Learning from Peers Stock Prices and Corporate Investment

Transcription

1 Learning from Peers Stock Prices and Corporate Investment Thierry Foucault HEC, Paris 1 rue de la Liberation Jouy en Josas, France [email protected] Laurent Frésard University of Maryland R.H. Smith School of Business College Park, MD [email protected] This Version: March 2013 Abstract We show that the stock market valuation of peers matters for firms investment decisions. In a large sample of firms, corporate investment is positively related to the market valuation of peer firms selling related products. Consistent with a model where managers use the stock prices of peers as a source of information, this relation is stronger when the level of informed trading in a firm s stock is weak. Also, the link between the investment of a firm and its own stock price is weaker when the level of informed trading in its peers stocks is high, or when the demand for its products is more correlated with that of its peers products. Furthermore the investment of private firms depends on their peers stock prices, but much less so after they go public. Overall, our results provide new insights on how financial markets affect the real economy. JEL Classification Numbers: G31, D21, D83 Keywords: Corporate investment, managerial learning, peers, informed trading We thank Rui Albuquerque, Laurent Bach, Francois Derrien, Maria Guadalupe, Alexandre Jeanneret, Pete Kyle, Rich Mathews, Sebastien Michenaud, Nagpurnanand Prabhala, Denis Sosyura, Jerome Taillard, David Thesmar, Philip Valta and seminar participants at Aalto University, Babson College, BI Oslo, Copenhagen Business School, McGill University, the University of Maryland, the University of Warwick and the 2013 Adam Smith Workshop in Oxford for valuable discussions and suggestions. We also thank Jerry Hoberg and Gordon Phillips for sharing their TNIC data, and Jay Ritter for sharing its IPO data. All errors are ours. 1

2 1 Introduction Firms managers, financial analysts, bankers, or investment professionals often rely on price multiples (e.g., price-to-book or price-to-earnings ratios) of peer firms to value new investments. For instance, survey evidence indicate that corporate executives use peers valuations for capital budgeting decisions (e.g., Graham and Harvey (2001)). Hence, one expects firms investment to be influenced by their peers market valuation (stock price). Whether and why this influence exists has not received much attention, however. In this article, we address these questions. Specifically, we test the hypothesis that firms investment choices are influenced by the market valuation of their peers (defined as firms exposed to common demand shocks), because this valuation informs managers about the value of their growth opportunities. Peers stock prices aggregate information on future cash-flow shocks that are common to a firm and its peers. Hence, we propose that managers can learn information from their peers market valuation, as they do from their own stock price (see Bond, Edmans, and Goldstein (2012) for a survey). 1 In some situations, peers valuation might even be the only market signal available to a manager (consider a private firm with publicly listed peers), or could be more informative about a particular investment project than the firm s own valuation. Indeed, the latter reflects the firm s portfolio of projects and is therefore less informative about the value of a particular project (e.g. the development of a new product line) than the stock price of firms focused on this particular project. If managers use the valuation of their peers to make investment decisions then firms investment and peers valuation should co-vary. Evidence thereof is however insuffi cient to conclude that managers learn information from peers stock prices since prices and investment can co-vary because of unobserved factors (e.g., correlated signals between managers and investors). To address this problem, we exploit the fact that our learning from peers hypothesis generates unique cross-sectional predictions for the relationship between corporate investment and stock prices. 1 Subrahmanyam and Titman (1999) argue that stock prices are particularly useful to managers because they aggregate investors dispersed signals about future product demand. This is the case for peers stock prices since product demands for related firms are affected by common shocks (e.g., Menzlis and Ozbas (2010) show that Return on Assets for individual firms are positively correlated with Returns on Assets of related firms). 2

3 These predictions derive from a simple model in which peers valuation complements managers knowledge about their investment opportunities. 2 In this model, a firm sells a product for which demand is uncertain and correlated with the demand for another firm s product (its peer). 3 The firm manager must decide whether to expand production capacity or not. Expansion is a positive net present value project if future demand for the firm s product (about which the manager is imperfectly informed) is strong enough. As investors trade on private information about future demand, the firm s stock price and its peer s stock price are informative about this demand. We compare the relation between the firm s investment and each stock price in three different scenarios: (i) when the manager uses the information contained in each stock price ( learning from peers ); (ii) when the manager only relies on his own stock price ( narrow managerial learning ); and (iii) when the manager ignores stock market information ( no managerial learning ). The learning from peers scenario delivers five predictions that do not hold in other scenarios. They all stem from the same mechanism: When a decision-maker learns information from multiple signals, his decision becomes less sensitive to one specific signal when others become relatively more informative. Accordingly, with learning from peers, the sensitivity of a firm s investment to its peer stock price is inversely related to (i) its own stock price informativeness and (ii) the quality of managerial information, that is, managers private information about their investment opportunities. Symmetrically, the sensitivity of a firm s investment to its stock price decreases with its peer s stock price informativeness. Furthermore, an increase in the quality of managerial information reduces this sensitivity if its peer s stock price informativeness is low enough, and increases it otherwise. Last, the sensitivity of a firm s investment to its own stock price is weakly decreasing in the correlation between the demands for its product and the product of its peer. 2 Existing models in which firms learn from stock prices have focused on the case in which firms learn from their own stock prices, not the case in which they also learn from their peers (see, for instance, Bresnahan, Milgrom and Paul (1992), Dow and Gorton (1997), Subrahmanyam and Titman (1999), Goldstein and Guembel (2007), Foucault and Gehrig (2008), Dow, Güembel and Goldstein (2011); see Bond et al.(2012) for a survey). 3 Peers are not necessarily competing firms. Firms can be exposed to common demand shocks because they are vertically related (suppliers/customers firms) or because their products are complements. For instance, if the demand for computer hardware is strong, the demand for softwares is likely to be strong as well. 3

4 As these predictions do not hold if managers ignore stock market information or if they only rely on their own stock price, they form the backbone of our empirical strategy. We test each prediction on a large sample of firms drawn from Compustat over the period 1996 to We define the peers of a given firm using the Text-based Network Industry Classification (TNIC) developed by Hoberg and Phillips (2011), which is based on firms products description (from their annual 10Ks). We document that firms investment is positively and significantly related to their peers valuation (market-to-book ratio) after controlling for their own valuation and other characteristics. 4 The economic magnitude of this correlation is substantial: A one standard deviation increase in peers value is associated with a 5.6% increase in corporate investment, about 14.5% of the sample average. The sensitivity of firm s investment to its peers stock price is about half the sensitivity to its own price (a one standard deviation increase in a firm s stock price is associated with a 12.80% increase in its investment in our sample). The sensitivity of a firm s investment to a peer s stock price disappears once the firm and its peer stop operating in the same product space. Furthermore, the investment of a firm turns out to be sensitive to its peer s stock price before the two firms start operating in the same product space. This finding suggests that managers may decide to launch a new product after learning information about its expected profitability from the stock prices of firms already selling related products. Importantly, we find empirical support for the cross-sectional implications specific to the learning from peers scenario. First, a firm s investment is less sensitive to its peers valuation when its own stock price is more informative. 5 The economic magnitude of this effect is large: A one standard deviation increase in peers market valuation is associated with a 1.24% increase in a firm s investment when its own stock price is highly informative versus a 6.80% increase when its stock price is uninformative. Symmetrically, a firm s investment is less sensitive to its own stock price when its peers market valuation is more informative. 4 Findings are qualitatively similar if we measure firms valuation with price-earnings ratio rather than marketto-book ratio. 5 We use a measure of a firms specific return variation as proxy for the level of informed trading in a stock (as, for instance, in Durnev, Morck and Yeung (2004), Chen, Goldstein and Jiang (2007), and Bakke and Whited (2010)). 4

5 We also study the effect of managerial information on investment-to-price sensitivities, using the trading activity of the main insiders of the firm (its top five executives) as a proxy for the quality of managerial information. The investment of a firm is more sensitive to its peers stock prices when its managers appear less informed. In addition, the sensitivity of a firm s investment to its own stock price is not significantly related to the quality of managerial information, on average, as found in Chen, Goldstein, and Jiang (2007). Yet, consistent with our hypothesis, when peer stock prices are not very informative, an increase in the amount of managerial information has a negative effect on the sensitivity of a firm s investment to its stock price. This effect is reversed when peer stock prices are highly informative. Furthermore, and as uniquely predicted by the learning from peers hypothesis, the sensitivity of a firm s investment to its own stock price increases when it is less similar to its peers (they share fewer common words in the description of their products or their cash flows are less correlated). Less surprisingly, the sensitivity of a firm investment to its peers market valuation increases when the firm is more similar to its peers or when its sales are more correlated with those of its peers. Finally, we look at the investment behavior of a sample of firms before and after they go public. We show that, prior to their IPO, the investment of these firms is highly sensitive to their public peers valuation. However, this sensitivity drops significantly once they become public. This evolution is consistent with our learning from peers hypothesis: Once publicly listed, a firm can learn information from its own stock price and should therefore put less weight on the price of its peers as a source of information. In contrast, if managers do not learn information from their peers, the sensitivity of a firm investment to its peers valuation should either remain unchanged (if managers do not learn from stock prices) or increase after going public (if managers only learn from their own stock price). Several empirical studies already show that the information contained in a firm s stock price affects its real decisions. 6 Our paper, however, is the first to establish that there is a link between 6 See for instance Durnev, Morck and Yeung (2004), Luo (2005), Chen, Goldstein, and Jiang (2007), Fang, Noe and Tice (2009), Bakke and Whited (2010), Ferreira, Ferreira, and Raposo (2011), Edmans, Goldstein and Jiang (2012), or Foucault and Frésard (2012). 5

6 a firm s investment, its peers market valuation, and the informativeness of this valuation. This link has far reaching implications. In particular, a shock to the stock price of a firm or to its informativeness should affect investment decisions of other firms and vice versa. This externality generates a new channel through which the stock market could affect aggregate investment and the allocation of resources in the economy (see Subrahmanyam and Titman (2013)). According to the learning hypothesis, variations in stock prices have a causal effect on corporate investment because managers actively learn from the stock market. We do not claim to have identified this effect. Identification is very challenging since stock price variations are endogenous and can be related to investment through various, non mutually exclusive, channels. As in related studies (e.g., Chen, Goldstein, and Jiang (2007)), our approach is to show that cross-sectional variations in the sensitivity of a firm investment to stock prices are consistent with implications of the learning hypothesis. Focusing on peer firms helps to sharpen tests of this hypothesis for two reasons. First, the learning hypothesis has unique cross-sectional predictions regarding the effect of stock prices informativeness on the sensitivity of a firm investment to its own stock price and its peers stock prices. Second, the sensitivity of a firm s investment to its stock price can be affected by financial constraints because stock overvaluation relaxes these constraints (see Baker, Stein, and Wurgler (2003), or Graham and Campello (2011)). The financial constraint channel, however, should not affect the sensitivity of a firm investment to the stock price of its peers. Thus, by looking at peers, we neutralize one possible confounding factor for the relationship between stock prices and investment. Overall, our findings indicate that peers market valuations matter in shaping the investment behavior of firms. Hence, they also add to the growing empirical literature emphasizing the importance of peers in firms decision making (e.g., Gilbert and Lieberman (1987) or more recently Leary and Roberts (2012), and Hoberg and Phillips (2011)). Fracassi (2012) and Dougal, Parsons, and Titman (2012) provide evidence of peer effects in investment decisions, that is, situations in which a firm investment is influenced by the investment of related firms. These papers consider different channels for these effects (CEOs social networks or geographical proximity). Our paper does not seek to identify such peer effects. It suggests, however, that investment decisions of 6

