NBER WORKING PAPER SERIES FEEDBACK EFFECTS AND THE LIMITS TO ARBITRAGE Alex Edmans Itay Goldstein Wei Jiang Working Paper 17582 http://www.nber.org/papers/w17582 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 November 2011 For helpful comments, we thank Philip Bond, Mike Fishman, Kathleen Hanley, Dirk Jenter, Pete Kyle, Sam Taylor, James Thompson, Dimitri Vayanos, Kostas Zachariadis, and seminar participants at the Federal Reserve Board, Wharton, the LSE Paul Woolley Centre Conference, and the Theory Conference on Corporate Finance and Financial Markets. We thank Ali Aram, Guojun Chen, Chong Huang and Edmund Lee for excellent research assistance. AE gratefully acknowledges financial support from the Dorinda and Mark Winkelman Distinguished Scholar award and the Goldman Sachs Research Fellowship from the Rodney L. White Center for Financial Research. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer- reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications. © 2011 by Alex Edmans, Itay Goldstein, and Wei Jiang. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Feedback Effects and the Limits to Arbitrage Alex Edmans, Itay Goldstein, and Wei Jiang NBER Working Paper No. 17582 November 2011 JEL No. G14,G34 ABSTRACT This paper identifies a limit to arbitrage that arises from the fact that a firm's fundamental value is endogenous to the act of exploiting the arbitrage. Trading on private information reveals this information to managers and helps them improve their real decisions, in turn enhancing fundamental value. While this increases the profitability of a long position, it reduces the profitability of a short position -- selling on negative information reveals that firm prospects are poor, causing the manager to cancel investment. Optimal abandonment increases firm value and may cause the speculator to realize a loss on her initial sale. Thus, investors may strategically refrain from trading on negative information, and so bad news is incorporated more slowly into prices than good news. The effect has potentially important real consequences -- if negative information is not incorporated into stock prices, negative-NPV projects may not be abandoned, leading to overinvestment. Alex Edmans Wei Jiang The Wharton School Graduate School of Business University of Pennsylvania Columbia University 2318 Steinberg Hall - Dietrich Hall 411 Uris Hall 3620 Locust Walk New York, NY 10027 Philadelphia, PA 19104 [email protected] and NBER [email protected] Itay Goldstein Wharton School University of Pennsylvania Philadelphia, PA 19104 [email protected] 1 Introduction Whether financial markets are informationally efficient is one of the most hotly-contested de- bates infinance. Proponents of marketefficiencyarguethatprofit opportunities inthe financial market will lead speculators to trade in a way that eliminates any mispricing. For example, if speculators have negative information about a stock, and this information is not reflected in the price, they will find it profitable to sell the stock. This will push down the price, caus- ing it to reflect speculators’ information. However, a sizable literature identifies various limits to arbitrage, which may deter speculators from trading on their information. (This notion of “arbitrage” is broader than the traditional textbook notion of risk-free arbitrage from trading two identical securities. Here, we use “arbitrage” to refer to investors trading on their private information.) For example, De Long, Shleifer, Summers, and Waldmann (1990) and Shleifer and Vishny (1997) show that the slow convergence of price to fundamental value may render arbitrage activities too risky. This in turn dissuades trading if the speculator has a short hori- zon, which may in turn arise from informational asymmetries with her own investors. Other explanations for limited arbitrage rely on market frictions such as short-sales constraints. All of these mechanisms treat the firm’s fundamental value as exogenous to the arbitrage process and rely on market imperfections to explain why speculators will not drive the price towards fundamental value. Thus, as financial markets develop, these limits to arbitrage may weaken. In this paper, we identify a quite different limit to arbitrage, which does not rely on exoge- nousforcesbutisinsteadgeneratedendogenouslyaspartofthearbitrageprocess. Itstemsfrom the fact that the value of the asset being arbitraged is endogenous to the act of exploiting the ar- bitrage. By trading, speculators cause prices to move, which in turn reveals information to real decision makers, such as managers, board members, corporate raiders, and regulators. These decision makers then take actions based on the information revealed in the