《金融经济学》（英文版）The Positive Role of Overconfidence and Optimism in Investment Policy.pdf_大学文库

1 Introduction A vast experimental literature finds that individuals are usually optimistic (i.e, they believe out comes favorable to themselves to be more likely than they actually are) and overconfident (i.e., they believe their knowledge is more precise than it actually is). Since optimism and overconfidence di rectly influence decision making, it is natural to ask how optimistic and overconfident managers will ffect the value of the firm. Are managerial optimism and overconfidence sufficiently detrimental to firm value that shareholders should actively avoid hiring optimistic and overconfident managers? What possible benefits might optimistic and overconfident managers bring to the firm? We use a simple model of capital budgeting to contrast the decisions of overconfident, optimistic managers with those of rational managers. We reach the surprising conclusion that managerial overconfidence and optimism can increase the value of the firm. Moderate overconfidence can align more closely with those of shareholders. However, extreme managerial overconfidence and optimism are detrimental to the firm. Our analysis starts with the observation that many capital budgeting decisions can be viewed as decisions whether or not to exercise real options(Dixit and Pindyck, 1994). Because of their greater risk aversion, rational managers will postpone the decision to exercise real options longer than is in the best interest of shareholders. As Treynor and Black(1976)write If the corporation undertakes a risky new venture, the stockholders may not be very concerned, because they can balance this new risk against other risks that they hold heir portfolios. The managers, however, do not have a portfolio of the corporation does badly because the new venture fails, they do not have any risks except the others taken by the same corporation to balance against it. They are hurt by a failure more than the stockholders, who also hold stock in other corporations, are hurt.” Since overconfident managers believe that the uncertainty about potential project is less than it actually is, they are less likely to postpone the decision to undertake the project. Thus moder ately overconfident managers make decisions that are in the better interest of shareholders than do rational managers. Overconfident managers also benefit the firm by expending more effort than rational managers, as they overestimate the value of that effort. Optimistic managers believe that the expected net present value of potential projects is greater than it actually is. Like overconfident managers, optimistic managers undertake projects more quickly than do rational managers. How

1 Introduction A vast experimental literature finds that individuals are usually optimistic (i.e., they believe outcomes favorable to themselves to be more likely than they actually are) and overconfident (i.e., they believe their knowledge is more precise than it actually is). Since optimism and overconfidence directly influence decision making, it is natural to ask how optimistic and overconfident managers will affect the value of the firm. Are managerial optimism and overconfidence sufficiently detrimental to firm value that shareholders should actively avoid hiring optimistic and overconfident managers? What possible benefits might optimistic and overconfident managers bring to the firm? We use a simple model of capital budgeting to contrast the decisions of overconfident, optimistic managers with those of rational managers. We reach the surprising conclusion that managerial overconfidence and optimism can increase the value of the firm. Moderate overconfidence can align managers’ preferences for risky projects more closely with those of shareholders. However, extreme managerial overconfidence and optimism are detrimental to the firm. Our analysis starts with the observation that many capital budgeting decisions can be viewed as decisions whether or not to exercise real options (Dixit and Pindyck, 1994). Because of their greater risk aversion, rational managers will postpone the decision to exercise real options longer than is in the best interest of shareholders. As Treynor and Black (1976) write: “If the corporation undertakes a risky new venture, the stockholders may not be very concerned, because they can balance this new risk against other risks that they hold in their portfolios. The managers, however, do not have a portfolio of employers. If the corporation does badly because the new venture fails, they do not have any risks except the others taken by the same corporation to balance against it. They are hurt by a failure more than the stockholders, who also hold stock in other corporations, are hurt.” Since overconfident managers believe that the uncertainty about potential project is less than it actually is, they are less likely to postpone the decision to undertake the project. Thus moderately overconfident managers make decisions that are in the better interest of shareholders than do rational managers. Overconfident managers also benefit the firm by expending more effort than rational managers, as they overestimate the value of that effort. Optimistic managers believe that the expected net present value of potential projects is greater than it actually is. Like overconfident managers, optimistic managers undertake projects more quickly than do rational managers. How- 1

