Costless Versus Costly Signaling: Theory and Evidence from Share Repurchases *

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1 Costless Versus Costly Signaling: Theory and Evidence from Share Repurchases * by Utpal Bhattacharya 1 and Amy Dittmar 2 JEL Classification: D80, G14, G30 Key Words: Cheap talk, costly signals, share repurchases First version: January 2001 This version: February Kelley School of Business, Indiana University, Bloomington, IN ubhattac@indiana.edu 2 Kelley School of Business, Indiana University, Bloomington, IN adittmar@indiana.edu * This paper has benefitted from the response of seminar participants at Alabama, Humboldt, Frankfurt, Illinois, Indiana, INSEAD, Norwegian School of Management, Notre Dame, Penn State and Pittsburgh.

2 COSTLESS VERSUS COSTLY SIGNALING: THEORY AND EVIDENCE FROM SHARE REPURCHASES Abstract When does a good firm separate itself from a bad firm by putting its money where its mouth is and when does it engage in cheap talk? We develop a simple model in this paper to find out which signaling mechanism will be used under what circumstances in a capital market. We find, as one would expect, that the good firm prefers cheap talk over costly signaling, because in the latter method, all of the cost of separation is being borne by the firm. However, costless signaling can only be used by good firms who are more undervalued and are more ignored. These restrictions exist because cheap talk will only attract attention from speculators when scrutiny is likely to uncover more opportunities for trading profits that will cover the costs of scrutiny. We then test the predictions of the model using a data set of open market share repurchases that contains firms that employ costless signals (announce share repurchases, but do not repurchase) as well as firms that employ costly signals (announce share repurchases, and repurchase). The evidence in favor of the predictions of the model is surprisingly robust.

3 COSTLESS VERSUS COSTLY SIGNALING: THEORY AND EVIDENCE FROM SHARE REPURCHASES When does a good firm separate itself from a bad firm by putting its money where its mouth is and when does it engage in cheap talk? Signaling theory predicts that a good firm can separate itself from a bad firm by giving a costly signal to capital markets; the bad firm will not mimic because the signal is costlier for the bad firm. A good firm can also separate itself by engaging in cheap talk to attract scrutiny; the bad firm will not mimic because the bad firm does not gain from being discovered. This paper explores, both theoretically and empirically, when do good firms use costly signals to separate and when they use costless signals to separate. The first contribution of this paper is to develop a simple theoretical model that gives a good firm the choice between costless and costly signaling in a capital market. This allows us to make precise the circumstances under which each signaling mechanism will be used. We obtain the following insights from our theoretical model. The good firm always prefers costless signaling over costly signaling because, in the latter method, all of the cost of separation is being borne by the firm; whereas, in the former method, all of the cost of separation is being borne by a speculator who, after his attention has been attracted, finds it optimal to expend search costs to find out more about the firm. The good firm is, thus, discovered. The bad firm does not gain from being discovered, and so it does not attract attention. Separation by costless signals, however, is effective only under very special circumstances in a stock market. This is because the speculator will only undertake search if he hopes to discover substantial material non-public information about a firm and then make substantial trading profits to cover the cost of scrutiny. As only good firms, i.e. only undervalued firms, signal in equilibrium, substantial material non-public information can only be obtained if the firm is deeply undervalued. Second, the discovery of substantial material non-public information about a firm is useless if many other speculators discover the same information and compete away all trading profits. In other words, if the size of informed trading increases, stock prices become more informative, and so the value of the additional information that can be obtained from costly search diminishes. To summarize, 1

4 our theoretical model predicts costless signals are effective for more undervalued firms and for more ignored firms. For other firms, this signaling mechanism will not work, and they have to put their money where their mouths are employ costly signals. The second contribution of our paper is to take the above two testable implications of our theoretical model to the data. To test our model, we need a signaling mechanism that allows a firm a choice between a costly and a costless signal. Our data set consists of a sample of firms that have announced open market share repurchases. This data set offers a unique opportunity to test the predictions of our theoretical model, because we find that 46% of all firms that announce share repurchase programs do not purchase a single share within the quarter of or the quarter following the announcement. As a matter of fact, 27% of firms that announce, do not repurchase within four fiscal years of the announcement or prior to dropping out of Compustat. Thus, if a repurchase announcement signals value, then these firms simply use the announcement, which is virtually costless, to attract scrutiny from speculators and have their true value discovered, whereas the rest of the firms repurchase their shares, which is costly, to signal their true value. The differences between these two sets of firms should shed some light as to which type of firms use costless signaling and which type of firms use costly signaling, enabling us to test the predictions of our model. We test the predictions of our theoretical model using proxies for measuring the two variables of interest. Our proxy for measuring our first variable of interest, undervaluation, is the amount of positive information that comes out at the announcement or between the announcement date and the time the firm reveals if it has used a costly or a costless signal. Since firms do not report stock repurchases until they file their quarterly statements, the market may not know the type of signal until the close of the next fiscal quarter. Thus, we assume that the signal corrects the undervaluation within t days after the announcement where we take t to be one day, one quarter or two quarters. A classical measure of the amount of undervaluation is the abnormal returns from the announcement till date t, and this is what we use. Our primary proxy for measuring our second variable of interest, ignorance, is the number of analyst following. We also use firm size since the market is typically better informed about large versus small firms. 2