7 related firms might be linked because they learn from each other stock prices. In the next section, we derive our main testable implications using a simple model of investment in which managers learn information from their stock price, the stock prices of their peers, and other sources. In Section 3 we describe the data and discuss the methodology. In Section 4 we present the empirical findings and in Section 5 we conclude. Proofs are collected in an appendix at the end of the paper. An Internet Appendix provides additional theoretical and empirical results. 2 Hypotheses Development 2.1 Model We consider two firms A and B that are exposed to common demand shocks for their product. The timing of the model is described in Figure 1. [Insert Figure 1 about here] At date 1, investors trade shares of firms A and B at prices p A1 and p B1. At date 2, firm A has the option to expand its production capacity. Capacity expansion requires making an irreversible investment, K, at date 2 before observing demands for firms A s and B s products. These demands and firms cash-flows are realized at date 3. Firms cash flows. At date 3, demand d j for the product of firm j can be High (H) or Low (L) with equal probabilities. Firms demands share a common factor, that is, Pr(d A = H d B = H ) = Pr(d B = H d A = H ) = ρ, (1) where ρ 1 2. The cash flow of firm B at date 3, θ B, is θ H B if demand for its product is high and θl B (< θh B ) otherwise. The cash flow of firm A is θ H A + I (Λ K) if demand for its product is high and θ L A I K if demand for its product is low, where I is a variable equals to 1 if firm A invests 7

8 at date 2 and zero otherwise. Thus, the net present value, Σ, of firm A s investment decision at date 2 is: Σ = Λ K (> 0) if d A = H, (2) K if d A = L, where Λ is the incremental sales revenues for firm A if it invests at date 2 and demand for its product is high at date 3. 7 The manager of firm A. When the manager of firm A invests at date 2, he has two sources of information about the demand for its product at date 3. First, he observes stock prices at date 1. Second, the manager receives a signal s m on demand at date 3. This signal is perfect with probability γ and uninformative with probability (1 γ). We refer to signal s m as direct managerial information and to γ as the quality of direct managerial information. This signal captures managers private information about their investment opportunities. At date 2, for a given investment decision, I, the expected value of firm A is: V A (I) = E(θ A s m, p A1, p B1 ) + I E(Σ s m, p A1, p B1 ). (3) The manager of firm A chooses I to maximize firm value and the firm faces no financing constraints. To focus on the interesting case, we assume that in the absence of any information, the expected NPV of capacity expansion is negative. That is: A.1 : E(Σ) = K( R H 2 1) 0, (4) where R H = Λ K. Hence, if the manager had no information, he would not invest at date 2. Moreover, for the moment, we assume that the correlation in demands for both firms is such that 7 For simplicity, we assume that expanding production capacity is useless if demand is low. The idea is that in this case the existing capacity of firm A is suffi cient to serve all its clients. It is straigtforward to extend the model to the more general case in which investing at date 2 generates additional sales revenues even when demand is low. The important point is that expanding capacity has a negative NPV in this case. 8

9 if the manager of firm A learns that demand for firm B is high then he invests. That is: A.2: E(Σ d B = H ) = K(ρR H 1) > 0, (5) or ρ > 1 R H > 1 2 (the second inequality follows from A.1). We relax assumption A.2 in Section 2.4. The Stock Market. There are three types of investors in the stock market: (i) a continuum of risk-neutral speculators, (ii) liquidity traders with an aggregate demand, z j, for firm j, and (iii) risk neutral dealers. Liquidity traders aggregate demand is uniformly distributed over [ 1, 1]. Subrahmanyam and Titman (1999) argue that individuals are well placed (e.g., through their consumption experience) to obtain information not readily available to managers about demand for a firm products. They view this information as being obtained serendipitously, that is, by luck and without cost and treat the number of investors with serendipitous information as exogenous. Following their approach, we take as given the fraction π j of speculators receiving a signal ŝ j {H, L} on demand for the product of firm j {A, B}. 8 For simplicity, we assume that this signal is perfect. Finally we denote by ŝ j =, the information set of a speculator who receives no signal about stock j. After receiving her information on stock j, a speculator decides to buy or to sell one share of this stock, or to stay put. We denote by x ij (ŝ j ) { 1, 0, +1} the size of the order submitted by speculator i when she has received signal ŝ j. Signal ŝ j is also informative about the payoff of the other stock since ρ 1 2, which opens the possibility that an informed investor trades in both assets. To simplify the analysis, we assume that a speculator only trades the stock for which she receives information. This is in fact optimal for speculators if there is a fixed cost of trading per asset (see Section A.5 in the Internet Appendix). 9 Let f j be the order flow (the sum of speculators and liquidity traders net demand) for stock 8 In the Internet Appendix (Section A.4), we consider the case in which speculators must pay a cost c to receive a signal. In this case, π j is endogenous and variations in π j across stocks are then driven by variations in the cost of information, c, and the volatility of firm cash flows (uncertainty on future demands). 9 Albuquerque et al. (2008) estimate a model in which investors receive both market-wide private information and firm-specific information. In our model, when ρ 1, private information is firm specific but it contains a market-wide component if ρ 1. The market wide component is a source of correlation in informed investors 2 trades across stocks, as found empirically by Albuquerque et al. (2008), even if informed investors are different across stocks. 9

10 j: f j = z j x ij (ŝ j )di (6) This order flow is absorbed by dealers at a price such that they just break even (as in Kyle (1985)) given the information contained in the order flow. That is, for a given investment policy I of firm A, p A1 (f A ) = E(V A (I) f A ), and p B1 (f B ) = E(θ B f B ). (7) Using the Law of Iterated Expectations, the stock prices of firms A and B at date 0 are: p A0 (I) =E(V A (I)) and p B0 (f B ) =E(θ B ). The change in price of stock j from date 0 to date 1 is denoted p j = p j1 p j Investment decisions and stock prices In this section, we study how the optimal investment policy of firm A is related to stock prices in equilibrium. This step is straightforward in our model but it is key for our empirical implications. For brevity, we provide the equilibrium in the market for stock B in the Appendix (see Lemma 1). For our purpose, the main feature of this equilibrium is that he stock price of firm B is informative about the demand for firm A s product if π B > 0 and even more so when the level of informed trading in stock B, π B, increases. Firm A s optimal investment decision at date 2, I (s m, p A1, p B1 ) solves I (s mj, p A1, p B1 ) Argmax I {0,1} V A (I), (8) where V A (I) is given in (3). The stock price of firm A depends on the manager s investment decision, which itself depends on the stock price of firm A. In equilibrium, speculators and dealers in stock A take this feedback into account. Formally, a stock market equilibrium for firm A is a set {x A ( ), p A1 ( ), I ( ))} such that (i) the trading strategy x A ( ) maximizes the expected profit for each speculator, (ii) the investment policy I ( ) maximizes the expected value of firm A at date 2 (solves (8)), and (iii) the pricing rule p A1 ( ) solves (7) given that speculators use the 10

11 trading strategy x A ( ), and the manager of firm A follows the investment policy I ( ). We provide the stock market equilibrium for firm A in Lemma 2 in the Appendix. The main property of this equilibrium is provided in Figure 2. This figure shows the optimal investment policy of the firm as a function of the change in its price and that of firm B between dates 0 and 1 when the manager does not receive direct managerial information. 10 The price changes can take three different values in equilibrium depending on the realization of the order flow in this stock (see Lemma 1 and 2). Clearly the optimal investment policy of firm A depends on both the price of stock A and the price of stock B as long as π B is not zero. In particular, if the price of stock A decreases moderately but the price of B increases then the manager of firm A optimally invests. Actually, an increase of the stock price of firm B is a good signal about future demand for the product sold by firm A, that compensates the bad signal sent by a moderate drop in price for stock A. Investment is also optimal, whatever the price of stock B, if the price of A increases. [Insert Figure 2 about here] 2.3 Empirical implications We now use the characterization of equilibrium stock prices for firms A and B and the optimal investment policy of firm A to derive predictions that we test in the next section. We focus on the implications of the model for the covariance between investment and stock prices. 11 This is natural since the influence of stock prices on investment is often measured by regressing investment on (normalized) stock prices. However, investment and stock prices can be correlated even in the absence of managerial learning from stock prices, for instance because speculators signals and managers signals are positively correlated. Hence, to isolate predictions that only arise when managers learn from peers prices, we compare the effects of π j, γ, and ρ on the covariance between investment and stock prices in three different scenarios: (i) managers ignore stock market information; (ii) managers learn solely 10 When the manager receives direct managerial information, his optimal investment policy is independent of stock prices: he invests if he learns that demand is high and does not invest if he learns that demand is low. 11 The model has other testable implications. For instance, the model implies that the order flow in stock A should forecast the return from date 1 to date 3 on stock B and vice versa. Tookes (2008) provide evidence of cross-stock price impacts of order flow for related firms. 11

12 from their own stock price; and (iii) managers learn from their stock price and that of their peers. Table 5 in Section 4.3 where we test the cross-sectional implications derived in this section provides a synoptic view of our predictions No managerial learning First consider the case in which managers ignore the information contained in stock prices, either because they are fully informed (γ = 1), or because they fail to realize that stock prices contain information. We focus on the latter case ( inattentive managers scenario ) because it encompasses the first as a special case when γ = Let σ j = ( θ H j θ L ) j /2. Corollary 1 (benchmark 1: no managerial learning) In the absence of managerial learning, the covariance between the price of stock B and the investment of firm A is equal to: cov(ki, p B1 ) = [γπ B (2ρ 1)] σ B K 2 0. (9) Hence, when ρ 1 2, this covariance is positive and it increases with (i) the quality of managerial information (γ), (ii) the fraction of informed speculators in stock B (π B ), and (iii) the correlation in demands for the products of firms A and B (ρ). Moreover the covariance between the price of stock A and the investment of firm A is also positive and equal to: cov(ki, p A1 ) = γπ A (σ A + γ 2 (Λ K))K 2 0. (10) Hence, this covariance increases with (i) the quality of managerial information (γ), (ii) the fraction of informed speculators in stock A (π A ), and (iii) is independent of the fraction of informed speculators in firm B(π B ). 12 In the absence of managerial learning, the stock price of firm B at date 1 is unchanged. The stock price of firm A is different because this price depends on the investment policy followed by the manager at date 2, which depends on whether or not the manager of firm A relies on stock prices as a source of information. In particular, when he ignores stock prices, the manager of firm A never invests unless s m = H (Assumption A.1). We account for this in deriving Corollary 1. 12

13 Thus, even in the absence of managerial learning, the investment of a firm is correlated with its peers stock price and its own stock price when π j > 0. The reason is simply that managers signals are correlated with speculators signals. Thus, we refer to this channel as the correlated information channel. When investment and stock prices are related only through this channel, cov(ki, p j ) increases with γ because a higher γ makes the correlation between speculators and the manager s signals stronger Narrow managerial learning Another possibility is that the manager only uses his stock price as a source of information, ignoring that of his peers. This scenario ( narrow managerial learning ) is another useful benchmark to better isolate the predictions that arise only when managers also learn from their peer stock prices. Corollary 2 (benchmark 2: narrow managerial learning). When the manager of firm A only uses the information contained in the price of his stock, the covariance between the price of stock B and the investment of firm A is equal to: cov(ki, p B1 ) = [(γ + (1 γ)π A )(2ρ 1)π B ] σ B K 2 0. (11) Hence, it is positive if ρ 1 2. It increases with the fraction of informed speculators in firm A and the effects of the other parameters (ρ, π B and γ) on cov(ki, p B1 ) are as when the manager of firm A does not learn information from prices (Corollary 1). Moreover the covariance between the price of stock A and the investment of firm A is also positive and equal to: cov(ki, p A1 ) = γπ A(σ A + γ (Λ K)) + π A (1 γ)(σ A + ( Λ K )((2 (1 γ)π A )) } {{ 2 } } 2 {{ } Correlated information Managerial learning from stock A K 2. (12) Hence, it decreases with the quality of managerial information (γ) while the effects of π A and π B on cov(ki, p A1 ) are as when the manager of firm A does not learn information from prices (Corollary 1). 13