ever, unlike overconfident managers, optimistic managers will sometimes undertake projects that actually have negative expected net present values. This error may be mitigated by raising hurdle rates While compensation contracts that increase the convexity of manager payoffs can be used to realign the decisions of a rational manager with those of shareholders, it may be less expensive to simply hire an overconfident, optimistic manager. The gains from overconfidence and optimism will at times be sufficient that shareholders actually prefer an overconfident, optimistic manager with less ability to a rational manager with greater ability. Extreme overconfidence or optimism is, however, always detrimental to the firm. Extremely overconfident or optimistic managers will perceive too little risk or too little chance of failure. They will greatly underestimate of delaying a project or greatly overestimate the likelihood of success. When such individuals in charge of a firm's capital budgeting decisions, they will destroy that firm's value in the long run Our research helps to explain a puzzle in corporate finance. If rational individuals make better decisions than those influenced by behavioral biases, such as overconfidence, why are many CEO verconfident(Audia, Locke and Smith, 2000; Malmendier and Tate, 2001)? This puzzle can be viewed from the perspective of the individual manager and that of the firm. Gervais and Odean(2001)demonstrate, in the context of investors, that the human tendency to take too much credit for success and attribute too little credit to chance can cause successful people to become erconfident. Thus, in a corporate setting, managers who successfully climb the corporate ladder to become CEOs are likely to also become overconfident. In the current paper, we address the puzzle of CEO overconfidence from the perspective of the firm. We show that it can be in the best interest of shareholders to hire managers(e. g, CEOs) who are overconfident Our paper proceeds as follows. Section 2 reviews some of the literature on optimism and verconfidence. Section 3 introduces a simple capital budgeting problem that is used throughout the paper to analyze the effects of behavioral biases on the value of the firm. The same section presents the first-best solution, which serves as a benchmark for later sections. Section 4 formally introduces the concepts of overconfidence and optimism, and shows how these individual traits can ffect the value of the firm when a manager's sole intention is to maximize firm value. The principal agent nature of the relationship between firm owners and managers is analyzed in section 5. This section shows how contracting interacts with manager biases to solve the firms agency problems section 6. we show how our basic model can be extended to accommodate other forces that are

ever, unlike overconfident managers, optimistic managers will sometimes undertake projects that actually have negative expected net present values. This error may be mitigated by raising hurdle rates. While compensation contracts that increase the convexity of manager payoffs can be used to realign the decisions of a rational manager with those of shareholders, it may be less expensive to simply hire an overconfident, optimistic manager. The gains from overconfidence and optimism will at times be sufficient that shareholders actually prefer an overconfident, optimistic manager with less ability to a rational manager with greater ability. Extreme overconfidence or optimism is, however, always detrimental to the firm. Extremely overconfident or optimistic managers will perceive too little risk or too little chance of failure. They will greatly underestimate the option value of delaying a project or greatly overestimate the likelihood of success. When such individuals are put in charge of a firm’s capital budgeting decisions, they will destroy that firm’s value in the long run. Our research helps to explain a puzzle in corporate finance. If rational individuals make better decisions than those influenced by behavioral biases, such as overconfidence, why are many CEOs overconfident (Audia, Locke and Smith, 2000; Malmendier and Tate, 2001)? This puzzle can be viewed from the perspective of the individual manager and that of the firm. Gervais and Odean (2001) demonstrate, in the context of investors, that the human tendency to take too much credit for success and attribute too little credit to