The Real E ects of Exchange Traded Funds

Transcription

1 The Real E ects of Exchange Traded Funds Frank Weikai Li y Xuewen Liu z Chengzhu Sun x This Draft: December 207 Abstract This paper investigates the e ects of exchange-traded funds (ETFs) on the real e ciency of the underlying securities. We document strong evidence that being held by ETFs increases the sensitivity of a rm s investment to its own stock price. This is consistent with the model prediction on the managerial learning channel. Higher ownership by ETFs increases the rm s stock price informativeness about systematic shocks but may decrease the informativeness about rm-speci c shocks; however, the rm manager cares most and wants to learn from the stock price mainly about systematic shocks in making investment decisions as he already privately knows much about rm-speci c shocks. Consistent with the learning channel, the positive e ect of ETF ownership on investment-to-price sensitivity is stronger among rms in which systematic information is more important and for rms with poorer information environment or higher trading costs. We also nd that rms operating performance improves after ownership by ETFs increases. Our study highlights the positive e ect of ETFs on real e ciency, despite their ambiguous e ect on informational e ciency of the underlyings. JEL classi cation: G4, G23, G3 Keywords: ETFs, Real E ciency, Informational E ciency, Managerial Learning We thank Harrison Hong and Inessa Liskovich for providing Russell index membership data. y Singapore Management University, Lee Kong Chian School of Business ( wkli@smu.edu.sg) z Hong Kong University of Science and Technology ( xuewenliu@ust.hk ) x Hong Kong University of Science and Technology ( csunab@connect.ust.hk)

2 Introduction The exchange-traded fund (ETF) industry has been growing spectacularly in the recent decade. According to Investment Company Institute, there were,75 ETFs managing 2.84 trillion USD in the US market at the end of April, 207. Around 0% of the market capitalization and 36% of the trading volume of securities traded on US stock exchanges are attributable to ETFs. While undoubtedly popular among investors, ETFs have been found to possibly destabilize nancial markets by increasing systemic risk and inducing non-fundamental volatility and excess co-movement. 2 The debate on the bene ts and the potential destabilizing e ects of ETFs is only just starting and a fuller understanding of the overall welfare implications of ETFs is critical for regulators. 3 As pointed out in a recent survey by Ben-David, Franzoni and Moussawi (206), missing to date is a welfare analysis exploring the net e ect of ETFs on market participants. So far the academic research has largely focused on studying the e ects of ETFs on the informational e ciency of the underlying securities. The empirical evidence is inconclusive. On the one hand, Israeli, Lee and Sridharan (207), among others, document the dark side of ETFs and nd that rms that are widely held by ETFs experience a deterioration in the informational e ciency regarding the rm-speci c information. On the other hand, Glosten, Nallareddy, and Zou (206) nd that ETF activity facilitates the timely incorporation of systematic earnings information into stock prices. However, the net e ect of ETFs on the informational e ciency of their constituents is ambiguous and di cult to evaluate. While studying the e ects of ETFs on informational e ciency is clearly important, a more complete examination of the welfare implication of ETFs must include a study of their e ects on real e ciency. In fact, as Bond, Edmans and Goldstein (202) argue, price e ciency should be evaluated as the extent to which prices re ect information useful for the e ciency of real decisions, rather than the extent to which they forecast future cash ows. In this paper, we deviate from the line of the prior studies on ETFs and contribute to the debate by studying from a di erent perspective the real e ciency. We document strong evidence of the positive e ects of ETFs on the real e ciency of the underlying securities. We rst develop a simple theoretical model to show that a rm s investment is likely to be more responsive to its own stock price when rm ownership by ETFs increases. This prediction is based on two premises. First, an increase in ownership by ETFs results in See Ben-David, Franzoni and Moussawi (206). 2 See, e.g., Ben-David, Franzoni and Moussawi (205) and Da and Shive (206). 3 See, e.g., Exchange-traded funds: Emerging Trouble in the Future? Regulators are worried that a trendy new product will sow instability (The Economist, Oct 25th, 204).

3 an increase in the rm s stock price informativeness about systematic shocks but possibly a decrease in the informativeness about rm-speci c shocks. Inclusion in ETFs introduces an arbitrage mechanism that minimizes the price discrepancy between ETFs and the underlying securities. The noise trader risk of a underlying stock is therefore reduced and thus informed speculators who have private information about the systematic shocks of a rm (e.g., the beta of the rm s projects) trade more aggressively and consequently inject more private information into the rm s stock price. Some informed speculators who originally acquire information about rm-speci c shocks may even switch to acquire information about systematic shocks. Second, the rm manager has an information advantage over outside investors about rm-speci c shocks (Benhabib, Liu and Wang (207)) and hence learns from the rm s stock price mainly about systematic shocks. 4 Therefore, when rm ownership by ETFs increases, the rm s investment becomes more responsive to its own stock price. Using a large sample of US equity ETFs from 2003 to 203, we nd strong evidence of an increase in investment-price sensitivity being associated with a higher degree of ETF ownership. A one-standard-deviation increase in Tobin s Q raises corporate investment by 4.5 percentage points for rms in the bottom quartile of ETF ownership and by 5.0 percentage points for rms in the top quartile of ETF ownership. This relative increase in investment represents 5% of the mean investment level. This e ect is robust to controlling for total institutional ownership, employing various estimation methodologies, as well as an extensive list of control variables. Since the majority of ETFs are passive investment vehicles tracking well-de ned benchmark indices, ETF ownership should be largely exogenous to other rm characteristics a ecting investment-price sensitivity. Nevertheless, to address endogenous concerns, we exploit the Russell index reconstitution as an exogenous shift in ETF ownership, and use the Regression Discontinuity Design to show that ETFs have a causal impact on the investment-price sensitivity of the underlying securities. To further understand the channels behind the aforementioned empirical ndings, we ask why the rm manager does not simply learn about the systematic information from the ETF prices and why the rm s investment decision relies more on its own stock price as ETF ownership increases. Our empirical exercises verify two channels of mechanism as our theoretical model predicts. First, the stock price contains additional information about systematic factors (e.g., the beta of the rm s projects) beyond that contained in the ETF prices and the amount of additional information is increasing in ETF ownership. Second, a manager may simply pay more attention to his own rm s stock price than to the ETF 4 As argued by Bond et al. (202), a rm manager may be the individual who is most informed about the rm s own fundamentals, but outside investors may possess an advantage over the manager in collecting and interpreting external information such as the state of the economy or industry demand. 2

4 prices, considering that on average a stock is held by more than 20 ETFs. The managerial learning explanation developed based on our model bears several crosssectional implications. First, the increase in investment-price sensitivity associated with a higher ETF ownership should be stronger among rms in which systematic information is more important. Using a stock s market beta as a proxy for the importance of systematic information, we nd evidence consistent with this conjecture. Second, the e ect of ETF activity on investment-price sensitivity should be more pronounced for rms with poorer information environment. The reason is that the improvement in stock price informativeness resulting from a higher ETF ownership for such rms should be more signi cant, considering that for other rms the stock price is reasonably informative even without being included in ETFs and the improvement cannot be substantial. Using rm size and analyst coverage as proxies for rms information environment, we nd consistent evidence. In a similar vein, ETFs improve investment-price sensitivity more for stocks that are more costly to trade. Finally, we test two other implications of our managerial learning explanation. First, since a higher ETF ownership results in an improvement in the quality of information relevant to real investment decisions for the rm manager, the rm can make better investment decisions, which should translate into higher future operating performance. Second, the managerial learning literature documents that a rm learns not only from its own stock price but also from its peers stock prices in making investment decisions, as the latter can contain industry-wide information not fully captured by its own stock price. 5 As a higher ETF ownership facilitates the incorporation of systematic information into the rm s own stock price, this should reduce the rm s learning from its peers stock prices. Our evidence supports these predictions. We explore several alternative explanations for our main ndings. First, recent literature documents that passive institutional ownership may improve corporate governance quality (Appel, Gormley and Keim, 206). The improvement in governance associated with a higher ETF ownership could by itself strengthen the relation between investment and stock prices. If this mechanism plays a role in our ndings, one should expect the increase in investment-price sensitivity to be especially large for rms with poor prior governance. However, we do not nd support for this prediction. Using various rm-level measures of corporate governance quality, we nd that ETFs improve investment-price sensitivity only among rms with strong corporate governance to begin with. Another alternative explanation for our ndings could be that ETF ownership enhances investors ability to forecast the cash ows of new investments. This is plausible because some 5 See Foucault and Frésard (204) and Dessaint, Foucault and Matray (206). 3

5 studies have shown that rms with a higher institutional ownership have better disclosure quantity and quality, 6 thus enabling investors to form more accurate forecasts. As a result, the stronger correlation between investment and stock prices associated with a higher ETF ownership may not be because managers use stock prices as a source of information but rather because investors can evaluate the net present value of new investments for these rms more precisely. If this mechanism is at work, the e ect of ETFs on investment-to-price sensitivity should be particularly strong for rms that experience a relatively large increase in disclosure quality. Using analyst forecast accuracy as a proxy for disclosure quality, however, we do not nd such an e ect. The third alternative explanation for our ndings could be the nancial constraint story. Firms held by more ETFs could have a higher degree of eased access to external nance and could face less nancial constraints. This could strengthen the investment-to-price sensitivity by raising investment when new growth opportunities arise. However, our evidence that ETF ownership does not a ect the equity issuance of a rm or the investment-cash ow sensitivity suggests that relaxed nancial constraints are unlikely to explain our ndings. While we cannot completely rule out alternative explanations for our main results, our combined ndings that ETF ownership increases a rm s investment sensitivity to its own stock price and decreases a rm s investment sensitivity to its peers prices are more uniquely predicted by the managerial learning channel and are di cult to be explained by alternatives. For example, the story of an improvement in corporate governance would predict that managers under stricter governance also learn more from peers prices which contain valuable information about industry investment opportunities. Similarly, if ETF ownership is merely a proxy for an improved information environment, investors should also be able to better evaluate the impact of a rm s investment decisions on its peers value, leading to a higher, not lower, investment sensitivity to peers stock prices. Also, if the e ect of ETF ownership on investment-price sensitivity is driven by the nancial constraint channel, rms investment under relaxed nancial constraints should respond more strongly to industry investment opportunities conveyed by peers stock prices, giving a higher, not lower, investment sensitivity to peers stock prices. The rest of this paper is organized as follows. Section 2 discusses how our paper is related to and contributes to the existing literature. Section 3 formulates a simple model featuring managerial learning from prices to develop testable hypotheses. Section 4 describes the sample and summary statistics. Section 5 presents empirical ndings. In Section 6, we probe alternative explanations for our ndings. Section 7 concludes. 6 See, e.g., Boone and White (205) and Bird and Karolyi (206). 4