5 The following are our results from our empirical tests. We find that firms that announce share repurchases and do not carry them out, have higher cumulative abnormal returns over the announcement period, have fewer analysts following them, and are smaller than firms which announce share repurchases and carry them out. These results indicate that firms that are more undervalued and are more ignored are more likely to use a costless signal. These two pieces of evidence provide strong support for our model. Our theoretical model liberally borrows insights from two strands of a vast signaling literature. The first strand, the costly signaling literature, began with Spence (1973). He showed that if the cost of the signal is higher for the bad type than it is for the good type, the bad type may not find it worthwhile to mimic, and so the signal could be credible. Riley (1979) formalized the conditions under which such costly signaling equilibria exist. Numerous papers giving examples of such costly signaling in capital markets followed. An early paper was by Ross (1977), who showed how debt could be used as a costly signal to separate the good from the bad. The second strand, the cheap talk literature which we call costless signaling in this paper, began with Crawford and Sobel (1982). They showed that cheap talk, defined as a costless, non-binding, and unverifiable message, could also be a credible signal. They modeled a two-player non-cooperative information transmission game between a Sender and a Receiver. They demonstrated that the optimal response of the Receiver after a signal is received may affect the utility of the Sender in a way that it may be optimal for the Sender to tell the truth. In capital markets, an early paper was by Brennan and Hughes (1991), who modeled how good firms doing costless stock splits could motivate brokers to provide favorable reports about them. In a recent paper, Austen-Smith and Banks (2000) have also allowed both costless and costly signaling. The main difference between their model and ours is that they view the two types of signals as complements in a general framework, whereas we model them as substitutes in the specific context of signaling to capital markets. This means that the focus in Austen-Smith and Banks (2000) is on how costly signals can improve cheap talk communication, whereas the focus in our model is on when costly signals have to be used because costless signals will not work. 3

6 Our empirical tests also liberally borrow insights from a growing literature. We are not the first to empirically examine stock repurchases as signals of firm value (see, for example, Asquith and Mullins (1986), Comment and Jarrell (1991), Dann, Masulis and Mayers (1991), Hertzel and Jain (1991), Lee, Mikkelson and Partch (1992), and Vermaelen (1981)). However, most of these investigations assume that the repurchase is a costly signal, which may not be true in an open market stock repurchase program if the firm does not repurchase stock. Additionally, signaling firm value is not the only reason firms repurchase stock. We use control variables in our empirical tests to account for the other reasons that firms repurchase stocks, and which the literature has documented. Dittmar (2000) surveys the hypotheses expounded in the literature to explain why firms repurchase shares and finds that three other motives are important at different times in the period 1977 to The three other motives are: one, share repurchases are an alternative means of distributing cash to shareholders (see, for example, Brennan and Thakor (1990), and Lucas and McDonald (1996)); two, share repurchases may be used to tilt leverage ratios towards a target leverage ratio (see, for example, Bagwell and Shoven (1988), and Havakimian, Opler and Titman (2001)); and three, share repurchases may be preferred to dividends when a firm has employee stock options outstanding because most stock options are not dividend-protected and share repurchases allow the firm to distribute cash without diluting the per-share value of the stock. This third motive is particularly important if managers hold a lot of stock options (see, for example, Jolls (1996), Kahle (2001), Fenn and Liang (2001), and Weisbenner (2001)). 1 Finally, our theoretical and empirical analyses also address two puzzles in the repurchase literature: one, why some firms announce open market share repurchases, but never repurchase any stock; and two, why stock prices increase at the announcement of an open market repurchase program, even though the announcement does not commit the firm to purchase any stock, and many firms do not. Our hypotheses for these two puzzles, as formalized in our theoretical model and evidence provided in our empirical investigation 1 Dittmar (2000) also finds that share repurchases deter takeovers by increasing share prices (see Bagwell (1991)). However, this method is most commonly linked to self tender offers, not open market repurchases. The latter is the subject of our paper. 4

7 are: in some special cases, the mere announcement of an open market share repurchase attracts scrutiny from speculators, who then discover the true value of the firm; and two, this causes stock prices to increase at the announcement of an open market repurchase program, even though the announcement does not commit the firm to purchase any stock. Oded (2000), like us, also puzzles as to why the announcement of an open-market share repurchase program, which involves no commitment, is regarded as good news by the market. Ikenberry and Vermaelen (1996) argue that this may be because announcements are tantamount to creations of valuable options of buying undervalued shares in the future, but Oded (2000) argues that, if this were the reason, all types of firms would make such announcements. So, in equilibrium, such cheap talk cannot create value. He then goes on to develop a three-period signaling model that delivers positive announcement returns. In our paper, we contend that cheap talk can create value when it attracts the attention of speculators, who go on to discover the true value of the firm. We then put our hypothesis to the test. The plan of the rest of the paper is as follows. We introduce the model in Section I. In Section II we analyze the choice between costless signaling and costly signaling. The testable implications are formalized in Section III. The data is discussed in Section IV. Section V is devoted to the empirical tests of the model. Section VI concludes. I. Model There are two types of firms, good firms and bad firms, and each are equally likely. The good firms as well as the bad firms are equally likely to have good projects or bad projects. The bad projects of both the good firms as well as the bad firms have a payoff of - :. The good project of the bad firm has a payoff of +:, whereas the good project of the good firm is equally likely to have a payoff of +: or a payoff of +a:. Here a > 1. This asymmetry ensures that good news is uncertain, but bad news is certain for the market, an 5

