NBER WORKING PAPER SERIES EXECUTIVE COMPENSATION AND SHORT-TERMIST BEHAVIOR IN SPECULATIVE MARKETS. Patrick Bolton José Scheinkman Wei Xiong

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1 NBER WORKING PAPER SERIES EXECUTIVE COMPENSATION AND SHORT-TERMIST BEHAVIOR IN SPECULATIVE MARKETS Patrick Bolton Joé Scheinkman Wei Xiong Working Paper 97 NATIONAL BUREAU OF ECONOMIC RESEARCH 050 Maachuett Avenue Cambridge, MA 038 May 003 We would like to thank Lucian Bebchuk, Alan Blinder, Gary Gorton, Harrion Hong, Rafael LaPorta, David Scharftein, Jeremy Stein, Ivo Welch and eminar participant at Baruch, Harvard, HEC, INSEAD, Pari- Dauphine, Princeton, and the Five Star Conference at NYU for dicuion and comment. Thi paper wa written while Scheinkman wa the Blaie Pacal Reearch Profeor at Univerite Pari Dauphine. He i grateful for financial upport provided by the National Science Foundation grant The view expreed herein are thoe of the author and not necearily thoe of the National Bureau of Economic Reearch. 003 by Patrick Bolton, Joé Scheinkman, and Wei Xiong. All right reerved. Short ection of text not to exceed two paragraph, may be quoted without explicit permiion provided that full credit including notice, i given to the ource.

2 Executive Compenation and Short-termit Behavior in Speculative Market Patrick Bolton, Joé Scheinkman and Wei Xiong NBER Working Paper No. 97 May 003, Revied November 005 JEL No. G3 ABSTRACT We preent a multiperiod agency model of tock baed executive compenation in a peculative tock market, where invetor are overconfident and tock price may deviate from underlying fundamental and include a peculative option component. Thi component arie from the option to ell the tock in the future to potentially overoptimitic invetor. We how that optimal compenation contract may emphaize hort-term tock performance, at the expene of long run fundamental value, a an incentive to induce manager to purue action which increae the peculative component in the tock price. Our model provide a different perpective for the recent corporate crii than the increaingly popular `rent extraction view' of executive compenation. Patrick Bolton Joé Scheinkman Wei Xiong Bendheim Center for Finance Princeton Univerity Princeton Univerity 6 Propect Avenue Princeton, NJ and NBER pbolton@princeton.edu

3 Introduction Following the collape of the recent technology bubble on NASDAQ and other exchange numerou torie have appeared in the nancial pre pointing out how executive and director of many companie managed to enrich themelve by elling their hare hortly before their company tock price crumpled. Thee triking report have raied concern about executive compenation and cat doubt on their intended incentive e ciency. The claical view of executive compenation a formulated by Mirrlee (975), Holmtrom (979) and more recently Holmtrom and Tirole (993) among other ret on two fundamental hypothee. Firt that CEO incentive cheme e ciently trade o rik-haring and incentive conideration, and econd that tock-price are unbiaed etimator of rm fundamental, on which CEO pay could be baed to reward managerial e ort. While the recent corporate crii ha led many commentator to entirely reject thi claical view, our paper take a di erent perpective. We examine the implication for optimal incentive contracting of relaxing the econd hypothei about tock market and are thu able to reconcile the incentive perpective of executive compenation with the recent event. Speci cally, in thi paper we depart from Holmtrom and Tirole (993) by introducing a ource for di erence of opinion among invetor which, in turn, aure that tock price re ect not only the fundamental value of the rm but alo a hort-term peculative component. In addition, we potulate that rik-avere manager can take peci c action that boot the peculative component in tock price, albeit at the expene of long run fundamental value. We olve thi modi ed principal-agent problem and how that optimal compenation contract will overemphaize hort-term tock performance to induce manager to take action that may increae the peculative component in tock price. We alo conider the role of controlling hareholder that have a longer-term outlook and argue that although they do not bene t directly from tock ale at the in ated hort run price, they may till encourage ome horttermit trategie to reduce their cot of capital. There i growing evidence that tock price can deviate from fundamental value for pro- The Financial Time ha conducted a urvey of the 5 larget nancially ditreed rm ince January 00 and found that, although hundred of billion of invetor wealth together with 00,000 job diappeared, top executive and director in thee rm walked away with a total of $3.3 billion by elling their tock holding early (ee Financial Time, July 3, 00).