chance can cause successful people to become overconfident. Thus, in a corporate setting, managers who successfully climb the corporate ladder to become CEOs are likely to also become overconfident. In the current paper, we address the puzzle of CEO overconfidence from the perspective of the firm. We show that it can be in the best interest of shareholders to hire managers (e.g., CEOs) who are overconfident. Our paper proceeds as follows. Section 2 reviews some of the literature on optimism and overconfidence. Section 3 introduces a simple capital budgeting problem that is used throughout the paper to analyze the effects of behavioral biases on the value of the firm. The same section presents the first-best solution, which serves as a benchmark for later sections. Section 4 formally introduces the concepts of overconfidence and optimism, and shows how these individual traits can affect the value of the firm when a manager’s sole intention is to maximize firm value. The principalagent nature of the relationship between firm owners and managers is analyzed in section 5. This section shows how contracting interacts with manager biases to solve the firm’s agency problems. In section 6, we show how our basic model can be extended to accommodate other forces that are 2

likely to play a role in capital budgeting problems. Finally, section 7 discusses our findings and concludes. All the proofs are contained in the appendix 2 elated work 2.1 perimental Studies For this paper, we define optimism to be the belief that favorable future events are more likely than they actually are. Researchers find that, generally, individuals are unrealistically optimistic about future events. They expect good things to happen to themselves more often than to their peers (Weinstein, 1980; Kunda, 1987). For example, Ito(1990)reports that foreign exchange companies are more optimistic about how exchange rate moves will affect their firm than how they will affect others. People overestimate their ability to do well on tasks and these overestimates increase when the task is perceived to be controllable(Weinstein, 1980) and when it is of personal importance (Frank, 1935). March and Shapira(1987) find that managers tend to believe that outcomes are largely controllable and that projects under their supervision are less risky than is actually the case. Finally, optimism is most severe among more intelligent individuals(Klaczynski and Fauth 1996)and, we expect, most top managers are intelligent For this paper, we define overconfidence to be the belief that the precision of one's information greater than it actually is, that is, one puts more weight on one's information than is warranted Studies of the calibration of subjective probabilities find that individuals do tend to overestimate the precision of their information(Alpert and Raiffa, 1982; Fischhoff, Slovic and Lichtenstein, 1977).2 Such overconfidence has been observed in many professional fields. Clinical psychologist (Oskamp, 1965), physicians and nurses( Christensen-Szalanski and Bushyhead, 1981; Baumann, er a ) investment bankers(Stael von Holstein, 1972), engineers(Kidd 1970), entrepreneurs(Cooper, Woo and Dunkelberg, 1988), lawyers(Wagenaar and Keren, 1986) negotiators(Neale and Bazerman, 1990), and managers(Russo and Schoemaker, 1992)have all been observed to exhibit overconfidence in their judgments The best established finding in the calibration literature is that people tend to be overconfident in answering questions of moderate to extreme difficulty(Fischhoff, Slovic and Lichtenstein, 1977; Over two years, the Japan Center for International Finance conducted a bi-monthly survey of foreign exchange experts in 44 companies. Each was asked for point estimates of future yen /dollar exchange rates. The experts in import-oriented companies expected the yen to appreciate(which would favor their company), while those in export- oriented companies expected the yen to fall(which would favor their company). People are even unrealistically optimistic about pure chance events(Marks, 1951; Irwin, 1953: Langer and Roth, 1975) See Lichtenstein, Fischhoff, and Phillips(1982)for a review of the calibration literature

likely to play a role in capital budgeting problems. Finally, section 7 discusses our findings and concludes. All the proofs are contained in the appendix. 