The Price Impact of Institutional Herding

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1 The Price Impact of Institutional Herding Amil Dasgupta LSE and CEPR Andrea Prat LSE and CEPR Michela Verardo LSE May 8 Preliminary. Comments welcome. Abstract We present a simple theoretical model of the price impact of institutional herding. In our model, career-concerned fund managers interact with pro t-motivated monopolistic market makers in a pure dealer-market. The reputational concerns of fund managers generate endogenous conformism, which, in turn, impacts the prices of the assets they trade. We show that assets persistently bought (sold) by fund managers trade at prices that are too high (low) and thus experience negative (positive) long-term returns, after uncertainty is resolved. The pattern of equilibrium trade is also consistent with increasing (decreasing) short-term transaction-price paths during or immediately after an institutional buy (sell) sequence. Our results provide a simple and stylized framework within which to interpret the empirical literature on the price impact of institutional herding. In addition, our paper generates several new testable implications. Introduction Professional money managers are the majority owners and traders of equity in today s markets. Leading market observers commonly allege that money managers herd and that such herding destabilizes markets and distorts prices. For example, Jean-Claude Trichet, President of the European Central Bank, commented on the incentives and behavior of fund managers as follows: Some operators have come to the conclusion that it is better to be wrong along with everybody else, rather than take the risk of being right, or wrong, alone... By its nature, We are grateful to Dilip Abreu, Markus Brunnermeier, Stephen Morris, Guillermo Ordonez, Hyun Shin, Dimitri Vayanos, and Wei Xiong as well as seminar audiences at Minnesota (Economics Department), Princeton (Bendheim Center), University of Chicago (Mathematical Finance seminar), and the University of Illinois- Chicago (Finance Department) for helpful comments.

2 trend following ampli es the imbalance that may at some point a ect a market, potentially leading to vicious circles of price adjustments and liquidation of positions. The empirical literature in nance generally concludes that fund managers do engage in conformist trading (i.e., trade in the direction of the recent trades of other fund managers). However, the literature has reached less clear conclusions regarding the price impact of such institutional conformism. Some authors nd that institutional herding drives prices towards fundamental value. 3 Others nd that following episodes of institutional herding, prices reverse, providing empirical evidence in favor of Trichet s view. 4 The theoretical literature lags behind its empirical counterpart in this area. While the well-known model of Scharfstein and Stein (99) shows that money managers may herd due to reputational concerns, there is no systematic theoretical analysis of the price impact of institutional herding. Scharfstein and Stein s original observation was made in partial equilibrium. This insight has recently been extended to settings with endogenous prices by Dasgupta and Prat (5). However, Dasgupta and Prat consider a market with unlimited arbitrage: in their model managers herd, and their herding a ects the informational content of prices, but prices never deviate from their information-based fair-values. In this paper, we present a simple yet rigorous model in which we can theoretically delineate the price impact of institutional herding. Our model extends the analysis of Dasgupta and Prat (5) into a market with limits to arbitrage, in which career-concerned money managers interact with pro t-motivated security dealers with market power. The interaction between these traders generates rich implications. Our model makes three main contributions. First, we show theoretically that money managers will trade in a conformist manner due to their reputational concerns, despite the fact that such conformism has a rst-order impact on the prices of assets that they trade. Second, we delineate the properties of the price impact of institutional conformism: we argue that, in markets dominated by institutional traders, assets persistently bought (sold) by money managers will trade at prices that are too high (low), and that this will generate return-reversals in the long-term, when uncertainty is resolved. We also show that our equilibrium is consistent with the existence of short-term positive (negative) price changes following an institutional buy (sell) sequence. Our analysis, therefore, provides a simple and stylized framework to interpret existing empirical results on the price impact of institutional herding at long and short horizons. Finally, our model Jean-Claude Trichet, then Governor of the Banque de France. Keynote speech delivered at the Fifth European Financial Markets Convention, Paris, 5 June : Preserving Financial Stability in an increasing globalised world. See Sias (4) for a recent comprehensive analysis that nds evidence of institutional herding. 3 See, for example, Wermers (999) and Sias (4). 4 See, for example, Dasgupta, Prat, and Verardo (7), and Sharma, Easterwood, and Kumar (6).

3 generates a number of new empirical predictions that represent potential directions for future empirical analysis.. Model and Results The building blocks of our theory can be traced back to the well-known model of reputational herding by Scharfstein and Stein (99), which has been recently extended to a setting with endogenous prices by Dasgupta and Prat (5). We extend Dasgupta and Prat s model into a setting with limits to arbitrage: in contrast to that model, where the trading counterparties of money managers were perfectly competitive, in the current set-up, these counterparties are endowed with market power. A number of career-concerned fund managers trade with monopolistic dealers over several trading rounds before uncertainty over asset valuation is resolved. Fund managers receive private signals about the liquidation value of the stock and they di er in the accuracy of their signal. Fund managers are evaluated by their investors based on their trades and the eventual liquidation value of their portfolios. The future income of a manager depends on how highly investors think of his signal accuracy. In contrast, market makers are motivated purely by trading pro ts. In equilibrium, when past purchases and sales balance each other, a fund manager s average willingness to pay for an asset depends only on its expected liquidation value. However, things change if past trade has a persistent sign. If, for instance, most managers have bought the asset in the recent past, a manager with a negative signal is reluctant to sell, because he realizes that: () his negative realization is in contradiction with the positive realizations observed by his colleagues; () this is probably due to the fact that his accuracy is low; and (3) by selling, he is likely to appear like a low-accuracy type to investors. The manager faces a tension between his desire to maximize expected pro t (which induces him to follow his private information and sell) and his reputational concerns (which make him want to pretend his signal is in accordance with those of the others). This tension drives a wedge between the price at which the manager is willing to sell and the maximum price at which a pro t-motivated dealer will trade with him. Thus, this pessimistic manager does not trade. Conversely, a manager with a positive signal who trades after a sequence of buys is even more willing to buy the asset, because his pro t motive and his reputational incentive go in the same direction. Monopolistic dealers take advantage of this manager s reputational motivation and o er to trade with him at prices that are above expected liquidation values based on available information. In turn, the manager is willing to buy at such excessively high prices because buying provides him with an expected reputational reward. Thus, when a number of traders have bought, indicating that the asset value is likely to be high, fund managers will either conform and buy, at unfavorable prices, or not trade. 3