4 longed period of time. While many economit believe in the long run e ciency of tock market they alo recognize that US tock market have diplayed an important peculative component during the period between 998 to In addition, everal recent tudie have hown that it i di cult to reconcile the tock price level and volatility of many internet and high-tech rm during thi period with tandard dicounted cah- ow valuation. 4 In ome highly publicized cae the market value of a parent company wa even le than the value of it holding in an internet ubidiary. The trading volume for thee tock wa alo much higher than that for more traditional companie, a likely indicator of di erence of opinion among invetor regarding the fundamental value of thee tock. 5 The general idea we build on in thi paper, that tock price may be higher than fundamental value when there are di erence of opinion and hort-ale contraint, actually ha a long ancetry in Economic and Finance. It ha been traced back to early writing by Keyne (936) and later reurfaced in the article by Miller (977), Harrion and Krep (978) and more recently Morri (996), Chen, Hong and Stein (00), and Scheinkman and Xiong (003). Several quetion arie concerning the ue of tock in CEO compenation contract when tock price may not alway re ect the fundamental value of the rm. For example, what kind of incentive would tock compenation provide to rm manager in uch an environment? Would invetor be willing to ue tock for compenating manager if they knew that tock price could deviate ubtantially from fundamental value? More generally, what i hareholder value in uch a peculative market? Our goal in thi paper i to et up a tractable theoretical model to addre thee quetion and to provide an analyi of optimal CEO compenation in peculative market. We conider an optimal contracting problem in a two-period principal-agent model imilar to Holmtrom and Tirole (993). We let a rik-avere CEO chooe ome cotly hidden action, which a ect both the long-run fundamental value of the rm (in period ) and it hort-run tock valuation (in period ). For rik diveri cation reaon, when the tock price i an unbiaed etimate of the fundamental value of the rm, the optimal (linear) CEO compenation cheme See Shleifer (000) and Shiller (000) for upporting argument and Fama (998) for a contrarian view. 3 e.g. Malkiel (003) 4 See Lamont and Thaler (003), Ofek and Richardon (003), and Cochrane (00). 5 An extreme example i the trading volume in Palm tock, which turned over once every day according to Lamont and Thaler (003, Table 8).

5 ha both a hort-run and a long-run tock participation component. Our rt departure from Holmtrom and Tirole (993) i the introduction of a peculative tock market. Speci cally, we build on the model of equilibrium tock-price dynamic in the preence of overcon dent invetor by Scheinkman and Xiong (003). 6 In thi model, overcon- dence provide a ource of heterogeneou belief among invetor, which lead them to peculate againt each other. The holder of a hare then ha not only a claim to future dividend but alo an option to ell the tock to a more optimitic invetor in the future. Stock price in thi model have two component: a long-run fundamental and a hort-term peculative component. Invetor are willing to pay more than what they believe to be the tock long-run fundamental value becaue they think they may be able to ell their hare in the hort-term to other invetor with more optimitic belief. 7 Our econd departure from Holmtrom and Tirole (993) i the introduction of a multitak problem for the CEO, imilar to Holmtrom and Milgrom (99). That i, we allow the CEO to divide hi time between increaing the long-term value of the rm and encouraging peculation in the tock in the hort-term by puruing project over which invetor are likely to have diverging belief. In time of great heterogeneity in invetor belief, the optimal incentive contract i deigned to partially or completely induce the CEO to purue the trategy that tend to exacerbate invetor di erence of opinion and to bring about a higher peculative option value. Importantly, both initial hareholder and the CEO can gain from thi trategy ince it may increae the tock price in the hort run. 8 Thu, CEO may be encouraged to purue hort-term peculative project even at the expene of long-term fundamental value. Although hort-termit behavior by manager ha been highlighted before (mot notably, Stein 988, 989, Shleifer and Vihny 990, and Von Thadden 995), managerial hort-termim in thee model i not induced by ome optimal incentive cheme, but rather due to information 6 Overcon dence i a frequently oberved behavioral bia in pychological tudie. See Daniel, Hirhleifer and Teoh (00) and Barberi and Thaler (003) for review of the related pychological tudie and the application of overcon dence in economic and nance. 7 In a thought-provoking account of the internet bubble, Michael Lewi (00) ha given a vivid decription of the thought proce of many invetor, when he explained the reaoning behind hi purchae of the internet company tock Exodu Communication at the end of 999: I gured that even if Exodu Communication didn t wind up being a big ucce, enough people would believe in the thing to drive the tock price even higher and allow me to get out with a quick pro t. [Michael Lewi, 00]. 8 In ome cae thee initial hareholder are venture capitalit, who typically tructure the manager contract in new rm. 3