2 Related Work 2.1 Experimental Studies For this paper, we define optimism to be the belief that favorable future events are more likely than they actually are. Researchers find that, generally, individuals are unrealistically optimistic about future events. They expect good things to happen to themselves more often than to their peers (Weinstein, 1980; Kunda, 1987). For example, Ito (1990) reports that foreign exchange companies are more optimistic about how exchange rate moves will affect their firm than how they will affect others.1 People overestimate their ability to do well on tasks and these overestimates increase when the task is perceived to be controllable (Weinstein, 1980) and when it is of personal importance (Frank, 1935). March and Shapira (1987) find that managers tend to believe that outcomes are largely controllable and that projects under their supervision are less risky than is actually the case. Finally, optimism is most severe among more intelligent individuals (Klaczynski and Fauth, 1996) and, we expect, most top managers are intelligent. For this paper, we define overconfidence to be the belief that the precision of one’s information is greater than it actually is, that is, one puts more weight on one’s information than is warranted. Studies of the calibration of subjective probabilities find that individuals do tend to overestimate the precision of their information (Alpert and Raiffa, 1982; Fischhoff, Slovic and Lichtenstein, 1977).2 Such overconfidence has been observed in many professional fields. Clinical psychologists (Oskamp, 1965), physicians and nurses (Christensen-Szalanski and Bushyhead, 1981; Baumann, Deber and Thompson, 1991), investment bankers (Sta¨el von Holstein, 1972), engineers (Kidd, 1970), entrepreneurs (Cooper, Woo and Dunkelberg, 1988), lawyers (Wagenaar and Keren, 1986), negotiators (Neale and Bazerman, 1990), and managers (Russo and Schoemaker, 1992) have all been observed to exhibit overconfidence in their judgments. The best established finding in the calibration literature is that people tend to be overconfident in answering questions of moderate to extreme difficulty (Fischhoff, Slovic and Lichtenstein, 1977; 1Over two years, the Japan Center for International Finance conducted a bi-monthly survey of foreign exchange experts in 44 companies. Each was asked for point estimates of future yen/dollar exchange rates. The experts in import-oriented companies expected the yen to appreciate (which would favor their company), while those in exportoriented companies expected the yen to fall (which would favor their company). People are even unrealistically optimistic about pure chance events (Marks, 1951; Irwin, 1953; Langer and Roth, 1975). 2See Lichtenstein, Fischhoff, and Phillips (1982) for a review of the calibration literature. 3

Lichtenstein, Fischhoff and Phillips, 1982; Yates, 1990; Griffin and Tversky, 1992). Exceptions to overconfidence in calibration are that people tend to be underconfident when answering easy questions, and they learn to be well-calibrated when predictability is high and when performing repetitive tasks with fast, clear feedback. For example, expert bridge players(Keren, 1987),race- track bettors(Dowie, 1976: Hausch, Ziemba and Rubinstein, 1981) and meteorologists(Murphy and Winkler, 1984)tend to be well-calibrated There are a number of reasons why we might expect the overconfidence of managers to exceed that of the general population. 1) Capital budgeting decisions can be quite complex. They often require projecting cash flows for a wide range of uncertain outcomes. Typically people are most erconfident about such difficult problems. 2)Capital budgeting decisions are not well suited for learning. Learning occurs "when closely similar problems are frequently encountered, especially if the outcomes of decisions are quickly known and provide unequivocal feedback?"(Kahneman encountered,outcomes are often delayed for long periods of time, and feedback is typically tip ind Lovallo, 1993). But the major investment policy decisions we study here are not frequentl noisy. Furthermore, it is often difficult for a manager to reject the hypothesis that every situation is new in important ways, allowing him to ignore feedback from past decisions altogether. Learnin from experience is highly unlikely under these circumstances(Brehmer, 1980; Einhorn and Hogarth 1978). 3)Unsuccessful managers are less likely to retain their jobs and be promoted. Those who do succeed are likely to become overconfident because of self-attribution bias. Most people overestimate the degree to which they are responsible for their own success(Miller and Ross, 1975; Langer and Roth, 1975; Nisbett and Ross, 1980). This self-attribution bias causes the successful to become overconfident(Daniel, Hirshleifer and Subrahmanyam, 1998; Gervais and Odean, 2001 ). 4) Finally, managers may be more overconfident than the general population because of selection bias. Those who are overconfident and optimistic about their prospects as managers are more likely to apply for these jobs. Firms, too, may select on the basis of apparent confidence and optimism, either because the applicants overconfidence and optimism are perceived to be signs of greater ability or because, as in our model, shareholders recognize that it is less expensive to hire overconfident, optimistic managers who suit their needs than it is to hire rational managers who do 2.2 Overconfidence and Optimism in Finance Recent studies explore the implications of overconfidence for financial markets. In Benos(1998) traders are overconfident about the precision of their own signals and their knowledge of the si