14 With narrow managerial learning, the manager obtains an informative signal about future demand (either directly or from the stock market) with probability γ + (1 γ)π A, rather than just γ as in the case with no managerial learning. For this reason, his investment decision becomes more strongly linked to the the future demand for firm B and therefore its peer stock price when π A increases (first part of Corollary 2). Thus, the model implies that an increase in the level of informed trading in a firm s stock (here π A ) should strengthen the sensitivity of its investment to peer stock prices, whether managers learn information from stock prices in a narrow sense, as assumed here, or in a broader sense (see Corollary 3 below). Now, consider the link (measured by cov(ki, p A1 )) between the stock price of firm A and its investment decision. With narrow managerial learning, this link is stronger than in the absence of managerial learning because a high stock price for A induces the manager to invest when he does not receive direct managerial information. This effect is captured by the second component in the expression for cov(ki, p A1 ). This component decreases with γ: the manager puts less weight on the signal conveyed by his stock price when direct managerial information is of higher quality. As a result, the net effect of an increase in the quality of managerial information on the covariance between the investment of firm A and its stock price is negative while the opposite prediction holds in the absence of managerial learning (Corollary 1) Learning from peers stock prices Now, we turn to the more general case in which both the stock price of firm A and the stock price of firm B influence the investment decision of the manager of firm A, as formalized in Lemma 2 in the Appendix and shown in Figure 2. Corollary 3 In equilibrium, the covariance between the investment of firm A and the stock price of firm B is equal to: cov(ki, p B1 ) = (γ + (1 γ)π A )(2ρ 1)π B } {{ } Correlated information + (1 γ)π B (1 π A ) } {{ } Managerial learning from stocks A and B σ BK 2. (13) 14

15 Thus, it is positive since ρ > 1 2 and it increases in the fraction of informed speculators in stock B (π B ). Moreover, it decreases in (i) the likelihood that the manager of firm A receives direct managerial information, γ, and (ii) the fraction of informed speculators in stock A (π A ) if γ < 1. Equation (13) splits the co-variation between the investment of firm A and the stock price of firm B in two components. The first component is the contribution of the correlated information channel: this contribution is just equal to the covariance between the investment of firm A and the price of its peer with narrow managerial learning. The second component is the incremental contribution of the learning from peers channel. It is positive because an increase in the stock price of firm B conveys a positive signal about future demand for firm A s product and can thereby induce the manager of firm A to scale up capacity at date 2. When the manager learns from his peer stock price and his own stock price, the covariance between the price of stock B and the investment of firm A decreases with the fraction of informed speculators in firm A, π A, and the quality of direct managerial information, γ. The same mechanism is at work in both cases. The manager has three sources of information: (i) direct managerial information, (ii) his stock price, (iii) the stock price of its peer. As γ or π A increase, the informativeness of the two first sources of information becomes relatively higher relative to the third. Hence, the manager relies relatively less on the third source of information and as a result its investment becomes less correlated with the stock price of firm B. This substitution effect is absent when the manager ignores the information contained in stock prices (no managerial learning) or when he only uses the information contained in his own stock price (narrow managerial learning). Thus, assessing the direction of the effect of γ and π A on cov(ki, p B1 ) empirically offers a sharp way to test for the learning from peers hypothesis. Indeed, a positive effect is consistent with other scenarios but not with the scenario in which managers learn from their peers. Corollary 4 In equilibrium, the covariance between the investment of firm A and the stock price 15

16 of firm A is given by: cov(ki, p A1 ) = γπ A (σ A + γ (Λ K)) } {{ 2 } Correlated information + π A (1 γ)(σ A + ( Λ K )((2 π B (1 γ)(π A (1 π B ) + π B )) } 2 {{ } Managerial learning from stocks A and B K 2. (14) For all parameter values, the covariance between the investment of firm A and the stock price of firm A is positive. This covariance increases in (i) the fraction of informed speculators in stock A (π A ), and (ii) it decreases in the fraction of informed speculators in stock B (π B ), if γ < 1. Moreover, it decreases in the likelihood that the manager of firm A receives managerial information, γ if π B < π B and increases in this likelihood if π B > π B where π B = 2(1 γ)(1 π A) 1+2(1 γ)(1 π A ). Hence, the co-variation between the investment of firm A and its own stock price is equal to a baseline component, due to the correlated information channel, plus an additional component due to the learning from peers channel. The covariance between the investment of firm A and its stock price increases in the fraction of informed speculators in stock A because this fraction has a positive effect on both components. We obtain two additional predictions that are specific to the learning from peers scenario. First, the covariance between the investment of firm A and its stock price should decline when the level of informed trading in stock B increases. Indeed, such an increase strengthens the informativeness of the price of stock B, which leads the manager of firm A to rely more on this price as a source of information. Second, the quality of direct managerial information, γ, has an ambiguous effect on the covariance between the investment of firm A and its stock price: it is negative if π B is small and positive otherwise. Indeed, an increase in the quality of direct managerial information strengthens the correlated information channel (the first component in Equation (14)) and weakens the learning from peers channel (the second component in Equation (14)). When π B is small, the second negative effect dominates (Corollary 2). As π B increases, the size of this negative effect 16

17 becomes smaller because the manager of firm A relies relatively less on his stock price. Hence, when π B is high enough, the first effect dominates and cov(ki, p A1 ) starts increasing with γ (as with no managerial learning). Chen, Goldstein, and Jiang (2007) find that the sensitivity of a firm investment to its stock price is negatively related with a proxy for managerial information (see their Table 3). However, this relationship is not statistically significant in their sample. Corollary 4 suggests a possible explanation. The effect of managerial information on the investment-to-price sensitivity of a firm depends on the level of informed trading in its peers. Hence, the unconditional effect (i.e., the average effect across firms with different π B s ) may well be indistinguishable from zero. According to Corollary 4, a stronger test should allow the effect of managerial information on the investment-to-price sensitivity to differ according to π B, the level of informed trading in peer firms. We implement such a test in Section The role of correlation in firm demands (ρ) So far we have assumed that ρ 1/R H (Assumption A.2). We now analyze the case in which ρ < 1/R H. First, suppose that 1 2 ρ < 1/RH. In this case, demands for products of firms A and B remain positively correlated. However, the informativeness of the price of stock B about the demand for firm A s product is too small to influence the manager s investment decision. 13 Hence, this decision only depends on his own signal and his own stock price, as in the narrow managerial learning scenario. The only difference is that when 1 2 ρ < 1/RH, manager s inattention to its peer stock price is rational. Hence, when 1 2 ρ < 1/RH, the predictions of the model regarding the effects of parameters π A, π B, and γ are given in Corollary 2. Second, suppose that ρ < 1 1/R H < 1 2. This case is symmetric to the case ρ > 1/RH. The demands for the products of both firms are negatively correlated. Thus, intuitively, a low (resp., high) realization of the stock price for firm B signals a strong (resp. low) demand for firm A. Accordingly, the covariance between the investment of firm A and the stock price of firm B is 13 Indeed, E(Σ A r B > 0 )=E(Σ A d B = H )= K(ρR H 1) < 0. Thus, even when the price of stock B reveals that the demand for product B is strong, the manager of firm A chooses not to invest. Thus, his decision cannot be influenced by the price of stock B. 17

18 negative. However, in absolute value, this covariance is identical to that obtained when ρ > 1 2, for all possible cases considered in previous sections (see the Internet Appendix, Section A.3). Thus, the predictions derived in the previous sections hold for Cov(KI, p B1 ). The expressions for Cov(KI, p A1 ) are also unchanged in the various cases considered in the previous section. Last, the case 1 1/R H < ρ 1 2 is symmetric to the case in which 1 2 ρ < 1/RH. Indeed, in this case, the price of firm B is not informative enough to influence the investment decision of firm A. Thus, the predictions of the model regarding the effects of parameters π A, π B, and γ are given in Corollary 2, except that they hold for Cov(KI, p B1 ). The correlated information and the learning components in the covariance between firm A investment and the stock price of B increase in ρ. Thus, the covariance between the investment of firm A and the stock price of firm B (cov(ki, p B1 ) increases in ρ whether or not the manager of firm A learns from the stock price of firm B (see equations (9), (11), and (13)). In contrast, the effect of ρ on the covariance between the investment of firm A and its stock price (cov(ki, p A1 ) depends on whether the manager learns information from its peer or not, as shown by the next corollary. Corollary 5 The covariance between the investment of firm A and its stock price (cov(ki, p A1 ) weakly declines in ρ 1 2 if and only if the manager of firm A uses peer stock prices as a source of information. Otherwise this covariance does not depend on ρ. When the manager of firm A uses information contained in the stock price of firm B, his investment is relatively less driven by his own stock price than when he does not use the information contained in his peer stock price. Hence, the covariance between a firm investment and its stock price should be smaller when the correlation between the demand for the firm product and the demand for its peer products becomes higher in absolute value (that is ρ 1 2 is higher), as claimed in the first part of Corollary 5. As this prediction is specific to the case in which managers learn both from their stock price and their peer stock price, it offers another way to test whether managers learn information from their peer stock prices. 18

19 2.5 Timing In the model, the markets for stocks A and B clear simultaneously. As a result, at date 1, the price of stock A does not reflect the information contained in the price of stock B when the manager makes his investment decision (at time t = 2). Suppose instead that dealers in stock A adjust their date 1 valuation after observing the price of stock B, at some date τ. If date τ is posterior to the date at which the investment decision is made, the model is obviously unchanged. If instead date τ occurs between dates 1 and 2 (the investment date), we have: p Aτ = E(V A (I ) p A1, p B1 ), (15) where p Aτ is dealers valuation for stock A at date τ. Given our assumptions, the manager of firm A makes exactly the same investment decisions whether he conditions his investment policy on p Aτ only or on {p Aτ, p B1 } because the price of stock A at date τ is a suffi cient statistic for the information contained in {p Aτ, p B1 } about the future demand for firm A. This case, however, is quite special for at least two reasons. First, in reality, information contained in prices diffuses only gradually across stocks (e.g., Hou (2007), Hong, Torous, and Valkanov (2007), Cohen and Frazzini (2008), Menzli and Ozbas (2010)), so that there is crossfirms return predictability. In these conditions, managers should improve their forecasts of fundamentals by using the information contained in their peers stock price, not yet impounded in their own stock price, as in the model. Second, and maybe most important, a firm stock price reflects the value of its product portfolio. Thus, it is a noisy signal of the incremental value of a growth opportunity in one specific product within the firm s portfolio, especially if the latter contributes little to the aggregate cash flow. 14 In this case, stock prices of pure players or at least firms with cash-flows more correlated with the firm investment project provide more accurate signals than the stock price of the firm, even if the latter reflects the information available in other stock prices. We provide a simple illustration of this point in the Internet Appendix (see Section A.6). 14 See Bresnahan, Milgrom, and Paul (1992) for a similar point. 19

20 3 Data and Methodology 3.1 Sample construction and definition of peer firms Our empirical analysis is based on a sample of U.S. public firms. To test the main predictions of the model (Corollaries 3 and 4), we must pair each firm in our sample with other firms (the empirical counterpart of firm B in our model) selling similar products. To this end, we use the new Text-based Network Industry Classification (TNIC) developed by Hoberg and Phillips (2011). 15 This classification is based on textual analysis of product descriptions from firms 10-K statements filed yearly with the Securities and Exchange Commission (SEC). Specifically, Hoberg and Phillips (2011) calculate firm-by-firm similarity measures by parsing the product descriptions from the firm 10-Ks and forming word vectors for each firm to compute a measure of product similarity for every pair of firms in each year. The similarity measure is based on the (relative) number of words that two firms product description have in common. It ranges between 0% and 100%. Intuitively, the more firms use common words in their product description, the more similar are their products. Using this similarity measure, Hoberg and Phillips (2011) construct TNIC industries using a minimum similarity threshold. They define each firm i s industry to include all firms j with pairwise similarities relative to i above a pre-specified minimum similarity threshold chosen to generate industries with the same fraction of industry pairs as 3-digit SIC industries (equals to 21.32%). We define as peers all the firms that belong to the same TNIC industry in a given year. The classification covers the 1996 to 2008 period because TNIC industries are based on the availability of 10-K annual filings in electronically readable format. Hoberg and Phillips (2011) s TNIC industries have three important features. First, unlike industries based on the Standard Industry Classification (SIC) or the North American Industry Classification System (NAICS), they change over time. In particular, when a firm modifies its product range, innovates, or enters a new product market, the set of peer firms changes accordingly. Second, TNIC industries are based on the products that firms supply to the market, 15 The data can be found at: 20