6 2 Related Literature and Our Contribuiton Our paper contributes to two strands of the literature. First, it contributes to the growing literature examining the e ect of ETFs. Several papers have documented the dark side of ETF investing as non-fundamental demand shocks might be transmit from the ETFs to their underlying securities. Theoretically, Bhattacharya and O Hara (206) show that information feedback between ETFs and their constituents could cause propagation of shocks unrelated to fundamentals and market instability, especially for ETFs that track hard-to-trade assets. Empirically, Ben-David, Franzoni, and Moussawi (206) provide evidence that arbitrage activities between ETFs and their underlying stocks increase the latter s volatility. Da and Shive (206) document that higher ETF trading activity leads to excess return co-movement among the constituent stocks. Hamm (204) and Israeli, Lee and Sridharan (207) argue that ETFs can deteriorate liquidity for their constituents. On the bright side, Subrahmanyam (99) and Cong and Xu (206) show theoretically that initiation of basket securities could reduce speculators incentives to acquire and trade on asset-speci c information, but facilitate trading on systematic information. Empirically, Boehmer and Boehmer (2003) nd that the initiation of three ETFs increases liquidity and market quality. Dannhauser (206) nds that corporate bond ETFs have a long-term positive valuation e ect on their constituents. Glosten, Nallareddy, and Zou (206) document that ETF trading increases informational e ciency for stocks with weak information environments. Li and Zhu (207) nd that due to the high liquidity and creation-redemption mechanism, ETFs could relax short-sale constraints for di cult-to-short stocks. Di erent from these existing contributions in this literature, our paper is the rst to study the real e ciency of ETF activity. By showing that ETFs improve the real e ciency of their constituents through facilitating the incorporation of new systematic information valuable to managers, our paper highlights the importance of distinguishing between real e ciency and informational e ciency in examining the e ects of ETFs. Although ETFs may have ambiguous overall e ects on informational e ciency as they may have opposite impacts on rm-speci c information and systematic information as documented earlier, we show that the e ect on real e ciency is always positive considering that systematic information is likely the incremental information that rm managers want to learn from stock prices. Second, this paper contributes to the long-standing and important debate on whether nancial markets a ect the real economy or is merely a sideshow. A list of theory papers have suggested the managerial learning hypothesis, which argues that when nancial speculators trade on their private information about a rm s future performance to make a pro t, the stock price aggregates a diverse set of information which is useful to real-investment 5

7 decision makers. 7 Some of the earlier empirical studies do not nd supporting evidence (e.g., Morck, Shleifer and Vishny, 990). In contrast, numerous recent works have documented evidence supporting the managerial learning hypothesis. Luo (2005) nds that managers are more likely to cancel acquisition plans when the market response to the deal announcement is negative. Zuo (206) documents that a manager s belief about rm fundamentals is positively a ected by stock price change. The majority of empirical studies on the managerial learning hypothesis use the sensitivity of corporate investment to stock price as evidence of the real e ect from nancial markets (Chen, Goldstein and Jiang, 2007; Barker and Whited, 200; Foucault and Frésard, 202; Foucault and Frésard, 204). More recent studies have documented supporting evidence for the managerial learning channel by using a rm s cross-listing status and the staggered enforcement of insider trading laws across countries to proxy for stock price informativeness (Foucault and Frésard, 202; Edmans, Jayaraman and Schneemeier, 206). Besides learning from the rm s own stock price, managers are also found to learn additional information from peers stock prices (Foucault and Frésard, 204). An important theoretical argument developed recently in this literature is that nancial markets and rm managers have a comparative advantage in producing di erent types of information (Bond, Edmans and Goldstein, 202; Benhabib, Liu and Wang, 207); managerial learning from stock prices does not mean that managers are less informed than outside investors, but rather means that managers want to learn some incremental information that nancial markets have a comparative advantage to produce. Our empirical investigation on the e ect of ETFs on the informational role of stock prices is an ideal setting to test the theory. As ETF activity changes the composition of systematic vs. rm-speci c information in a stock price, our paper provides supporting evidence that real decisions depend on the type of information in a price, rather than only the total amount of information. 8 3 Theoretical Model and Hypothesis Development This section presents a simple model to organize all of the empirical hypotheses in a uni ed framework and in a structural manner. The model also helps clarify the economic intuition and guide the empirical speci cation and interpretation. For these purposes, we keep the model simple as in Dessaint et al. (206) while relegating more microfoundation of the model to Appendix A. The model is sketched as follows. Conditional on learning from ETF prices, the rm 7 See, e.g., Dow and Gorton (997) and Subrahmanyam and Titman (999). 8 See also Goldstein and Yang (207). 6

8 manager learns more from the rm s stock price in making investment decisions when the rm is more widely owned by ETFs. This is because a higher degree of ETF ownership results in the stock price s informaiveness about the systematic risk being higher while the rm manager already has precise information about the rm-speci c risk. The reason is that inclusion in ETFs, introducing an arbitrage mechanism that minimizes the price discrepancy between ETFs and the underlying securities, lowers the noise trader risk and thus encourages informed traders having private information about systematic risk (for example, the beta of the rm) to conduct price discovery. 3. A Simple Model of Managerial Learning There are two dates: t = and 2. At t =, rm j has a real investment project (or a growth opportunity). After making investment K j at t =, the rm realizes the project s payo at t = 2 as Y (K j ) = ( m j j ) K j, where m j denotes the macro-related or industry-related productivity shock and j denotes the rm-speci c productivity shock, and measures the importance of shock m j (relative to j ). For example, m j takes the form of m j = j a or m j = a j, where a is the common productivity shock to all rms and j represents the impact factor of the common productivity shock to rm j. For simplicity and without loss of generality, we set = in the main analysis of our model. The prior distribution of m j is m j N ( m ; = m ). The prior distribution of j is j N ( ; = ). The cost of the investment is C (K j ) = 2 K2 j. The (gross) interest rate between t = and t = 2 is normalized to. 3.. The rm s information At t = when the manager of rm j makes the investment decision, he has several pieces of information. First, he has private signals regarding j and m j, namely, s = j " with " N (0; = s ) and s m = m j " m with " m N (0; = sm ). 7

9 Second, the price of ETF(s) with a stake in the rm is available, which gives (imperfect) information about m j, that is, q = m j e m;j with e m;j N (0; = qm ), where q is called the ETF price-based signal about rm j (e.g., the ETF return coupled with the historic beta of rm j). For example, q can be interpreted as the information based on the historic beta of rm j coupled with the available macro-level or industry-level information inferred from the ETF price, while the relevant fundamental m j depends on rm j s future/forward-looking beta. The rm manager might pay only limited attention to the ETF price signal. Speci cally, under limited attention, as in Peng and Xiong (2006), the rm manager s signal is instead q 0 = q M j with M j N (0; = q 0 q), where q 0 q measures the degree of attention. A higher q 0 q corresponds to a higher degree of attenion, and q 0 q = corresponds to full attention (i.e., M j = 0). 9 Third, the stock price of rm j is available. In the stock market of rm j, there are two types of speculators: those who have private information about m j and those who have private information about j. Importantly, speculators also know the public signal q (containing information about m j ) in trading the stock. As in Grossman (976) and Hellwig (980), the stock price aggregates the dispersed information held by speculators and thus reveals information about m j and j. The stock price also incorporates the public signal q. In Appendix A, we show that the stock price of rm j at t =, denoted by p j, is given by 0 p j 2 q = 3 m j 4 j n j, () where 0,, 2, 3 and 4 are coe cients, and n j N (0; = n ) is the endogenous degree of noise trading at t =. Lemma follows. Lemma Firm j s stock price at t = is given by (). Let! denote the ETF ownership of rm j (i.e., the proportion of rm j s shares held by ETFs). We examine how! a ects the stock price s information content about m j and j. By (), the stock price p j (combined with q) provides an additional signal about m j, that is, p(q; p j ) = m j % m;j with % m;j N (0; = pm ) (2) 9 The rm manager is rational and is fully aware that he may su er limited attention. 8

10 where p(q; p j ) ( 0 2 follows. 4 ) p j 2 q, % 3 m;j 4 ( j )n j, and pm = n. Lemma Lemma 2 The stock price provides an independent signal (orthogonal to signal q) about m pm Its precision, pm, is increasing in ETF ownership! (i.e., > The intuition behind Lemma 2 is as follows. A higher degree of inclusion in ETFs causes that the stock price will converge to its fundamentals more likely in the next period, thanks to the arbitrage mechanism introduced by inclusion in ETFs. Consequently, informed speculators of m j face less noise trader risk in the next period, and thus these speculators will trade more aggressively in the current period, crowding out the noise traders and injecting more private information about m j into the stock price. Therefore, the stock price s informativeness increases. There is another channel through which the stock price s informativeness about m j can increase. As ETF ownership increases, more speculators may endogenously choose to acquire private information about m j ; that is, the number of informed speculators of m j may also increase with!. Because signal p is orthogonal to signal q and hence provides additional information about m j beyond that contained in q, pm measures the amount of additional information. Formally, we have which is increasing in!. V ar (m j jq; p j ) V ar (m j jq) = pm, Similarly, the stock price p j (combined with q) provides an additional signal about j, that is, p(q; p j ) = j % ;j with % ;j N (0; = p ), (3) where p(q; p j ) ( 0 3 m ) p j 2 q, % 4 ;j 3 (m j m )n j and p = m. 4 n Lemma 3 follows. Lemma 3 The stock price provides an independent signal about j. Its precision, p, is decreasing or slightly increasing in ETF ownership!. The intuition behind Lemma 3 is as follows. Less noise trader risk in the next period due to inclusion in ETFs results in an increase in the stock price s informativeness about j. However, there is a counterforce: a higher ETF ownership may induce some informed speculators who originally acquire information about j to switch to acquiring information about m j, so the number of informed speculators of j goes down, which results in a decrease in the stock price s informativeness about j. 9

11 We also consider a special case of (). If none of the nancial speculators has private information about m j, then they can only extract information about m j from the ETF pricebased signal q in trading the stock. For simplicity and without loss of generality, it is also assumed that none of the nancial traders has private information about j. In this case, the stock price becomes 0 p j 2 q = n j. (4) That is, the stock price is a function of q and noise trading n j. In other words, the stock price p j is a noisy signal about q, namely, p (p j ) = q 2 n j, where p (p j ) 0 p j, p (p j ) N (q; = pq ), and pq = n. Therefore, for this special case, the stock price contains less information about m j than the ETF price-based signal. Considering that n is increasing in! (i.e., inclusion in ETFs also reduces the noise trader risk in the current period; see Appendix A), pq is increasing in!. However, V ar(m j jq;p j ) = V ar(m j jq) = m qm, which is independent of pq or! The rm s investment decision We work out the rm manager s investment decision. The rm manager s information set at t = is I = fp j ; q 0 ; s ; s m g. Hence, maxe (m j j ) K j K j 2 K2 j ji To have a clean analysis of (5), we proceed with two cases. =) K j = E [m j j ji] (5) Case : The rm manager has full attention to q and there are some informed speculators trading on their private information about m j. In this case, q 0 = q and the stock price p j is given by (). Then, K j = E [m j j jp j ; q; s ; s m ] = 0 p j 2 q 3 s 4 s m (6) 0

12 where 0 is a constant coe cient, and = 2 = 3 = 4 = pm p (7) m qm pm sm 3 s p 4 pm 2 m qm pm sm 3 s s p sm : m qm pm sm qm m qm pm sm p s p 2 4 When s result:! (the rm manager has perfect information about j ), we have a cleaner lim = s! lim 2 = s! lim 3 = : s! pm m qm pm sm 3 pm 2 qm m qm pm sm 3 m qm pm sm Considering that pm is increasing in! (Lemma 2), is increasing in! and 2 is decreasing in! (by noting that 2 is negative). 0 Proposition follows. Proposition Suppose the rm manager has full attention to the ETF price. If in the nancial market there are informed speculators of m j and if the rm manager s private information about j is precise enough, the rm manager s investment decision is more responsive to the stock price p j and less responsive to the ETF price as the ETF ownership of the stock! > 0 < 0). As the ETF ownership of the stock! increases, the stock price contains more information about m j and less information about j. However, the rm manager already has precise private information about j and does not rely too much on the stock price to learn j anyway. Therefore, the rm manager s investment decision becomes more responsive to the qm Also, it is easy to show that has the following additional properties: < 0; when qm is su ciently qm < 0; when m is not m < 0 m < 0. Case 2: The rm manager pays limited attention to q and there are no informed spec- 0 Coe cients and 2 3 also change with!, but their e ects are dominated by the terms before them 3 (see the proof in Appendix A).