Lichtenstein, Fischhoff and Phillips, 1982; Yates, 1990; Griffin and Tversky, 1992). Exceptions to overconfidence in calibration are that people tend to be underconfident when answering easy questions, and they learn to be well-calibrated when predictability is high and when performing repetitive tasks with fast, clear feedback. For example, expert bridge players (Keren, 1987), racetrack bettors (Dowie, 1976; Hausch, Ziemba and Rubinstein, 1981) and meteorologists (Murphy and Winkler, 1984) tend to be well-calibrated. There are a number of reasons why we might expect the overconfidence of managers to exceed that of the general population. 1) Capital budgeting decisions can be quite complex. They often require projecting cash flows for a wide range of uncertain outcomes. Typically people are most overconfident about such difficult problems. 2) Capital budgeting decisions are not well suited for learning. Learning occurs “when closely similar problems are frequently encountered, especially if the outcomes of decisions are quickly known and provide unequivocal feedback” (Kahneman and Lovallo, 1993). But the major investment policy decisions we study here are not frequently encountered, outcomes are often delayed for long periods of time, and feedback is typically very noisy. Furthermore, it is often difficult for a manager to reject the hypothesis that every situation is new in important ways, allowing him to ignore feedback from past decisions altogether. Learning from experience is highly unlikely under these circumstances (Brehmer, 1980; Einhorn and Hogarth, 1978). 3) Unsuccessful managers are less likely to retain their jobs and be promoted. Those who do succeed are likely to become overconfident because of self-attribution bias. Most people overestimate the degree to which they are responsible for their own success (Miller and Ross, 1975; Langer and Roth, 1975; Nisbett and Ross, 1980). This self-attribution bias causes the successful to become overconfident (Daniel, Hirshleifer and Subrahmanyam, 1998; Gervais and Odean, 2001). 4) Finally, managers may be more overconfident than the general population because of selection bias. Those who are overconfident and optimistic about their prospects as managers are more likely to apply for these jobs. Firms, too, may select on the basis of apparent confidence and optimism, either because the applicant’s overconfidence and optimism are perceived to be signs of greater ability or because, as in our model, shareholders recognize that it is less expensive to hire overconfident, optimistic managers who suit their needs than it is to hire rational managers who do so. 2.2 Overconfidence and Optimism in Finance Recent studies explore the implications of overconfidence for financial markets. In Benos (1998), traders are overconfident about the precision of their own signals and their knowledge of the sig- 4

nals of others. De Long, Shleifer, Summers, and Waldmann(1991)demonstrate that overconfident traders can survive in markets. Hirshleifer, Subrahmanyam and Titman(1994)argue that over confidence can promote herding in securities markets. Odean(1998) examines how the overconfi- dence of different market participants affects markets differently. Daniel, Hirshleifer, and Subrah- manyam(1998), and Gervais and Odean(2001)develop models in which, due to a self-attribution bias, overconfidence increases with success. Kyle and Wang(1997) and Wang(1997) argue that mutual funds may prefer to hire overconfident money managers, because overconfidence enables money managers to "pre-commit"to taking more than their share of duopoly profits. While we conclude that there are advantages to hiring overconfident managers in a corporate setting,our reasoning is quite different from that of Kyle and Wang(1997) and Wang(1997). These authors rely on assumptions about the timing of trading and information signals, and they require that competing money managers have knowledge of the information and overconfidence of each other. Our basic findings are based simply on the assumptions that shareholders are less risk-averse than are managers regarding the fate of the firm, and that overconfidence causes managers to perceive less risk than is there Fewer studies have looked at overconfidence in corporate settings. Roll (1986)suggests that verconfidence(hubris) may motivate many corporate takeovers. Kahneman and Lovallo(1993) argue that managerial overconfidence and optimism stem from managers taking an"inside view of prospective projects. The inside view focuses on project specifics and readily anticipated scenar ios while ignoring relevant statistical information such as"how often do projects like this usuall succeed? "Heaton(2002)examines the implications of managerial optimism for the benefits and osts of free cash How. He points out that in the corporate environment, irrational managers are not likely to be arbitraged away. Transactions costs for the most obvious " arbitrage"of man- erial irrationality-the corporate takeover-are extremely large, due primarily to high legal and regulatory hurdles. The specialized investors who do pursue takeovers must bear very large id- iosyncratic risks. These factors severely limit the power of arbitrage(Pontiff, 1996; Shleifer and Vishny, 1997). Consequently, there is no reason to believe that corporate financial decisions cannot manifest managerial irrationality within the large arbitrage bounds these limits create. Malmendier nd Tate(2001) provide empirical evidence that optimistic managers invest more aggressively