21 rather than its production processes as, for instance, is the case for NAICS. Thus, firms within the same TNIC industry are more likely to be exposed to common demand shock, as in our model. Third, unlike SIC and NAICS industries, TNIC industries do not require relations between firms to be transitive. Indeed, as industry members are defined relative to each firm in the product space, each firm has its own distinct set of similar firms. This provides a richer definition of similarity and product market relatedness. For the set of firms with available TNIC industries, we gather firms stock price and return information from the Center for Research in Securities Prices (CRSP), investment and other accounting data from Compustat. We exclude firms in the financial industries (SIC code ) and utility industries (SIC code ). We also exclude firm-year observations with negative sales, missing information on total assets, capital expenditure, fixed asset (property, plant and equipment), and (end of year) prices. We detail the construction of all the variables in Table 1. To reduce the effect of outliers all ratios are winsorized at 1% in each tail. [Insert Table 1 about here] Table 2 presents descriptive statistics on the sample. The sample includes 46,162 firm-year observations (7,521 distinct firms). For a given firm, the average number of peers is 65 (#peers), while the median is 28. Summary statistics for the main variables used in the analysis resembles those reported in related studies. The average (median) rate of investment (capital expenditures divided by lagged PPE) is 39.2% (24.2%). Following other studies on the sensitivity of investment to stock price, we use Tobin s Q as a proxy for a firm (normalized) stock price. Q is defined as a firm s stock price times the number of shares outstanding plus the book value of assets minus the book value of equity, scaled by book assets. There is a large heterogeneity in Q in our sample: It ranges from 0.55 to with a mean of 2.18 and a median of Also, the average and median values of total assets are $1.4 billion and $169 million, respectively. We also report summary statistics for peers characteristics (average across all peers for each firm-year). They are very close from their own firm counterpart, although aggregation lowers their standard deviation. 21

22 [Insert Table 2 about here] 3.2 Empirical methodology To empirically measure the co-variation between a firm s investment and (i) the stock prices of its peers (cov(ki, p B1 )) and/or (ii) its own stock price (cov(ki, p A1 )), we adapt a standard linear investment equation. Specifically, we estimate several specifications of the following baseline equation: I i,t = α i + δ t + ηq i,t 1 + βq i,t 1 + ϕx i,t 1 + γx i,t 1 + ε i,t, (16) where the subscripts i and t represent respectively firm i (firm A in the model) and the year, while the subscript i represents a (equally-weighted) portfolio of peer firms based on the TNIC industries (firm B in the model). The dependent variable I i,t is a measure of corporate investment in year t, which in the baseline specification, is the ratio of capital expenditure in that year scaled by lagged fixed assets (property, plant, and equipment). The variable Q i,t 1 is the normalized stock price of firm i in year t 1 as defined above. The variable, Q i,t 1, is the normalized stock price of firm i s peers, computed as the average Q of all firms belonging to the same TNIC industry as firm i in year t 1, except firm i. 16 In the baseline specification, the vector X i,t 1 includes control variables known to correlate with investment decisions. Following previous research, we include the natural logarithm of assets (ln(t A i,t 1 )) to control for the impact of size on corporate investment. Moreover, to account for the well documented relationship between cash flows and investment, we include cash flows (CF i,t 1 ) as an additional control variable. We also include the characteristics of peers (their average size, ln(t A i,t 1 ), and cash flows, CF i,t 1 ) to further control for product market characteristics. In addition, we account for time-invariant firm heterogeneity by including firm fixed effects (α i ) and time-specific effects by including year fixed effects (δ t ). As a result, the coeffi cient η measures how, over time, the average firm s investment is tied to its peers stock price. We allow the error term (ε i,t ) to be correlated within firms and correct the standard errors 16 Following common practice, we impose a lag of one year between the measurement of investment and the measurement of Q (e.g., Chen, Goldstein, and Jiang (2007)). In the Internet Appendix (Table IA1), we show that the findings holds when we consider no lag between investment and Q. 22

23 as in Petersen (2009). Coeffi cients η and β in equation (16) measure respectively the co-variation between the investment of firm i and the (average) stock price of its peers and the co-variation between the investment of firm i and its stock price, holding other variables affecting investment constant. We use estimates of these coeffi cients to test the main implications of the model. We proceed in two steps. First, we establish that estimates for η and β are both statistically significant in our sample. This is indeed a necessary condition for the learning from peers channel to play a role (see Corollaries 3 and 4). This condition is not suffi cient, however. Indeed, the investment of a firm should co-vary with its stock price and the stock price of its peers in part because investors information is correlated with managers information about their investment opportunities (this is captured by the correlated information component in the expressions for covariances between stock prices and investment in our model). Thus, Q i and Q i in equation (16) play a dual role: they are both (i) proxies for unobserved managers private information about their investment opportunities and (ii) determinants of investment if managers learn information from stock prices. Hence, in a second step, we test whether cross-sectional patterns for η and β are related to measures of price informativeness or proxies for managerial information as predicted by Corollaries 3 and 4, with a special focus on predictions specific to the scenario in which stock prices influence investment (the learning from peers scenario). 4 Empirical Findings 4.1 Corporate investment and stock market prices Table 3 presents estimates for various specifications of the baseline investment equation (16). The sensitivity of a firm investment to its peers stock price (η) is positive (equal to 0.051). It is highly significant with a t-statistic of and the economic magnitude of the relationship between the investment of a firm and the stock price of its peers is substantial as well. To see this, consider a one standard deviation increase in the stock price of peers (1.109). This shock 23

24 is associated with a 5.6% increase in investment on average, about 14.5% of the sample average ratio of capital expenditures on fixed capital (η sd(q i )= =5.6%). As found in many other studies (e.g. Baker, Stein, and Wurgler (2003), Chen, Goldstein, and Jiang (2007), or Campello and Graham (2011)), our estimation reveals a positive and significant relation between a firm s stock price (Q i,t 1 ) and its investment (I i,t ). On average, the estimated investment-to-price sensitivity, β, is with a t-statistic of In terms of magnitude, the effect of peers price on a firm investment is about half that of its own stock price. Indeed, a one standard deviation increase in the firm own price (1.919) is associated with a 12.8% increase in investment (β sd(q i )= =12.8%). 17 [Insert Table 3 about here] The rest of Table 3 checks the robustness of these findings to several changes in the baseline specification. In column 3, we modify the proxy for peers stock price and characteristics (size and cash flow) by using their median values instead of their average values. In Columns 4 and 5, peers of a given firm are defined as firms within the same 3-digit SIC or 4-digit NAICS instead of firms within the same TNIC industry. We continue to observe that the investment of a firm co-varies positively with the stock price of its peers. We perform additional robustness tests that we report in the Internet Appendix. We show that our inference is robust to various forms of fixed effects (e.g. the inclusion of industry and industryyear fixed effects), different forms of clustering, and different definitions of corporate investment (Tables IA2-IA4). Also, our conclusions remain identical if we use price-to-earning ratio (PE) or (idiosyncratic) stock returns instead of the market-to-book ratio as alternative proxies for stock prices (Table IA5). We also check that the investment of a firm is not sensitive to the stock price of unrelated firms (Figure IA1), that is, randomly selected firms, which therefore should not be exposed to common demand shocks (that is, ρ = 1 2 in the model). The Internet Appendix presents additional specifications (Table IA6) where we include a larger set of control variables (such as leverage, cash holdings, asset tangibility, sale growth, lagged capital expenditures, and 17 The correlation between Q i and Q i is 0.40 in the sample. Thus the coeffi cient on Q i captures an information that is distinct from the information in Q i. 24

25 future (3 years) returns of firms and their peers). The main results remain unaffected. As pointed by Erickson and Whited (2000, 2012), Q i imperfectly measures the information in stock prices relevant to managers, which biases the estimate of β downward and may lead to spurious correlation of investment with other variables (e.g., cash-flows or, in our case, peers valuation). They propose an estimator of β that accounts for this error-in-measurement problem. The estimation of equation (16) using this technique is reported in the Internet Appendix, for brevity (see Table IA7). 18 As expected, we find that estimates of β are significantly larger when we use the Erickson and Whited s estimator. However, we still find a positive and significant coeffi cient for η. Moreover, the magnitude of this coeffi cient is similar to that reported in Table 3. Overall, the investment of a firm is positively and significantly correlated with its market valuation and its peers market valuation. The first empirical finding is well known. The second is new to our paper. 4.2 Dynamic peers classification By using TNIC industries, the set of peers for each firm is changing over time. So we can gauge how the investment of a firm is related to the stock price of past, present, and future peers. Consider a firm B which becomes a peer of firm A at date t. This entry of firm B in the set of peers is like a positive shock on ρ in the model. Hence, we should observe an increase in the sensitivity of firm A investment to the stock price of firm B. Symmetrically, the investment of firm A should become less sensitive to the stock price of a peer when this firm exits its set of peers. These effects should hold whether or not managers learn information from stock prices (see Corollary 5) as long as the price of a peer (new or old) contains information correlated with the cash flows of firm A s incremental investment projects. Now consider the case in which firm B is not yet a peer of firm A at date t but will become one at some point in the future, say date t + 2. This might happen because the manager of firm A decides to enter the product space of firm B at date t + 1, after learning information from firm 18 We thank Toni Whited for providing the Erickson and Whited estimator for unbalanced panel (stata command XTEWreg) on her website. 25

26 B s stock price (and other sources of information) at date t. In this case, the investment of firm A should co-vary with the stock price of firm B before firm B becomes a peer of firm A. To test these implications, we construct for each firm-year four distinct sets of peers: (i) new peers, (ii) still peers, (iii) past peers, and (iv) future peers. For firm i and year t, we define new peers as firms that are in the same TNIC industry as firm i in year t but that were not in year t 1. Following the same logic, past peers are firms that were in the TNIC industry of firm i in year t 1 but that are not anymore in year t while still peers are firms that were in the TNIC industry of firm i in year t 1 and continue to be in year t. Finally future peers are firms that are not in the TNIC industry of firm i in year t but will be therein in year t + 1 (or t + 2, depending on specification). Then, we compute the average price (market-to-book ratio) for each set of peers and use this price instead of the average stock price of all current peers in equation (16). [Insert Table 4 about here] Table 4, present the results. In columns 1, we observe a positive and significant relation between firms investment and the stock price of their new peers. The estimated coeffi cient is with a t-statistic of In contrast, column 2 shows that the investment of firms stop being sensitive to the stock price of firms that exit their set of peers (the sensitivity is with a a t-statistic of 1.77). Finally, results regarding still peers largely mirror the baseline results (presented in Table 2) with a large coeffi cient on the stock price of still peers (0.036 with a t-statistic of 7.02). In columns 4 and 5, we report the sensitivity of investment to the stock price of one year or two years ahead f uture peers. The sensitivity of firms investment to the prices of their one year ahead (respectively two years ahead) future peers is equal to (0.014) and is statistically significant. These empirical findings fit well with a scenario in which firms managers extract information about the profitability of breaking into a new product space from the valuation of firms already active in this space. 19 The sample size is smaller than that used in previous tests because we exclude from the analysis firms that keep the same peers over the entire sample period. 26

27 4.3 Cross-sectional tests We now turn to the cross-sectional implications that are unique to the learning from peers hypothesis. We examine how the co-variation between investment and stock prices varies crosssectionally with (i) measures of informed trading (π A and π B ), (ii) measures of managerial information other than stock prices (γ), and (iii) measures of the correlation in demand shocks between a firm and its peers (ρ). [Insert Table 5 about here] Table 5 summarizes the cross-sectional predictions of the model for η and β. We highlight with an the predictions that enable us to distinguish the scenario ( learning from peers ) in which firms investment decisions are influenced by their peers market valuation from the scenarios in which this influence does not exist ( no managerial learning, and narrow managerial learning ). As discussed in Section 2.4, our cross-sectional predictions for the effects of peer stock prices hold for the absolute value of η. Empirically, we always find that η is positive, which suggests that, for the average peer, the case in which ρ > 1 2 is the relevant one empirically Informed trading (π j ) We first examine how investment-to-price sensitivities (η and β) varies with the level of informed trading in the stock of a firm (π A ) and the stocks of its peers (π B ). We use a measure of price informativeness as proxy for the level of informed trading in a stock. As in many other papers (e.g., Durnev, Morck, and Yeung (2004), or Chen, Goldstein, and Jiang (2007)), we measure the informativeness of a firm stock price by its firm-specific return variation (or price non-synchronicity), defined as Ψ i,t = ln((1 Ri,t 2 )/R2 i,t ), where R2 i,t is the R2 from the regression in year t of firm i s weekly returns on the market portfolio returns and the peers portfolio returns (both portfolios being value-weighted). The idea, due to Roll (1988), is that trading on firmspecific information makes stock returns less correlated and thereby increases the fraction of total volatility due to idiosyncratic returns. The level of informed trading in a stock is higher when Ψ is high. 27