4 Thus, the willingness to pay for an asset on the part of career-driven investors can di er systematically from the expected liquidation value. It is higher (lower) if past trade by other managers has been persistently positive (negative). This discrepancy between the willingness to pay and the fair price translates into mispricing. Each stock develops a reputational premium. Stocks that have been persistently bought (sold) trade at prices that are higher (lower) than their fair value, leading to a correction when the true value is revealed. Our theory, therefore, predicts a negative correlation between net trade between the institutional and individual sectors of the market and long term returns. On the other hand, our theory is consistent with a positive correlation between the balance of fund manager trade and the short-term changes in the transaction price of the asset. To see this, note that when a number of managers have bought, market beliefs about the asset become quite positive. Managers who arrive to trade at this point will either buy (which pushes prices further up) or not trade. While non-trading will reveal negative information, bringing down potential transaction prices, we show that at least two periods of market inactivity must precede a reversal in realized transaction prices. Thus, measured during an institutional herd, or immediately following one, short-term transaction price paths are likely to be increasing when institutions have been net buyers, and decreasing when they have been net sellers. Our model leads to several other implications, which we selectively summarize here. We show that the degree of asset mispricing based on career concerns is an increasing function of the degree to which contractual incentives of institutional traders put weight on their career concerns. Money managers who care more about reputation (relative to pro ts), will be willing to buy at even higher prices and to sell at even lower prices, leading to greater mispricing. We also show that, as long as managers are su ciently concerned about their reputations, the expected mispricing increases monotonically along a buy or sell sequence. Thus, a non-trivial sequence of institutional buying can engender a bubble. Finally, we link fund manager conformism and price reversals to the level of market turnover. Price run-ups due to institutional buying are reversible in our model: they can be reversed by su ciently many fund managers receiving negative signals, leading them not to trade, and thus revealing to the market the existence of such negative news, and leading to a drop in public beliefs about asset values. However, as this informal discussion suggests, for such a reversal to occur, a number of fund managers must choose not to trade in a sequence: thus, price reversals following a managerial herd are likely to be preceded by episodes of reduced turnover. 4

5 . Related Literature Our paper is related to a number of recent empirical studies on institutional herding. There is now ample evidence that institutions herd. Lakonishok, Shleifer and Vishny (99) show that the trades of a sample of pension funds tend to be correlated over a given quarter, especially among small stocks. Grinblatt, Titman and Wermers (995) and Wermers (999) examine a larger sample of holdings by mutual funds and nd evidence of herding in small stocks. Sias (4) nds stronger evidence of herding behavior among institutional investors. He estimates a strong and positive correlation between the fraction of institutions buying the same stock over adjacent quarters. The evidence on the impact of such herding behavior on prices is mixed. Wermers (999) nds that stocks heavily bought by mutual funds outperform stocks heavily sold by them during the following two quarters, and interprets this result as evidence of a stabilizing e ect of institutional trade on prices. Sias (4) shows that institutional demand is weakly positively correlated with returns over the following year. Other papers nding evidence of a positive correlation between institutional demand and future returns include Nofsinger and Sias (999), Sias, Starks and Titman (), Grinblatt, Titman and Wermers (995), and Cohen, Gompers and Vuolteenaho (). A number of recent studies show that institutional demand is negatively correlated with returns. Dasgupta, Prat, and Verardo (7) analyze stock returns conditional on the persistence of trading by institutional investors. They nd that returns of stocks persistently bought (sold) by institutions over a period of three to ve quarters exhibit strong reversals at long horizons (two-three years). Sharma, Easterwood and Kumar (6) examine herding by institutional investors for a sample of internet rms during the period They nd strong evidence of one-quarter reversals after the cessation of institutional buy herding. Focusing on mutual fund ows, Braverman, Kandel and Wohl (5), Frazzini and Lamont (7), and Coval and Sta ord (7) nd a negative relationship between institutional trading and long-horizon returns. At a theoretical level, our paper is related to the large literature on herding (e.g., Banerjee 99, Bikhchandani, Hirshleifer, and Welch 99, and Avery and Zemsky 998) and to the growing literature on the agency con icts and asset pricing (e.g., Allen and Gorton 993, He and Krishnamurthy 7, and Kondor and Guerrieri 7). The rest of the paper is organized as follows. In the next section we present the model, and derive the equilibrium. In section 3 we discuss the properties of the equilibrium and delineate the connection with existing empirical results. Section 4 discusses possible micro-foundations for the payo structure assumed in the baseline model. Section 5 concludes. 5