price, and these actions change the underlying asset value. This may make the initial trading less profitable, deterring it from occurring in the first place. To fix ideas, consider the following example. Suppose that a firm (acquirer) announces the acquisition of a target. Also assume that some speculators conducted some analysis suggesting thatthisacquisitionwillbevalue-destructive. Traditionaltheorysuggeststhatthesespeculators should sell the acquirer’s stock. However, large-scale selling will convey to the acquirer that speculatorsbelievetheacquisitionisabadidea. Asaresult, theacquirermayendupcancelling the acquisition. In turn, cancellation of a bad acquisition will boost firm value, reducing the speculator’s profit from her short position and in some cases causing her to suffer a loss. Put differently, the acquirer’s decisionto cancel the acquisition means that the negativeinformation possessed by speculators is now less relevant, and hence they should not trade on it. Thus, the information ends up not being reflected in the price. Our mechanism is based on the presence of a feedback effect from the financial market to real economic decisions — that real decision makers learn from the market when deciding their actions. A common perception is that managers know more about their own firms than 2 outsiders (e.g. Myers and Majluf (1984)). While this is likely plausible for internal information about the firm in isolation, optimal managerial decisions also depend on external information (suchas market demandfor a firm’s products, orpotential synergies with atarget) about which outsiders may be more informed. A classic example of how information from the stock market can shape real decisions is Coca-Cola’s attempted acquisition of Quaker Oats. On November 20, 2000, the Wall Street Journal reported that Coca-Cola was in talks to acquire Quaker Oats. Shortlythereafter, Coca-Colaconfirmedsuchdiscussions. Themarketreactednegatively, sendingCoca-Cola’ssharesdown8%onNovember20thand2%onNovember21st. Coca-Cola’s board rejected the acquisition later on November 21st, potentially due to the negative market reaction. The following day, Coca-Cola’s shares rebounded 8%. Thus, speculators who had short-sold on the initial merger announcement, based on the belief that the acquisition would destroy value, lost money — precisely the effect modeled by this paper. In the same context, Luo (2005) provides large-sample evidence that acquisitions are more likely to be cancelled if the market reacts negatively to them, and that the effect is more pronounced when the acquirer is more likely to have something to learn from the market, e.g., for non-high-tech deals and where the bidder is small. Relatedly, Edmans, Goldstein, and Jiang (2011) demonstrate that a firm’s market price affects the likelihood that it becomes a takeover target, which may arise because potential acquirers learn from the market price. More broadly, Chen, Goldstein, and Jiang (2007) show that the sensitivity of investment to price is higher when the price contains more private information not known to managers. Moreover, our model can apply to corrective actions (i.e., actions that improve firm value upon learning negative information about firm prospects) undertaken by stakeholders other than the manager. Such stakeholders likely have less information than the manager and may be more reliant on information held by outsiders. Examples include managerial replacement (undertaken by the board, or by shareholders who lobby the board), a disciplinary takeover (undertaken by an acquirer), or the granting of a subsidy or a bail-out (undertaken by the government). We demonstrate a barrier to the feedback effect, that hinders decision makers from learning from the market. An important aspect of our theory is that it generates asymmetry between trading on positiveandnegativeinformation. Thefeedbackeffectdeliversanequilibriumwherespeculators trade on good news but do not trade on bad news. Yet, it does not give rise to the opposite equilibrium, where speculators trade on bad news only. The intuition is as follows. When speculators trade on information, they improve the efficiency of the firm’s decisions — regardless of the direction of their trade. If the speculator has positive information on a firm’s prospects, trading on it will reveal to the manager that investment is profitable. This will in turn cause the firm to invest more, thus increasing its value. If the speculator has negative information, trading on it will reveal to the manager that investment is unprofitable. This will in turn cause the firm to invest less, also increasing its value as contraction is the correct decision. When a speculatorbuysandtakesalongpositioninafirm, shebenefitsfurtherfromincreasingitsvalue 