28 In our sample, the correlation between Ψ i and Ψ i (the average firm-specific return variation of the peers for stock i) is equal to To test the model s predictions, we need to measure the effect of Ψ i on the co-variation between investment and stock prices, while holding constant Ψ i and vice versa. To do so, we first regress Ψ i on Ψ i each year and define the regression residuals as Ψ + i. Similarly, we regress Ψ i on Ψ i each year and define the regression residuals as Ψ + i. In our tests, we analyze how a change in Ψ + i or Ψ+ i affects the estimates of of β and η. As the variation of, say, Ψ + i is independent of Ψ i by construction, this amounts to varying the level of informed trading in firm i s peers while keeping the level of informed trading in stock i, Ψ i, fixed. Thus, to sum up, we use Ψ + i as a proxy for π B and Ψ + i as a proxy for π A. [Insert Table 6 about here] To gauge the effect of informed trading in peers stocks on the co-variation between a firm s investment and stock prices, we assign observations that are in the bottom and top quintiles of the distribution of Ψ + i into low and high groups, each year. Then, we estimate our baseline regression (equation (16)) for each group and compare the coeffi cient estimates of η and β across groups. 20 Panel A of Table 6 presents the results. For brevity, we only display the estimated coeffi cients for η and β, their statistical and economic significance, as well as the average values of Ψ i and Ψ i (bottom two lines). 21 A prediction specific to the learning from peer hypothesis is that the sensitivity of a firm s investment to its own stock price should be lower when the level of informed trading in its peers is high. This is indeed what we find in Panel A: the estimate of β is lower in the high group than in the low group (0.070 versus 0.059). The difference in β between the two groups is marginally significant (p-value of 0.063). In economic terms, the difference is significant: a one standard deviation increase in a firm s stock price is associated with a 13.12% increase in investment when the level of informed trading in peers stocks is low while the same shock raises investment by 11.12% when the level of informed trading in peers stocks is high. 20 We partition firms based on the informativeness variable measured at date t 1, i.e., contemporanously to the stock price (Q) in equation (16). Moreover, we focus on only the lowest and highest quintile to limit the impact of measurement errors in the price informativeness proxies (see Greene (2008)). 21 By construction the average Ψ i is similar across the low and high groups (2.514 vs ), but the average is not. It amounts to in the low group vs in the high group. Ψ i 28

29 Moreover, a firm s investment turns out to be more sensitive to the stock prices of its peers when peers markets have a higher level of informed trading, as implied by both the learning channel and the correlated information channel (Corollaries 1 and 2). All else equal (i.e., keeping Ψ i fixed), these results show that firms rely less on their own stock price and more on the stock prices of their peers when peers stock prices are more informative. In Panel B, we study how changes in the level of informed trading in a firm s own stock (π A ) affects the sensitivity of its investment to its own stock price and the stock price of its peers (holding π B constant). The first row shows that the co-variation between a firm s investment and the stock price of its peers decreases in the amount of informed trading in its own market, as uniquely predicted by the scenario in which firms learn from their peers stock price. Indeed, the coeffi cient on η is large and significant in the low group (0.064 with a t-statistic of 10.31), but insignificant in the high group (0.011 with a t-statistic of 1.621). The difference is economically large. A one standard increase in peers stock prices generates a modest 1.24% increase in a firm s investment when its own market has a high level of informed trading. In contrast, the same shock is associated with a 6.80% increase in a firm s investment when the level of informed trading in its own stock is low. The second row confirms the results of Chen, Goldstein, and Jiang (2007) and Bakke and Whited (2010): a firm s investment is markedly more sensitive to its own stock price when its market displays a higher level of informed trading. This observation is consistent both with the correlated information channel and the learning channel. The general picture that emerges from Table 6 supports the hypothesis that managerial learning explains part of the positive correlation between corporate investment and stock market prices. In the Internet Appendix (Table IA8), we show the robustness of the findings in Table 6 using two other proxies for the level of informed trading in a stock: one based on Llorente, Michaely, Saar, and Wang (2002) and another one based on the P IN measure developed by Easley, Kiefer, and O Hara (1996). 29

30 4.3.2 Managerial information (γ) According to the learning from peers hypothesis, an increase in the quality of managerial information (γ) should decrease the sensitivity of a firm s investment to its peers valuation. Moreover, the effect of a higher γ on the sensitivity of a firm s investment to its own stock price should depend on the level of informed trading in its peers stocks. If this level is high, the effect should be positive while if this level is low, the effect should be negative. None of these predictions are obtained if the learning from peers hypothesis does not hold (see Table 5). We test these two predictions using the trading activity of corporate insiders as a proxy for managerial information, following Chen, Goldstein, and Jiang (2007). Intuitively, managers should be more likely to trade their own stock if they possess more private information (γ higher). We measure the intensity of managers insider trading activity (Insider i,t ) in a given year as the total number of insider transactions for that year divided by the total year s transactions. We obtain the trades of corporate insiders from the Thomson Financial Insider Trading database and the total number of trades (turnover) from CRSP. 22 We follow previous studies (e.g. Beneish and Vargus (2002), or Peress (2010)) and limit insider trades to open market stock transactions initiated by the top five executives (CEO, CFO, COO, President, and Chairman of the Board). [Insert Table 7 about here] Table 7 reports the results from the estimation of equation (16) where observations in the bottom and top quintiles of the distribution of Insider i are assigned into low and high groups respectively. 23 In the first row, we observe that the investment of a firm is significantly more sensitive to its peers stock price when managers have little private information. The estimated coeffi cient for η is in the low group, and in the high group. The difference between these estimates is significant (p-value of 0.036). This finding is consistent with the learning from peers hypothesis and inconsistent with the absence of managerial learning from peers (see Table 22 The Thomson Financial Insider Filing database compiles all insider activity reported the the SEC. Corporate insiders include those that have "access to non-public, material, insider information" and required to file SEC form 3, 4, and 5 when they trade in their firms stock. 23 The last row of Table 7 indicates that the average fraction of insider trading is 0% in the low group, while it amounts to 9.85% in the high group. The sample average is 1.85%. 30

31 5). The estimates for β are not significantly different between the low and the high group (0.066 vs ). Chen, Goldstein, and Jiang (2009) also find that the sensitivity of a firm s investment to its own stock price is not significantly related to the extent of insider trading. The learning from peers hypothesis however predicts that the sign of the relation between the quality of managerial information and the co-variation between a firm s investment and its stock price should depend on the level of informed trading in its peers stocks (Corollary 4). To test whether the data uphold this prediction and to better understand the role of managerial information in explaining investment-to-price sensitivities, we double-sort firm-year observations based on (i) the level of informed trading in peers (measured by Ψ + i ; see Section 4.3.1) and (ii) the quality of managerial information for each firm. As in Section 4.3.1, in each year, we keep the firms that are in the lowest and highest quintiles of the distribution of Ψ + i and, in each of these two groups, we further separate firms in two groups based on the median value of Insider i (in each initial group). We then estimate η and β for each of the four subgroups separately. [Insert Table 8 about here] Panel A of Table 8 displays the results. For low level of informativeness in peers stock prices (low Ψ + i ), firms investment is less sensitive to their own price when managers enjoy more private information. The coeffi cient on Q i, β, is when the value of Insider is below the median (column 1), and when the value of Insider is above the median (column 2). In contrast, when the level of informativeness in peers stock prices is high (high Ψ + i ), the ranking of the estimates for β between the two groups is reversed: A firms investment is more sensitive to its own stock price when managers enjoy more private information. In either case, the difference between groups in estimates for coeffi cient β is not significant at conventional levels, maybe because of lack of power due to smaller sub-samples. Yet, remarkably, the direction of the effects is consistent with the predictions of the learning from peers hypothesis. Furthermore, the estimates for the coeffi cients on Q i (η) are as expected: Corporate investment co-varies more with peers valuation when managers have less private information (columns 1 and 3), and even 31

32 more so when peers valuation is highly informative Correlated demand for products (ρ) If firms learn information from their peers valuation, the sensitivity of a firm investment to its own stock price should decrease when the correlation in product demands between the firm and its peers increases in absolute value (Corollary 5). We now test this prediction. We use two different variables to proxy for the correlation between the demands for firms products. First, we use the correlation of cash-flows (CF correlation) between a firm and its peers. We compute this correlation for each firm-year using quarterly cash flows over the previous three years. Second, we use a direct measure of product similarity based on firms product description. As explained in section 3.1, the TNIC industries developed by Hoberg and Phillips (2011) are constructed based on similarity scores (ranging from 0% to 100%) for each pair of firms that are above a minimum similarity threshold (21.32%). We use these scores to compute the average similarity score (denoted similarity) of a firm with its peers in a given year. 24 This is another proxy for ρ. [Insert Table 9 about here] For each proxy, we group firms in quintiles and estimate equation (16) separately for the lowest and the highest quintiles of firms. Results are reported in Table 9. The investment of firms in the lowest quintile is less sensitive to their peers valuation than the investment of firms in the highest quintile. For instance, the estimate for η is (with a t-statistic of 5.72) when the correlation between a firm s cash flow and that of its peers is relatively high and (with a t-statistic of 3.89) when this correlation is relatively low. This ranking of the estimate for η between the two extreme quintiles is consistent with the learning hypothesis but it could also arise even if firms do not learn from their peers (see Table 5). In contrast, the ranking of the estimates for β between the high and the low quintiles is consistent with the learning hypothesis only. For each proxy for ρ, the investment of firms in the 24 We are especially grateful to Jerry Hoberg and Gordon Phillips for sharing the data required for this test with us. 32

33 low quintile is significantly more sensitive to their stock price. For instance, the estimate for β is (with a t-statistic of ) when the average similarity between a firm and its peers is low and (with a t-statistic of 12.40) when this average similarity is high. This difference in sensitivity between firms with low and high values of ρ cannot be explained if firms do not rely on peers stock prices as a source of information (see Table 5). 4.4 Going public and learning from peers stock prices Finally, we provide an additional piece of evidence in favor of our learning from peers hypothesis by looking at the investment behavior of a subset of firms before and after they go public. By definition private firms cannot learn from their own stock price. Hence, they are likely to rely on their peers stock price as a source of information. More importantly for our purpose, when these firms go public, they obtain the possibility of learning information from their own stock price. Thus, going public is similar to an increase in π A in our model (a move from a situation where a firm stock price is completely uninformative to a situation in which it is informative). If the investment decision of a firm is influenced by its peers valuation because managers extract information from these prices, we should therefore observe a drop in the sensitivity of a firm investment to its peers valuation after a firm IPO. In contrast, we should observe no change in this sensitivity after an IPO if managers do not learn information from stock prices or an increase in this sensitivity if they learn information only from their own stock price (see the predictions regarding π A in Table 5). Hence, we compare the investment behavior of firms before and after their IPO using a sample of 3,166 U.S. IPOs (provided to us by Jay Ritter) for the 1996 to 2008 period. In this sample, we identify 1,342 firms for which we can obtain data on investment and peers stock prices before and after these firms go public (we consider a maximum of five years post-ipo). 25 We examine whether the investment of these firms is sensitive to the stock price of their public peers before they go public and how this sensitivity changes after firms become public. To this end, we regress 25 The investment data are from Compustat. As observed in Teoh, Welch and Wong (1998), Compustat typically contains information for firms prior to their public offering. We follow their approach and concentrate on firms for which we can obtain data for at least one year before the IPO. 33