6 Model The rst ingredient of our analysis is a model of nancial markets with asymmetric information. We use an adapted and abridged version of Glosten and Milgrom (985). Consider a sequential trade market in which in each period there is a large number of delegated traders (fund managers). There are T trading periods. Each trader is able to trade at most once, if he is randomly selected to trade in one of the T rounds. There is a single Arrow asset, with equi-probable liquidation values v = or. realized value of v is revealed at time T +. The trader who is selected at t faces a shortlived monopolistic market maker (MM), who trades at time t only, and posts a bid (p b t) and an ask price (p a t ) to buy or sell one unit of the asset. 5 The Each trader has three choices: he can buy one unit of the asset from the MM (a t = ), sell one unit of the asset to the MM (a t = ), or not trade (a t = ). We consider a pure quote-driven dealer market (e.g., the London Stock Exchange s SEAQ system) where the market maker is a monopolist. 6 In Glosten and Milgrom (985) the market is made by a number of Bertrand-competing uninformed traders. Hence, Glosten and Milgrom s model is characterized by unlimited arbitrage: the price never deviates from the expected liquidation value based on public information. Our monopoly setting is a crude (but tractable) way to allow for limited arbitrage. We deviate from Glosten and Milgrom in another, less important aspect: there is no noise trade in our set-up. However, noise traders could be added to our model without modifying the qualitative properties of our price dynamics, at the cost of substantial algebraic complexity. The manager chosen to trade at t can be either smart (type = g) with probability or dumb (type = b), with probability. Managers do not know their own types. 7 The smart manager observes a perfectly accurate signal: s t = v with probability. The dumb manager observes a purely noisy signal: s t = v with probability. Signals are independent conditional on the state. As in many signalling games, the presence of potential out-of-equilibrium actions can 5 Formally, our model has features of both Glosten and Milgrom (985), which is a multi-period model with a competitive market maker, and Copeland and Galai (983) which is a single-period model with a monopolistic market maker. Needless to say, it is complex to model a monopolistic market maker in a multi-period setting, and our assumption of short-livedness simpli es the problem. 6 The assumption of a monopolistic market maker is a simpli cation for imperfect competition amongst dealers. Only the latter is necessary to support our qualitative results. Imperfectly competitive dealer markets are not uncommon in the context of relatively illiquid securities. 7 Dasgupta and Prat (5) consider a related model in which managers receive informative signals about their types, and show that the core e ects of career concerns are una ected as long self-knowledge is not very accurate. 6

7 result in multiple equilibria, some of which are supported by implausible out-of-equilibrium beliefs. To overcome this problem, we assume that there is an exogenous probability (; ) that the manager selected at t is unable to trade, in which case he is replaced by a di erent randomly selected manager (so that some manager always has a chance to trade with the market maker in any given period). This guarantees that non-trading occurs on the equilibrium path. can be as small as desired. The investor observes that whether his manager was selected to trade, and if so, at what time t: But, if the manager did not trade, the investor cannot tell whether he was unable or unwilling to trade. Manager t maximizes a linear combination of his trading pro ts ( t ) and his reputation ( t ), which are de ned below. Trading pro t is given by: 8 >< v p a t if a t = t = p >: b t v if a t = if a t = The reputational bene t is given by the posterior probability (at T + ) that the manager is smart given his actions and the liquidation value: The manager s total payo is t = Pr [ t = gja t ; v] t + t where > measures the importance of career concerns. Let us rst introduce some notation. Let h t denote the history of prices and trades up to period t (excluding the trade that occurs at t). Let v t = E [vjh t ], denote the public expectation of v. Finally, let v t = E [vjh t ; s t = ] and v t = E [vjh t ; s t = ] denote the private expectations of v of a trader at t who has seen signal s t = or s t = respectively. Simple calculations show that v t = It is clear that, v t < v t < v t and ( + )v t v t + and v t = ( )v t + v t Pr(s t = jh t )vt + Pr(s t = jh t )vt = v t As a benchmark, we rst analyze the case in which =, that is, there are no career concerns. In this case, it is easy to see that the only possibility is that all traders trade sincerely in equilibrium, that is, buy if they see s t = and sell if they see s t =. The MM, in turn, sets prices to extract the full surplus: bid price p b t = vt and ask price p a t = vt. We summarize: 7

8 Proposition When =, managers trade as follows: ( if s t = a t = if s t = and the market maker sets prices p b t = v t and p a t = v t. Thus the average transaction price when = is v t. We now analyze the more general case when >. We rst introduce some additional notation for useful equilibrium quantities. Let w st a t = E[ t (a t )js t ]; the expected posterior reputation of a manager who observes signal s t and takes action a t. This is clearly an equilibrium quantity, and turns out to be useful in summarizing prices when >. The following is an equilibrium of the game with >. Proposition There exists an equilibrium in which, if selected to trade at t a manager trades as follows: ( () If v t = then a if s t = t = if s t = ( () If v t > then a if s t = t = otherwise ( (3) If v t < then a if s t = t = otherwise The market maker quotes the following prices at t: () If v t = p a t = v t p b t = v t () v t > p a t = vt + w w p b t = v t (3) v t < p a t = vt p b t = vt + w w 8

9 where w = w = w = w = + v t ; + ( v t ); + ( + ) ( ) v t + + ( + ) ( ) v t ; + ( + ) ( ) v t + + ( + ) ( ) v t : The proof of this result is lengthy, and is presented in full detail in the appendix. Here, we comment on the main ingredients that drive the result. We focus on the case in which v t >. The intuition for v t < is symmetric. The proof is trivial for v t = ; as then the net reputational value of buying or selling the asset for the fund managers is zero: thus, the equilibrium for v t = is identical to the case with no career concerns ( = ). When v t >, the market is optimistic about the asset payo, and the equilibrium strategies prescribe that the manager with s t = should buy while the manager with s t = should decline to trade. The equilibrium also speci es that, in this scenario, the ask price is higher than expected liquidation value conditional on a buy order, while the bid price is equal to expected liquidation value conditional on a sell order. When v t >, it seems to fund managers that there are reputational rewards to be reaped (in equilibrium) from buying. Thus, the fund manager who receives s t = wishes to buy this asset from pro t motivations, and for reputational reasons. Thus he is willing to pay a price above the fair informational value of the asset at t in order to own it. The monopolistic market maker sees this as an opportunity for extracting rents, and sets ask prices strictly above expected liquidation value to make positive pro ts. The fund manager who receives s t = wishes to sell for pro t reasons, but to buy for reputational reasons. The price at which he would sell will be higher than v t, which is the highest price the market maker would ever be willing to pay him. Thus, this manager does not trade. Could the market maker deviate to increase his pro ts? It is clear that he would never wish to make fund managers with s t = change their behavior, since he can already extract maximal surplus from these traders. However, as long as fund managers with s t = buy, it is also not optimal for him to induce fund managers with s t = to also buy (for which he would have to lower prices). Intuitively, the market maker makes pro ts by selling reputation to fund managers. However, if he persuades all managers to always buy, there is no reputational bene t to buying. In turn, therefore, the market maker cannot extract any positive rents from his trades with fund managers, and therefore makes zero pro ts. It will generally be in the interest of the market maker to extract reputational rents only from a strict subset of 9