3 via the feedback effect. By contrast, when she sells and takes a short position, she loses from increasing the firm’s value via the feedback effect. Note that, for the speculator to lose from the feedback effect, she must end up with a short position. If she ends with a long position, the value of the shares she still holds onto are enhanced by the feedback effect. Thus, the model implies that investors are less likely to engage in short-sales than sales — even though the model contains no short-sale constraints. Even though the speculator’s trading behavior is asymmetric, in general it is not automatic that the impact on prices is asymmetric. The market maker is fully rational and takes into accountthefactthatthespeculatorbuysonpositiveinformationanddoesnottradeonnegative information. Thus, he adjusts his pricing function accordingly. Therefore, it may seem that negative information will be impounded in prices to the same degree as positive information — even though it may lead to a neutral rather than negative order flow, the market maker knows that a neutral order flow can stem from the speculator having negative information but choosing not to trade, and may decrease the price accordingly. By contrast, we show that the asymmetry in trading behavior does translate into asymmetry in price impact. The crux is thatthemarketmakercannotdistinguishthecaseofaspeculatorwhohasnegativeinformation but chooses to withhold it, from the case in which the speculator is absent (i.e. there is no information). Thus, a neutral order flow does not lead to a large stock price decrease, and so negative information has a smaller effect on prices. Indeed, Hong, Lim, and Stein (2000) show empiricallythatbadnewsisincorporatedinpricesmoreslowlythangoodnews. Theyspeculate that this arises because it is firm management that possesses value-relevant information, and they will publicize it more enthusiastically for favorable than unfavorable information. Our paper presents a formal model that offers an alternative explanation. Here, key information is held by a firm’s investors rather than its managers, who “publicize” it not through public news releases, but by trading on it. They also choose to disseminate good news more readily than bad news, but for a very different reason from firm management, i.e., because of the feedback effect. In standard models of underreaction, if bad news has a smaller effect on short-run returns (i.e. between  = 0 and  = 1) than good news, this must be counterbalanced by bad news generating a larger long-run drift (between  = 1 and  = 2) than good news. We show that this need not be the case in a model with feedback. It is indeed true that, if the state is bad and little bad news comes out in the short-run (due to the speculator not trading on it), there is more bad news still to come out in the long-run. However, in a feedback model where firm value is endogenous, the manager can take a corrective action to mitigate the negative impact of the state on firm value. If the feedback effect is sufficiently strong, bad news has a smaller effect than good news in both the short-run and the long-run. While the above considers the returns to good and bad news, the model also generates predictions regarding the returns to good and bad investment decisions. Naturally, the returns to investment are positive (both in the short-run and long-run) if the state is good and negative 4 if the state is bad. More interestingly, we show that the returns to good investment are more front-loaded than the returns to a bad investment — i.e., a higher proportion of the returns manifestsat = 1thanat = 2. Thisresultagainstemsfromtheasymmetryofthespeculator’s trading strategy. Even if the speculator is aware that the investment is bad at  = 1, she may not trade on this information due to the feedback effect. Thus, the value-destructiveness of the investment seeps out ex post at  = 2. Thus, our model provides an explanation for the negative long-run returns to M&A, documented by Agrawal, Jaffe, and Mandelker (1992) and Rau and Vermaelen (1998). In addition to its interesting effects on stock returns, the asymmetry of the speculator’s trading strategy can also generate important real consequences. Since negative information is not incorporated into prices, it does not influence management decisions. Thus, while positive- NPV projects will be encouraged, some negative-NPV projects will not be canceled — even though there is an agent in the economy who knows with certainty that the project is negative- NPV—leadingtooverinvestmentoverall. Incontrasttostandardoverinvestmenttheoriesbased on the manager’s private benefits (e.g., Jensen (1986), Stulz (1990), Zwiebel (1996)), here the managerisfullyalignedwithfirmvalueandtherearenoagencyproblems. Themanagerwishes to maximize firm value by learning from prices, but is unable to do so since speculators refrain from revealing their information. Applied to M&A as well as organic investment, the theory may explain why M&A appears to be “excessive” and a large fraction of acquisitions destroy value (see, e.g., Andrade, Mitchell, and Stafford (2001).) Asmentionedabove, theprimarymotivationforour paper is to identifya limittoarbitrage. Different authors have emphasized different factors that lead to limits on arbitrage activities. Campbell and Kyle (1993) focus on fundamental risk, i.e., the risk that firm fundamentals will changewhilethearbitragestrategyisbeingpursued. Intheirmodel, suchchangesareunrelated to speculators’ arbitrage activities. De Long, Shleifer, Summers, and Waldmann (1990) argue that noise-trading risk, i.e., the risk that noise trading will increase the degree of mispricing, may render arbitrage activities unprofitable. Noise trading only affects the asset’s market price and not its fundamental value, which is again exogenous to the act of arbitrage. Shleifer and Vishny (1997) show that, even if an arbitrage strategy is sure to converge in the long-run, the possibility that mispricing may widen in the short-term may deter speculators from trading on it, if they are concerned with redemptions by their own investors. Similarly, Kondor (2009) demonstrates that financially-constrained arbitrageurs may stay out of a trade if they believe that it may become more profitable in the future. Many authors (e.g., Pontiff (1996), Mitchell and Pulvino (2001), and Mitchell, Pulvino, and Stafford (2002)) focus on the transaction costs and holding costs that arbitrageurs have to incur while pursuing an arbitrage strategy. Others (Geczy, Musto, and Reed (2002), and Lamont and Thaler (2003)) discuss the importance of short-sales constraints. While these papers emphasize market frictions as the source of limits to arbitrage, our paper shows that limits to arbitrage arise when the market performs its utmost efficient role: guiding the allocation of real resources. Thus, while limits to arbitrage based 5 on market frictions tend to attenuate with the development of financial markets, the effect identified by this paper may strengthen — as investors become more sophisticated, managers will learn from them to a greater degree. Our model deliberately shuts down the sources of the limitstoarbitrageidentifiedbypriortheories: thespeculatorisrisk-neutral, therearenoagency problems due to portfolio delegation, and there is no exogenous friction on trading (other than astandardtransactioncost), suchasshort-saleconstraints. Withall theseforcesswitchedoff, a limit to arbitrage nevertheless arises because the speculator endogenously chooses not to trade due to the feedback effect. Our paper is related to the literature exploring the theoretical implications of the feedback effects from market prices to real decision making. Several papers in this literature have shown that the feedback effect can be harmful for real efficiency. Most closely related is Goldstein and Guembel (2008), whoshowthatitprovidesanincentiveforuninformedspeculators toshortsell a stock, reducing its value by inducing a real decision (investment) based on false information. Their paper also highlights an asymmetry between buy-side and sell-side speculation, but only with respect to uninformed trading; here, we show that informed speculators are less likely to trade on bad news rather than good news, in turn generating implications for the speed of incorporation of news into prices.1 Bond, Goldstein, and Prescott (2010), Dow, Goldstein, and Guembel (2010), and Goldstein, Ozdenoren, and Yuan (2011) also model complexities arising from the feedback effect. Overall, the point in our paper — that negatively informed speculators will strategically withhold information from the market, because they know that the release of negativeinformationwillleadmanagerstofixtheunderlyingproblem—isnewinthisliterature. This paper proceeds as follows. Section 2 presents the model. Section 3 contains the core analysis, demonstrating the asymmetric limit to arbitrage. Section 4 investigates the extent to which information affects beliefs and prices, Section 5 discusses potential applications of the model, and Section 6 concludes. Appendix A contains all proofs not in the main text. 2 The Model The model has three dates,  012 . There is a firm whose stock is traded in the financial ∈ { } market. The firm’s manager needs to take a decision as to whether to continue or abandon an investment project. The manager’s goal is to maximize expected firm value; since there are no agencyproblemsbetweenthemanagerandthefirm,wewillusethesetwotermsinterchangeably. At  = 0, a risk-neutral speculator may be present in the financial market. If present, she is informed about the state of nature  that determines the profitability of continuing vs. abandoning the project. Trading in the financial market occurs at  = 1. In addition to the speculator, two other types of agents participate in the financial market: noise traders whose trades are unrelated to the realization of , and a risk-neutral market maker. The latter collects 1In addition, while they require two trading periods to generate the asymmetry, our model is simpler and requires only a single period. 