6 or other form of imperfection, and it arie againt the wihe of hareholder. In contrat, the managerial hort-termim analyzed in our paper i conitent with the peculative motive of incumbent hareholder, and therefore would not be eliminated even with active hareholder intervention. More cloely related to our paper i Froot, Perold and Stein (99) who provide a dicuion of the potential link between the hort-term horizon of hareholder and hort-term managerial behavior. They point out that the e ective horizon of intitutional invetor, a meaured by the frequency of their hare turnover, i about one year, much horter than the neceary period for them to exert long-term dicipline on rm manager. However, their paper doe not provide a formal model or analyi of optimal incentive compenation in an environment in which controlling hareholder have a hort-term objective. 9 Our model, thu, provide a way of reconciling the agency perpective on tock compenation with the recent corporate crii. We can explain why it i optimal for hareholder to o er compenation contract under which CEO can make early gain from a peculative tock price upwing, even though at a later date the rm market value may collape. We alo provide a rationalization for the oberved increae in tock-baed compenation during peculative phae. Our theory of executive compenation in peculative market, therefore, give an alternative explanation for the recent corporate crii than the increaingly in uential view emphaizing managerial power and abue brought about by a lack of adequate board uperviion (ee Bebchuk, Fried and Walker 00, and Bertrand and Mullainathan 00). 0 Rent-eeking behavior by manager i alway preent, but the exiting rent eeking theorie fail to explain why rent-eeking behavior would have trended upward over the 990 even though corporate governance wa generally trengthened over thi period. In contrat, our model ugget a link between hort-termit behavior and di erence of opinion a meaured by hare turnover. High turnover i likely to be oberved in rm in new indutrie, where it i uually more di cult to evaluate fundamental and therefore eaier for diagreement among potential invetor to arie. 9 Gervai, Heaton and Odean (003) provide another tudy of nancial contracting problem in the preence of behavioral biae. They how that rational invetor can hire modetly overcon dent and optimitic manager to mitigate the agency problem. Our tudy emphaize that peculative motive by invetor can caue hort-termit managerial behavior through an optimal contract. 0 Murphy (00) and Jenen and Murphy (004) propoe intead that compenation committee have under-etimated the cot of iuing tock and option to manager. 4

7 An implication of our analyi i that a failure to maximize long-run rm value i not necearily a ymptom of weak corporate governance, but may be a re ection of a more hort-term, peculative, orientation of hareholder. Thu, if the goal i to enure the maximization of longrun fundamental value then one may want to not only trengthen corporate governance, but alo lengthen tock-option veting period, lengthen director term, inulate the board of director more from market wing, and more generally take tep enuring that controlling hareholder (or the board of director) have a longer-term outlook. Indeed, we how that the more long-term oriented hareholder are, the le likely they are to encourage the CEO to engage in hort-termit behavior. Having aid thi, however, we alo how that even long-term oriented hareholder may want to purue hort-termit trategie in particularly peculative tock-market environment a a way of reducing the rm cot of capital. Our model provide a mechanim for invetor peculative motive to drive rm overinvetment, a many argued for the invetment boom in the telecom indutry in the late 990. Thu, our tudy echoe the growing literature on the e ect of ine cient tock market on rm invetment deciion. For example, Morck, Shleifer, and Vihny (990), Blanchard, Rhee, and Summer (993), Stein (996), Baker, Stein, and Wurgler (003), Polk and Sapienza (003), Gilchrit, Himmelberg and Huberman (005), and Panagea (004) have emphaized that when tock are overvalued, rm overinvet by taking advantage of a cheap ource of capital. A in our model a link i thu etablihed between equity over-valuation and rm behavior. However, unlike our paper, thi literature doe not explain why rm run by manager on behalf of their invetor would engage in ine cient invetment behavior that i detrimental to their invetor interet. In independent work to our Jenen (004) and Jenen and Murphy (004) have alo pointed to what they refer to a the agency cot of overvalued equity a the main caue of the recent corporate crii. They argue that when manager have large holding of tock or option they have trong incentive to engage in long-term value-detroying action to boot or maintain tock price at in ated level in the hort run. Again, their view lack a coherent theoretical Another related literature deal with the incentive e ect of early exit by manager or large hareholder (for example Maug 998, Kahn and Winton 998, Bolton and von Thadden 998, and Aghion, Bolton and Tirole 000). However, thi literature aume that tock market are e cient. More recently, Bebchuk and Bar-Gill (003) have analyzed the cot of permitting better informed manager to ell hare early, but they do not tudy the optimal compenation cheme that would be choen by hareholder in their framework. 5