10 the group of fund managers. 3 Equilibrium Trades and Prices In this section we delineate the properties of the equilibrium just identi ed. 3. Conformist Trading Fund managers never trade against popular opinion. If their private information agrees with the public belief (for example, if s t = when v t > ) then they trade in the direction of the public belief (e.g., buy when v t > ). If their private information contradicts the public belief (for example, if s t = when v t > ) then they choose not to trade. 3. The Reputational Premium The willingness of fund managers to trade at unfavorable prices in order to enhance their reputation can lead to prices deviating from expected liquidation value. We de ne the reputational premium as the di erence in expected transaction prices, conditional on trade taking place, in the presence and absence of career concerns. When =, p a t = v t, p b t = v t, and trade always occurs. Thus, the expected transaction price is v t. When >, prices and equilibrium behavior depend on the public belief v t. For concreteness, we focus on the case where v t > (the case where v t < is symmetric, and it is easy to verify that there is no reputational mispricing at v t = ). Trade occurs only if the selected fund manager observes s t =, in which case there is a buy order. Therefore, the expected transaction price with >, conditional on a trade taking place, is: vt + w w Thus, the reputational premium is given by: RP (; v t ) = vt + w w v t : We now consider some properties of RP (; v t ): 3.. The e ect of contractual incentives The degree of reputational concerns for fund managers depend on their contractual incentives. In our model, this is measured by. When v t >, increasing clearly increases RP (; v t), because it increases the ask price in the presence of career concerns without a ecting either

11 the probability of trade or any other prices. Similarly, when v t <, increasing clearly decreases RP (; v t ), i.e., increases the reputational discount. 3.. The e ect of the public belief Fixing v t >, how does RP (; v t) change as a function of v t? While the relationship between RP (; v t ) and v t can be non-monotone, when fund managers career concerns are su ciently strong, the reputation premium is strictly increasing in v t. To see this, observe that: RP (; v t ) = vt + w w v t = vt v t + w w While the expression vt v t may be non-monotone, it is easy to see that w w is strictly increasing in v t, because w increases while w decreases in v t. Thus, the overall expression strictly increases in v t as long as is large enough. 3.3 The cost of conformism As our discussion above has made clear, fund managers only trade in the direction of the public belief (thus, in a conformist manner), and do so at prices that are too high or too low, depending on whether the public belief is optimistic or pessimistic. Our model allows us to quantify the price that fund managers pay for their conformism, as a function of when they buy (sell) in a given sequence of buy (sell) orders. We restrict attention to the case where v t >. The other case is symmetric. When a fund manager (with s t = ) buys, his trading pro ts are given by: v t p a t = v t v t (w w ) < : Thus, this manager makes an expected trading loss, for which he is compensated by an expected reputational bene t. Note that w w is increasing in v t, and thus the higher is the public belief when the manager buys, the higher are his expected trading losses. But high v t is achieved in this equilibrium only by persistent net buying. Thus, the later a manager buys in a sequence with a set of net buy orders, the greater will be his losses. In other words, the larger the group of traders that the manager chooses to conform with, the higher is the price of conformism that he must pay. 3.4 Institutional conformism, price reversals, and market inactivity It is clear that institutional buy or sell sequences are reversible in our model. When fund managers buy in a sequence following a neutral public belief of v t =, this ensures that v t >,

12 and the price rises. However, following such purchases, fund managers with s t = may arrive, and they will choose not to trade or to sell respectively. Such actions will (eventually) lead to a reversal of the price pattern. Our analysis has important joint implications for the degree of market activity (as measured by the number of transactions per period for a given asset) and reversals in realized transaction prices, which we comment on here. Suppose that two or more fund managers have bought in a sequence up to and including period t, leading to a pattern of increasing public beliefs ( v t < v t ) and realized transaction prices (p a t < pa t ). How can such a pattern be reversed? That is, when is it possible to see a transaction occur at a price smaller than p a t, the most recent transaction price? Since v t+ >, the equilibrium strategies dictate that no fund manager will sell, the only possible cases are (a) there is a further purchase at t + (which continues the pattern of increasing prices, so that v t+ > v t+ and p a t+ > pa t ) or (b) there is no trade at t +. The latter reveals that a fund manager with s t+ = faced the market maker. This, in turn, lowers public beliefs to v t+ = v t > so that quoted prices at t + are identical to the prices in the most recent period (t) in which a transaction took places: p a t+ = pa t and p b t+ = pb t. Now, since v t+ > ; again the only possibilities are (a) a further buy order at t +, which implies that realized transaction prices do not fall, or (b) no trade at t +, which leads to v t+3 < v t, and thus lowers the potential transaction prices below the most recent transaction price. Thus, only following two periods of no-trade at t + and t +, is it possible that a transaction will occur (at t + 3) at a price strictly lower than the most recent transaction price; p a t. Thus, a reversal in transaction prices following an institutional buysequence must be preceded by at least two successive periods of no-trade. Market inactivity precedes transaction-price reversals. Consistent with the results in this section, recent empirical studies nd that an abnormally low trading volume predicts return reversals. For example, Connolly and Stivers (3) document that the weekly returns of a portfolio of large U.S. stocks exhibit reversals following a period of low abnormal turnover. Avramov, Chordia and Goyal (6) nd that monthly returns of low turnover stocks exhibit more reversals than high turnover stocks. Finally, Cooper (999) examines weekly returns for large U.S. stocks and nds that low volume stocks exhibit greater reversals than high volume stocks. 3.5 The short-term and long-term price impact of institutional herding: interpreting existing results To conclude our discussion of the properties of the equilibrium identi ed in Proposition, we now consider existing empirical results on the price impact of institutional conformism.