6 theordersfromthespeculatorandnoisetraders,andsetsapriceatwhichheexecutestheorders out of his inventory. At  = 2, the manager takes the decision, which may be affected by the trading in the financial market at  = 1. Finally, all uncertainty is resolved and payoffs are realized. Wenowdescribethefirm’sinvestmentproblemandthetradingprocessinmoredetail. 2.1 The Firm’s Decision Suppose that the firm has an investment project that can be either continued or abandoned at  = 2. We denote the firm’s decision as   , where  =  represents continuing ∈ { } the investment and  =  represents no investment (also referred to as “abandonment” or “correction”). The firm faces uncertainty over the realization of value under each possible action. In particular, there are two possible states  Θ  (“high” and “low”). We ∈ ≡ { } denote the value of the firm realized in  = 2 as  = , which depends on both the state of  nature  and the manager’s action . We assume that whether continuation or abandonment is desirable depends on the state of nature (i.e., there is no dominant action). Without loss of generality, we set:    (1)       (2)   that is, continuation is optimal in state , while abandonment is optimal in state . We also set:   , (3)   that is, under the optimal action, the highest firm value is achieved in state , consistent with this being labeled as the “high” state. This assumption is also without loss of generality as, if it is not satisfied, the highest firm value is achieved in state  and we can simply reverse notations. Note that equations (1) and (2) imply:      (4)     − − Equation (4) is the driving force behind our results. It means that taking the corrective action reduces the negative effect of state  on firm value. Put differently, if the state is  rather than , the reduction in firm value is lower if the manager has taken action . In turn, equation (4) incorporates two cases, depending on whether firm value is monotonic in the underlying state: Case 1:   . In this case, state  is better for firm value, no matter what action   has been taken by the firm. Hence, the corrective action attenuates, but does not eliminate, the effect of the state on firm value. Abandonment reduces the volatility of firm value, i.e., the dependence of firm value on the state. For example, state  can represent high demand for the firm’s products, while state  represents low demand. Whether the firm continues to invest in 7 its production process or not, its value will be lower in state , but the negative effect of state  is attenuated if the firm does not invest. Case 2:   . In this case, if the corrective action is taken, firm value is higher in state   . Put differently, the corrective action is sufficiently powerful to overturn the effect of the state on firm value. Importantly, this second case does not require that abandonment reduces the volatility of firm value: it could be that ( )  (  ) so volatility is  −   −  higher under correction. Instead, the case    implies non-monotonicity of firm value   in the state: one state does not dominate the other. For example, consider the case where continuation implies proceeding with a takeover decision, and abandonment implies keeping the cash for future opportunities. State  corresponds to a state in which current acquisition opportunities dominate future ones, and state  refers to the reverse. Under continuation, firm valueishigherinstate,whereasifthefirmchoosestopostponeacquisitions,itsvalueishigher in state  where future acquisition opportunities are superior. Another example is related to Aghion and Stein (2008):  =  corresponds to a growth strategy, and  =  corresponds to a strategy focused on current profit margins. Growth prospects are good if  =  and bad if  = . If the firm eschews the growth strategy ( = ), its value is higher in the low state where there are no growth opportunities, since in the high state, its rivals could pursue the growth opportunities, in turn worsening its competitive position. The prior probability that the state is  =  is  = 1, which is common knowledge. We