13 ulators trading on private information about m j. In this case, the stock price is given by (4). Because the stock price contains less information about m j than the ETF price-based signal q, the rm manager would not learn from the stock price at all if he has full attention to the ETF price. However, because the rm manager only pays limited attention to q (that is, he has only a noisy signal about q), he will learn from the stock price. Denote q = = m= qm. Formally, we have K j = E [m j j jp j ; q 0 ; s ; s m ] = 0 p j 2 q 0 3 s 4 s m, where = qm pq m qm sm q pq q 0 q 2 (8) 2 = qm q0q. m qm sm q pq q 0 q Considering that pq is increasing is!, Proposition 2 follows. Proposition 2 Suppose the rm manager pays limited attention to the ETF price (i.e., q 0 q < ). Even if in the nancial market there are no speculators who have and trade on private information about m j, the rm manager s investment decision is more responsive to the rm s stock price and less responsive to the ETF price as the ETF ownership of the stock! > 0 < 0). The intuition behind Proposition 2 is easy to understand. As ownership by ETFs of the stock increases, the stock price informativeness about q increases. In other words, the stock price becomes more correlated with the ETF price (i.e., V ar(qjp j is increasing in! ) considering that pq is increasing in!). Because the rm manager pays limited attention to the ETF price, his investment decision becomes more responsive to the stock price. Also, it is easy to show that has the following additional property: when q 0 q is su ciently q 0 q < The rm s pro t Now we can examine the ex-ante expected pro t of the rm. The rm s realized pro t at t = 2 is (m j j ) E [m j j ji] 2 2 (E [m j j ji]) 2.

14 By exploiting the law of iterated expectations, the ex-ante unconditional expected pro t of the rm, denoted by, is ( pm ; qm ; sm ; s ; p ) = E 2 (E [m j j ji]) 2 = ( 2 m ) 2 m m qm pm sm : s p When s! (the rm manager has perfect information about j ), we have ( pm ; qm ; sm ; s ; p ) = 2 ( m ) 2 : m m qm pm sm Considering that pm is increasing in! (Lemma 2), is increasing in!. Proposition 3 follows. Proposition 3 If the rm manager s private information about j is precise enough, the rm s future expected pro t is increasing in rm ownership by ETFs! > Proposition 3 shows the information value for the rm. When the rm has a more precise signal about m j or j, it makes a better investment decision because its investment can be more closely aligned with the realized productivity shock; otherwise, there is more severe under- or over-investment, reducing the rm s pro t. 3.2 Empirical Predictions We derive several direct predictions of the model. First, based on Propositions and 2, Prediction follows. Prediction : A higher degree of ETF ownership of a rm leads to the rm s investment responding more strongly to the rm s own stock for rm learning from the ETF price. > 0), after controlling In particular, Propositions and 2 separate two channels of mechanism for Prediction. Proposition together with Lemma 2 implies the rst channel. Prediction 2 (Channel ): The increase in investment-stock price sensitivity associated with a higher ETF ownership can occur through the channel where the stock price contains additional information about systematic risk beyond that contained in the ETF price (i.e., > V ar(m j jq;p j ) V ar(m j ) and the amount of additional information is pm increasing in ETF ownership (i.e., > 3

15 To test the rst channel, the model also gives a cross-sectional prediction. If the ETF price-based signal already conveys a lot of information about m j, informed speculators can add little additional information to the stock price. So the rm manager can simply learn from the ETF price, rather than from the stock price. Formally, qm Proposition. Prediction 3 follows. < 0 following Prediction 3: For a rm with its beta being less time-varying and more stable (i.e., qm is higher), the positive e ect of ETF ownership on investment-stock price sensitivity is weaker qm < 0). Proposition 2 implies the second channel. Prediction 4 (Channel 2): The increase in investment-stock price sensitivity associated with a higher ETF ownership can occur through the channel where the stock price does not contain additional information about systemic risk beyond that contained in the ETF price (i.e., = V ar(m j jq;p j ) V ar(m j ) but the rm manager pays limited attention to jq) the ETF price (i.e., q 0 q < ). For this channel, a higher degree of attention leads to the positive e ect of ETF ownership on investment-stock price sensitivity becoming weaker q 0 q < 0). Next, either through the rst or the second channel or both, the model implies some cross-sectional predictions. In the main model, for simplicity, we have set = (where measures the relative importance of the systematic shock m j ). If is not set as, it is easy to derive > 0. Prediction 5 follows. Prediction 5: The increase in investment-stock price sensitivity associated with an increase in ETF ownership is stronger among rms in which systematic information (relative to rm-speci c information) is more > 0). Moreover, in a weaker information environment (a lower m ), the e ect should be stronger. Formally, m < 0. Prediction 6 follows. Prediction 6: The increase in investment-stock price sensitivity associated with an increase in ETF ownership is stronger among rms with a weaker information environment m < 0). To avoid complicating the algebra, we have assumed in the main model that the rm does not learn from other rms stock prices. It is easy to relax this assumption by adding 4

16 another signal which provides noisy information about m j. Denote by 5 the coe cient in front of this new signal for the investment decision (6). This signal has a similar e ect as signal q. < 0 in Propositions and 2, Prediction 7 follows. Prediction 7: A rm s investment responds less to its peers stock prices when its ownership by ETFs increases (i.e., d 5 d! < 0). Finally, the model has implications for rms operating performance. By Proposition 3, Prediction 8 follows. Prediction 8: A rm s future operating performance increases with its ownership by > 0). 4 Data and Summary Statistics 4. Sample Construction We obtain a list of all U.S. domestic equity ETFs that physically replicate the indices. We do so by rst merging all ETFs (etf ag=f) in the CRSP mutual fund database with securities in CRSP monthly stock le with the share code of 73. We parse the fund name manually to tease out non-equity or non-domestic ETFs. 2 Finally, we limit our analysis to ETFs that physically replicate the indices by ensuring at least 20 underlying stocks with holdings information available from the Thomson Reuters Mutual Fund holdings database (S2). Our nal sample contains 343 ETFs from 2003 to 203. We construct ETF ownership (ET F it ) of each stock i using the following equation: ET F it = P J j= SHARES ijt T SO it where SHARES ijt is the number of shares of rm i held by ETF j at the end of year t and T SO it is rm i s total number of shares outstanding at the end of year t. We merge the ETF ownership of each stock with data on stock returns, accounting information, analyst coverage and earnings forecast at the scal year end obtained from the Center for Research in Security Prices (CRSP), Compustat and I/B/E/S, respectively. We restrict Most ETFs in the U.S. tend to physically replicate their underlying index. The Investment Act of 940 requires ETFs to hold 80% of their assets in securities matching the fund s name. 2 We search for terms in fund names such as international, world, ex-us, treasury, or municipal. 5

17 our sample to common stocks (share codes 0 and ) traded on NYSE, AMEX and NAS- DAQ, and exclude nancial (SIC codes ) and utility industries (SIC code 4200). To control for the confounding e ect of institutional ownership, our sample only includes rm-year observations with institutional ownership data available from the Thomson-Reuters Institutional Holdings (3F) database. After excluding observations without the necessary data (investment and standard control variables) for our analysis, our nal sample contains 26,270 rm-year observations from 2003 to Summary Statistics Table reports the summary statistics of the variables used in our analysis. Appendix B provides their de nitions in detail. We winsorize all variables at % and 99% of their respective distributions to mitigate the potential e ect of outliers. Figure shows that the average ETF ownership in our sample has been rising continuously, from about.2% in 2003 to 5.0% in 203, with a mean value (standard deviation) of 2.7% (2.6%). These numbers are comparable to the ones reported in Israeli, Lee and Sridharan (207). The increase in ETF ownership is consistent with the tremendous investment ow to ETF markets in the recent decade. The dependent variables used in our analysis consist of the sum of capital expenditures and R&D expenses (CAPXRND), capital expenditures (CAPX) and R&D expenses (RND), all scaled by lagged total asset. The means (standard deviation) of these investment measures are 0. (0.2), 0.05 (0.06) and 0.05 (0.0). This indicates that a rm s annual investment represents about % of its total assets, and is attributed equally to capital expenditures and R&D expenses. 5 Empirical Analyses 5. ETF Ownership and Investment-Price Sensitivity Investment sensitivity to stock price, as measured by the correlation between corporate investment and Tobin s Q, is a commonly used measure of managers (unobserved) learning from stock price when making investment decisions (Chen, Goldstein and Jiang, 2007; Foucault and Frésard, 202). Adopting this standard measure, we estimate the following 3 Our sample ends in 203 because we need to include the stock return for the next three years as an important control variable in the investment-q regression. Our result remains if we drop that control and extend the sample period to

18 baseline equation to test whether ETF ownership (ET F it ) positively a ects the sensitivity of a rm s investment (Investment it ) to its own (normalized) stock price (Q it ): Investment it = t i Q it 2 Q it ET F it 3 ET F it X it it ; (9) where t and i represent the year- and rm- xed e ects, respectively. Investment it is rm i s investment in year t measured by the sum of capital expenditures and R&D expenses, capital expenditures and R&D expenses, all scaled by lagged total assets. Q it is rm i s Tobin s Q in year t, de ned as the market value of equity plus the book value of asset minus the book value of equity scaled by the book value of asset at the end of year t. The key independent variable is the interaction term of Q it and ET F it, and the coe cient 2 captures the incremental e ect of ETF ownership on investment-price sensitivity. If ETF activity indeed increases the sensitivity of corporate investment to stock price as we hypothesized, we should observe a signi cant and positive 2. We follow the existing literature to control for rm characteristics X that could potentially a ect investment-price sensitivity and may also correlate with ETF ownership (Bushee, 998; Lamont, 2000; Bates, 2005; Richardson, 2006; Biddle and Hilary, 2006; Almeida and Campello, 2007; Beatty, Liao and Weber, 200; Panousi and Papanikolaou, 202). They consist of () rm size and its interaction with Tobin s Q (SIZE it and SIZE it Q it ); (2) (residual) institutional ownership and its interaction with Tobin s Q (INST R it and INST R it Q it ); (3) cash ow and its interaction with Tobin s Q (CF it and CF it ET F it ); (4) three-year future return, RET it3 ; (5) other control variables including the reciprocal of total assets, book leverage, return on assets, cash holding and sales growth (=ASSET it, LEV it, ROA it, CASH it and SG it ). The inclusion of institutional ownership enables accounting for the constraints that institutional investors imposed on rm investment. We do not have signed prediction on it because the e ect of institutional ownership on corporate investment could either be positive or negative. 4 We also include its interaction with Tobin s Q because institutional ownership could a ect the informational e ciency of stock price (Boehmer and Kelley, 2009) and hence investment-price sensitivity. In addition, a higher institutional ownership could improve corporate governance and force managers to make investment decisions that are more aligned with shareholder value. Given the positive correlation between institutional ownership and ETF ownership, we follow Glosten, Nallareddy and Zou (206) and use the residual 4 On one hand, institutional investors can lead to investment reduction by restricting managers overinvestment tendencies or forcing managers to reduce long-term investments for short-term bene ts (Bushee, 998; Ferreira and Matos, 2008). On the other hand, they can also lead to an increase in investment by mitigating managers under-investment behaviors due to risk aversion (Bushee, 998; Panousi and Papanikolaou,202). 7