8 assumption that is critical for delivering a cheap talk equilibrium. 2 Who knows what and when? This is given in Figure 1 below. Insert Figure 1 about here A. At time t At time t, the world comes to know that all firms will have access to a positive net present value project at time t+4. The NPV of this project is ". The investment required to start this project at time t+4 is I, which, with some loss of generality, we normalize to - :. This ensures that, if the firm does not do a costly signal, the project can be funded from payoffs in all states for all types of firms. B. At time t+1 At time t+1, a firm is born. As mentioned before, this firm could be good or bad with equal probability. The manager of the firm knows the type of her firm. She may decide to keep quiet or to signal its value. Value could be signaled in one of two ways: signal costlessly by attracting scrutiny or do a costly signal by spending money m. The manager will take the action that maximizes the expected price of her firm s share. In other words, there are current shareholders who employ the manager to maximize the expected share price, with agency problems, if any, resolved by the optimal contract between shareholders and the manager. C. At time t+2 At time t+2, it becomes known to all market participants whether a firm has a good project or a bad project, though it is not publicly known who this project belongs to, a good firm or a bad firm. 2 The reason we need the good news is uncertain, but bad news is certain assumption for a cheap talk equilibrium is that we need the search strategy of the trader to be state-contingent: search only the good firm that is attracting attention. The same critical assumption drives the results of the Bhattacharya and Krishnan (1999) paper. How valid is this assumption? Bhattacharya and Krishnan (1999) tested this. They obtained a sample of 1259 firms, each of which had data for fifteen quarters of 5-day returns after an earnings announcement. They then computed, for each firm, the mean and the skewness of cumulative abnormal returns (CAR) in this 5-day event window. The cross-sectional statistics of these firm-specific metric were as follows. The mean of the mean was indistinguishable from zero; the skewness ranged from a high of 0.67 to a low of -0.71, with a mean of Thus, good news is more uncertain than bad. 6

9 D. At time t+3 At time t+3, after receiving the public signal at time t+2, and after observing the action of the firm at time t+1 which, recall, could be a costless signal or a costly signal or inaction a risk-neutral trader can acquire, at a cost c, additional private information about the firm. This additional private information is a costly private signal he gets telling him exactly what the project payoff at t+4 will be. This information cost could be interpreted as the time and money spent doing further investigations by consulting an in-house expert or an outside expert. The information set of the trader will therefore consist of his observation of the manager s actions, a piece of public information, and the outcome of incremental costly information acquisition if he does any search. E. At time t+3.5 At time t+3.5, there is a market for shares of these firms. The details of this market are inspired by the extensive form introduced in Glosten and Milgrom (1985). 3 There is a risk-neutral market maker who commits himself to offer a liquidity supply schedule. To be specific, he commits himself to offer share prices that are conditioned on the manager s action, the public information, and his observation of order flows. We allow only three order flows: +q, +1 and -1. We exogenously restrict the size of the order flows, as did Glosten-Milgrom (1985), to prevent infinite orders from risk-neutral traders. Share prices are set such that the market maker s conditional expected profit in this competitive market is zero. In other words, the share price equals the conditional expected value of the firm, a conditioning that is done with respect to the market maker s information set. The market maker s information set is his observation of the manager s actions, the public information, and his observation of order flow. Order flows are noisy. They could be information-based or non-information based. The logic for making this assumption on order flow noise is now standard (see, for example, Grossman and Stiglitz (1980)). Without it, the informed trader s order would fully reveal his private information, and thus there would be 3 The Kyle (1985) model gives the same results in our binary framework. Krishnan (1992) uses a binary framework to show the equivalence between Glosten-Milgrom (1985) and Kyle (1985), given identical parametric assumptions. 7