8 framework to pit againt the e cient market paradigm. In particular, they do not explain how tock overvaluation arie and how value-detroying managerial action can temporarily utain overvalued equity. Our theoretical framework addree thee weaknee and highlight how both the notion of overvalued equity and the con ict between hort-term and long-term value emerge from di erence of opinion among hareholder coupled with hort ale contraint. There i by now a whole body of evidence conitent with at leat the weak form of our theory, which how how for a xed executive compenation contract, CEO orientation become more hort-termit in peculative market (Propoition 4). In particular, there i growing evidence that CEO have engaged in more value-detroying activitie to boot hort-term tock price performance, in period when di erence of opinion among invetor were more pronounced. We dicu thi evidence more ytematically in Bolton, Scheinkman and Xiong (004). It i worth mentioning here one prevalent form of value-detroying activity that ha rien with tockoption baed compenation throughout the technology bubble: earning manipulation, either in the form of accounting manipulation (ee Peng and Roell, 004) or in the form of wateful action, uch a ine cient merger or delayed invetment and R&D expenditure (ee Graham, Harvey and Rajgopal, 004). One tet of the trong form of our theory, which aume that the contracting partie optimally adapt the compenation contract to market condition, would be whether the hortterm performance weighting in CEO compenation increae with high level of peculation, a, ay, meaured by econdary-market trading. Thi greater hort-term weighting may be characterized by horter veting period or horter CEO tenure, for example. Precie meaure of thee variable may be di cult to contruct and we are not aware of any tudy that ha attempted to do thi. Interetingly, ome policy implication emerging from our analyi echo the argument upporting the protection of target rm againt hotile takeover by Martin Lipton (987) and other legal cholar. The central iue in the policy debate on hotile takeover in the 980 wa whether tock market valuation accurately re ected rm fundamental value. Mot legal cholar and economit were arguing that market value were the bet available meaure of a rm long-term value and that any value-increaing takeover, a meaured by hort-term tock price movement, hould go forward. The contrarian view wa that many hotile takeover were 6

9 purely peculative tranaction eeking to realize a quick pro t by breaking up undervalued rm in pite of the lo of long-run e ciency that reulted from plitting up the rm. Thi view ha been ghting an uphill battle, becaue it lacked a coherent theory of aet pricing in peculative market. A variation of our model, however, can be the bai of a theoretical framework for thi view. The paper proceed a follow. Section decribe the model. Section 3 derive the optimal CEO compenation contract under the claical aumption that tock market are e cient. In Section 4, we introduce invetor with heterogeneou belief and characterize the optimal contract in the preence of a peculative market. Section 5 analyze whether a long-term oriented board can remedy the hort-termim generated by a peculative tock market. In Section 6, we dicu ome implication from our model. Section 7 conclude the paper. An appendix contain mot proof and numerical illutration of ome comparative tatic. The model We conider a publicly traded rm run by a rik-avere CEO. There are three date: t = 0; ;. The rm i liquidated at t =. At t = 0, the manager can pend time or e ort between two project: a project with a higher long-term expected return and a project with an inferior long-run expected return but which i more likely to be overvalued by ome future invetor in the econdary market. For implicity, we et the interet rate to zero. We alo aume that hareholder and potential invetor are rik-neutral while the CEO i rik-avere. 3 The rm long-term value at t =, thu, ha three additive component: e = u + v +, where, u repreent the realized value of the rt project. It i a normally ditributed random variable with mean h and variance (or preciion = = ). Here 0 denote the Example of thi type of project can be making an acquiition or pending a fortune on an internet venture to atify the whim of an irrational market" (ee Jenen (004)). 3 The tandard juti cation for hareholder rik-neutrality i that they can diverify rm peci c rik, while the CEO cannot. 7

10 CEO hidden e ort, and h > 0 i a parameter meauring the expected return of e ort. The variance i outide the manager control. v i the terminal value of the inferior project, which we refer to a a catle-in-the-air venture. It i alo a normally ditributed random variable. To be able to de ne a imple benchmark under an e cient tock market with no peculative trading, we aume that the unit return on thi project, which we denote by z, ha a xed mean which we normalize to 0. The unit variance of thi project i l. Thi project can be caled up by the CEO by raiing the obervable level of managerial time! devoted to the project. Then, for a given choice of!; the total variance of the project i! l. In ummary, the catle-in-the-air venture i a contant return to cale project with an inferior long-term mean return. The attraction of thi project, however, i that it might become over-valued by ome invetor in a peculative market. We will how that in an e cient tock market, optimal compenation deign would lead the CEO to pend no time on thi project. However thi will not be the cae in a peculative tock market. i a pure noie term; it i a normally ditributed random variable with mean 0 and variance (or preciion = = ). If we let the random variable W denote nancial take of the CEO in the rm then the CEO payo i repreented by the uual additively eparable utility function: E 0 u(w ) (;!) where (;!) i the CEO hidden cot of e ort function, which we aume to take the imple quadratic form: (;!) = ( +!). We make the additional implifying aumption that the CEO attitude toward rik can be ummarized by the following mean-variance preference. E 0 u(w ) = E 0 (W ) V ar 0(W ), where > 0 meaure the CEO averion to rik. 8