19 institutional ownership INST R it (after orthogonalizing it w.r.t. ETF ownership) as control. Cash ow is included as a control because a large literature documents the positive sensitivity of corporate investment to cash ow (Fazzari et al., 988). Prior literature also documents that managers tends to increase investment when the rm is overvalued by the stock market (Baker, Stein and Wurgler, 2003; Polk and Sapienza, 2009). We use a rm s stock return for the next three years to control for the misevaluation channel and expect a negative coe cient. Following Chen, Goldstein and Jiang (2007), we also add the reciprocal of total assets to control for the mechanically positive relation between investment and the regressor caused by the same de ator (ASSET it ). Table 2 presents the regression results. Consistent with prior studies, a rm s investment shows a signi cant positive relation with its own stock price for all three measures of investment. Column () shows that for a rm not held by any ETFs, a one-standard-deviation increase in Tobin s Q leads to an increase of about 4.4 percentage points in rm s investment measured by the sum of capital expenditures and R&D expenses. Columns (2) and (3) suggest that both capital expenditures and R&D expenses are positively related to Tobin s Q. Consistent with the hypothesis, the coe cient on our key independent variable (Q it ET F it ) is positive and signi cant for all three investment measures, with a magnitude of 0.05 (t-stat=3.92) for CAP XRND it, 0.04 (t-stat=2.70) for CAP X it and (tstat=3.5) for RND it. To see the economic e ect, consider a one-standard-deviation increase in Tobin s Q (.30). This is associated with an increase of 4.5 percentage points in corporate investment for rms in the bottom quartile of ETF ownership, against an increase of 5. percentage points for rms in the top quartile of ETF ownership. This relative increase in investment represents 5% of the mean investment level. Moreover, 2 is similar in magnitude for capital expenditures and R&D expenses. This suggests that ETF activity has a similar positive e ect on the sensitivity of capital expenditures and R&D expenses to stock price. Our baseline results are robust when we replace the residual institutional ownership with the raw institutional ownership measure, when we vary the estimation methods by replacing rm- xed e ects with industry- xed e ects or excluding all control variables, and when we use alternative de nitions of corporate investment (e.g., scaled by property, plant and equipment). The strong and robust positive e ect of ETF ownership on investment-price sensitivity supports our main argument that ETF ownership of a rm has e ects on its real investment behavior. One thing worth noting is that although ETF ownership increases rm s investment sensitivity to its own stock price, the overall e ect of ETF ownership on the rm s investment 8

20 is negative with a magnitude of ( 3 2 AverageQ it ) = 0:53). Similarly, institutional ownership exerts an overall negative e ect on corporate investment. This is consistent with the idea that institutional investors discipline managers overinvestment tendencies through various governance mechanisms. The coe cients on other control variables have the expected signs, except for the coe cient on cash ow. The positive investment-cash ow sensitivity as documented by the literature is only observed for capital expenditures, but not for R&D expenses. Lastly, we want to point out that in the regression (9), ideally, we would like to control for managers own information set (i.e., fs m ; s g as in our model). But because managers private information is not observable to econometricians, we cannot control for it. However, the omission of managers own information, a common issue in this literature, will only cause the true e ect of ETFs on investment-price sensitivity to be underestimated Do Managers Learn from Stock Prices in addition to ETF Prices and Why? Our goal is to show that a rm manager learns more from the information contained in his own rm s stock price when the rm s ownership by ETFs increases (or his information set improves). However, the result in the last subsection does not provide support for this point yet. The reason is that we did not control for a manager s learning from ETF prices. As a result, we cannot rule out the possibility that the manager learns only from the ETF prices and not from his own stock price. Investment responds more to the stock price simply because the stock price becomes more correlated with the ETF prices when its ETF ownership increases. More concretely, let us consider the following scenario: the stock price does not contain more (systematic) information than the ETF prices and the manager learns only from the ETF prices. If the stock price becomes more correlated with the ETF prices when the stock s ETF ownership increases, investment that is only responsive to the ETF prices mechanically will appear to be more responsive to the stock price. In that 5 Intuitively, after controlling for a rm manager s private rm-speci c information, the manager mainly infers systematic information from the stock price; an increase in ETF ownership, resulting in an increase in the stock prices informativeness about systematic factors, means that the response of the investment to the stock price is stronger (i.e., 2 is positive). Without controlling for the manager s private information, however, a counterforce is introduced. The manager infers from the stock price rm-speci c as well as systematic information; because an increase in ETF ownership can slightly reduce the stock prices informativeness about rm-speci c shock, investment sensitivity to the stock price will drop slightly (i.e., 2 is biased toward zero). In short, if anything, the omission of managers private information will cause the true e ect of ETF ownership on investment-price sensitivity to be underestimated (formally, in our model, without controlling for s, the term p s p in (7) becomes p p, which is more rapidly decreasing in!). 9

21 case, however, the rm manager s set of systematic information does not increase with ETF ownership. 6 In this subsection, we conduct an additional test to address the aforementioned issue. Speci cally, we test Prediction of our model, which states that the e ect of ETF ownership on investment-price sensitivity should be positive after controlling for the manager s learning from ETF prices. To test whether managers learn from stock price of their own rms in addition to ETF prices, we add annual ETF-level returns in the baseline regression. As a typical stock is held by multiple ETFs, we average the annual returns of the top ve ETFs in terms of ownership of the stock. 7 We also add the interaction of ETF-level return with the stock s beta because the e ect of ETF prices on investment should be di erent for stocks with di erent levels of exposure to systematic factors, noting that this interaction term maps to the signal q in our model. Speci cally, we run the following panel regression: Investment it = t i Q it 2 Q it ET F it 3 ET F it 4 ET F RET it 5 ET F RET it BET A it 6 BET A it X it it ; where ET F RET it is the average annual return of the top- ve ETFs in terms of ownership of stock i and BET A it is the stock s market beta estimated at the end of year t. Table 3 reports the results. As we can see, the coe cient of ET F RET it BET A it is signi cantly positive for capital expenditures, but insigni cantly negative when the dependent variable is R&D expenses. This suggests that investment also responds to information in ETF prices (corresponding to the signal q in our model), especially when a rm is highly exposed to systematic factors. More importantly, the coe cient of Q it ET F it barely changes and is still signi cant for all three measures of investment. These results suggest that a rm manager increasingly learns from his own rm s stock price as ETF ownership of his rm increases even when ETF prices are available. Next, we examine the two (non-mutually exclusive) channels through which managers learn from the stock price in addition to ETF prices. The rst channel (Prediction 2) states 6 Formally, this case is illustrated in our model. When none of the nancial speculators has private information about m j, the stock price is given by (4), where the stock price contains less information about m j than the ETF prices. Under the condition that the rm manager pays full attention to ETF price (i.e., q0 q = ), the investment sensitivity to the stock price is = 0 when controlling for the ETF price signal q, given by (8). Without controlling for ETF prices, however, the response would be = qm pq m qm sm q pq, which is increasing in!. 2 7 Our results are similar if we use the top-three or the top-0 ETF returns as the explanatory variable. (0) 20

22 that the stock price contains incremental systematic information beyond what is contained in ETF prices and the amount of incremental systematic information is increasing with ETF ownership. To test this channel, we regress rm-level earnings at year t on past-year stock return (RET it ) and its interaction with ETF ownership (RET it ET F it ), controlling for ETFlevel return (ET F RET it ) and its interaction with the stock s market beta BET A it. Table 4 reports the results. Column () shows that the coe cient of RET it ET F it is signi cantly positive, suggesting that the stock price indeed contains additional fundamental information beyond what is contained in the ETF prices. In columns (2) and (3), we further decompose earnings into systematic and rm-speci c components and examine the earningsreturn relation separately. The coe cient of RET it ET F it is much larger and more signi cant for systematic earnings than for rm-speci c earnings. This result thus supports the rst channel that the stock price contains incremental systematic information beyond what the ETF prices contain and that the incremental systematic information increases with ETF ownership. To check the robustness of our result regarding the stock prices informativeness in Table 4, we also use annual data to replicate the main results of Glosten, Nallareddy, and Zou (206) and Israeli, Lee and Sridharan (207). Consistent with Glosten, Nallareddy, and Zou (206), we nd that ETF ownership has a signi cantly positive e ect on the contemporaneous earnings-return relation, and the e ect is driven entirely by the systematic earnings component (see Panel A of Table A). More timely incorporation of systematic earnings information also predicts higher return co-movement, so we examine the e ect of ETF ownership on stock return synchronicity, following Israeli, Lee and Sridharan (207). Consistent with their study, Panel B of Table A shows a signi cant positive e ect of ETF ownership on return synchronicity. The rst channel also gives a cross-sectional prediction based on our model (Prediction 3), which states that for a rm whose beta is more time-varying and less stable, the positive e ect of ETF ownership on investment-price sensitivity should be stronger. Intuitively, if a rm s beta is stable, the macro- or industry-level information conveyed by the ETF prices coupled with the historic beta can already reveal a lot of information about the rm s systematic factor, so its own stock price adds less new information. To test this prediction, we create a dummy BET AV OL that is equal to one when the volatility of a rm s estimated beta is above the sample median. We then interact this dummy with Q it ET F it. Prediction 3 implies the coe cient of Q it ET F it BET AV OL it 2 should be positive. Results from Table A2 supports this prediction. The rst channel is also supported by the result in Table 2

23 3, where the weak signi cance of the interaction between ETF return and the stock s past beta suggests that the ETF price-based signal does not reveal enough information about the rm s exposure to the systematic factor. 8 The second reason why the managers learn from their own rms stock price in addition to ETF prices could be that managers simply pay less attention to ETF prices than to their own rms price. This is a reasonable conjecture since managers, like everyone else, have limited attention. Since a typical stock is held by more than 20 ETFs, it is di cult to determine the systematic information contained in each ETF. This limited attention channel predicts that when managers pay more attention to ETF prices, they will learn less from their own rm s stock price, i.e., the positive e ect of ETF ownership on investmentstock price sensitivity becomes weaker (Prediction 4). To test this, we use the size of a ETF as a proxy for the salience of the ETF to rm managers, as larger ETFs are more likely to attract managers attention. We then create a dummy variable Dum that is equal to one when the average size of the top- ve ETFs holding the stock is above the sample median. We interact this dummy with Q it ET F it. Prediction 4 implies that conditional on the stock being held by ETFs, managers learn less from their own rm s stock price when the ETF size is larger. That is, the coe cient of Q it ET F it Dum it should be negative. Our result in Table 5 is consistent with this hypothesis. 5.3 Identi cation Using Regression Discontinuity Design 5.3. Russell Index Reconstitution Setting The identi cation based on cross-sectional and time-series variation in ETF ownership, which underlies the baseline results in Table 3, can raise doubts if the rm-level controls fail to capture characteristics that co-determine ETF ownership and investment-price sensitivity. Our prior is that this is unlikely because most ETFs are passive investment vehicles following well-de ned benchmark indexes. In addition, our regression speci cation includes rm- xed e ects, thus capturing time-invariant (unobserved) rm characteristics. Nevertheless, to address the potential endogeneity of ETF ownership, we exploit the Russell index reconstitution setting and use the Regression Discontinuity Design (RDD) to establish the causal e ect of ETF ownership on investment-price sensitivity. The Russell index reconstitution setting has been used by several recent studies to examine the causal impact of passive institutional ownership on various corporate policies, including corporate governance (Appel, Gormley, 8 Indeed, there is a large literature discussing the time-varying nature of beta (see, e.g., Fama and French, 992, 997). 22