13 Our simple model provides a stylized framework within which it is possible to rationalize two important sets of existing empirical results in this area of the literature. A core conclusion that emerges out of our theoretical analysis is that, in markets dominated by fund managers, stocks that have been persistently bought (sold) by career-concerned fund managers are overpriced (underpriced), and thus are likely to have below (above) average returns in the long-term (at horizon T + ), once uncertainty has been resolved and prices adjust to fundamental value. This observation follows from the existence of the reputational premium: in section 3., we show that the reputational premium is strictly positive for persistently bought assets, and negative for pursistently sold ones. This nding provides a theoretical grounding for the results of Dasgupta, Prat, and Verardo (7). They consider the aggregate portfolio holdings of money managers who le 3F reports at a quarterly frequency, and identify those stocks that have been persistently bought or sold (over several quarters) by institutions as a whole. They examine the returns to such stocks at long (two year) horizons and nd evidence of negative performance for peristently bought stocks and positive performance for persistently sold stocks. Complementary evidence for such negative long-term predictability can be found in Braverman, Kandel and Wohl (5), Frazzini and Lamont (7), and Coval and Sta ord (7). In contrast to Dasgupta, Prat, and Verardo (7), an earlier strand of the literature has found positive return predictability from institutional conformism at short horizons. In particular, Wermers (999) and Sias (4) nd that stocks that institutions herd into (and out of) exhibit positive (negative) abnormal returns at horizons of a few quarters. The results of section 3.4 show that our model can also generate equilibrium outcomes consistent with these ndings. The analysis in section 3.4 showed that following an institutional buy (sell) sequence up to time t, in a market dominated by fund managers, expected transaction prices at t + and t + could not be lower than the transaction price at t. Thus, stocks bought ex post at realized transaction prices at t and then sold at realized transaction prices at t + or t + will, on average, have positive expected returns. 4 Discussion We have seen that the presence of career concerns on the part of fund managers can be shown to have important consequences for short and long-term prices and returns of assets that they trade. To date, we have assumed that fund managers care about their reputation. In this section we brie y discuss a microfoundation for fund-manager payo s. A more detailed approach to such microfoundations in related models can be found in the related model of Dasgupta and Prat (5). 3

14 There are a large number, N F, of islands. On each island i live an investor and two fund managers: an incumbent fund manager and a challenger. The investor cannot trade directly and must use a fund manager. There are two long periods ( years ). In year, the investor is (exogenously) assigned to the incumbent fund manager. In each year, one asset is traded, with equiprobable liquidation value or. The trading process and the information structure in the rst year are exactly as described in the reduced-form model. The number of periods of trading in the rst year is very small in comparison to the number of islands. At the end of the rst year, each investor i observes whether his fund manager has traded, but he does not observe whether his fund manager had the opportunity to trade. The investor is unable to distinguish between a manager who did not have the chance to trade and one who did but chose a t =. Also at the end of the rst year, a new generation of fund managers appear, one in every island. Their ability ~ is uniformly distributed over [; ]. In the second period, trading occurs again in the same format as the rst period, with two exceptions: in this second period, (a) fund managers do not have career concerns and thus prices do not rise above or below the fair information-based levels, and (b) there are some noise traders, the presence of whom make it optimal for investors to wish to retain fund managers only if he believes that they are better than average. If the fund manager is paid a fraction of the rst year s pro ts along with a xed wage, this formulation generates a payo function that is a special case of the baseline model. The discerning reader will have already concluded that a shortcoming of our analysis to date is that investors who use delegated portfolio managers earn negative expected returns in the rst period, and thus delegation is not optimal for fully rational investors. There is, of course, a fair amount of evidence to suggest that retail investors place their money in actively managed funds despite the fact that the after-cost return of these funds is lower than those of index funds. For example, Carhart (997) nds evidence of mutual funds underperformance on a style-adjusted basis. Daniel, Grinblatt and Titman (997) use a characteristics-based measure of performance for a large sample of mutual funds and nd that the amount by which the average fund beats a passive strategy is approximately equal to the average management fee. Wermers () documents that mutual funds on average beat the market index, but not by enough to cover their expenses and transactions costs. Nevertheless, it is worth discussing this point from a theoretical angle. The suboptimality of delegation to fund managers is a consequence of the absence of liquidity-driven traders in our model. Such traders are standard in models of nancial markets with asymmetric information, but in our setting with career concerned traders and monopolistic market makers, the introduction of this third class of 4

15 traders would lead to substantial modelling complexity, which is beyond the scope of this paper. However, such an extension presents no conceptual di culties, and we can sketch the basic idea here. For example, we could augment the model to include noise traders who buy from and sell to the market maker with probabilities b and s, respectively. In addition, as in Copeland and Galai (983), we could posit that liquidity driven traders trade with lower probability when prices are unfavorable, i.e., b decreases in the ask-price, and s increases in the bid-price. 8 Finally, in order to suitably enrich the model, we could consider a continuum of types of fund managers di erentiated by private signals about the precision of their own information. Now consider a situation in which v t >. Consider the set of traders who have received signal s t =. Let v t and v t denote the expected values of the asset from the perspective of the most informed and least informed traders respectively. The managers willingness to pay for the asset, however, is higher due to reputational concerns (since v t > ). Let the corresponding minimal and maximal willingness to pay be denoted by p a t (> v t ) and p a t (> v t ). Imagine that the market maker is considering whether to increase prices above v t. Raising the price has three e ects at the margin: () it discourages noise trading, which diminishes the market maker s pro ts; () it reduces his losses against well-informed fund managers; and (3) it increases his pro ts against badly informed career concerned traders (for example, the market maker pro ts from tradingh withimanagers with expected value v t and willingness to pay p a when the price p a lies in v t t ; p a ). E ect () discourages high prices, while e ects t () and (3) encourage them. It is clear that, under reasonable assumptions, the optimal ask price will lie in the interval v t ; v t. Then, badly informed managers will make expected losses and well informed managers will make expected pro ts. On average, delegation will be rational, and it will be in the investor s interest to monitor their fund managers in order to learn their types. Finally, note that if we replaced a given set of fund managers by an identially informed set of non-career concerned traders, then e ects () and () delineated above will still exist, but e ect (3) will vanish. This will lead to a lower ask price. Thus, the presence of career concerned managers would lead to a reputational premium as in the baseline model. However, as the preceding discussion makes clear, the fully formal modelling of such an enriched market is very complex and is well beyond the scope of this paper. 8 Implicitly, the assumption that supports this is that there is are di erences in the willingness of noise traders to pay for liquidity, with some of them willing to pay very unfavourable prices while others stop trading at such prices. 5