nals of others. De Long, Shleifer, Summers, and Waldmann (1991) demonstrate that overconfident traders can survive in markets. Hirshleifer, Subrahmanyam and Titman (1994) argue that overconfidence can promote herding in securities markets. Odean (1998) examines how the overconfi- dence of different market participants affects markets differently. Daniel, Hirshleifer, and Subrahmanyam (1998), and Gervais and Odean (2001) develop models in which, due to a self-attribution bias, overconfidence increases with success. Kyle and Wang (1997) and Wang (1997) argue that mutual funds may prefer to hire overconfident money managers, because overconfidence enables money managers to “pre-commit” to taking more than their share of duopoly profits. While we conclude that there are advantages to hiring overconfident managers in a corporate setting, our reasoning is quite different from that of Kyle and Wang (1997) and Wang (1997). These authors rely on assumptions about the timing of trading and information signals, and they require that competing money managers have knowledge of the information and overconfidence of each other. Our basic findings are based simply on the assumptions that shareholders are less risk-averse than are managers regarding the fate of the firm, and that overconfidence causes managers to perceive less risk than is there. Fewer studies have looked at overconfidence in corporate settings. Roll (1986) suggests that overconfidence (hubris) may motivate many corporate takeovers. Kahneman and Lovallo (1993) argue that managerial overconfidence and optimism stem from managers taking an “inside view” of prospective projects. The inside view focuses on project specifics and readily anticipated scenarios while ignoring relevant statistical information such as “how often do projects like this usually succeed?” Heaton (2002) examines the implications of managerial optimism for the benefits and costs of free cash flow. He points out that in the corporate environment, irrational managers are not likely to be arbitraged away. Transactions costs for the most obvious “arbitrage” of managerial irrationality—the corporate takeover—are extremely large, due primarily to high legal and regulatory hurdles. The specialized investors who do pursue takeovers must bear very large idiosyncratic risks. These factors severely limit the power of arbitrage (Pontiff, 1996; Shleifer and Vishny, 1997). Consequently, there is no reason to believe that corporate financial decisions cannot manifest managerial irrationality within the large arbitrage bounds these limits create. Malmendier and Tate (2001) provide empirical evidence that optimistic managers invest more aggressively. 5

3 The model 3.1 The Firm An all-equity firm initially consists of half a dollar in cash, and is considering the possibility to invest that money in a risky project. At the beginning of the period, one such project becomes vailable. All risky projects return one or zero dollar with equal probabilities one period fror now;we denote this end-of-period cash flow by 0. For simplicity, we assume that the risk of these ects is completely idiosyncratic, and that the correct discount rate, the riskfree rate, is zero Given this, the net present value of any risky project is exactly zero, and so the value of the firm is one half The potential value from a risky project comes from the possibility of acquiring information about it. This can be done in two stages: the firm can gather an imperfect signal about the project's payoff in the first stage, and a perfect signal in the second stage. Before each stage, the firm learns the probability that the project will still exist at the end of that stage. The cost of gathering information in this real options framework is therefore the potential loss of a project that is likely to be good. The qualitative implications of our model extend to real options settings in which the draw back to delaying exercise is foregone revenue from the project or an explicit cost to thering additional information introducing these additional cash hows into the model howey greatly complicates the formal analysis, without contributing intuition. We denote the probability that the project will still exist at the end of the first(second)stage by p( @. We assume