24 and Keim, 206), disclosure and information environment (Boone and White, 206; Bird and Karolyi, 206) and payout policy (Crane, Michenaud, and Weston, 205). The Russell 000 and the Russell 2000 index represent the largest,000 and the next 2,000 largest stocks in U.S. and are widely followed by institutional investors as benchmark indices. At the end of June each year, Russell Investments will announce the index membership of stocks based on their end-of-may market capitalizations. At the same time, Russell also assigns a portfolio weight to each individual stock within the index based on its end-of- June oat-adjusted market capitalization. 9 Because of this value-weighting mechanism, rms at the top of the index are assigned larger portfolio weights than rms at the bottom of the index. The di erence in portfolio weight is quite large, with a di erence of about 0 times between stocks at the top of Russell 2000 and those at the bottom of Russell 000 (Chang, Hong and Liskovich, 204). ETFs tracking Russell 000/2000 will follow the portfolio weights of Russell indices closely to minimize the tracking errors. Consequently, for every dollar invested in ETFs, a very small portion is invested in rms at the bottom of the Russell 000 index, while a large portion would be put into rms at the top of the Russell 2000 index, even though these rms are very close in terms of market capitalizations. This leads to a sharp discontinuity in ETF ownership for rms near the,000 cut-o, as shown in Figure 2. The underlying idea of this identi cation strategy is to exploit the discontinuous change in ETF ownership when rms at the bottom of the Russell 000 index are reshu ed to the top of Russell 2000 index. The validity of this identi cation relies on two key assumptions. The rst is that rms cannot precisely manipulate the index assignment. This assumption is plausible because Russell follows an arbitrary rule based on the relative rank of a rm s market capitalization, which is di cult to manipulate. The second is that rm s other (unobserved) characteristics should change continuously around the,000 cut-o. This assumption will be satis ed when we use the ranking calculated based on the CRSP end-of-may market capitalization as the instrument. However, the challenge with this methodology is that the rankings cannot perfectly predict a stock s index assignment because Russell makes proprietary adjustments to determine index membership. Hence this methodology will su er from weak instrument concerns. However, we cannot use the actual Russell-assigned ranking as instrument either, because stock liquidity and inside ownership around the,000 threshold will no longer be continuous, 20 violating the underlying assumption of continuous rm 9 Shares that are not available to the public including shares held by another company or individuals that exceed 0% of shares outstanding, by another member of a Russell index, by an employee stock ownership plan, or by a government. 20 After index membership assignment, Russell will resort stocks within an index according to their endof-june- oat-adjusted market capitalizations to form Russel-assigned ranking. This arbitrary process will 23

25 characteristics in the RDD framework (Lee and Lemieux, 200). To overcome the above shortcomings in the Russel index reconstitution setting, Appel, Gormley and Keim (206) adopt an empirical speci cation taking into account both the end-of-may market capitalization from CRSP and the end-of-june oat-adjusted market capitalizations from Russell Regression Discontinuity Design and Empirical Results Following the regression discontinuity design in Appel, Gormley and Keim (206), we use an instrumental variable strategy to establish the causal e ect of ETF ownership on investmentto-price sensitivity. In the rst-stage regression, we use actual inclusion in the Russell 2000 (Incl2000 it ) as an instrument to isolate the exogenous variation in ETF ownership (ET F (IV )). Speci cally, we instrumentalize ETF ownership using the following equation (with a polynomial order of 2) with year- xed e ect 2 and standard error clustered at the rm level: ET F it = t Incl2000 NX n (LnMktcap it ) n Ln(F loat it ) X it it ; () n= where LnMktcap it is the natural logarithm of end-of-may market capitalization from CRSP for stock i in year t, Ln(F loat it ) is the natural logarithm of end-of-june oat-adjusted market capitalization of stock i in year t and X are standard controls in our baseline equation (9). We include stocks end-of-may market capitalization because market capitalization is the criterion of index assignment which might a ect ETF ownership independently in addition to index reconstitution. We also include end-of-june oat-adjusted market capitalization because it determines a stock s portfolio weight within the index which will directly a ect ETF ownership. This instrument variable regression is valid because inclusion into Russell 2000 index does not directly a ect our outcome variable (investment-price sensitivity) after controlling for market capitalization other than through its e ect on ETF ownership. The exclusion restriction assumption appears reasonable. There is no theoretical or empirical work suggesting a shift from Russell 000 to Russell 2000 will directly a ect the rm s investment-price sensitivity after robustly controlling for rm market capitalization and other characteristics. The instrument relevance condition can be measured by the signi cance and magnitude of the coe cient on Incl2000 in equation (). result in stocks at the bottom of Russell 000 having a much lower liquidity and a higher inside ownership than those ranked at the top of Russell We do not include rm- xed e ects because very few rms in our sample have index shift event between Russell 000 and Russell 2000 more than once. 24

26 We estimate the rst-stage regression using three narrow bandwidths (50, 200 and 250) around the Russell 000 cut-o. The results in Panel A of Table 6 show that the instrument Incl2000 has a signi cant positive e ect on ETF ownership for all three bandwidths, con- rming Russell index membership is a strong instrument for ETF ownership. On average, inclusion in the Russell 2000 leads to a percentage-point increase in ETF ownership, which is about a 30% increase in average ETF ownership. The robust results from the rst-stage regression suggest that our instrument is valid. The predicted ETF ownership identi es the exogenous variation in ETF ownership conditioning on market capitalization and rm-speci c controls. In the second stage, we use the predicted ETF ownership (ET F (IV )) from the rststage regression to re-examine the relation between ETF ownership and investment-price sensitivity: 22 Investment it = t i Q it 2 Q it ET F (IV ) it 3 ET F (IV ) it NX n (LnMktcap it ) n Ln(F loat it ) X it it ; n= The second-stage regression results are reported in Panel B of Table 6. It shows that instrumentalized ETF ownership has a signi cant positive e ect on the investment-price sensitivity. Again, the results are robust to using di erent measures of investment and for all three bandwidth choices. Moreover, the positive e ect of ETF ownership estimated from IV regression is larger than that estimated from OLS regression. Take the 250 bandwidth as an example. When investment is measured by CAP XRND it, the coe cient on Q it ET F (IV ) it is around eight (0.893/0.0=8.8) times larger than that on Q it ET F it in Table 3, while the standard deviation of ET F (IV ) is about a third of the standard deviation of ET F. The di erence means that the causal e ect of ETF ownership on investment-toprice sensitivity is about 2-3 times stronger than that estimated from panel regression. Overall, the strong positive e ect of ETF ownership on investment-price sensitivity from a regression discontinuity analysis helps further establish the causal impact of ETF ownership on the real e ciency of underlying securities. 5.4 Cross-Sectional Heterogeneity The e ect of ETF ownership on investment-price sensitivity bears several cross-sectional implications, as predicted by our model. First, the e ect of ETF ownership on investment- 22 In this regression, we also control for managers learning from ETF prices as we do in regression (0). 25

27 price sensitivity is expected to be stronger among rms in which systematic information is more important (Prediction 5). Second, the e ect of ETF ownership should be more pronounced for rms with weak information environment (Prediction 6). The reason is that the improvement in stock price informativeness will be larger for rms with poor information environment to begin with. Similarly, the e ect of ETF ownership should be stronger among rms with high trading costs because these rms are more likely to incorporate new information with delay when not held by ETFs (Hou and Moskowitz 2005). To test the above predictions, we re-examine our regression for subsamples di ering in the importance of systematic information, strength of the information environment and level of trading costs. We use market beta (Beta) as a proxy for the importance of systematic information to the rm, the rm s market capitalization (SIZE) and analyst coverage (Analyst) as proxies for the rm s information environment, and Amihud (2002) illiquidity (Illiquidity) and bid-ask spread (Bid-ask) as proxies for trading frictions. We also account for managers learning from ETF prices in the regression. We de ne a dummy (Dum it 2 ) that equals one for rm i when its beta, illiquidity or bidask spread is above the median level of the entire sample in year t 2, and zero otherwise. 23 For SIZE or Analyst, the dummy is equal to one when the variable is below the sample median. We interact this dummy indicator with our key independent variable Q it ET F it and investigate the coe cient of this triple interaction term (Q it ET F it Dum it 2 ), which captures the incremental e ect of ETF ownership on investment-price sensitivity for rms with a higher exposure to systematic factors, worse information environment and higher trading costs. We expect a positive coe cient on Q it ET F it Dum it 2. Consistent with our expectation, Table 7 shows that the coe cient on Q it ET F it Dum it 2 is signi cantly positive for all partitioning variables. Column () reports the results conditional on the rm s market beta. The coe cients on Q it ET F it Dum it 2 and Q it ET F it are and 0.064, respectively. This means that the e ect of ETFs on investment-to-price sensitivity among high-beta rms is.2 times larger than that among low-beta rms. The result thus supports our model s prediction that ETFs create more bene t for rms in which systematic information is more important. Columns (2) and (3) report the results conditional on the rm s information environment, as measured by rm size and analyst coverage, respectively. We nd signi cant positive coe cients on Q it ET F it Dum it 2, and the magnitude of this coe cient is much larger than that of Q it ET F it. For example, when rm size is the partitioning variable, the coe cients 23 Note that we de ne the dummy indicator one year before the measure of ETF ownership because ETF activities may a ect rm liquidity, market beta and analyst following (Israeli, Lee and Sridharan, 207; Da and Shive 206). 26

28 on Q it ET F it Dum it 2 and Q it ET F it are 0.73 and 0.044, respectively. This suggests the e ect of ETF ownership on investment-price sensitivity in small rms is about 5 times (( )/0.044=4.9) larger than that in big rms. Columns (4) and (5) further show the results conditional on trading costs, as measured by Amihud (2002) illiquidity and bid-ask spread, respectively. We nd that the positive e ect of ETF ownership on investment-price sensitivity is about 3 to 4 times stronger among rms with high trading costs than among lower trading cost rms. Taken together, our subsample analysis suggests that the e ect of ETF ownership on investment-to-price sensitivity is more pronounced for rms in which systematic information is more important, for rms with poor information environment and incurring higher trading costs. The evidence substantializes the prediction that ETFs could improve investmentto-price sensitivity by incorporating more systematic information into stock prices that is valuable to managers. 5.5 The E ects of Di erent Types of ETFs on Investment-Price Sensitivity Our results so far suggest that ETFs improve the real e ciency of underlying securities by facilitating the incorporation of systematic information into stock prices. Given that a variety of ETFs have emerged in recent years, the nature of systematic information being incorporated into stock prices and its usefulness to rm managers may depend on the type of ETFs holding the stock. To test this, we classify all U.S. equity ETFs into three types: market ETFs, sector ETFs and factor ETFs, which represent the majority of ETFs currently existing in nancial markets. 24 We then decompose the total ETF ownership for each stock into three components and interact each with Tobin s Q, controlling for managers learning from ETF prices. The magnitude and signi cance of the three interaction coe cients should reveal the di erential usefulness of the systematic information contained in three types of ETFs for real investment decisions. Table 8 reports the results. Column () suggests that industry information contained in sector ETFs is most useful for investment decisions, as indicated by the signi cant and positive coe cient in front of Tobin s Q interacting with sector-etf ownership. Factor-level information is also incrementally useful to managers, as the interaction of Q with factor- 24 Market ETFs are those tracking broad indices like S&P 500. Typical market ETFs include the SPDR S&P 500 ETF (SPY) and the ishares Russell 2000 ETF (IWM). Sector ETFs are those tracking speci c industry or sectors. A typical sector ETF is the SPDR Oil & Gas Exploration & Production ETF (XOP). Factor ETFs are those ETFs tilting towards stocks with speci c characteristics such as size, quality and dividend yield. A typical factor ETF is the ishares MSCI USA Value Factor ETF (VLUE). 27