34 the investment of IPO firms (I i ) on the stock price of their peers (Q i ), a dummy variable P ost i that equals one for the years that follow the IPO, the interaction between Q i and P ost i, and the usual control variables (including firms own post-ipo stock price). [Insert Table 10 about here] Table 10 presents the results of this event-time analysis. Consistent with the idea that the stock market matters for private firms, we find that their investment is sensitive to their public peers stock price. The coeffi cient on Q i is positive (0.026) and significant (t-statistic of 4.54). More importantly, the coeffi cient on Q i P ost i is significantly negative ( with a t-statistic of 2.93). Thus, firms investment becomes less sensitive to their peers valuation once they are publicly listed. The same result obtains when we add sales growth to further control for firms investment opportunities before they are publicly listed. As explained previously, this evolution of the sensitivity of investment to peers valuation is consistent with the scenario in which managers learn information from their peers stock prices but not with other scenarios in our model. 5 Conclusion In this article, we document that a firm s investment is positively related to its peers valuation. Our hypothesis is that this relationship arises in part because peers valuation conveys information to managers about their growth opportunities. We formalize this idea in a simple model and we derive several cross-sectional predictions about the relationship between investment and stock prices that hold only if firms extract information from their peers valuation. For instance, the sensitivity of a firm investment to its peers valuation should decrease with the quality of managers private information if the latter learn from their peers valuation but should increase with this quality if they don t. Our tests do not reject the cross-sectional predictions specific to the learning from peers hypothesis. If firms learn information about future demand from their peers valuation then product market choices by firms exert an externality on other firms. For instance, if a firm increases the differentiation between its products and those of its peers, the ability of peers to learn from its 34

35 stock price is weaker. Analyzing the effects of these learning externalities on product market choices and firm valuations is an interesting venue for future research. In particular, they could be one channel through which the stock market affects product market choices and the degree of competition within an industry. 26 From a different perspective, learning externalities could also affect the behavior of privately held firms. The precision and nature of the information they can gather from the stock prices of publicly-listed peers could impact their willingness to go public, the type of securities issued, their listing location, and the type of investors they want to attract. More generally, it would be interesting to better understand the characteristics (firm, product, or stock markets) that determine the extent to which firms can learn from each other stock prices. We plan to investigate these questions in future research. 26 Some papers suggest that the degree of competition within an industry affects stock market returns and price effi ciency (see Peress (2010) and Tookes (2008)). If firms learn from their peers valuation, there might also be an effect of the stock market on firms product choices and therefore the degree of competition in an industry. 35

36 Appendix Appendix A: Stock market equilibrium for firms A and B. In this appendix, we solve for equilibrium prices at date 1 and the manager s optimal investment decision at date 2. The results in this section are used for the discussion in Section 2.2 and the empirical predictions, in particular those in Section We provide the equilibrium in the markets for stocks A and B in Lemma 1 and 2 below and then we provide a proof of these two lemma. Lemma 1 : The stock market equilibrium for firm B is as follows: 1. A speculator: (i) buys when she knows that demand for firm B s product is high (x ib (H) = +1) and (ii) sells when she knows that demand for firm B s product is low (x ib (L) = 1). 2. The stock price of firm B at date 1 is an increasing step function of investors net demand for this stock, f B. Specifically, the stock price of firm B, p B1 (f B ), is θ H B when f B > 1 π B ; E(θ B ) when 1 + π B f B 1 π B ; and θ L B when f B < 1 + π B. If investors net demand is relatively strong (f B 1 π B ), dealers infer that speculators have received a good signal about the demand for firm B s product and the price of stock B is therefore θ H B. If instead, investors net demand for stock B is relatively low (f B 1 + π B ), dealers infer that speculators have received a bad signal and the price of stock B is θ L B. Intermediate realizations for investors net demand are not informative and therefore the price of stock B is just equal to the unconditional expected cash-flow of this firm. Remember that p B = p B E(θ B ) is the change in the price of stock B from date t = 0 to date t = 1. Lemma 1 implies: Pr( p B 0 d A = H ) Pr( p B 0 d A = H ) = ρ + (1 ρ)(1 π B) ρ(1 π B ) + (1 ρ) = 1 (1 ρ)π B. (17) 1 ρπ B 36

37 When ρ > 1 2 (i.e., firm A and B have positively correlated demand), this likelihood ratio is strictly greater than 1 and increases in π B. That is, as π B increases, a high stock price for B at date t = 1 is more likely to occur when the demand for the product of firm A is high than a low stock price (and vice versa when the demand for firm A is low). Hence, the stock price of firm B is informative about the demand for firm A s product and its informativeness increases with π B, as claimed in the text. Let denote p H A = θh A + (Λ K); pm A =E(θ A) (γ + (1 γ)π B) (Λ K); and p L A = θl A. Note that p H A > pm A > pl A. Lemma 2 : There is a stock market equilibrium for firm A in which: 1. A speculator: (i) buys when she knows that demand for firm A s product is high (x ia (H) = +1) and (ii) sells when she knows that demand for firm A s product is low (x ia (L) = 1). 2. The stock price of firm A at date 1, p A1 (f A), is an increasing step function of investors net demand for this stock, f A. Specifically, this price is p H A when f A > 1 π A ; p M A when 1 + π A f A 1 π A ; and p L A when f A < 1 + π A. 3. The manager of firm A optimally invests at date 2 (I = 1) if and only if: (i) his managerial information indicates a high demand at date 3 (s m = H), or (ii) its stock price at date 1 is p H A or (iii) the stock price of firm B is θh B. Investors net demand for stock A, f A, affects its stock price because this demand is informative about the future demand for firm A s product, as for stock B. Moreover, as the level of informed trading (π A ) in stock A increases, investors demand for this stock becomes more informative. Hence, the informativeness of the stock price of firm A for its manager increases with π A. As the last part of the proposition shows, the investment decision of the manager of firm A depends on its own stock price and the stock price firm B The last part of the proposition implies that if the manager of firm A does not receive managerial information then he does not invest, except for high realizations of the price for stock A or stock B. Thus, it specifies the manager s optimal decision for all possible prices for stocks A and B, even those that cannot be observed in equilibrium (prices that are out of the equilibrium path). For these prices, the manager s beliefs regarding future demand cannot be computed by Bayes law. We choose these beliefs so that they are identical to those that the 37

38 Using equation (7) and Lemma 2, we obtain: p A0 (I ) = E(E(V A (I ) f A )) = E(p A1 (f A )) = E(θ A ) (Λ K) (γ + (1 γ)(π A + π B )). (18) Thus, the value of firm A at date 0 (before trading) is higher than p M A and pl A and less than p H A. We conclude from the last part of Lemma 2 that when the manager has no information, he invests if and only if (a) the change in price of stock A, p A, is positive or (b) the change in price of stock B is positive and the change in price of stock A is moderately negative ( p A = p M A p A0(I )). These observations yield Figure 2. Proof of Lemma 1. We show that the strategies described in the lemma form an equilibrium. Let Π(x ib, ŝ B ) be the expected profit of a speculator who trades x ib { 1, 0, +1} shares of firm B when his signal is ŝ B and let σ B = θ H B E(θ B ) = E(θ B ) θ L B = θh B θl B. 2 First, consider an informed speculator who observes ŝ B = H. If he buys the asset, his expected profit is: Π(+1, H) = E(θ B p B1 (f B ) ŝ B = H, x ib = 1 ) = Pr( 1 + π B < f B < 1 π B ŝ B = H, x ib = 1 )(σ B ) + Pr(f B < 1 + π B ŝ B = H, x ib = 1 )(2σ B ). When ŝ B = H, the informed speculator expects other informed speculators to buy the asset and uninformed speculators to stay put. Hence, using equation (6), he expects: f B = z B + π B when ŝ B = H. (19) manager would have if he could directly observe investors demands, f A and f B, in each stock (see the proof of the proposition). In this way the equilibrium described in Lemma 2 is identical to the equilibrium that would be obtained if the manager could observe investors demand. 38

39 We deduce that Pr( 1 + π B < f B < 1 π B ŝ B = H, x ib = 1 ) = Pr( 1 < z B < 1 2π B )=(1 π B ). and Pr(f B < 1 + π B ŝ = H, x ib = 1 ) = Pr(z B < 1) = 0. Thus, Π(+1, H) = (1 π B )σ B > 0. If instead, the speculator sells, his expected profit is: Π( 1, H) = E(θ B p B1 (f B ) ŝ B = H, x ib = 1) = (1 π B )σ B < 0, where we have used the fact that each speculator s demand has no impact on aggregate speculators demand since each speculator is infinitesimal. Thus, the speculator optimally buys the asset when he knows that demand for firm B is strong at date 3. A symmetric reasoning shows that the the speculator optimally sells the asset when he knows that this demand is low at date 3. Now consider dealers prices at date t = 1. Remember that p B1 (f B ) =E(θ B f B ). If ŝ B = L, then π B 0 x ib (ŝ B )di = π B. Thus, equation (6) implies that f B > 1 π B is impossible if ŝ B = L. In contrast, if ŝ B = H, then π B 0 x ib (ŝ B )di = π B. Thus, equation (6) implies that f B > 1 π B happens when z B > 1 2π B. As a result, when dealers observe f B > 1 π B, they deduce that ŝ B = H. This implies: p B1 (f B ) = E(θ B f B ) = E(θ B ŝ B = H ) = θ H B for f B > 1 π B. A symmetric reasoning implies: p B1 (f B ) = E(θ B f B ) = E(θ B ŝ B = L) = θ L B for f B < 1 + π B. 39

40 Finally, for 1 + π B f B 1 π B, we have: p B1 (f B ) = E(θ B 1 + π B f B 1 π B ) = θ B +(2Pr(d B = H 1 + π B < f B < 1 π B ) 1)σ B. Now: Pr(d B = H 1 + π B < f B < 1 π B ) Pr( 1 + π B < f B < 1 π B d B = H ) = Pr( 1 + π B < f B < 1 π B d B = H ) + Pr( 1 + π B < f B < 1 π B d B = L ) ( ) 1 π B = = 1 1 π B + 1 π B 2. Hence, p B1 (f B ) = E(θ B ) for 1 + π B f B 1 π B. Proof of Lemma 2. Speculators optimal trading strategy. It can be shown that speculators order placement strategy is optimal following the same steps as in the proof of Lemma 1. Hence, we skip this step for brevity. The manager s optimal investment policy. Now consider the investment policy for the manager of firm A given the equilibrium price function p A1 ( ). If the manager receives managerial information, he just follows his signal since this signal is perfect. Hence, in this case, he invest if s m = H and does not invest if s m = L. If he receives no managerial information (that is, s m = ), the manager relies on stock prices. If he observes that p A1 = p H A, the manager deduces that f A > 1 π A. In this case, investors net demand in stock A reveals that demand for product A is strong, i.e., d A = H (the reasoning is the same as that followed for firm B when f B > (1 π B ); see the proof of Lemma 1). Thus the manager optimally invests. If instead the manager observes that p A1 = p L A then the manager deduces that f A < 1 + π A and he infers that the demand for the product sold by firm A will be low at date 3. In this case, the manager 40

41 optimally abstains from investing at date t = 2. Finally if he observes p A1 = p M A then the manager infers that 1 + π A f A 1 π A. In this case, investors demand in stock A is uninformative (that is, Pr(d A = H 1 + π A < f A < 1 π A )= 1 2 ). Hence, the manager of firm A relies on the price of stock B as a source of information. If p B1 = θ H B, he deduces that f B > 1 π B and that the demand for product B will be high. We deduce that E(Σ p B = θ H B, p A = p M A ) = E(Σ d B = H ) > 0, (20) where the last inequality follows from Assumption A.2. If p B1 < θ H B, the manager deduces that f B 1 π B, in which case either investors demand in stock B is uninformative or it signals that the demand for product B will be low. Hence, when p B1 < θ H B and p A1 = p M A, the manager of firm A assigns a probability less than or equal to 1 2 to demand for product A being high at date 3. Using Assumption A.1, we deduce that the manager of firm A does not invest in this case. We have considered the manager s optimal decision for prices that can be observed on the equilibrium path, that is, p H j, pm j, pl j for j {A, B}. Other prices for stocks A and B are out-of the equilibrium path and, for these prices, the manager s belief about the demand for its product cannot be computed by Bayes rule. Consider the following specification of the manager s belief about investors demand for prices out of the equilibrium path: (i) if he observes p M A p A1 < p H A, the manager of firm A believes investors demand for stock A to be 1 + π A f A 1 π A, (ii) if he observes p A1 < p M A, the manager of firm A believes investors demand for stock A to be less than 1 + π A, and (iii) if he observes p B1 < θ H B, the manager believes that f B 1 π B. It is straightforward, using the same reasoning as in the previous paragraph that this specification of the manager s out-of-equilibrium beliefs leads to the optimal investment policy prescribed by Lemma 2 for out-of-equilibrium prices. Collecting these observations, we deduce that the manager s optimal investment policy at date 2 is as given in the last part of Lemma 2. Equilibrium prices. Now consider the stock price of firm A. We must check that the following 41