that p and q are uniformly distributed on [0, 1] and are independent. These two variables can be thought of as describing the ease with which the firm can learn about the project's profitability. Alternatively they capture the amount of competition that the firm faces when deciding whether to invest in a project immediately or to delay the decision. In that sense, a larger(smaller) probability that the project still exists represents a situation in which few(many)other firms are likely to unde the project before more information can be gathered Upon learning p, the imperfect signal that the firm can gather in the first stage is given by 8=E0+(1 where n has the same distribution as u, but is independent from it, and E takes a value of one ith probability a E(0, 1), and zero otherwise. This signal s is more informative for larger values of a, as the true value of the project is then observed more often. The parameter a can in fact be interpreted as the ability of the individual making the capital budgeting decision, whom we refer

3 The Model 3.1 The Firm An all-equity firm initially consists of half a dollar in cash, and is considering the possibility to invest that money in a risky project. At the beginning of the period, one such project becomes available. All risky projects return one or zero dollar with equal probabilities one period from now; we denote this end-of-period cash flow by ˜v. For simplicity, we assume that the risk of these projects is completely idiosyncratic, and that the correct discount rate, the riskfree rate, is zero. Given this, the net present value of any risky project is exactly zero, and so the value of the firm is one half. The potential value from a risky project comes from the possibility of acquiring information about it. This can be done in two stages: the firm can gather an imperfect signal about the project’s payoff in the first stage, and a perfect signal in the second stage. Before each stage, the firm learns the probability that the project will still exist at the end of that stage. The cost of gathering information in this real options framework is therefore the potential loss of a project that is likely to be good. The qualitative implications of our model extend to real options settings in which the drawback to delaying exercise is foregone revenue from the project or an explicit cost to gathering additional information. Introducing these additional cash flows into the model, however, greatly complicates the formal analysis, without contributing intuition. We denote the probability that the project will still exist at the end of the first (second) stage by ˜p (˜q). We assume that ˜p and q˜ are uniformly distributed on [0, 1] and are independent. These two variables can be thought of as describing the ease with which the firm can learn about the project’s profitability. Alternatively, they capture the amount of competition that the firm faces when deciding whether to invest in a project immediately or to delay the decision. In that sense, a larger (smaller) probability that the project still exists represents a situation in which few (many) other firms are likely to undertake the project before more information can be gathered. Upon learning ˜p, the imperfect signal that the firm can gather in the first stage is given by s˜ = ˜εv˜ + (1 − ε˜)˜η, where ˜η has the same distribution as ˜v, but is independent from it, and ˜ε takes a value of one with probability a ∈ (0, 1), and zero otherwise. This signal ˜s is more informative for larger values of a, as the true value of the project is then observed more often. The parameter a can in fact be interpreted as the ability of the individual making the capital budgeting decision, whom we refer 6

to as the manager of the firm. At the same time that the manager observes s, he learns g, the probability that the project will still exist should he decide to keep gathering information(i.e. delay the decision to undertake the project for one more period). If he chooses to gather more information, the manager learns i perfectly. In the event that the project disappears at any stage (probability 1-p in the first stage, and 1-q in the second stage), the firm's cash is simply invested at the riskfree rate until the end of the period; no other risky projects are available The sequence of events is illustrated in Figure 1. The manager of the firm makes three decisions(which are represented by open circles in the figure) during the period. At utset the first stage, he must choose whether to undertake the risky project, drop it, or gather some information about it. If information is gathered and if the project does not disappear while it is gathered, the manager makes his second-stage decision: the project can again be undertaken dropped, or the manager can choose to gather more (i.e, in this case, perfect) information about it. If more information is gathered and the project remains available, the manager then chooses in