29 ETF ownership is also positive albeit less signi cant. The least useful type of systematic information is market-wide information, as the coe cient of the interaction between Tobin s Q and market-etf ownership is insigni cantly negative. Overall, the results shed further light on the type of ETF that is more likely to reveal new information to managers and hence more valuable from the real e ciency perspective. 5.6 ETF Ownership and Investment Sensitivity to Peers Prices Our preferred interpretation of the positive e ect of ETF ownership on investment-price sensitivity is that the price of a stock with higher ETF ownership contains more systematic information that is useful for manager s investment decisions. The managerial learning literature nds that a rm s investment depends not only on its own stock price, but also on its peers valuations, especially when its own stock price is less informative (Foucault and Frésard 204; Dessaint, Foucault and Matray, 206). The reason is that peers stock prices contain industry-wide information not fully captured by a rm s own (noisy) stock price, and hence is valuable for decision makers. As ETFs facilitate the incorporation of systematic information into its own stock price, peers prices become less useful to managers for the systematic information extraction purpose. As a result, managers will rely less on peers prices when making investment decisions. Thus, we predict that the investment of rms with higher ETF ownership will be less responsive to peers stock prices (Prediction 7). To test the above implication, we estimate the baseline regression (9) by including the average Tobin s Q of peer rms (P Q it ) and its interaction with the rm s ownership by ETFs (P Q it ET F it ). The coe cient on P Q it ET F it captures the impact of ETF activity on the sensitivity of the rm s investment to its peers valuation. Following the literature, we use the Text-based Network Industry Classi cation (TNIC) to identify peer rms. 25 This data is developed by Hoberg and Phillips (200, 206) through a textual analysis of business descriptions of rms 0-K lings from 996 to If managers indeed reduce their reliance on the information contained in peers prices due to the improved (systematic) informativeness of their own stock prices due to higher ETF ownership, we should observe a signi cantly negative coe cient on P Q it ET F it. The 25 The data can be obtained from 26 We choose TNIC over other industry classi cations, such as the SIC and the North American Industry Calci cation system (NAICS), for two reasons. First, TNIC has less measurement error in industry classi cation because it is dynamic and captures changes in rms product market space in a timely manner. Second, unlike the SIC or NAICS which are based on similarity in rms production processes, TNIC is more likely to identify the set of rms exposed to the same industry demand shocks. 28

30 result in Table 9 strongly supports our hypothesis. First, the signi cant positive coe cients on the rm s own Tobin s Q and peers average Tobin s Q are consistent with the literature that managers learn new information from both their own prices and their peers prices. However, the coe cient on P Q it is smaller than that on Q it, suggesting that on average, managers rely more on their own prices than their peers prices for new information. More importantly, a rm s investment responds less to its peers prices when it is heavily owned by ETFs. The coe cient on P Q it ET F it is signi cantly negative for all three investment proxies. Moreover, the e ect of ETF ownership on the sensitivity of investment to the rm s own price is still signi cantly positive and even shows a stronger magnitude. In sum, the evidence in Table 9 supports the managerial learning hypothesis that managers of rm with high ETF ownership nd peers prices less useful because ETF activities facilitate the incorporation of systematic information into their own prices. As we discussed in the introduction, this negative e ect of ETF ownership on investment sensitivity to peers prices is more di cult to be explained by alternative explanations. 5.7 ETF Ownership and Future Operating Performance A nal implication of our model is that ETF ownership should improve a rm s future operating performance (Prediction 8). The intuition is that if ETFs indeed improve the quality of information relevant to real investment decisions, then that should translate into better future operating performance. To test this prediction, we regress the rm s future operating performance on ETF ownership and standard controls with rm- and year- xed e ects: OP itj = t i ET F it X it itj (2) where the rm s future operating performance (OP itj ) is measured by return on assets (ROA it ) and sales growth (SG it ) in year t and their three-year averages (AvgROA it3 and AvgSG it3 ). We include rm size (SIZE it ), market-to-book ratio (MB it ), book leverage (LEV it ), cash holding (CASH it ), and institutional ownership (INST R it ) as standard controls. If rms with a higher ETF ownership experience better future operating performance, we should nd a signi cant positive. The results in Table 0 support this prediction for various measures of operating performance. The coe cient on ETF ownership is signi cantly positive for three out of four operating performance measures. The only exception is when the dependent variable is ROA it, which is positive but marginally insigni cant. Furthermore, the positive relation between ETF ownership and the rm s future operating performance is economically meaningful. A 29

31 one-standard-deviation increase in ETF ownership is associated with a 0.54-percentage-point increase in annual ROA and a.23-percentage-point increase in annual sales growth over the next three years. These numbers represent 6.5% and 2.8% of the average annual ROA and the sales growth rate, respectively. The results are consistent with the managerial learning hypothesis that more informative stock prices facilitate more e cient corporate investment (Durnev, Morck and Yeung, 2004; Benhabib, Liu and Wang, 207). 6 Alternative Explanations 6. Improvement in Corporate Governance Prior literature documents that passive institutional investors could improve corporate governance (Appel, Gormley and Keim, 206). Improved governance associated with a higher ETF ownership could by itself strengthen the sensitivity of investment to prices. Better governance can help align managers interests with those of shareholders and lead to valuemaximizing investment decisions (John, Litov and Yeung, 2008; Frésard and Salva, 200). Furthermore, under stronger governance managers may be more responsive to the price movements because these movements partly re ect shareholders views toward a rm s strategies (Foucault and Frésard, 202). If the said mechanism plays a role in our ndings, we should expect the e ect of ETF ownership on investment-price sensitivity to be especially large for rms that have weak governance to begin with. The reason is that these rms are expected to experience a large improvement in corporate governance due to the disciplinary role of ETFs. In addition, the e ect of ETF ownership on investment-price sensitivity should be much weaker among rms not experiencing any governance improvement. To test whether our results are driven by the improved corporate governance channel, we partition rms into strong, neutral and weak governance subsamples based on rm-level G-index and E-index. 27 G-index (E-index) is constructed by adding one index point for each of the 24 (six) (anti-)takeover provisions listed in Gompers, Ishii and Metrick (2003). Higher index values imply weaker governance. We only use rm-year observations from in this test because the G-index and E-index data are available up to Panel A of Table reports the results of our baseline regression conditional on a rm s governance quality. When G-index is used as the partitioning variable, the coe cient of the interaction term (Q it ET F it ) is positive and signi cant (0.423) for the subsample with strong corporate 27 Governance is strong when the value of G-index is below 6 and weak when the value is above 3, otherwise it is (de ned as) neutral. Governance is strong when the value of E-index is 0 and weak when the value is 5 and 6, otherwise it is (de ned as) neutral. 30

32 governance but insigni cantly negative (-0.444) for the subsample with weak corporate governance. The results are similar when we use E-index as the corporate governance measure. This result indicates that ETFs improve investment-to-price sensitivity only among rms with strong corporate governance to begin with, which is contradictory to the prediction from the improved governance story. Instead, the result suggests that good governance is necessary if managers are to use information contained in prices to maximize the value of investment decisions. To further rule out the improved governance channel, we examine whether our ndings are signi cantly weaker among rms without improvement in governance. Speci cally, we examine the e ect of ETFs on investment-price sensitivity for rms that do not experience governance improvement. The result is reported in Panel B of Table. Column () reports the estimation results for the full sample after merging with the governance measures. Column (2) reports the coe cient on Q it ET F it for rms that do not experience governance improvement in our sample. The coe cient of 0.77 (0.82) under G-index (E-index) is not economically or statistically di erent from that reported in the full sample. Overall, our tests point in the same direction that the higher investment-to-price sensitivity associated with ETF ownership does not occur through the mechanism of corporate governance improvement. 6.2 Investors Enhanced Ability to Forecast Future Investment Recent studies (Boone and White 205; Bird and Karolyi, 206) nd that institutional investors could improve rms disclosure quality, resulting in higher transparency and lower information asymmetry. As an increasingly sizeable part of institutional investors, ETFs could potentially improve a rm s information environment, thus enabling investors to form more accurate forecasts. Thus a plausible alternative explanation for our nding is that ETF ownership enhances investors ability to forecast the cash ows of new investments. In other words, the correlation between investment and stock prices could be stronger among high- ETF-ownership rms, not because managers use stock prices as a source of information but because investors can evaluate the net present value of new investments for these rms more precisely. If this mechanism is at work, the positive e ect of ETFs on investment-to-price sensitivity should be particularly high for rms experiencing a relatively large increase in disclosure quality. We use the accuracy of analyst forecast as a measure of the improvement in investors ability to forecast future cash ows. We measure the improvement in analysts forecast accuracy in a given year using both the absolute change (Accuracy) and percentage change (P Accuracy) in the median analyst 3

33 forecast error for each rm. The forecast error is de ned as the negative of the absolute difference between forecasted earnings and actual earnings dividend by actual earnings. Thus, higher Accuracy (P Accuracy) values imply a larger improvement in investors ability to forecast a rm s future cash ows. Depending on whether the (percentage) change in analysts forecast accuracy is below or above the median value of all rms in each year, we partition our sample into high and low forecast improvement groups, respectively. As shown in Table 2, we nd no signi cant di erence in the impact of ETF ownership on investmentto-price sensitivity between these two groups. The coe cient on Q it ET F it for rms experiencing a larger improvement in analysts forecast accuracy is similar to that for rms experiencing a smaller improvement. In sum, the ndings in Table 2 show that there is no discernible relation between investors ability to forecast cash ows and the increased investment-price sensitivity induced by ETF activities. Thus, our ndings are unlikely driven by investors enhanced ability to evaluate future investment. 6.3 Relaxed Financial Constraints A third alternative explanation for why ETFs improve investment-price sensitivity is that rms held by more ETFs have eased access to external nance and face less nancial constraints. Easier access to external capital could by itself strengthen the investment-to-price sensitivity by raising investment when new growth opportunities arise on the one hand and raising stock prices on the other hand, as the latter should re ect the net present value of new growth opportunities. In this section, we conduct several tests to investigate such possibilities. First, we test whether ETFs could actually improve rms access to external nance as we are not aware of any existing studies showing the relation. To that end, we regress the composite equity issuance of stock i at year t on its ETF ownership at year t, and control for other rm-level variables associated with equity issuance. The result is reported in Table 3. The coe cient on ETF ownership is insigni cant with a t-statistic of This result casts doubt on the idea that ETFs improve investment-price sensitivity mainly because they help relax nancial constraints. Second, the literature (Fazzari, Hubbard and Petersen, 988) nds that the investments of nancially constrained rms respond positively to cash ows, suggesting investment-cash ow sensitivity as a measure of nancial constraints. If ETFs help ease rms nancial constraints, they should reduce the reliance of rms investment on internally generated cash ows. However, our results in Table 2 show that this is not the case. The interaction 32