10 no incentive to collect costly information to trade. We will assume that the small orders, +1 and -1, are information-based, whereas the large order, +q, is information-based with a probability B. This asymmetry ensures that good news is uncertain, but bad news is certain for the market-maker as well, an assumption that is critical for delivering a cheap talk equilibrium. 4 At t+3.5, the risk-neutral trader gives an order flow to maximize his expected profits. This order could be, as mentioned before, -1, +1, or +q. F. At time t+4 At t+4, since the -: funding required for the positive net present value project comes from the payoffs of the projects, and since the manager used up cash m for signaling (m equals zero for costless signaling or if the manager keeps quiet) at time t+1, the manager may have a shortfall of cash for the funding. This shortfall is s = Max [(-:) - (Project payoff at time t+4 m), 0] (1). She will have to borrow this shortfall s; otherwise, the positive NPV project will not be financed. External borrowing, as opposed to internal financing, is costly. Let the cost of borrowing the shortfall s be denoted by b(s). We shall assume that b(0) =0, and that b is increasing in s. The payoffs are revealed. Portfolios are consumed. 4 It is standard in market micro structure models and noisy rational expectations models to introduce noise in the order flow in this way. In some models, the non information-based noise is modeled, whereas in other models, it is assumed to be coming from noise traders. In most models, the non information-based noise is symmetric: there are as many buy non information-based orders as there are sell non information-based orders. There is no conceptual reason for assuming symmetry. Allen and Gorton (1982) derive intriguing results on price manipulation when non informationbased orders are asymmetric. 8

11 II. Equilibria From the point of view of the manager of the good firm, it is apparent in our model that if she could, she would like to separate her firm by attracting scrutiny rather than incurring the deadweight cost of a costly signal. The reason this is true is because in the former case, the cost of separation is being borne by the strategic trader, who may find it in his interest to expend search costs and differentiate these firms, whereas in the latter case, the cost of separation is being borne entirely by the firm. It should be mentioned here that this unambiguous preference for costless signals over costly signals is an artifact of our model; in more general models, this result may not hold. The reason this result may not hold in more general models, as in the model of Austen-Smith and Banks (2000), is because the Receiver of the signal can pass all of the costs of search to the Sender. As these search costs are passed entirely to the noise traders in our model, this will not happen here. This allows us to claim that the manager of the good firm will always like to separate by attracting scrutiny, but if that is not possible, costly signaling is the last resort. What are the special circumstances under which costless signaling is possible? We now explore this question. A. Separating by costless signaling Assume that q> 2/(1-B) and c < 0.25(a-1):[q(1-B) -2]. Conjecture that at time t+1 only good firms attract attention. If a firm has attracted attention at time t+1, and if the public information is good project at time t+2, conjecture that the trader searches at time t+3. If his search reveals the project payoff to be +: (+a:), conjecture that the trader gives an order +1 (+q) at time t+3.5. If a firm has attracted attention at time t+1, and if the public information is bad project at time t+2, conjecture that the trader does not search, and he gives an order of - 1 at time t+3.5. If a firm has not attracted attention at time t+1, and if the public information is bad project ( good project ) at time t+2, conjecture that the trader does not search, and he gives an order of - 1 (+1) at time t+3.5. Conjecture that the posted prices of the market maker, which are set at time t+3.5, are P(firm has attracted attention, good project, +q) = " + 0.5:{(a+1)+(a-1)B} > " + :; P(firm 9

12 has attracted attention, good project, +1) = "+:, P(firm has attracted attention, good project, -1) = " - :; P(firm has not attracted attention, good project) = " + : and P(bad project) = " - :. Finally, conjecture that at time t+4, the positive NPV project of value +" is undertaken by all types of firms. Will these conjectures hold in a subgame perfect equilibrium? To check, we work backwards. Assume that we are at time t+3.5. The various possibilities of the market maker s information set at t+3.5, his posterior beliefs given this information set and his conjectures, and the resultant prices that he posts are given in Table I below. Insert Table I about here Given the above posted prices of the market maker at t+3.5, we now examine the trader s expected profits for his various order flows under his possible information sets at t+3.5 in Table II below. Insert Table II about here As q> 2/(1-B) by assumption, 0.5 q:(a-1)(1-b) > :(a-1). Therefore, from Table II, our conjectures on the trader s order flow strategy is upheld. Specifically, if a firm has attracted attention at time t+1, and if the public information is good project at time t+2, and if a traders s search at t+3 reveals the project payoff to be +: (+a:), the trader gives an order +1 (+q) at time t+3.5. If, on the other hand, a firm has attracted attention at time t+1, and if the public information is bad project at time t+2, and if the trader does not search at t+3, the trader gives an order of - 1 at time t+3.5. If a firm has not attracted attention at time t+1, and if the public information is bad project ( good project ) at time t+2, and if the trader does not search at t+3, the trader gives an order of - 1 (+1) at time t+3.5. Table I tells us that the conjectures on the market maker s posted prices are upheld as well. Specifically, P(firm has attracted attention, good project, +q) = " + 0.5:{(a+1)+(a-1)B} > " + :; P(firm has attracted attention, good project, +1) = " + :, P(firm has attracted 10