16 5 Conclusion In this paper, we have presented a simple yet rigorous model in which we can theoretically delineate the price impact of institutional herding. Our model extends the analysis of Dasgupta and Prat (5) into a market with limits to arbitrage, in which career-concerned money managers interact with pro t-motivated security dealers with market power. The interaction between these three classes of traders generates rich implications. Our model makes three main contributions. First, we show theoretically that money managers will trade in a conformist manner due to their reputational concerns, despite the fact that such conformism has a rst-order impact on the prices of assets that they trade. Second, we delineate the properties of the price impact of institutional conformism: we argue that, in markets dominated by institutional traders, assets persistently bought (sold) by money managers will trade at prices that are too high (low), and that this will generate return-reversals in the long-term, when uncertainty is resolved. We also show that our equilibrium is not inconsistent with the existence of short-term increasing (decreasing) transaction-price paths following an institutional buy (sell) sequence. Our analysis, therefore, provides a simple and stylized framework to interpret existing empirical results on the price impact of institutional herding at long and short horizons. Finally, our model generates a number of new empirical predictions that represent potential directions for future empirical analysis. 6

17 6 Appendix Proof of Proposition : We rst demonstrate the proof for the case in which v t >. The case for v t < is symmetric. The proof for v t = is presented after the proof for v t >. Case: v t > Fund manager s strategy: We begin by computing some equilibrium posteriors. because w = Pr (gjv = ; a = ) Pr (v = js = ) + Pr (gjv = ; a = ) Pr (v = js = ) = Pr (gjv = ; s = ) vt + Pr (gjv = ; s = ) vt = + v t w = Pr (gjv = ; a = ) Pr (v = js = ) + Pr (gjv = ; a = ) Pr (v = js = ) = + ( + ) ( ) v t + + ( + ) ( ) v t Pr (gjv; a = ) = = = = = Pr (a = jg; v) Pr (gjv) Pr (a = jg; v) Pr (gjv) + Pr (a = jb; v) Pr (bjv) Pr (a = jg; v) Pr (a = jg; v) + Pr (a = jb; v) ( ) ( + ( ) Pr (s = jg; v)) ( + ( ) Pr (s = jg; v)) + ( + ( ) Pr (s = jb; v)) ( ) 8 < if v = +(+ ( ))( ) : (+( )) if v = (+( ))+(+( ) )( ) ( +(+)( ) if v = +(+)( ) if v = The expressions for w and w are analogous Suppose the fund manager has received signal s t =. If he buys, he receives: If he does not trade, he also receives w. v t p a t + w = w Finally, if he sells (an o equilibrium action) we assume that the investor believes that it was because he received signal s t =, so that w = ( v t ) +.9 Thus, the manager s expected payo from selling is p b t v t + w = v t v t + w < w 9 This is the natural o -equilibrium belief, that is robust to the presence of a small number of naive fund managers who always trade sincerely. 7

18 We show next that w < w, which will imply that the expected (deviation) payo from selling is strictly smaller than the expected (equilibrium) payo from buying. Recall that w = + + ( ) v t + + ( + ) ( ) v t It is clear that at =, w = w. We shall demonstrate that, for v t >, w is increasing in, which implies that for v t > and > it must be the case that w > w. To do so, we take the derivative of w with respect to = v + + t + ( ) + ( + ) ( ) v A t B = ( + + ( ) v t ( + ( + ) ( )) v t This expression is increasing in vt. Whenever v t >, it is clear that v t >. Evaluating this expression at vt = gives B ( = ( ) + + ( ) C ( + ( + ) ( )) A ( + ( + ) ( )) ( + ( + ) ( )) > Which then establishes that w < w, and thus selling is dominated for the manager with s t =. is: Suppose instead that the fund manager has received signal s t =. His payo from buying C A v t p a t + w = v t v t w w + w = v t v t + w w + w < w < w The penultimate inequality follows from the fact that vt vt < and w w <. To see why the latter is true, note that w = + v t < + v t = w. The nal inequality follows from the fact that w = + + ( ) v t + + ( + ) ( ) v t 8

