional investors.

Appendix A. Mathematical proofs Proof of Proposition 1. The first order condition for institutional investors is:

"

#

cX Ij ð2 þ mj 2aj X Ij Þ lj  Q j  cSj  ¼0 2ð1 þ mj 2aj X Ij Þ2 ðhj þ Nj hB Þ

ðA1Þ

and the first order condition for retail investors is:

lj  Q j  cSj 



cX Rj

ð1 þ mj 2aj X Ij Þðhj þ Nj hB Þ

 ¼ 0;

ðA2Þ

where Acknowledgments We thank Tarun Chordia, Valentin Dimitrov, Ed Dyl, Andrew Ellul, Sridhar Gogineni, Scott Linn, Ike Mathur (the editor), Bill Megginson, Tom Noe, Russ Robins, Arturo Rodriguez, Laura Starks, Wayne Thomas, Sheri Tice, Vahap Uysal, Pradeep Yadav, Martin Young, an anonymous referee, and seminar participants at Tulane University, University of Oklahoma, the Financial Management Association (FMA) meetings, the FMA European meetings, and the Financial Intermediation Research Society (FIRS) Conference for valuable discussions and comments on previous versions of this paper. Anthony May provided excellent research assistance. We are responsible for any remaining errors.

Nj ¼

cSj f

ðA3Þ

The market clearing condition for any firm j is:

hIj þ hRj ¼ 1

ðA4Þ

Furthermore, by definition we have that:

hIj ¼ 2aj X Ij

ðA5Þ

hRj ¼ 2ð1  aj ÞX Rj

ðA6Þ

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Substituting (A3), (A4), (A5), and (A6) into (A1) and (A2), and solving (A1) and (A2) for Qj we get:

2

Q j ¼ lj  cSj  4

3

chIj ð2 þmj hIj Þ  5 cS

4aj ð1 þ mj hIj Þ2 hj þ

j

f

ðA7Þ

hB

and

2 Q j ¼ lj  cSj  4

cð1  hIjÞ

2ð1  aj Þð1 þ mj hIj Þ hj þ

3   5 cSj hB f

ðA8Þ

Equating Eqs. (A7) and (A8) and then simplifying and solving the resulting expression yields the following two solutions for hIj:

0

hIj ¼ @aj þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ a2j mj ð2 þ mj Þ  ð1 þ a2j mj Þ

ð1 þ aj Þmj qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 þ a2j mj ð2 þ mj Þ þ ð1 þ a2j mj Þ A aj  ð1 þ aj Þmj

;

ðA9Þ

The corresponding two solutions for hRj become:

0

hRj ¼ @1  aj 

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ a2j mj ð2 þ mj Þ  ð1 þ a2j mj Þ

ð1 þ aj Þmj qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 þ a2j mj ð2 þ mj Þ þ ð1 þ a2j mj Þ A 1  aj þ ð1 þ aj Þmj

;

ðA10Þ

However, only the first solution in each case satisfies the second order conditions for institutional and retail investors, which permits us to eliminate the second solution. h Proof of Lemma 2. From (A8) we have that:

2

cð1  hIjÞ

3

  5 cSj hB f " # cf ð1  hIj Þ ¼ lj  cSj  ðfhj þ cSj hB Þ 2ð1  aj Þð1 þ mj hIj Þ

Q j ¼ lj

 cSj  4

2ð1  aj Þð1 þ mj hIj Þ hj þ

ðA11Þ

Substituting for hIj and simplifying, we get:

Q j ¼ lj  cSj  where

C1 ðmj Þ ¼

cf C1 ðmj Þ; ðfhj þ cSj hB Þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 þ mj Þ 1 þ a2j mj ð2 þ mj Þ  ð1 þ aj mj ð2 þ mj ÞÞ 2mj ð1  aj Þ2

ðA12aÞ

: ðA12bÞ

h Proof of Proposition 2. The first order condition for Qj (A12a) with respect to Sj is:

c

!

cfhB ðfhj þ cSj hB Þ2

C1 ðmj Þ  1 ¼ 0

ð13Þ

Solving for Sj yields two solutions

0

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 cfhB C1 ðmj Þþfhj  chB B C Sj ¼ @ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi A cfhB C1 ðmj Þfhj

ð14Þ

chB

The first solution does not satisfy the second order condition for maximizing the market value of the firm. h

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