13 attention, good project, -1) = " - :; P(firm has not attracted attention, good project) = " + : and P(bad project) = " - :. Let us now go to time t+3, where the trader has to make a decision on whether to incur an additional cost c to find out more about the firm. We need to show that the trader s search strategy to search only when a firm has attracted attention at t+1 and the public information at t+2 is good project is optimal. It is clear from the market maker s posted prices in Table I that share prices are fully-revealing in all states except the state where a firm has attracted attention at t+1 and the public information at t+2 is good project. We know from Grossman and Stiglitz (1980) that costly search is unprofitable under fully revealing prices. This implies that the only state where search could be profitable is the state where a firm has attracted attention at t+1 and the public information at t+2 is good project. If the trader searches in this state he is equally likely to discover a: or :. From Table II, his optimal order flow would be, respectively, +q or +1, and the consequent gross expected profits would be, respectively, 0.5 q:(a-1)(1-b) and 0. Therefore, the net expected profits from search is 0.25q:(a-1)(1-B) - c (2). If he does not search, and gives an order of +1, his net expected profit is going to be 1 [0.5(a:+"-(:+")) + 0.5(:+" -(:+"))] = 0.5:(a-1) (3). If he does not search, and gives an order of +q, his net expected profit is going to be q [0.5(a:+" -0.5:{(a+1)+(a-1)B}+" ) + 0.5(:+" -0.5:{(a+1)+(a-1)B} +" )] < 0 (4). Therefore, search when the firm has attracted attention and the public information is good project is optimal if (2) > (3). This gives us c < 0.25(a-1):[q(1-B) -2] (5). This was the assumption on the upper bound of c we had made earlier. As we had also assumed that q> 2/(1-B) (6), the right-hand side of inequality (5) is positive. Therefore, if inequalities (5) and (6) hold, the trader will only search the firm that has separated by attracting scrutiny and the public information is good news. He will 11

14 not search the firm in any other case. His optimal orders will be as given before, and the market maker s prices will be posted as shown in Table I. Let us now go to time t+1. To complete the proof, we have to show that, given these strategies of the other agents in the future, their conjectures on the signaling behavior of the managers at time t+1 will be upheld in equilibrium. Specifically, we need to check that the conjectures that only the good manager attracts attention at t+1, and that both types of firms undertake a project of positive NPV +" at t+4, are upheld. At time t+1, if the manager of the good firm is expected to separate herself by attracting scrutiny and she does, the price of her firm at t+3.5 will be (-:+") half the time, (+:+") a quarter of the time, and 0.5:{(a+1)+(a-1)B} +" a quarter of the time. So the expected price of this expected price maximizing good manager, if she attracts attention, is going to be 0.125:(a+(a-1)B) + " > ". If the manager of the bad firm is expected to keep quiet and she does, the price of her firm at t+3.5 will be (-:+") half the time and (+:+") half the time. So the expected price of this expected price maximizing bad manager, if she keeps quiet, is going to be ". If the manager of the good firm is expected to attract attention, but she decides to keep quiet, she will not invite search from the trader if she gets a good project. The trader will give an order of +1 here, which will beget a price of (+:+"). So the price of her firm at t+3.5 will be (-:+") half the time and (+:+") half the time, giving her an expected share price of of +". This is less than the expected share price she would get if she attracted attention. So she would separate herself by attracting attention. However, if the manager of the bad firm, who is expected to keep quiet but she does not, will invite search from the trader if she gets a good project. The search will reveal a payoff of +: to the trader, who will give an order of +1, which will beget a price of (+:+"). So the price of her firm at t+3.5 will be (-:+") half the time and (+:+") half the time. So the expected price of this expected price maximizing bad manager, if she decides to attract attention, is going to be ". This is the same expected share price she would obtain if she kept quiet. Assuming an epsilon fixed cost of attracting scrutiny, the bad manager will prefer to keep quiet. PROPOSITION 1: If the cost of search is below an upper bound, and there is an epsilon fixed cost of attracting scrutiny, we obtain a costless signaling equilibrium. In this equilibrium, the good type will 12

15 separate by attracting scrutiny, and will be discovered to be good. The bad type will keep quiet, and no one will investigate it. If the cost of search is greater than the upper bound, that is inequality (5) is violated, there will not be any search. If there is no search, traders will not be able to induce separation. Under this situation, the good firm will have no recourse other than to resort to costly signaling to separate itself. We now consider this equilibrium. B. Separating by costly signaling Our model on costly signaling follows the classic structure laid out by Spence (1973). The good firm separates itself by spending money m, whereas the bad firm does not do anything. At time t+4, the positive NPV project of value +" is undertaken by all types of firms. Suppose these are the conjectures of the market. We will now show that these conjectures will be upheld in a separating equilibrium. Assume that financing is not needed only when the project payoff is a:. Later we will give the condition on exogenous parameter values that will guarantee this assumption. If the bad firm stays true, does not spend cash m at t+1, and is regarded as a bad firm, its value, is " + 0.5(:) + 0.5(-:) = " (7). If the good firm stays true, spends cash m at t+1, and is regarded as a good firm, its value, is " + 0.5(-:) + 0.5(0.5(:) + 0.5(a:)) b(m) = " :(a-1) b(m) (8). If the bad firm deviates by spending cash m at t+1, and is perceived as a good firm, its value, is " :(a-1) - b(m) (9). If the good firm deviates by not spending cash m at t+1, and is perceived as a bad firm, its value, is " (10). Solve for m that makes (7) = (9). It will solve b(m*) = 0.25:(a-1) (11). It is easy to see that if m* solves (11), (8) > (10). As the good type will not like to spend more money than is needed to separate, it will spend just m*. The bad type will be indifferent. Finally, to ensure that 13