11 Intuitively, one can think of and! a time pent on the two eparate project. Under thi formulation the two activitie are ubtitute and there are diminihing return to pending more time on each tak. At t =, two ignal are publicly oberved by all invetor. Signal provide information about u (the value of the rm fundamental project), and ignal about z (the per unit return of the catle-in-the-air project). We aume that, = u + ; = z + ; where and are again normally ditributed random variable with mean 0 and repective variance and, (or preciion = = and = = write = z = l ). To implify our notation, we where, i a contant meauring the informativene of ignal. The two ignal allow invetor to revie their belief about the long-term value of the rm. After oberving the ignal, invetor can trade the rm tock, in a competitive market, at t =. The determination of invetor belief and the reulting equilibrium price in the econdary market p are a central part of our analyi. We normalize the initial number of hare held by invetor to one. The central problem for hareholder at t = 0 i to deign a CEO compenation package to motivate the CEO to allocate her time optimally between the two tak and between work and leiure, without expoing her to too much rik. A i tandard in the theoretical literature on executive compenation we will only conider linear compenation contract. 4 Our compenation contract pecify both a hort-term and a long-term equity take for the manager and take the form: 5 W = ap + be + c; () 4 A few recent attempt have been made to explore more general non-linear (option-like) contract (ee e.g. Hemmer et al. 000, and Huang and Suarez 997). 5 An implicit aumption in our linear peci cation of the CEO compenation package i that hareholder do not write forcing contract on the CEO obervable level of managerial activity devoted to the catlein-the-air project. Thi i a realitic impli cation a in reality a catle-in-the-air project may well involve many dimenion which are di cult to decribe accurately and exhautively in a contract. 9

12 where: p repreent the rm tock value at t =, a denote the hort-run weighting of the CEO compenation (the fraction of non-veted CEO hare), b i the long-run weighting (the fraction of CEO hare ownerhip that i tied up until t = ), and c i the non-performance baed compenation component. The initial hareholder problem i then to chooe the contract fa; b; cg (through the board of director, or the compenation committee) to maximize the rm tock price at t = 0, ubject to atifying the manager participation and incentive contraint. Formally, the initial hareholder problem i given by: max a;b;c p 0 ubject to max ;! E 0 (ap + be + c) where W i the manager reervation utility. 6 V ar 0(ap + be + c) ( +!) W, The timing of event i a follow: At t = 0, initial hareholder determine the managerial contract fa; b; cg. Then the manager chooe her action and!. At t =, market participant trade tock baed on the realized ignal and and the oberved value of!. At t = ; the rm i liquidated and the nal value e i divided among hareholder after deducting the CEO pay. 6 Sometime thi formulation i miinterpreted a meaning that hareholder have all the bargaining power (a patently counterfactual aumption) and can force the CEO down to her reervation utility level. But the olution to the dual problem max fe0(w ) a;b;c V ar0(w ) ( +!) g ubject to p 0 p 0, would be the ame up to a contant. In the tandard agency problem the bargaining power of the manager determine the level of her total compenation (c), but not the tructure of the compenation package (a and b). 0

13 3 Optimal executive compenation in an e cient market To et a benchmark, we begin by olving for the optimal CEO compenation contract under the aumption that all invetor hare the ame correct belief. Thi ection motly build on and adapt the analyi of Holmtrom and Tirole (993). In an e cient market, the tock price p incorporate all the information contained in the hort-term ignal and that invetor oberve. Since, however, and are noiy ignal of u and z, the hort-term tock price p cannot be a u cient tatitic for the manager e ort choice and!. Therefore, ince the CEO i rik-avere, one hould expect her compenation package to have both a hort-run and long-run component. 3. Informationally e cient tock market More formally, if all the market participant are fully rational, equilibrium tock price at t = 0 and t = are given by: p 0 = E 0 (p ) and p = E(e W j; ;!), where W i the compenation to the manager. The manager e ort choice in the fundamental project i not obervable. However, in a rational expectation equilibrium, hareholder correctly expect the manager to chooe the optimal e ort under the CEO compenation contract, and form the following conditional expectation: E(ej; ;!) = E(uj) + E(vj;!) = h + + ( h ) + z +! () = h + (u h + ) +! (3) + + Equation () i the tandard expreion for the conditional expectation given that u; ; v; and are normally ditributed random variable with repective preciion ; ; z, and (ee, e.g. DeGroot 970). Equation (3) follow immediately upon ubtitution of z = = and = u +.

