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
undertake drot project project P observed disappears U Is ③3 undertake drop off of u yoff of a Figure 1: Sequence of events. The open circles represent stages at which the manager of the firm must make a decision; at each of these stages, the manager must decide whether to undertake the project, drop the project, or gather more information(only in the first two stages). The closed circles represent nodes at which random events occur: the project disappears with probability p( 9) in the first(second)of these nodes. At the end of the period, the firm will get its payoff either from the risky project(a)if the manager chose to undertake it at any point, or from the safe investment
1 2 3 p˜ is observed drop project drop project drop project undertake project undertake project undertake project gather imperfect information gather perfect information p˜ 1−p˜ q˜ 1−q˜ project disappears project disappears s˜ and ˜q observed v˜ is observed payoff of ˜v payoff of 1 2 Figure 1: Sequence of events. The open circles represent stages at which the manager of the firm must make a decision; at each of these stages, the manager must decide whether to undertake the project, drop the project, or gather more information (only in the first two stages). The closed circles represent nodes at which random events occur: the project disappears with probability ˜p (˜q) in the first (second) of these nodes. At the end of the period, the firm will get its payoff either from the risky project (˜v) if the manager chose to undertake it at any point, or from the safe investment ( 1 2 ). 8