16 financing is not needed only in the best state, when the payoff is a:, our exogenous parameters have to satisfy the following condition: : - (-:) = 2: < m*, i.e., : < 0.5m* = 0.5 b -1 {0.25:(a-1)} (12) PROPOSITION 2: If c is above a lower bound, we have a costly signaling equilibrium. In this equilibrium, the good type will separate by spending money m*. The bad type will not spend any money. Note that in the above model demonstrating costly signaling, in the interest of consistency, we retained the critical assumption that drives the costless signaling result: good news is uncertain, but bad news is certain. This asymmetry is not needed for our costly signaling result. The only critical assumption needed for the costly signaling result is that good firms have a lower probability of a cash shortfall than bad firms at t+4. This ensures that if bad firms try to mimic the good firm, they will have to undertake costly refinancing more often. 5 III. Testable Implications Our theoretical model tells us that the good firm prefers costless signaling over costly signaling because, in the former method, all of the cost of separation is being borne by the speculator who, after his attention has been attracted, finds it optimal to expend search costs to find out more about the firm. The good firm is discovered. The bad firm does not gain from being discovered; so it does not attract attention. Speculators will only undertake search if they hope to discover substantial material non-public information about a firm and then make substantial trading profits to cover the cost of scrutiny. As only good firms, i.e. undervalued firms, signal, substantial material non-public information can only be obtained if the firm is deeply undervalued. The parameter a distinguishes the good firm from the bad firm. If a is 1, both firms are equivalent. As a increases, their difference increases, and, if the firms are pooled, the higher is the undervaluation of the good firm. Note that the upper bound of c given in (5) for which costless signaling 5 In this paper, repurchasing stock is costly because this leads to a cash shortfall, which in turn leads to costly external financing. The extant literature has modeled this cost in different ways. In Brennan and Thakor (1990), for example, share repurchase are costly because they redistribute wealth from uninformed shareholders to informed shareholders. Our results depend on share repurchases being costly; they do not depend on why they are costly. 14

17 works increases as a increases. This is depicted in Figure 2. Insert Figure 2 here Figure 2 gives us the first testable implication of our model. Everything else equal, especially holding the cost of search equal, more is the undervaluation of the good firm, greater is the likelihood of the good firm separating itself by a costless signal rather than a costly signal. The discovery of substantial material non-public information about a firm is useless if many other speculators discover the same information and compete away all trading profits. In other words, if the size of informed trading increases, stock prices become more informative, and so the value of the additional information that can be obtained from costly search diminishes. To put it another way, more is the informed trading, less is the benefit from search. The parameter B is a measure of the magnitude of informed trading. If B increases, informed trading increases, and if B equals 1, all prices are fully revealing, and there is no incentive to collect costly information. Note that the upper bound of c given in (5) for which costless signaling works decreases as B increases. This is depicted in Figure 3. Insert Figure 3 here Figure 3 gives us the second testable implication of our model. Everything else equal, especially holding the cost of search equal, more is the level of informed trading, less is the likelihood of the good firm separating itself by a costless signal rather than a costly signal. 6 6 The mass of informed traders, B, is exogenous in our model. It could be argued that the mass of informed traders is endogenous, and it should depend on the cost of search. We claim that this is not going to make any difference to the comparative statics. The reason is the following. If the only barrier to becoming a speculator is the cost of gathering information, the number of speculators in equilibrium will be such that if an additional speculator entered, he will lose money. Now suppose there is a shock in firm value which leads to a temporary disequilibrium. The additional speculator can now, perhaps, make short-term profits. He will make more short-term profits in the firm which had fewer speculators to begin with because there is less competition. Such firms will, therefore, attract the marginal speculator more. 15

18 IV. Sample and Data It is essential to the tests of the implications of our model that the firm has a choice of using a costless signal, which means that it has the freedom not to carry through an announced transaction. It is equally essential that some firms actually make this choice of not carrying through an announced transaction. The announcement of open market stock repurchases meets both of these requirements. When the board of directors approves an open market stock repurchase program, the firm typically announces the program to the public. They do this because, if they do not, the repurchase may be a violation of the safe harbor provisions under the stock price manipulation provisions of the Securities and Exchange Commission. According to Stephens, Jagannathan and Weisbach (2000), there is little evidence of firms repurchasing stock without first announcing the program. However, once the firm announces the repurchase program, it is not obligated to repurchase stock. Further, as will be shown in Table III, a significant proportion of firms announcing a stock repurchase never actually repurchase stock. This means that these firms signal with the announcement, but never incur the cost of the signal. Thus, open market stock repurchase announcements provide a unique opportunity to test the choice between costless and costly signals, and to investigate why some firms announce a share repurchase program and never repurchase any stock, whereas other firms announce and repurchase. 7 The initial sample consists of all firms announcing an open market stock repurchase between 1985 and 1995 as listed on Securities Data Corporation s Mergers and Acquisitions database. We exclude announcements in the last quarter of 1987, because the magnitude of the number of announcements suggests that these announcements may differ from typical repurchase programs. Netter and Mitchell (1989) show that twice as many repurchases were announced in this quarter than the prior three quarters of We do not consider repurchase announcements subsequent to 1995 because we wish to examine if the firm 7 Note that we do not claim that announcement of open market share repurchases is the only costless signal available to firms. Our claim is simply that announcement of open market share repurchases is that rare corporate signal that could be either costly or costless, depending on whether the firm repurchases its own shares or it does not. 16