the third and final stage-the last decision node--whether or not to undertake the project In this and the next sections, we assume that the manager's utility is a function of the firms value exclusively. This is equivalent to assuming that the manager is compensated with firm's stock. In section 5, we take a closer look at the manager's incentives and analyze how more general compensation contracts can be used to align the manager's decisions with the interests of shareholders. This two-step approach allows us to disentangle the effects of risk aversion, behavioral biases, and compensation on decision-making Clearly, even if the project can be dropped in favor of a safe investment in the first two stages this will never be considered by the manager: the worst possible outcome from gathering more information is that the risky project disappears; the safe investment can then be made any way.It is also clear that the decision to undertake or drop the risky project in the third stage is trivial: at that point, the risky project's payoff is known with certainty, and so the project will be undertaken if and only if v= 1. Effectively therefore, the manager makes active decisions in each of the first two stages only, and the decision involves a comparison between undertaking the project at that stage or acquiring more information about it. This simple two-period framework thus captures the idea that a firm may choose to wait to invest in a risky project(McDonald and Siegel, 1986), but waiting may be costly(Grenadier, 2002), since a good project may be lost to competition. Suppose that, when making his second-stage decision, the manager knows that q is close to This results from the fact that information can be gathered without the firm or manager incurring any direct onetary or effort costs. Such costs are considered in section 6.2

to as the manager of the firm. At the same time that the manager observes ˜s, he learns ˜q, the probability that the project will still exist should he decide to keep gathering information (i.e., delay the decision to undertake the project for one more period). If he chooses to gather more information, the manager learns ˜v perfectly. In the event that the project disappears at any stage (probability 1−p˜ in the first stage, and 1−q˜ in the second stage), the firm’s cash is simply invested at the riskfree rate until the end of the period; no other risky projects are available. The sequence of events is illustrated in Figure 1. The manager of the firm makes up to three decisions (which are represented by open circles in the figure) during the period. At the outset, the first stage, he must choose whether to undertake the risky project, drop it, or gather some information about it. If information is gathered and if the project does not disappear while it is gathered, the manager makes his second-stage decision: the project can again be undertaken, dropped, or the manager can choose to gather more (i.e., in this case, perfect) information about it. If more information is gathered and the project remains available, the manager then chooses in the third and final stage—the last decision node—whether or not to undertake the project. In this and the next sections, we assume that the manager’s utility is a function of the firm’s value exclusively. This is equivalent to assuming that the manager is compensated with firm’s stock. In section 5, we take a closer look at the manager’s incentives and analyze how more general compensation contracts can be used to align the manager’s decisions with the interests of shareholders. This two-step approach allows us to disentangle the effects of risk aversion, behavioral biases, and compensation on decision-making. Clearly, even if the project can be dropped in favor of a safe investment in the first two stages, this will never be considered by the manager: the worst possible outcome from gathering more information is that the risky project disappears; the safe investment can then be made anyway.3 It is also clear that the decision to undertake or drop the risky project in the third stage is trivial: at that point, the risky project’s payoff is known with certainty, and so the project will be undertaken if and only if ˜v = 1. Effectively therefore, the manager makes active decisions in each of the first two stages only, and the decision involves a comparison between undertaking the project at that stage or acquiring more information about it. This simple two-period framework thus captures the idea that a firm may choose to wait to invest in a risky project (McDonald and Siegel, 1986), but waiting may be costly (Grenadier, 2002), since a good project may be lost to competition. Suppose that, when making his second-stage decision, the manager knows that ˜q is close to 3This results from the fact that information can be gathered without the firm or manager incurring any direct monetary or effort costs. Such costs are considered in section 6.2. 7