19 while w = v + + t + ( ) + ( + ) ( ) v t and, clearly < + + ( ) +(+)( ) and v t < v t. If he does not trade, his payo is w. Thus, buying is dominated. Finally, if he chooses to sell (an o -equilibrium action), then, as before, the investor assumes (correctly in this case) that the signal received was s t =, and thus the expected reputational payo associated with selling is w = v t +. His total payo from selling is p b t v t + w = w To show that selling is dominated by non-trading, we need to show that w < w. This is analogous to the proof of w < w, shown above, and we brie y summarize it here. First note that for =, w = w. Now we shall show that w is increasing in for v B = ( + + ( ) v t ( + ( + ) ( )) v t This expression is increasing in vt. When v t >, the lowest equilibrium value it can take (following a buy order, which comes from a trader with s t = ) is vt (v t = ) = ( + ). For v t = ( + ), it is easy to see that v t =. Thus, for v t >, v t. Now, substituting in vt = into the above derivative, we note that it is clearly positive, > for all v t >, which establishes that w < w. Therefore, it is optimal for the manager with s t = not to trade. Market maker s strategy: By using the equilibrium strategies, the MM can extract positive (maximal) surplus from s t = fund managers, but gets zero surplus from interacting with s t = fund managers. It is clear that he will not wish to change the behavior of s t = managers. We rst show that as long as s t = managers buy, the MM will never wish to have s t = managers sell with positive probability. In any putative equilibrium in which the s t = managers buy, and the s t = sell with positive probability, the posterior for non-trading is identical to the original equilibrium posterior w (because non-trading reveals that the manager either got signal s t = or did not receive a trading opportunity. Similarly, the putative equilibrium posterior for selling is identical to the sincere o -equilibrium belief used above: w (because sales in the putative equilibrium identify the manager as having received signal s t = ). In order to sell with positive probability, the manager with s t = C A 9

20 must at least weakly prefer selling to non-trading. Denoting the bid price in this putative equilibrium by ep b t, we now can write down: This, in turn, implies that ep b t v t + w w ep b t v t + w w > v t since we have shown earlier that w > w. But bidding such a price can never be incentive compatible for the MM, which rules out this possible deviation. The only remaining alternative is that the market maker prices to induce both s t = and s t = managers to buy. We need to check that his pro ts in this potential deviation are smaller than his (strictly positive) equilibrium pro ts. Suppose that the market maker prices to induce the s t = manager to buy with probability (; ], and to not trade with probability. The expected reputational payo s from buying in this putative equilibrium are as follows:! bw = vt + ( v t ) + ( ) ( + )! bw = vt + ( v t ) + ( ) ( + ) It is easy to see that bw > bw. By a similar set of computations, the reputational payo s from not trading in this putative equilibrium are as follows: bw = vt + + ( ) ( ) +( v ( + ( ) ( )) t ) ( ) ( + ( ) ( )) + + ( ) ( ) ( ) bw = vt + + ( ) ( ) +( v ( + ( ) ( )) t ) ( ) ( + ( ) ( )) + + ( ) ( ) ( ) It is easy to see that bw < bw. Denote the revised ask price in such a putative equilibrium by bp a t. Since the fund manager with s t = must weakly prefer buying to not trading, it must be the case that bw v t bp a t + bw i.e., bp a t v t + bw bw : The MM s expected pro t under the equilibrium strategy is: E Pr(s t = )(p a t vt ) = Pr(s t = ) w w

21 The MM s expected pro t under the putative deviation is: Since bp a t vt + bw bw D Pr(s t = )(bp a t v t ) + Pr(s t = )(bp a t v t ): D Pr(s t = )(vt + bw bw vt ) + Pr(s t = )(vt + bw bw v t ) = Pr(s t = ) v t v t + Pr(st = ) bw bw + Pr(st = )( bw bw ) < Pr(s t = ) bw bw + Pr(st = )( bw bw ) = (Pr(s t = ) + Pr(s t = )) bw bw = Pr(a t = ) bw bw UBD () We show below that UB D () < E for all [; ], which implies that the deviation is unpro table for the MM. First, note that bw bw = < Pr(v = js = ) (Pr ( = gja t = ; v = ; ) Pr ( = gja t = ; v = ; )) + Pr(v = js = ) (Pr ( = gja t = ; v = ; ) Pr ( = gja t = ; v = ; )) Pr(v = ja t = ) (Pr ( = gja t = ; v = ; ) Pr ( = gja t = ; v = ; )) + Pr(v = ja t = ) (Pr ( = gja t = ; v = ; ) Pr ( = gja t = ; v = ; )) where the inequality follows from the fact that, since managers with s t = also buy, Pr(v = ja t = ) > Pr(v = js = ). The expression to the right of the inequality can, in turn, be written as follows: Pr(v = ja t = ) Pr ( = gja t = ; v = ; ) + Pr(v = ja t = ) Pr ( = gja t = ; v = ; ) = Pr ( = gja t = ; ) Pr(v = ja t = ) Pr ( = gja t = ; v = ; ) + Pr(v = ja t = ) Pr ( = gja t = ; v = ; )! C A Pr(v = ja t = ) Pr ( = gja t = ; v = ; ) + Pr(v = ja t = ) Pr ( = gja t = ; v = ; )!!! Thus, UB D () can be written as: Pr(a t = ) Pr ( = gja t = ; ) Pr(v = ja t = ) Pr ( = gja t = ; v = ; ) + Pr(v = ja t = ) Pr ( = gja t = ; v = ; )!!

22 which, by adding and subtracting Pr(a t = ) Pr ( = gja t = ; ), can be further written as: Pr(a t = ) Pr ( = gja t = ; ) + (Pr(a t = ) Pr ( = gja t = ; ) Pr(a t = ) Pr ( = gja t = ; ))! Pr(v = ja t = ) Pr ( = gja t = ; v = ; ) C A Pr(a t = ) + Pr(v = ja t = ) Pr ( = gja t = ; v = ; )! Pr(v = ja t = ) Pr ( = gja t = ; v = ; ) Pr(a t = ) = + Pr(v = ja t = ) Pr ( = gja t = ; v = ; )! Pr(v = ja t = ) Pr ( = gja t = ; v = ; ) C A + Pr(a t = ) + Pr(v = ja t = ) Pr ( = gja t = ; v = ; )! Pr(a t = ) Pr(v = ja t = ) = Pr ( = gja t = ; v = ; ) + Pr(a t = ) Pr(v = ja t = )! Pr(a t = ) Pr(v = ja t = ) Pr ( = gja t = ; v = ; ) + Pr(a t = ) Pr(v = ja t = ) Claim 3 = (Pr(v = ) Pr ( = gja t = ; v = ; ) + Pr(v = ) Pr ( = gja t = ; v = [Pr(v = ) Pr ( = gja t = ; v = ; ) + Pr(v = ) Pr ( = gja t = ; v = ; )] > Proof of claim: From the expressions delineated above we know that: and Pr ( = gja t = ; v = ; ) = Pr ( = gja t = ; v = ; ) = Direct computation shows that + + ( ) ( ) ( ) ( + ( ) ( )) ( + ( ) ( )) + + ( ) ( ) ( ) Pr ( = gja t = ; v = ; Pr ( = gja t = ; v = ; Pr ( = gja t = ; v = ; Pr ( = gja t = ; v = ; ) > : Since, for v t >, by de nition, Pr(v = ) > > Pr(v = ), the claim is proved. From Claim 3 it follows that UB D () is decreasing in, and thus is maximized for =. But, since at =, bw = v t +, and bw = w (the equilibrium expected posterior for a