42 equilibrium condition is satisfied: p A1 (f A ) = E(V A (I ) f A ), (21) where I (s m, p A, p B ) = 1 if s m = H, or p A = p H A, or p B1 = θ H B and I (s m, p A, p B ) = 0, otherwise (last part of Lemma 2). We check that the price function given in the second part of Lemma 2 satisfies Condition (21). Suppose first that f A (1 π A ). In this case, investors net demand in stock A reveals that demand for product A is strong, i.e., d A = H (the reasoning is the same as that followed for firm B when f B > (1 π B ); see the proof of Lemma 1). Moreover, the stock price of firm A is p H A according to the conjectured equilibrium. Hence, I = 1 and we deduce that: E(V A (I ) f A ) = θ H A + (Λ K) for f A (1 π A ), which is equal to p H A, so that for f A > (1 π A ), Condition (21) is satisfied. Now suppose that f A 1 + π A. In this case, investors net demand in stock A reveals that demand for product A is low, i.e., d A = L. Moreover, the stock price of firm A is p L A according to the conjectured equilibrium. Hence, I = 0 and we deduce that: E(V A (I ) f A ) = θ L A for f A 1 + π A, which is equal to p L A. Hence, for f A 1 + π A, Condition (21) is satisfied. Last, consider the case in which 1+π A f A 1 π A. In this case the investors demand for stock A is uninformative about the demand for product A, that is Pr(d A = H 1 + π A < f A < 1 π A )= 1 2 (the reasoning is as for firm B). Moreover, the stock price of firm A is pm A according to the conjectured equilibrium. Hence, the manager of firm A will invest (I = 1) if and only if (i) he receives a signal that demand for product A is strong or (ii) he observes a high price for stock B. 42

43 We deduce that: E(I (Λ K) 1 + π A f A 1 π A ) = Pr(s m = H 1 + π A < f A < 1 π A )(Λ K) +Pr(s m = f B > 1 π B 1 + π A < f A < 1 π A )(Λ K). Now, Pr(s m = H 1 + π A < f A < 1 π A )= γ 2, and Pr(s m = f B > 1 π B 1 + π A < f A < 1 π A ) = (1 γ)pr(f B > 1 π B d B = H )Pr(d B = H 1 + π A < f A < 1 π A ) = (1 γ) π B 2 We deduce from the expression for V A (I ) (equation (3)) that, ( γ E(V A (I ) 1 + π A f A 1 π A ) = E(θ A ) (1 γ)π ) B (Λ K), 2 which is equal to p M A, so that for 1 + π A f A 1 π A, Condition (21) is satisfied. Appendix B: Empirical Implications Proof of Corollary 1. When the manager of firm A does not learn information from prices, his investment policy, I b ( ), is 1 if s I b m = H (s m ) = 0 if s m H. (22) As this investment policy differs from that obtained when the manager accounts for the information in stock prices (I b ( ) I ( )), the equilibrium price of stock A in the no managerial learning 43

44 scenario is different from that given in Lemma 2. In the Internet appendix (Section A.1), we show that this price is given by: θ H A + γ(λ K) when f A 1 π A, p b A1(f A ) = E(θ A ) + γ(λ K)/2 when 1 + π A < f A < 1 π A, (23) θ L A when f A 1 + π A. By definition, the covariance between the price of stock A and the investment of firm A in the benchmark case is: K cov(i b, p b A1) = K [ ] E(I b p b A) E(I b )E(p b A). Using equations (22) and (23), we deduce that cov(k I b, p b A1 ) = γπ A(σ A + γ 2 (Λ K)) K 2, as announced in the corollary. The cash flow for firm B is the same whether or not the manager of firm A relies on stock prices as a source of information. Hence, even if when the manager of firm A does not use stock prices as a source of information, the stock price of firm B is given by Lemma 1. Using this observation, we easily derive the covariance between the price of stock B and the investment of firm A, I b, when there is no managerial learning. Proof of Corollary 2. For brevity, we derive the expressions for cov(k I, p j1 ) when the manager only learns from his stock price in the internet appendix (see Section A.2). Proof of Corollary 3. The covariance between the price of stock B and the investment of firm A in equilibrium is: K cov(i, p B1 ) = K [E(I p B1 ) E(I )E(p B1 )]. The last part of Lemma 2 implies that I (s m, p A1, p B1 ) = 1 if s m = H, or p A = p H A, or p B = θ H B 44

45 and I (s m, p A1, p B1 ) = 0, otherwise. Using Lemma 1, we deduce that: E(I p B1 ) = γ 2 (θ B + π B (2ρ 1)) + (1 γ) (θ B π A + σ B π B (1 2π A + π A ρ)). 2 Moreover, E(p B1 ) = E(θ B ) and E(I ) = γ 2 (1 γ) + (π A + π B (1 π A )). (24) 2 Thus, after some algebra, we obtain cov(ki, p B1 ) = ((γ + (1 γ)π A )(2ρ 1)π B + (1 γ)π B (1 π A )) σ BK 2. We deduce that: cov(i, p B1 ) π B = ((2ρ 1)(γ + (1 γ)π A ) + (1 γ)(1 π A )) σ B /2 > 0, cov(i, p B1 ) π A = (1 γ)π B (1 ρ) < 0, if γ < 1, cov(i, p B1 ) γ = (1 π A )π B (1 ρ)σ B < 0. This proves Corollary 3. Proof of Corollary 4. The covariance between the price of stock A and the investment of firm A is given by: K cov(i, p A1 ) = K [E(I p A1 ) E(I )E(p A1 )]. (25) Calculations yield: E(I p A1 ) = γ 2 ( πa p H A + (1 π A )p M A ) 1 γ + ( ) ( π A p H A + (1 π A )π B p M ) A. 2 Equation (24) gives the expression for E(I ). By definition, p A0 = E(p A ). Hence, the expression for E(p A ) is given by equation (18). Using these observations, we obtain equation (14) from equation (25). 45

46 Differentiating equation (14), it is straightforward that cov(i,p A1 ) π B < 0 and cov(i, p A1 ) π A = 1 2 σ A + (Λ K) ((1 γ)(1 + π A + π B ) + 1 γ 2 π A + (1 γ) 2 π B π B ) > 0, and cov(i, p A1 ) γ ( ) Λ K = π A ((1 γ)(1 π A )(1 π B ) π B 2 2 ). Clearly, cov(i,p A1 ) γ increases in π B. Moreover, for π B = 1, cov(i,p A1 ) γ is positive while for π B = 0, it is negative. Thus, there exists a value π B such that cov(i,p A1 ) γ > 0 if π B > π B, cov(i,p A1 ) γ < 0 if π B < π B and cov(i,p A1 ) γ corollary. Calculations yield π B = 2(1 γ)(1 π A) 1+2(1 γ)(1 π A ). Proof of Corollary 5. = 0 for π B = π B, as claimed in the last part of the As explained in the text, when 1 1 R H ρ < 1 R H, the equilibrium is identical to the case in which the manager ignores the information contained in the price of stock B. Thus, in this case, cov(ki, p A1 ) is given by equation (12) in Corollary 2. In contrast, when ρ < 1 1 R H or ρ > 1 R H, investment is influenced by the stock price of B and, as explained in the text, cov(ki, p A1 ) is given by equation (14) in Corollary 4. Calculations show that the expression for cov(ki, p A1 ) in (14) is smaller than in (12). The first part of Corollary 5 follows. When the manager of firm A ignores the information contained in the stock price of firm B, cov(ki, p A1 ) is given by equations (12) or (10). In either case, it does not depend on ρ, which yields the last part of the corollary. 46

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51 Figure 1: Timing of the model Date 1 Date 2 Date 3 1. Investors trade shares 1. The manager of firm A Demands and firms' of firms A and B observes stock prices, p A1 and p B1 cash flows are and his private signal s ma realized 2. Stock prices, p A1 and p B1, are 2. The managers of firm A realized decides to invest or not

52 Figure 2: Equilibrium Figure 2 shows for each realization of the order flow in stock A (Y axis) and B (X axis), the sign of the changes in prices realized between dates 0 and 1 in each stock and the corresponding investment decision for firm A.

53 Table 1: Variable definition Variable Definition Source Capex Capital expenditures (capx) Compustat PPE Property, Plant and Equipement (ppent) Compustat Q [Book value of assets (at) book value of equity (ceq) + market value of equity (csho*prcc_f)] / book value of assets (at) Compustat TA Book value of total assets (at) Compustat Size Logarithm of the book value of assets (at) Compustat CF (cash flow) Income before extraordinary items (ib) plus depreciation (dp) divided by total assets Compustat Sale Total sales (sale) Compustat Ψ Insider CF Correlation Similarity Fluidity Firm specific return variation computed as ψ i,t = ln[(1 R 2 i,t)/ R 2 i,t], where R 2 i,t represents the R 2 from a regression of firm i weekly returns on the returns on the (value weighted) market portfolio and a (value weighted) portfolio of peers, where peers are defined using the TNIC industries. Total number of insider transactions in a given year divided by the total year s transaction. We only consider open market stock transactions initiated by the top five executives (CEO,CFO, COO, President, and Chairman of the board) Correlation between firm i s cash flow and the average cash flow of its peers (using quarterly observation over the past three years) Average similarity score across the peers of firm i. Similarity scores (ranging from 0% to 100%) are from the detailed textbased analysis of Hoberg and Phillips (2010) Measure of the stability of a firm s product mix compared to that of its peers (from Hoberg, Phillips, and Prabhala (2012) CRSP Thomson Financial Insider Trading Datavase and CRSP Compustat Hoberg Phillips data library Hoberg Phillips data library

54 Table 2: Descriptive statistics This table reports the summary statistics of the main variables used in the analysis. We present the mean, median, 25 th and 75 th percentiles, standard deviation and the number of non missing observations. All variables are defined in the Appendix. In the upper panel, we present the statistics for firm level observations. In the lower panel, we present statistics for peers average (i.e. the average of peers for each firm year observation). Peers are defined using the TNIC industries developed by Hoberg and Phillips (2010). The sample period is from 1996 to Mean 25th Median 75th St. Dev. Obs. Own firm Capital expenditures (I i ) ,162 Q i ,162 Cash Flow (CF i ) ,074 Total assets (mio.) 1, , ,162 Average of peers # Peers ,162 Capital expenditures (I i ) ,035 Q i ,162 Cash flow (CF i ) ,155 Total assets (mio) 1, , , ,162

55 Table 3: Investment to price sensitivities: Baseline Results This table presents the results from estimations of equation (16). The dependent variable is investment, defined as capital expenditures divided by lagged property, plant and equipment (PPE). Q i is the market to book ratio of firm i, defined as the market value of equity plus the book value of debt minus the book value of assets, scaled by book assets. Q i is the average market to book of the peers of firm i, where peers as defined using the TNIC industries developed by Hoberg and Phillips (2010). The subscript i refers to (the average across) firm i s peers. The other explanatory variables are defined in Table 1. Columns (1) and (2) present the baseline estimations. In column (3) we use the median peers characteristics instead of the average. In column (4) the peers of firm i are all the firms that belong to firm i s 3 digit SIC industry. In column (5) the peers of firm i are all the firms that belong to firm i s 4 digit NAICS industry. The sample period is from 1996 to The standard errors used to compute the t statistics (in squared brackets) are adjusted for heteroskedasticity and within firm clustering. All specifications include firm and year fixed effects. Symbols ** and * indicate statistical significance at the 1% and 5% levels, respectively. Investment (capex over lagged PPE) Baseline Median SIC 3 NAICS 4 (1) (2) (3) (4) Q i 0.051** 0.054** 0.044** 0.050** [11.09] [9.75] [7.09] [7.64] CF i 0.145** 0.133** 0.211** 0.183** [4.31] [3.96] [4.68] [3.802] Size i [0.97] [1.26] [144] [0.73] Q i 0.067** 0.068** 0.070** 0.069** [23.68] [24.07] [24.45] [23.98] CF i 0.356** 0.356** 0.356** 0.355** [18.66] [18.66] [18.42] [18.22] Size i 0.063** 0.061** 0.060** 0.060** [8.51] [8.25] [7.98] [8.08] Firm FE Yes Yes Yes Yes Year FE Yes Yes Yes Yes Obs. 43,861 43,861 43,867 43,867 Adj. R