34 of ETF ownership with the cash ow measure is positive not negative. Overall, the results suggest that changes in access to external nancing alone is unlikely to explain the positive e ect of ETF ownership on investment-to-price sensitivity. 7 Conclusion This paper examines the e ect of rising ETF ownership on the real e ciency of the underlying constituents. We develop a theoretical model featuring managerial learning from prices, and show that ETFs could increase the investment-price sensitivity because they facilitate the incorporation of systematic information into a stock price, which is valuable to rm managers. Consistent with the main predictions of our model, we nd that ETF ownership exerts a strong positive e ect on the sensitivity of corporate investment to stock prices. This nding is robust to a host of estimation methods, di erent measures of corporate investment and an extensive list of controls. Using Russell index reconstitution as an exogenous shock to ETF ownership, we establish that ETFs have a causal impact on the real e ciency of the underlying stocks. We also document supporting evidence for the cross-sectional implications of our model. We further test two additional implications of the managerial learning channel that our model studies. First, we examine whether ETFs can indeed improve a rm s future operating performance as the model predicts. The evidence is supportive. Second, we look at the e ect of ETF ownership on managers learning from their peers prices. Consistent with the prediction, managers reduce their reliance on peers stock prices to guide their investment decisions when the ownership by ETFs of their own rm increases. Our results have important policy implications that ETFs help improve the real e ciency of the underlying securities, even though their net e ect on the informational e ciency of the underlyings is likely ambiguous. 33

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38 Appendix A Proofs Proof of Lemmas -3: We provide a micro-foundation for the stock price formation in (). Note that the feedback literature shows that when a rm s stock price a ects and re ects investment decisions, the stock price is typically non-linear (e.g., Goldstein, Ozdenoren and Yuan (203) and Sockin and Xiong (205)). For simplicity and for our purpose of guiding the empirical analysis, we follow the approach of Subrahmanyam and Titman (999) and Dessaint et al. (206), where the rm s investment is a growth opportunity, traded separately from its assets in place. That is, the stock price of the established business (i.e., assets in place) only in uences the investment decision of developing a new product/business (i.e., growth opportunity). The fundamentals of the new business are the same as or similar to those of the established business. The fundamentals (i.e., cash ow) of the assets in place at t = 2 are represented by m j j. We work out the trading stock price at t =. We assume that there are two types of speculators: those who have private information about m j and those who have private information about j. For the rst type, speculator i 0 s signal is x mi = m j m i, where m i N (0; = xm ); for the second type, speculator k 0 s signal is x k = j k, where k N (0; = x). The measure of the rst type is and the measure of the second type is 2. All speculators are short-lived and maximize the utility at the end of the next period. The utility function of a speculator is assumed to be U(W i ) = exp ( W i ), where W i is the wealth of speculator i at t = 2 and is the risk aversion (CARA) coe cient. The (gross) interest rate between t = and t = 2 is normalized to. The total supply of the stock is normalized to unit. As in Cong and Xu (206), we assume that there are two types of noise traders: macro-related and rm-speci c ones. The demand from the rst type is n M jt N 0; = nt M and that from the second type is n F jt N 0; = nt F at time t, where n M jt and n F jt are independent and each is independent across time t. Denote the total demand by noise traders at t by n jt n M jt n F jt, where n jt N (0; = nt ) and nt. = M nt = F nt Because of the presence of noise trading at t = 2 as well as at t =, the stock price at t = 2 is a linear function of m j, j and n j2. For simplicity and without loss of generality, the stock price at t = 2 is speci ed as p j2 = m j j n j2. So speculators who trade at t = face fundamental risk and noise trader risk (i.e., the term n 2j ) at t =. We conjecture that the stock price at t =, denoted by p j, takes the form: 0 p j 2 q = 3 m j 4 j n j, (A.) where 0,, 2, 3, and 4 are coe cients. Combined with q, price q j is converted into a signal about m j, that is, p(q; p j ) ( 0 4 ) p j 2 q 3 = m j % m;j with % m;j N (0; = pm ), (A.2) 37

39 )n j where % m;j 4 ( j and pm = 3 4 about j, that is, n. Similarly, price q j provides a signal p(q; p j ) ( 0 3 m ) p j 2 q 4 = j % ;j with % ;j N (0; = p ), (A.3) where % ;j 3 (m j m )n j and p = m 4 2 At t =, for the rst type speculator i, his information set is fx mi ; q; p j g, which one-toone maps to fx mi ; q; p; pg, so the utility maximization gives his demand for the stock: n. d i = E[p 2jjm j m i ; q; p; p] p j V ar[p 2j jm j m i ; q; p; p] = m qm pm xm [ m m qm q pm p xm (m j m i )] h m qm pm xm p M n2 p ( p p) p j i ; (A.4) In (A.4) the rst type of speculator who holds a diversi ed portfolio faces only the macrorelated noise trader risk at t = 2, the term = M n2. Similarly, for the second type speculator k, his information set is fx k ; q; p j g or fx k ; q; p; pg at t =, so his demand for the stock is d k = E[p 2jj j k ; q; p; p] p j V ar[p 2j j j k ; q; p; p] = m qm pm [ m m qm q pm p] h m qm pm p x p p x j k p j i : p x n2 (A.5) In (A.5), the second type of speculator cannot diversify away the macro-related noise trader risk at t = 2 and thus face the total noise trader risk corresponding to = n2. The market clearing of the stock market at t = implies Z d i 2 Z d k n j =. (A.6) 38

40 Plugging (A.4) and (A.5) into (A.6) yields 8 >< >: mqmpmxm mqmpm where = h m m qm q pm ( 0 4 ) p j 2 q 3 m m qm q pm ( 0 4 ) p j 2 q 3 m qm pm xm p xm m j ( 0 p p 7 ( 5 p 0 p x 2 M n2 i and 2 = 2 h Comparing the terms of (A.7) with those of (A.), we obtain 8 >< >: 3 = 4 = 2 8 < = 2 = xm m qm pm xm x p x m qm pm xm pm 3 p p 4 : 2 m qm pm pm 3 p x p 8 h 4 < m qm pm xm qm 2 pm h 3 : 2 m qm pm qm 2 pm 3 3 m ) p j 2 q 4 3 m ) p j 2 q x j 4 p j p j (A.7) m qm pm p x 9 = ; i p 2 p 4 i p x 2 p 4 9 = ; : (A.8) 9 >= n j = ; >; n2 i. Plugging pm = and p = 3 n 4 2 m 4 2 n into 3 in (A.8) yields 3 = 20 m qm m qm ( 4 3 ) 2 ( 3 ) 2 xm ( 4 3 ) 2 ( 3 ) 2 n xm xm n ( 3 4 ) 2 m ( 4 ) 2 n A M n2 3. (A.9) 5 Similarly, plugging the expression of pm and p into 4 in (A.8) yields 4 = 2 20 m qm ( 4 3 ) 2 ( 3 ) 2 x ( 3 4 ) 2 m ( 4 ) 2 n x n ( 3 4 ) 2 m ( 4 ) 2 x n A M n2 3 5 F n2 : (A.0) The system of equations (A.9)-(A.0) solves the pair ( 3 ; 4 ). After obtaining the solutions 39

41 of 3 and 4, pm and p are known. Furthermore, (A.8) gives the solutions of and 2 : = 2 = pm xm 2 p x p p 2 m qm pm xm x qm m qm pm xm 2 h i pm xm 2 p x p p x m qm pm qm m qm pm pm xm p 2 x h i: m qm pm xm pm 2 m qm pm xm p x (A.) (A.2) To obtain the analytical properties of the solutions of, 2, 3, 4 as well as pm and p, we proceed with our analysis in three steps. First, we consider the extreme case that only the rst type of speculator exists, not the second type. This corresponds to 2 = 0 and therefore 2 =, 4 = 0, p = 0 and p = 0. 4 Hence, (A.9) can be transformed into a cubic function with respect to 3, that is, M n 33 ( n2 M m qm xm ) 3 xm = 0: (A.3) n2 (A.3) clearly has a unique positive solution with respect to 3. In fact, if we write the LHS of (A.3) as function ( 3 ), it is easy to show that equation ( 3 ) is monotonically increasing in 3 and ( 3 = 0) < 0. Hence, equation ( 3 ) = 0 has a unique positive solution, 3 increasing in. 3 d 3 3 M n2 > 0. We also prove that this unique positive solution of 3 is > < 0, so by the implicit function theorem we have > 0. Similarly, the unique positive solution of 3 is increasing in M n2. In fact, < 0 and thus d 3 d M n2 = Moreover, plugging 3 > 0. Because pm = 2 3 n, pm is increasing in and M n2. pm 2 n into (A.3), we have an equation with respect to pm : 3 2 pm M n ( n2 n M m qm xm ) n2 pm If we write the LHS of (A.4) as function ~ ( pm ; n ), it is easy to show pm > 0, so by the implicit function theorem we have following n n n xm = 0: (A.4) < 0 and > 0. In short, we have the d 3 d > 0, d 3 d M n2 > 0, d pm d > 0, d pm d M n2 > 0, d pm d n > 0. (A.5) 40

42 For the case of 2 = 0, and 2 in (A.) and (A.2) can also be simpli ed as Hence, = xm xm pm qm xm 2 = : m qm pm xm xm pm = m qm 3 xm pm 2 qm = : 3 xm pm (A.6) (A.7) Second, we consider the other extreme case that only the second type of speculators exists, not the rst type. This corresponds to = 0 and therefore =, 3 = 0, pm = 0 and pm = 0. By symmetry, we can prove that 3 4 is increasing in 2 and M n2 and that p is increasing in 2, M n2 and n. In short, we have the following properties: d 4 d 2 > 0, d 4 d M n2 > 0, d p d 2 > 0, d p d M n2 > 0, d p d n > 0. (A.8) Third, the analysis on (A.8) is just the combination of the analyses on the two extreme cases in steps and 2. Because all functions are continuous, when 2 is su ciently close to 0, all of the properties in (A.5) for the case of 2 = 0 remain. In addition, it is easy to prove that when 2 is su ciently close to 0, the property d p d 2 > 0 holds. 28 Let! denote the ETF ownership of rm j (i.e., the proportion of rm j s shares held by ETFs). ETF ownership (!) a ects macro-related noise trading ( M n and M n2) as well as the measure of di erent types of speculators ( and 2 ). Speci M > M > < 0. Because the properties in (A.5) and the property d p d 2 > 0 hold when 2 is small enough, we conclude that under the su cient condition that 2 is small enough, pm is increasing in! and p is decreasing or slightly increasing in! (Lemmas 2 and 3). We can also endogenize and 2 as a function of!. Speci cally, we study the ex ante endogenous decision of information acquisition of speculators. First, we assume that a speculator chooses to acquire information either about m j or about j, that is, to acquire 28 This is easy to prove. In fact, when 2 = 0, p = 0; when 2 is slightly positive, p must be positive. 4