23 manager who does not trade when he receives signal s t = ). UB D () = Pr(s t = ) vt + w < Pr(s t = ) w w = E + > v t because, it is clear that w = v t Thus the deviation is unpro table. This completes the proof for v t >. Case: v t = When v t =, we can compute that v t = +, and we have shown earlier than w < w. ( + )v t v t + = ( + ) + = + and we can then compute the expected reputation from buying for a manager who has received signal s t =. In this equilibrium, w = v t + = Thus, the highest price that the FM with s t = is willing to pay is v t, at which price he is indi erent between buying and not trading, and strictly prefers both to selling. Thus, the MM is indi erent, and it is a best response for him to set p a t = v t. The sell side is symmetric. 3

24 References [] Franklin Allen and Gary Gorton. Churning Bubbles. Review of Economic Studies 6(4): [] Christopher Avery and Peter Zemsky. Multidimensional Uncertainty and Herd Behavior in Financial Markets. American Economic Review, 88(4): [3] Avramov, Doron, Tarun Chorida, and Amit Goyal, 6, Liquidity and Autocorrelations in Individual Stock Returns, Journal of Finance 6, [4] Abhijit Banerjee. A Simple Model of Herd Behavior. Quarterly Journal of Economics, 7: [5] Braverman, Oded, Shmuel Kandel, and Avi Wohl, 5, The (Bad?) Timing of Mutual Fund Investors. Working paper, Tel Aviv University. [6] Sushil Bikhchandani, David Hirshleifer and Ivo Welch. A Theory of Fads, Fashion, Custom, and Cultural Change as Information Cascades. Journal of Political Economy, : [7] Carhart, Mark M., 997, On persistence in mutual fund performance, Journal of Finance 5, [8] Cohen, Randolph B., Paul A. Gompers, and Tuomo Vuolteenaho,, Who underreacts to cash- ow news? Evidence from trading between individuals and institutions, Journal of Financial Economics 66, [9] Connolly, Robert, and Chris Stivers, 3, Momentum and Reversals in Equity-Index Returns during Periods of Abnormal Turnover and Return Dispersion, Journal of Finance 58, [] Cooper, Michael, 999, Filter rules based on price and volume in individual security overreaction, Review of Financial Studies, [] Thomas Copeland and Dan Galai. Information E ects on the Bid-Ask Spread. Journal of Finance, 38, [] Coval, Joshua, and Erik Sta ord, 7, Asset re sales (and purchases) in equity markets, Journal of Financial Economics, forthcoming. 4

25 [3] Daniel, Kent, Mark Grinblatt, Sheridan Titman, and RussWermers, 997, Measuring mutual fund performance with characteristic-based benchmarks, Journal of Finance 5, [4] Amil Dasgupta and Andrea Prat. Information Aggregation in Financial Markets with Career Concerns, 5, Journal of Economic Theory, forthcoming. [5] Amil Dasgupta and Andrea Prat. Financial Equilibrium with Career Concerns. Theoretical Economics, 6. [6] Amil Dasgupta, Andrea Prat, and Michela Verardo. Institutional Trade Persistence and Long-Term Equity Returns. Working Paper, 7. [7] Andrea Frazzini and Owen Lamont, 7. Dumb money: Mutual fund ows and the cross-section of stock returns, Journal of Financial Economics, forthcoming. [8] Lawrence R. Glosten and Paul R. Milgrom. Bid, Ask and Transaction Prices in a Specialist Market with Heterogeneously Informed Traders. Journal of Financial Economics 4(): 7-, 985. [9] Grinblatt, Mark, Sheridan Titman, and Russ Wermers, 995, Momentum investment strategies, portfolio performance, and herding: a study of mutual fund behavior, American Economic Review 85, [] Zhiguo He and Arvind Krishnamurthy. Intermediation, Capital Immobility, and Asset Prices. Working paper, Northwestern University, 6. [] Peter Kondor and Veronica Guerrieri. Emerging Markets and Financial Intermediaries. Working paper, 7. [] Lakonishok, Josef, Andrei Shleifer, and Robert W. Vishny, 99, The Impact of Institutional Trading on Stock Prices, Journal of Financial Economics 3, [3] Nofsinger, John, and Richard Sias, 999, Herding and feedback trading by institutional and individual investors, Journal of Finance 54, [4] David Scharfstein and Jeremy Stein. Herd behavior and investment. American Economic Review 8: , 99. [5] Vivek Sharma, John Easterwood, and Raman Kumar. Institutional Herding and the Internet Bubble. Working paper, University of Michigan Dearborn and Virginia Polytechnic Institute. 6. 5

26 [6] Sias, Richard, 4, Institutional Herding, Review of Financial Studies 7, [7] Sias, Richard, Laura Starks, and Sheridan Titman,, The Price Impact of Institutional Trading, Working Paper. [8] Wermers, Russ, 999, Mutual Fund Herding and the Impact on Stock Prices, Journal of Finance, 54, [9] Wermers, Russ,, Mutual fund performance: An empirical decomposition into stockpicking talent, style, transaction costs, and expenses, Journal of Finance 55,