use 2  to denote the posterior probability the manager assigns to the case  = . The manager’s decision is conditioned on , which in turn is calculated using information arising from trades in the financial market. Let  denote the posterior belief that the state is  such that the manager is indifferent between continuation and abandonment, i.e.:  +(1 ) =  +(1 ) (5)     − − The value of  represents a “cutoff” that determines the manager’s action. If and only if   , he will continue the project. We will distinguish between two cases. The first case is where   1. Since the prior  is 1, the manager would continue the investment without further 2 2 information, i.e., ex ante, the investment has a positive net present value. The second case is where   1, and so the ex-ante net present value of the investment is negative. 2 2.2 Trade in the Financial Market In  = 0, with probability 0    1, a speculator arrives in the financial market. Whether the speculatorispresentornotisunknowntoanyoneelse.2 Ifthespeculatorispresent, sheobserves the state of nature  with certainty. We will use the term “positively-informed speculator” to 2Since private information is not public knowledge, its existence is also unlikely to be public knowledge. ChakrabortyandYilmaz(2004)alsofeatureuncertaintyonwhetherthespeculatorispresent,inanequilibrium in which informed insiders manupulate the market by trading in the wrong direction. 8 describe a speculator who observes  = , and “negatively-informed speculator” to describe a speculator who observes  = . The variable  is a measure of market sophistication or the informedness of outside investors and will generate a number of comparative statics. Trading in the financial market happens in  = 1. Always present is a noise trader, who trades  = 1, 0, or 1 with equal probabilities. If the speculator is present, she makes an − endogenous trading choice  101 . Trading either 1 or 1 is costly for the speculator ∈ {− } − and entails paying a cost of . Unless otherwise specified, we refer to trading profits and losses gross of the cost . If the speculator is indifferent between trading and not trading (because her expected profits from trading exactly equal ), we assume that she will not trade. Following Kyle (1985), orders are submitted simultaneously to a market maker who sets the price and absorbs order flows out of his inventory. The orders are market orders and are not contingent on the price. The competitive market maker sets the price equal to expected asset value, given the information contained in the order flow. The market maker can only observe total order flow  = +, but not its individual components  and . Possible order flows are  2 1012 and the pricing function is () = ( ). A critical departure from ∈ {− − } | Kyle (1985) is that firm value here is endogenous, because the manager’s action is based on information revealed during the trading process. Specifically, themanager observes total orderflow, and uses theinformationin  toform his posterior , which is then used in the investment decision. Allowing the manager to observe order flow , rather than just the price , simplifies the analysis without affecting its economic content. In the equilibria that we analyze, there is a one-to-one correspondence between the price and the order flow so it does not matter which variable the manager observes. Under the alternative assumptionthat the managerobserves , other, non-interesting, equilibriacan arise, where the price is essentially uninformative. Since this paper’s focus is to analyze the feedback effect, which requires the price to be informative, we do not analyze such equilibria here. It is also realistic to assume that managers have access to information about trading quantities in the financial market: first, market making is competitive and so there is little secrecy in the order flow; second, microstructure databases (such as TAQ) provide such information at a short lag — rapidly enough to guide investment decisions. 2.3 Equilibrium The equilibrium concept we use is the Perfect Bayesian Nash Equilibrium. Here, it is defined as follows: (i) A trading strategy by the speculator:  : Θ 101 that maximizes his → {− } expected final payoff ( )  , given the price setting rule, the strategy of the manager, − −| | and his information about the realization of . (ii) An investment strategy by the firm  :  (where = 2 1012 ), that maximizes expected firm value  =  given Q → { } Q {− − }  the information in the order flow and all other strategies. (iii) A price setting strategy by the market maker  : R that allows him to break even in expectation, given the information Q → in the price and all other strategies. Moreover, (iv) the firm and the market maker use Bayes’ 9