56 Table 4: Investment to price sensitivities: Dynamic peers classification This table presents the results from estimations of equation (16) where we change the definition of peers to include dynamic relationships. The dependent variable is investment, defined as capital expenditures divided by PPE. Q i is the market to book ratio of firm i. Q i is the average market to book of the peers of firm i, where peers as defined using the TNIC industries developed by Hoberg and Phillips (2010). The subscript i refers to (the average across) firm i s peers. The other explanatory variables are defined in Table 1. In column (1), peers are defined as firms in the same TNIC industry in year t that we not in year t 1 (new peers). In column (2), peers are defined as firms that were in the same TNIC industry in year t 1 but not in year t (past peers). In column (3), peers are defined as firms in the same TNIC industry in year t that we in year t 1 (old peers). In columns (4) and (5) peers are defined as firms that are not in the same TNIC industry in year t but will be in year t+1 and t+2 respectively (future peers). The sample period is from 1996 to The standard errors used to compute the t statistics (in squared brackets) are adjusted for heteroskedasticity and within firm clustering. All specifications include firm and year fixed effects. Symbols ** and * indicate statistical significance at the 1% and 5% levels, respectively. Investment (capex over lagged PPE) New Past Still Future (+1) Future (+2) (1) (2) (3) (4) (5) Q i 0.022** ** 0.018** 0.014** [7.39] [1.77] [7.02] [5.69] [3.93] CF i 0.156** 0.140** 0.153** 0.142** 0.156** [4.33] [3.87] [4.33] [3.38] [3.37] Size i [1.44] [1.43] [1.25] [1.28] [1.83] Q i 0.071** 0.062** 0.058** 0.072** 0.074** [23.03] [19.33] [18.28] [22.13] [21.21] CF i 0.347** 0.320** 0.314** 0.361** 0.359** [17.26] [15.56] [15.49] [16.66] [15.13] Size i 0.048** 0.043** 0.044** 0.040** 0.035** [4.33] [5.12] [5.53] [4.35] [3.37] Firm FE Yes Yes Yes Yes Yes Year FE Yes Yes Yes Yes Yes Obs. 37,579 34,013 35,533 33,713 28,432 Adj. R

57 Table 5: Investment to price sensitivities: Cross sectional predictions This table summarizes the cross sectional predictions of the model as explained in Section 2.3. The model generates predictions for the co variation between a firm s investment and its own stock price (β) and the covariation between a firm s investment and the price of its peers (η) as a function of four parameters: the fraction of informed trading in a firm s stock π own (π A in the model), the fraction of informed trading in the peer s stock π peer (π B in the model), the private information of managers (γ), and the correlation between the demands for firms products. We present the predictions for three scenarios: (i) managers ignore stock market information: (ii) managers only rely on the information contained in their own stock price, and (iii) managers rely on their stock price and the stock price of their peers. We highlight with an * the predictions that are unique the scenario in which managers learn from the stock prices of their peers (iii). Sensitivity of Investment to: Own stock price (β) Peer stock price (η) Effect of π own π peer γ ρ-1/2 π own π peer γ ρ-1/2 (i) No managerial learning (ii) Narrow managerial learning (iii) Learning from peers + * +/ * * * + * +

58 Table 6: Investment to price sensitivities: Stock price Informativeness (π A and π B ) This table presents the results from estimations of equation (16) across different partitions based on a price informativeness proxy. The dependent variable is investment, defined as capital expenditures divided by PPE. Q i is the market to book ratio of firm i. Q i is the average market to book of the peers of firm i, where peers as defined using the TNIC industries developed by Hoberg and Phillips (2010). The subscript i refers to (the average across) firm i s peers. The other explanatory variables (not reported) are defined in Table 1. The low (high) partition corresponds to the bottom (top) quintile of the partitioning variable (in year t 1). The partitioning variable is peers average (firm) firm specific return variation Ψ i + (Ψ i + ). The partitioning variables are de correlated (superscript + ) as explained in section The sample period is from 1996 to The standard errors used to compute the t statistics (in squared brackets) are adjusted for heteroskedasticity and within firm clustering. We report the economic effects (the coefficient estimate multiplied by the standard deviation of the explanatory variable in the relevant partition) in italic. We report p values corresponding to (unilateral) tests for difference in coefficients across low and high partitions. All specifications include firm and year fixed effects. Symbols ** and * indicate statistical significance at the 1% and 5% levels, respectively. Panel A : Investment to price sensitivities as a function of Ψ i + (Low) (High) (p value) Q i (η) 0.029** 0.051** 0.018** [3.93] [4.29] 2.98% 6.06% Q i (β) 0.070** 0.059** [15.74] [14.95] 13.12% 11.12% Obs. 7,994 7,992 Mean (Ψ i ) Mean (Ψ i ) Panel B : Investment to price sensitivities as a function of Ψ i + (Low) (High) (p value) Q i (η) 0.064** ** [10.31] [1.21] 6.80% 1.24% Q i (β) 0.047** 0.069** 0.000** [16.57] [12.32] 9.87% 11.73% Obs. 8,011 7,982 Mean (Ψ i ) Mean (Ψ i )

59 Table 7: Investment to price sensitivities: Managerial Information (γ) This table presents the results from estimations of equation (16) across different sample partitions based on a proxy for managerial information. The dependent variable is investment, defined as capital expenditures divided by PPE. Q i is the market to book ratio of firm i. Q i is the average market to book of the peers of firm i, where peers as defined using the TNIC industries developed by Hoberg and Phillips (2010). The subscript i refers to (the average across) firm i s peers. The other explanatory variables (not reported) are defined in Table 1. The low (high) partition corresponds to the bottom (top) quintile of insider trading (Insider) in year t 1, defined as the number of insider transactions in year t divided by the total year t s transactions. We limit insider trades to open market stock transactions initiated by the top five executives (CEO, CFO, COO, President, and Chairman of the board). The sample period is from 1996 to The standard errors used to compute the t statistics (in squared brackets) are adjusted for heteroskedasticity and within firm clustering. We report the economic effects (the coefficient estimate multiplied by the standard deviation of the explanatory variable in the relevant partition) in italic. We report p values corresponding to (unilateral) tests for difference in coefficients across low and high partitions. All specifications include firm and year fixed effects. Symbols ** and * indicate statistical significance at the 1% and 5% levels, respectively. Investment to price sensitivities as a function of Insider (γ) (Low) (High) (p value) Q i (η) 0.050** 0.038** 0.036** [6.57] [4.89] 6.15% 4.06% Q i (β) 0.066** 0.062** [16.73] [13.69] 13.92% 12.02% Obs. 9,648 8,759 Mean (Insider )

60 Table 8: Investment to price sensitivities: Peers stock price informativeness (π B ) and Managerial Information (γ) This table presents the results from estimations of equation (16) across different sample partitions based on a proxy for managerial information and three proxies for price informativeness of peers. The dependent variable is investment, defined as capital expenditures divided by PPE. Q i is the market to book ratio of firm i. Q i is the average market to book of the peers of firm i, where peers as defined using the TNIC industries developed by Hoberg and Phillips (2010). The subscript i refers to (the average across) firm i s peers. The other explanatory variables (not reported) are defined in the Table 1. The sample is first partitioned into low and high groups based on the bottom and top quintiles of the (de correlated) peers average price informativeness in year t 1 (Ψ i +, LRMV i +, and APIN i + as defined in section 4.3.1). Then, we further partition the (low and high) groups in two sub groups based on whether the value of Insider is below or above the median. Insider corresponds to the number of insider transactions divided by the total number of transactions. The sample period is from 1996 to The standard errors used to compute the t statistics (in squared brackets) are adjusted for heteroskedasticity and within firm clustering. We report the economic effects (the coefficient estimate multiplied by the standard deviation of the explanatory variable in the relevant partition) in italic. We report p values corresponding to (unilateral) tests for difference in coefficients across low and high partitions. All specifications include firm and year fixed effects. Symbols ** and * indicate statistical significance at the 1% and 5% levels, respectively. Panel A: Investment to price sensitivities as a function of Ψ i + and Insider (γ) Low Ψ i + High Ψ i + Low Insider High Insider p value Low Insider High Insider p value Q i (η) 0.039** ** ** [3.22] [2.36] [5.43] [0.40] 4.13% 1.48% 11.13% 1.16% Q i (β) 0.073** 0.062** ** 0.064** [10.62] [7.85] [8.29] [9.67] 11.38% 10.10% 11.27% 14.78% Obs. 3,943 3,947 3,953 3,960 Mean (Ψ i ) Mean (Ψ i ) Mean (Insider i )

61 Table 9: Investment to price sensitivities: Correlation between demands ( ) This table presents the results from estimations of equation (16) across different sample partitions based on proxies for the correlation between the demands for firms products. The dependent variable is investment, defined as capital expenditures divided by PPE. Q i is the market to book ratio of firm i. Q i is the average market tobook of the peers of firm i, where peers as defined using the TNIC industries developed by Hoberg and Phillips (2010). The subscript i refers to (the average across) firm i s peers. The other explanatory variables (not reported) are defined in Table 1. The low (high) partition corresponds to the bottom (top) quintile of each partitioning variable (in year t 1). We use two proxies. CF correlation is the correlation between a firm s cash flows and the average cash flows of its peers (using quarterly information over the past three years). Similarity is the similarity score (based on firms description of their products) provided by Hoberg and Phillips (2010). The sample period is from 1996 to The standard errors used to compute the t statistics (in squared brackets) are adjusted for heteroskedasticity and within firm clustering. We report the economic effects (the coefficient estimate multiplied by the standard deviation of the explanatory variable in the relevant partition) in italic. We report p values corresponding to (unilateral) tests for difference in coefficients across low and high partitions. All specifications include firm and year fixed effects. Symbols ** and * indicate statistical significance at the 1% and 5% levels, respectively. Investment to price sensitivities as a function product relatedness ( ) CF Correlation Product Similarity (Low) (High) (p value) (Low) (High) (p value) Q i (η) 0.030** 0.052** 0.065** 0.031** 0.050** [3.89] [5.72] [5.74] [4.32] 3.33% 5.35% 3.56% 6.10% Q i (β) 0.058** 0.050** ** 0.047** 0.000** [14.71] [10.95] [16.91] [12.40] 11.48% 8.40% 11.40% 10.24% Obs. 7,546 7,543 8,767 8,720 CF Corr Similarity

62 Table 10: Going public firms In this table, we use a subsample of 1,342 firms that go public at some point during our sample period ( ). We compare the sensitivity of investment to peers stock prices for these firms before and after they go public by regressing investment on peers stock price, a dummy variable equal to one after a firm goes public and the interaction between this dummy variable and peers stock price. Investment is defined as capital expenditures divided by PPE. Peers stock price (Q i ) is the average market to book of firm i s peers, where peers as defined using the TNIC industries developed by Hoberg and Phillips (2010). Post is a dummy variable that equals one after firm i IPO, and zero otherwise. The other control variables (including the firm own stock price post IPO, measured by market to book) are defined in Table 1. In Column 2, we also control for firms sales growth before and after their IPO. The standard errors used to compute the t statistics (in squared brackets) are adjusted for heteroskedasticity and within firm clustering. All specifications include firm and year fixed effects. Symbols ** and * indicate statistical significance at the 1% and 5% levels, respectively. Investment (capex over lagged PPE) IPO Firms (1) (2) Q i 0.026** 0.020** [4.54] [3.44] Post [0.78] [0.67] Q I x Post 0.016** 0.011* [2.93] [2.00] Sales Growth i 0.039** [5.29] Control variables Yes Yes Firm FE Yes Yes Year FE Yes Yes Obs. 5,878 5,728 Adj. R