14 The equilibrium tock price at t = i de ned by the following equation: Or, olving out for p, where the factor take. p = E(e W j; ;!) = E[e (ap + be + c)j; ;!] b +a and p = b + a E(ej; ;!) c (4) + a repreent the reidual tock value net of the manager c +a Subtituting thi expreion for the equilibrium price p into the equation () de ning the manager compenation, we obtain: with, and given by: = W = E(ej; ;!) + e + ; a c ( b); = b; = + a + a : Thu, denote the percentage ownerhip in the rm that the manager i allowed to ell in the rt period, the percentage ownerhip in the rm that the manager mut hold until the end, and the manager non-performance baed compenation. In practice, CEO compenation package typically atify 0 < and 0 < <. That i, CEO are not allowed to hort the tock of their company and CEO do not hold the entire equity of the rm. Accordingly, we hall retrict attention to contract uch that 0; 0 and The Manager optimization problem Given a contract f; ; g, the manager chooe her action and! to olve max ;! E 0 [E(ej; ;!) + e] ( +!) V ar 0 [E(ej; ;!) + e] ; where E 0 () and V ar 0 () are unconditional expectation and variance of the manager at t = 0. It i immediately apparent from thi objective that it i optimal for the manager to et! = 0 under any contract f; ; g. Thi i to be expected. Since pending e ort! on the catle-inthe-air project doe not a ect the equilibrium tock price in an informationally e cient market,

15 it never pay to et! > 0. A higher! only increae the variance of the manager payo and involve a higher e ort cot. Thu, in an informationally e cient tock market, the CEO would not engage in any hort-termit behavior. 7 Setting! = 0 and ubtituting for the expreion for E(ej; ) in equation (3), the CEO problem can then be reduced to chooing to olve: max + h + And the rt order condition to thi problem fully characterize the CEO optimal action choice: (; ) = h + + Note that any combination of long-term and hort-term tock participation which keep + +. (5) contant would give the ame incentive to chooe. Note alo that ince the tock price p i built on noiy information about the fundamental value of the rm u, the incentive e ect of the hort-term tock participation i dampened to t = 0 : +. Next, ubtituting for! and in (3) we obtain the unconditional expected rm value at E 0 [e] = E 0 [E(ej; )] = h where i the e ort choice of the CEO, a given in equation (5). In addition, the manager individual rationality contraint i binding under an optimal contract, o that E 0 [W ] ( (; )) V ar 0 [E(ej; ) + e] = W, (6) where: V ar 0 [E(ej; ) + e] = V ar 0 + (u h (; )) = ( + ) + : (7) 7 Thi reult contrat with Stein (989) and Von Thadden (995) where hort-termit behavior can take place in an e cient tock market for ignal jamming reaon. 3

16 3.3 The hareholder optimization problem Combining equation (5), (6), and (7), we can formulate the hareholder optimal contracting problem a follow: max ; p 0 = max f;g E 0[e W ] = max f;g ( h W Since any contract with the ame value for " #) ( + ) + : (8) + + would give the ame incentive to the manager, and hould be determined to reduce the manager rik " # min + + f;g + ( + ) + ; ubject to h + + = : Thu, we can rt olve for the optimal and for any given level of, and then olve for the optimal level of. The optimal incentive contract we obtain in thi way i decribed by the following propoition. (9) Propoition When the manager i u ciently rik-avere that > h + +, the optimal level of e ort i given by = h 3 h and the optimal weighting of hort and long term tock participation i 8 >< y ( = h +)h i; + >: y = ( + ) h + + h h ( + ) h + i; + + When the manager i not too avere to rik, o that h + +, the optimal level of e ort i given by = h3 + h ( + + ) h + ( + + )( + ) 4

17 and the optimal weighting of hort and long term tock participation i 8 >< y = (+ )(+ + ) h +(+ )(+ + ) ; >: y = h h +(+ )(+ + ) ; For both cae, the cah component y i choen o that the manager participation contraint in equation (6) i binding. Proof: ee the Appendix. In the cae where the manager i not very rik-avere the contraint + i binding becaue the manager ha a high rik tolerance. Indeed, a one would expect in thi cae, it i optimal to e ectively ell the rm to the manager and let her take on all the rik. Thi olution involve only a mall inurance cot but provide maximal e ort incentive. Note, however, the di erence in the optimal contract relative to the tandard reult that the rm hould be old entirely to the manager when he i rik neutral. Here, when the manager i cloe to being rik neutral it may be optimal to have her own the entire rm at time 0. However, for diveri cation reaon he will want to ell part of her holding at time t =. When the manager rik tolerance i low, on the other hand, it i optimal to et + < and to chooe and to minimize the manager inurance cot. 4 Optimal CEO compenation in a peculative market A critical aumption in exiting model of executive compenation i that tock market are informationally e cient and that tock price re ect the expected fundamental value of the rm. If tock price re ect fundamental value and if the CEO action a ect the rm long run fundamental value then it eem quite enible to incentivize the CEO through ome form of equity baed compenation. But how hould CEO be compenated when tock price can ytematically deviate from fundamental value? Thi i the quetion we now addre. To be able to analyze thi problem, however, we need a model of equilibrium tock price which ytematically depart from fundamental. We will ue a impli ed verion of Scheinkman and Xiong (003). 8 8 There are a number of other behavioral model of tock market, uch a De Long et al (990), Daniel, Hirhleifer and Subrahmanyam (998), Barberi, Shleifer and Vihny (998), and Hong and Stein (999) that 5