19 repurchases stock for four fiscal years following the announcement. We limit our analysis to the first repurchase announcement by each firm during the sample period. This is because these subsequent announcements result in overlapping event windows when we consider the actual repurchases for the years following the repurchase. Additionally, the information content of subsequent announcements may differ from that of the initial announcement. We further require that the firms are listed on Compustat in the quarter of the announcement. This results in a sample of 2297 firm repurchase announcements. To determine if a firm repurchases stock, we use the Compustat data item Purchase of Stock. As discussed in Stephens and Weisbach (1998), these data overstate stock repurchases because they include: 1) conversions of class A, class B, and special stock into common stock; 2) conversions of preferred stock into common stock; 3) purchases of treasury stock; 4) retirement or redemption of common stock; 5) retirement of preferred stock; and 6) retirement or redemption of redeemable preferred stock. 8. In this paper, we are only interested in item 3, the purchase of treasury stock. We therefore adjust stock repurchases by reducing Purchase of Stock by any decrease in preferred stock that occurs. This removes items 2, 5, and 6. The resulting number may still be overstated by the amount of class A, class B, and special stock converted into common stock, and the amount of retired common stock. However, most firms have only a single class of stock and the retirement of stock is much less frequent than stock repurchases. Additionally, we measure if the firm repurchases stock, not the amount of the repurchase; thus, these errors should have little impact on our results. Data on the number of analysts following the stock are from IBES. The market capitalization and accounting data are from Compustat. The daily and quarterly stock returns are from CRSP. All explanatory variables, except returns, are measured as of the fiscal year end prior to the year of the repurchase announcement. Panel A of Table III shows that of the 2,297 firms that announce repurchase programs between This measure is the same as that used in Dittmar (2000) and Grullon and Michaely (2002). 17

20 and 1995, the majority (1,248 firms) make their first repurchases within the quarter of or the quarter following the announcement. This finding is consistent with the findings in Cook, Krigman, and Leach (2002), who show that the length of the average repurchase program is 116 days for NASDAQ firms and 195 days for NYSE firms. Panel B of Table III dissects what happens to the rest 1049 firms that do not make their first repurchase within the quarter of or the quarter following the announcement. A surprising 409 firms (18% of total sample) do not repurchase stock in any of the four years following the announcement. Additionally, 218 (9% of total sample) firms drop off of Compustat without repurchasing stock. Thus, 27% of the firms in our sample appear to never repurchase any stock. The previous statistics show that a significant 18% of the firms announcing a stock repurchase do not repurchase stock in the four fiscal years following the announcement. This percentage is surprising in light of the evidence in Stephens and Weisbach (1998). Stephens and Weisbach (1998) show that 10% of the firms announcing a repurchase program purchase less than 5% of their stock. Our results differ from Stephens and Weisbach (1998) for two reasons. First, Stephens and Weisbach (1998) look at Wall Street Journal Announcements; we use all announcements on Security Data Corporation, which relies on several news sources to track announcements, and is likely to include smaller firms. Second, our sample period is later than the sample period used in Stephens and Weisbach (1998), who look at the 1981 to 1990 period. Fewer announcing firms repurchase their stock in the later years of our sample. Panel C of Table III illustrates the percentage of firms repurchasing stock by the year of the announcement. In 1985 and 1986, only 8% and 9% of the firms did not repurchase stock in the four fiscal years after an announcement. It is likely that in the period prior to 1985, the percentage of firms announcing but not repurchasing stock was even lower, since the type of repurchase and types of firms repurchasing differ prior to 1984 (Dittmar (2000) and Grullon and Michaely (2002)). In the later years of our sample, the number of non-repurchasers increased. In 1991, for instance, the percentage of firms announcing but not repurchasing stock in the next four fiscal years peaked at 27%. 18