43 either signal x mi or signal x k. 29 So 2 = : (A.9) Second, the cost of acquiring signal x mi is higher than the cost of acquiring signal x mi by c in terms of wealth. So and 2 are determined such that the two types of speculators have the same ex ante utility (i.e., indi erence condition). As in Grossman and Stiglitz (980), the indi erence condition is EV (W i ) EV (W k ) =, (A.20) where EV (W i ) E [U(W i )jq; p j ]. Hence, it follows that 30 EV (W i ) EV (W k ) = ec v () e c u t s V ar[p 2j jq; p j ; x mi ] V ar[p 2j jq; p j ; x k ] = m qm pm xm m qm pm p p x M n2 M n2 F n2 =. (A.2) Conditions (A.9) and (A.2) together solve and 2. An increase in!, causing an increase in M n2, leads to a decrease in the LHS of (A.2), 3 so the equality is broken; to restore the equality, needs to be increased to have an increase in pm and a decrease in p. That is, is increasing in!. Intuitively, an increase in!, which lowers the macro-related noise trader risk on the next date, causes the expected payo for the rst type of speculator to increase by a higher proportion than the expected payo for the second type of speculators, so the second type has incentives to switch to being the rst type. For the special case that there are no informed nancial speculators of m j or j and speculators can use only the ETF price-based signal q as public information to extract information about m j in trading the stock, (A.8) becomes 3 = 4 = 0 and where = h 8 < : m qm = 2 = n2 i 2 qm m qm 2 and 2 = 2 h qm m qm m qm n2 i. (A.22) 29 We assume that the information acquisition cost for either signal is su ciently low so that a speculator always chooses to acquire at least one signal. 30 Note that the sign of U(W i ) or EV (W i ) is negative. 3 An increase in! also impacts on M n and thereby pm and p. This channel may further make the second type have incentives to switch to being the rst type. 42

44 Proof of Proposition : We have = K j = E [m j j jp j ; q; s ; s m ] 8 >< >: 8 >< = 0 >: m m qm pm sm m pm ( 0 4 ) p j 2 q m qm pm sm 3 qm m qm pm sm q sm m qm pm sm s m s p p ( 0 3 m ) p j 2 q s p s 4 s p s h pm m qm pm sm 3 sm m qm pm sm s m p s p 4 i p j s s p s " 9 >= >; pm 2 m qm pm sm qm 3 m qm pm sm p 2 s p 4 # q 9 >= : >; So we obtain, 2, 3 and 4 in (6). Under s!, we have a cleaner result: By (A.6), lim = s! lim 2 = s! lim 3 = : s! lim = s! pm m qm pm sm 3 pm 2 qm m qm pm sm 3 m qm pm sm pm m qm pm sm m qm xm pm xm pm, (A.23) which is increasing in pm under the su cient condition that xm > sm, by noting that the rst-order derivative of (A.23) with respect to pm is positive i ( m qm sm ) ( xm pm m qm ) ( xm pm ) ( m qm ) ( m qm pm sm ) pm Therefore, by > 0 under the su cient condition that 2 is small enough, it follows > 0 under the su cient condition s is high enough, 2 is small enough, and xm > sm. Similarly, by (A.7), lim 2 = s! qm xm m qm pm sm xm pm which is decreasing in pm. Therefore, it follows 2 < 0 under the su cient that s is high enough and 2 is small enough. By (A.23), it m < qm < 0 under the su cient condition that xm > sm, s is high enough, and 2 is small enough. Also, when xm!, it follows that 43

45 3!. Hence, lim = s!; xm! pm m qm pm sm, which pm@ qm < 0 pm@ m when pm < m qm sm. Therefore, when qm is su ciently high such that pm < m qm sm, it follows pm@ qm < 0 and thus < 0 under the su cient condition that s and xm are high enough and 2 is small enough. Similarly, when m is not too low such that pm < m qm sm, it follows < 0 and thus m < 0 under the su cient condition that s and xm are high enough and 2 is small pm@ m Proof of Proposition 2: We have = K j = E [m j j jp j ; q 0 ; s ; s m ] 8 >< >: m m qm sm m s sm m qm sm s m s s p s qm m qm sm 2 4 q q pq q 0 q m q 0 q q pq q 0 q q 0 pq q pq q 0 q 0 p j >= >; So = qm pq m qm sm q pq q 0 q 2 2 = qm q0q. m qm sm q pq q 0 q Because pq is increasing in! and by considering > 0 2 q 0 q is su ciently high such that pq < q q 0 q, it follows q 0 q < 0. Proof of Proposition pq@ q 0 q < 0. Also, when < 0 and thus By exploiting the law of iterated expectations, we obtain ( pm ; qm ; sm ; s ; p ) = E (m j j ) E [m j j ji] = EE (m j j ) E [m j j ji] = 2 E (E [m j j ji]) 2. 2 (E [m j j ji]) 2 2 (E [m j j ji]) 2 ji 44

46 Then 2 E (E [m j j ji]) 2 0( = m 2 m qm pm sm m pm m qm pm sm p s p p s p p s s p s = ( 2 m ) 2 m m qm pm sm qm m qm pm sm q : s p sm m qm pm sm s m ) 2 A 45

47 B Variable Definitions CAPXRNDATit: The sum of capital expenditures and R&D expenses at the end of fiscal year t divided by beginning-of-year total asset. CAPXAT it: Capital expenditures at the end of fiscal year t dividend by beginning-of-year total asset. RND it: R&D expenses at the end of fiscal year t dividend by beginning-of-year total asset. Missing value was set to zero. Q it-: Market value of equity plus book value of asset minus book value of equity at the end of fiscal year t- scaled by beginning-of-year total asset. The book value of equity follows the definition of Fama and French (992). ETF it-: ETFs ownership of firm i at the end of fiscal year t-. INST it-: Institutional ownership at the end of fiscal year t-. The Institutional ownership is defined as the sum of shares held by institutions from 3F filings in the fourth quarter divided by total shares outstanding. CFit: Net income before extraordinary items plus depreciation and amortization expenses at the end of fiscal year t divided by beginning-of-year total asset. RET it3: Three-year cumulative monthly-return of firm i starting from January of year t. SIZE it-: Natural logarithm of market capitalization at the end of fiscal year t-. SG it-: Annual growth rate in sales revenue at the end of fiscal year t-. CASH it-: The ratio of cash and cash equivalent at the end of fiscal year t- to beginning-of- year total asset. LEVit-: The sum of long-term liability and current liability scaled at the end of fiscal year t- by beginning-of-year total asset. ROA it-: Operating income before depreciation (oibdp) at the end of fiscal year t- scaled by beginning-of-year total asset. /ASSET it-: The inverse of total asset at the end of fiscal year t-. Beta it-2: Following Fama and French (992), market beta of an individual stock i within fiscal year t-2 is estimated by running a time-series regression based on the daily return observations over the prior 2 months if available. BETAVOLit-2: Dummy variable that equals one if the standard deviation of Beta it-2 is above the median level for the entire sample, and zero otherwise. Analyst it-2: Analyst coverage is defined as the2-month average number of analysts following firm i within fiscal year t-2. Data are obtained from I/B/E/S. Illiqud it-2: Following Amihud (2002), we measure the illiquidity of stock i within fiscal year t-2 as the average daily ratio of the absolute stock return to the dollar trading volume. Bid-Ask it-2: Following Chung and Zhang (204), we measure the bid-ask spread of stock i within fiscal year t-2 as the average daily CRSP bid-ask spread calculated with the following formula: 46

48 CRSP_Spread id = (Ask id Bid id)/m id where Ask id is the ask price of stock i on day d from the CRSP daily data, Bid id is the bid price of stock i on day d from the CRSP daily data, and M id is the mean of Ask id and Bid id. We exclude all CRSP_Spread id that are larger than 50% of the quote midpoint to reduce the effect of data errors and outliers. Gindex: G-index is constructed by adding one index point for each of the 24 (anti-)governance provisions listed in Gompers, Ishii, and Metrick (2003). Higher index values imply weaker governance. Eindex: The E-index consists of six of the 24 provisions listed in Gompers, Ishii, and Metrick (2003). Accuracy it-: The change in the median value of analyst forecast error (Accuracy) for firm i within fiscal year t- where forecast error is defined as the absolute difference between estimated earnings and actual earnings dividend by the actual earnings. PAccuracy it-: Percentage change in Accuracy within year t-, which is defined as Accuracy it- divided by Accuracy it-2. Earn_Sysit: Systematic components of annually-adjusted earnings innovation within fiscal year t (EARNit). It is calculated as the fitted value from the annual regression of stock i bellow: EARNit= α0 β MKTEARNit β2 INDEARNit εit, where EARNit is the annually change in earnings per share excluding extraordinary items (EPSPX) of firm i at the end of fiscal year t scaled by the stock price at the end of fiscal year t- (PRCC_f), MKTEARNit and INDEARNit are the weighted averages of annually-adjusted earnings innovation of all firms traded on NYSE/AMEX/NASDAQ and firms with the same two-digit SIC code as firm i, respectively. Earn_Firmit: Firm-specific components of the annually-adjusted earnings innovation at the end of fiscal year t (EARNit). It is calculated as the residual value from the annual regression of stock i bellow: EARNit= α0 β MKTEARNit β2 INDEARNit εit Loss it-: Dummy variable that equals one if EARNit is negative, and zero otherwise. Earnvol it-: Standard deviation of earnings per share excluding extraordinary items of firm i over the 0 years prior to fiscal year t. TURN it: Turnover is the total daily trading volume over shares outstanding within fiscal year t. Since the nature of dealers in the NASDAQ makes difficult to compare its turnover with the turnover observed in the NYSE and AMEX, we follow Gao and Ritter (200) to adjust the trading volume for NASDAQ stocks. SYNCH it: For each firm-year observation, we regress daily returns on the value-weighted market return and the value-weighted two-digit SIC industry return, with a minimum of 200 daily observations, as follows: 47

49 RET it= α0 β MKTRETit β2 MKTRETit- β3 INDRETjt β4 INDRETjt- εit Following the definition in Morck, Yeung, and Yu (2000), we define synchronicity as SYNCH it=log (R 2 /(- R 2 )) where R 2 is the coefficient of determination estimated from the equation. Negative adjusted R 2 numbers are trimmed at The log transformation of R 2 creates an unbounded continuous variable out of a variable originally bounded by zero and one. 48

50 Average ETF ownership Figures and Tables Figure : Time Series of Average ETF Ownership This figure plots, by calendar year, the average fraction of shares outstanding held by ETFs for firms in our sample from 2000 to 203. The vertical axis represents the magnitude of average ETF ownership and the horizontal axis represents the year. The calculation of ETF ownership is described in Section

51 Average ETF ownership Distance from Russell 000 cutoff Figure 2: ETF Ownership around the Russell 000 Cutoff This figure reports the average ETF ownership for stocks with a bandwidth of 200 around the Russell 000 threshold in our sample period where the vertical line denotes the 000 th cutoff. The horizontal axis indicates the distance of a firm s ranking to the 000 th cutoff determined by its end-of-may market capitalization from CRSP. The vertical axis represents the average ETF ownership calculated as of one quarter after the June index reconstitution and in bins of five stocks. 50