18 More peci cally, their model of peculative econdary tock market involve trading between overcon dent invetor, who may diagree about the value of the rm. The introduction of invetor with heterogeneou belief i the only change we bring to the claical model of the previou ection. All invetor are till aumed to be rik-neutral, but now they di er in their etimate of the informativene of the ignal, which in turn lead to di erence in their belief at t = about the rm terminal value, even if all invetor tart with the ame prior belief at t = 0. If > 0; ( < 0,) invetor that overetimate the preciion of will buy (ell) hare from other invetor who are either rational or are le overcon dent with repect to that ignal. Thu, thi di erence in belief generate econdary market trading, and, due to the contraint on hort-elling all invetor face, thi alo give rie to a peculative price premium. In hort, di erence of opinion combined with limit on hort elling give rie to equilibrium price that may deviate from the rm fundamental at t =. Since thee deviation are anticipated at t = 0 and priced in by initial hareholder, they alo give rie to deviation from fundamental value at t = 0. In other word, tock price at t = 0 will re ect both the fundamental value of the rm and a peculative component. Critically, for our purpoe, the ize of thi peculative component can be in uenced by inducing the manager to devote more e ort to the catle-in-the-air project, which i the main ource of potential diagreement among invetor at t =. A particularly telling example of uch a catle-in-the-air project i Enron venture into broadband video-on-demand. Thi venture, along with the partnerhip with Blockbuter video, wa valued at everal billion dollar, while Enron wa till perceived a a model company: According to the New York Time, (January 7, 00) The tart of the broadband diviion helped end the tock leaping till further from $40 in January [00] to $90 everal month later, when Enron announced a 0-year partnerhip with Blockbuter Entertainment to provide video-on-demand ervice for conumer and ubequently announced a high-peed Internet deal with the Microoft Network. In addition the ame New York Time article mention that a pokeman for the company aid that Enron hoped to capitalize on the dot-com frenzy for online we could have ued. We have opted for the approach of Scheinkman and Xiong (003) becaue they explicitly model the non-fundamental component in price and the endogenou hort-term horizon of invetor a reulting from peculative trading by overcon dent invetor. 6

19 entertainment tock, at the time, people were actually raiing capital on weird concept Equilibrium aet price in a peculative market To model peculative trading, we aume that there are two group of invetor: A and B. Each group tart with the ame prior belief but may end up with di erent poterior belief due to diagreement on the informativene of ignal. Speci cally, we aume that group-a invetor treat the preciion of the ignal a A, and group-b invetor treat it a B. Under thi formalization, if A! and B! we are back in the cae of e cient market with homogeneou belief. What i crucial for our analyi i the di erence between A and B, which we aume each group i fully aware of. Thi diagreement i conitent with the notion of overcon dence that everal recent nance model have built on to explain invetor overreaction and exceive trading. 0 For the ake of conitency with thi overcon dence interpretation, we hall alo aume that A > and/or B >. To implify the contracting problem at t = 0 we hall aume that all controlling hareholder and the CEO are of the ame group, ay, group A, and B-invetor buy into the rm only at t =. Thi aumption allow u to avoid the puriou iue of aggregation of hareholder objective with di erent form of heterogeneou belief. But alo, it allow u to avoid modelling explicitly another poible round of trading of hare between A-invetor and B-invetor at t = 0. In e ect, we are looking at the rm at t = 0, a if it had already gone through an initial round of trading, which reulted in the group which value the rm the mot holding all the tock. For implicity we con ne invetor diagreement to jut the preciion of ignal. Invetor make the ame obervation of the cale of the catle-in-the-air project! and ue the correct preciion for ignal. Thu, in accordance with Baye rule invetor in group A and B hare 9 Interetingly, even though Enron i now mainly remembered a a cae of agrant fraud it clearly i alo an example of a rm aggreively playing into tock market bubble. 0 See, for example, Daniel, Hirhleifer and Subrahmanyam (998), Odean (998), and Scheinkman and Xiong (003). The aumption that the CEO and hareholder belong to the ame group i purely for technical convenience. Our main reult would till hold if, ay, the CEO belong to a third group. However, under uch an aumption additional conideration arie at t = 0 if, ay, a more optimitic CEO contract with more keptical hareholder. In uch a ituation it i likely that the optimal incentive cheme would be even more hort-term oriented, a hareholder may then bene t from rewarding the CEO with what in their eye i overvalued tock. 7