21 V. Empirical Tests Our theoretical model relies on investors being able to determine if a firm uses a costless or a costly signal. Thus, in the context of stock repurchases, it is important that investors know if the firm repurchased stock. Unfortunately, in the U.S., firms do not disclose repurchases until their quarterly statements. We therefore define a repurchaser (non-repurchaser) as a firm that has announced an open market share repurchase and has repurchased (has not repurchased) in the quarter of or following the announcement. We examine two quarters because the announcement may occur late in the first quarter and we need to allow sufficient time for the firm to repurchase stock. 9 Robustness checks with different time windows are conducted in Table VII. The results do not change. Our theoretical model predicts that a firm will chose a costless signal if the signal attracts scrutiny; otherwise, the firm must put its money where its mouth is, and provide a costly signal. The signal will attract scrutiny if the benefit to search is high. This is true for deeply undervalued firms, because the potential capital gains to be realized from discovering large undervaluations and trading on that information is high. Thus, our theoretical model predicts that more undervalued firms use a costless signal (announce share repurchases without actually repurchasing) for separating, whereas less undervalued firms, where the benefits to search are low, will use a costly signal (announce share repurchases and actually repurchase) for separating. Vermaelen (1981), Dann (1981), Comment and Jarell (1991) and Grullon (2000) show that firms announcing stock repurchases are undervalued, and that the announcement is a signal of their undervaluation. Obviously, some firms are more undervalued than others. We measure undervaluation as the abnormal return over the announcement period using three windows. The first window is the three days surrounding the announcement, t-1 to t+1. We measure the cumulative abnormal return over this window using a market model, the CRSP value-weighted market return, and a comparison period of 200 to 50 trading days. There are two problems with a three day window: first, it may take more than three days to resolve the 9 If the announcement occurs in the last 2 trading days of the quarter, the quarter of the announcement is defined as the following quarter. 19

22 undervaluation and, second, as share repurchases are not disclosed immediately, shareholders will not be able to distinguish between costly and costless signals. Our second measure of undervaluation is the buy and hold abnormal return over the quarter of the announcement. We calculate the abnormal returns by subtracting out the expected return, calculated using the CRSP value-weighted market return over the quarter and the firm beta calculated over the 1985 to 1995 sample period. Finally, as the primary definition of a repurchaser (nonrepurchaser) in our paper is a firm that has announced an open market share repurchase and has repurchased (has not repurchased) in the quarter of or following the announcement, our third measure of undervaluation is the buy and hold abnormal return over these two quarters. The abnormal returns over these two quarters are computed in the same way we computed abnormal returns over one quarter. 10 Our theoretical model also predicts that the benefit to search is high when the ignorance in the market about the firm is high. Thus, our theoretical model predicts that more ignored firms use a costless signal (announce share repurchases without actually repurchasing) for separating, whereas less ignored firms, where the benefits to search are low, will use a costly signal (announce share repurchases and actually repurchase) for separating. In this paper, we use the number of analysts and two measures of firm size, the natural log of the market capitalization and the natural log of assets, as measures for the lack of market ignorance about a firm. A. Summary Firm Characteristics of the Two Sub-Samples Table IV presents summary statistics and tests for differences between the repurchasing and nonrepurchasing firms using t-tests for unequal, unpaired samples and Wilcoxon Rank-sum tests. 11 Panel A describes our measures of ignorance; it depicts the number of analysts and firm size of the repurchasing and non-repurchasing firms in the year prior to the repurchase announcement. Unfortunately, 10 Ikenberry, Lakonishok, and Vermaelen (1995) show that these narrow windows may not be sufficient to measure the full extent of undervaluation. They provide evidence that repurchasing firms outperform non-repurchasing firms in the three years following the announcement. However, because our theoretical model relies entirely on investors interpreting one particular signal, we find it prudent to curtail the influence of confounding events by using a shorter window. 11 Several of the variables investigated are not available for all sample firms. 20

23 IBES only follows 1,405 of the 2,297 sample firms. Thus, we assume that any firm not covered by IBES has no analyst following. Though this assumption is not perfect, it is likely that firms not on IBES have significantly less analyst following. To check the impact of this assumption, we repeat all the analysis presented in this paper using only those firms that IBES covers. The results are unchanged. The mean (median) repurchasing firm has 5.74 (2) analysts following it in the year before the announcement. The mean (median) non-repurchasing firm has 3.39 (1) analysts following it in the year before the announcement. The difference between the repurchasing and non-repurchasing firms mean and median number of analysts is statistically significant. Thus, non-repurchasing firms are more ignored. It could be argued that any analyst following will improve information and, thus, the proper metric is a dummy variable if the firm has at least one analyst following it. Based on this dichotomous variable, the repurchasing firms are more followed: 38% of repurchasing firms have no analyst following, whereas 50% of the non-repurchasers have no analyst following. We repeat all the analysis presented in this paper using this alternative measure. The results are unchanged. These statistics support the implications of the theoretical model: firms that announce but do not repurchase are the ignored firms. Consistent with this interpretation, repurchasing firms are also significantly larger than non-repurchasing firms, as measured by the natural log of market capitalization or total assets. Panel B of Table IV shows our measures of undervaluation. The three-day abnormal returns for repurchasers and non-repurchasers are not significantly different. However, the one and the two quarter abnormal mean or median returns for non-repurchasing firms are significantly higher than those for repurchasing firms. This indicates that firms using stock repurchases as a costless rather than a costly signal are more undervalued than those using a costly signal. Specifically, the median two quarter abnormal return is six percent for the non-repurchasing firms and one percent for the repurchasing firms. Both sub-samples median abnormal returns are significantly greater than zero. Our theoretical model focuses only on the signaling motive for repurchasing stock. However, there are several other reasons why firms may repurchase stock. We control for these motives. Summary statistics 21

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