20 the ame poterior belief about u at t = : ^u = E A (uj) = E B (uj) = h + + ( h): In the remainder of thi paper we hall ue upercript A and B to denote the variable aociated with the repective group of invetor. At t =, the invetor poterior on v di er a follow: ^v A = E A (vj;!) = A z + A! = A + A!; ^v B = E B (vj;!) = B z + B! = B + B!: Thu, the di erence in poterior belief i ^v A ^v B A = + A B + B!: (0) Thi di erence in invetor belief induce tock trading at t = : A-invetor ell their hare to B-invetor when they have higher poterior, and vice vera. Under rik-neutral preference, one would then expect to ee unbounded bet between invetor with heterogeneou belief. We rule out uch bet by auming that invetor cannot engage in hort-elling. Thi i a reaonable aumption a, in practice, it i uually di cult and cotly to ell tock hort. When tock elling i limited by hort ale contraint, the price of a tock will be driven up to the valuation of the mot optimitic invetor. The hort ale contraint prevent rational arbitrageur from eliminating the upward biaed price et by optimitic invetor. In practice, there are many other contraint that retrict arbitrage trading even in abence of explicit hort ale contraint (See Shleifer and Vihny 997). Initial hareholder and the CEO (in group A) thu have an option to ell their hare at t = to invetor in group B when thee invetor have higher valuation. Under thee aumption, we are able to derive the following imple expreion for the expected value of the rm at t = and t = 0. For a given action choice (;!) the equilibrium What i important for our analyi i that there are ome limit on hort ale. Setting thee limit to zero i a technical convenience. Several empirical tudie, e.g. Jone and Lamont (00), D Avolio (00), and Geczy, Muto and Reed (00), have documented that it i cotly to hort-ell tock, epecially for over-valued tech tock in the recent bubble period. 8

21 value of the rm at t = to group-a invetor i: V = max(^e A ; ^e B ) = max(^u + ^v A ; ^u + ^v B ) and the expectation of V at t = 0 i = h + + ( h) + ^va + max(^v B ^v A ; 0); V 0 = E A 0 [V ] = h + E A 0 [max(^v B ^v A ; 0)]: That i, the value of the rm at t = 0 now alo include the value of the option to ell to group-b invetor, E A 0 [max(^vb ^v A ; 0)]. Thi option i analogou to a tandard nancial option, except that it underlying aet i now the di erence in belief: ^v B ^v A. From equation (0) we note that (^v B ^v A ) ha a normal ditribution with a mean of zero and a tandard deviation of 3 : A B q + A + B!l + = A Now, oberve that the expected value of an option, max(0; y), for a random variable y with Gauian ditribution y N(0; y) i given by E[max(0; y)] = Z 0 y q e y y y dz = y p. We have thu etablihed that the value of the rm at t = 0 ati e: Propoition The equilibrium value of the rm at t = 0, given the e ort vector (;!), i: V 0 = h + Kl!; () with K = p A + A B q + B + = A : () 3 Recall that = z + ", where z and " are normally ditributed random variable with mean zero and repective variance l and l. But, group-a invetor overetimate the preciion of themelve and believe that " only ha a variance of l = A. 9

22 Thu, a critical di erence with the value under e cient market conidered before i that now the tock price at t = 0 i alo an increaing function of!, while before the gro tock valuation wa independent of!. Notice that in the limit, when A B i approaching 0, the tock price i independent of!, a before. In other word, in the preence of heterogeneou belief among invetor, the value of the catle-in-the-air project to initial hareholder increae becaue of the option to ell to group-b hareholder at t =. 4 The parameter K meaure the extent that invetor belief might di er at t =, and can be referred to a the peculative coe cient. A can be een from Propoition, thi coe cient K i a ected both by the di erence in A and B and by the informativene of the ignal. Thi change in the valuation of the rm at t = 0 i the key ditortion introduced by peculative market. A we hall illutrate below, thi ytematic bia in tock price, far from dicouraging rational hareholder from expoing the CEO to tock baed remuneration, will intead induce them to put more weight on hort run tock performance. Indeed, incumbent hareholder would now be willing to acri ce ome long-term value in for a higher!, in order to exploit hort-term peculative pro t. 4. The CEO problem Under any incentive contract fa; b; cg the market value of the rm at t = i now given by: p = max fe A [e (ap + be + c)]; E B [e (ap + be + c)]g; or, p = b + a ^u + maxf^va ; ^v B g c + a : Making the ame change of variable a before, = a c ( b); = b; = + a + a (3) we then have p = ( ) ^u + maxf^v A ; ^v B g : (4) 4 Note that if invetor alo had diagreement on the preciion of ignal, then the peculative option value would be attached to the long-run venture u a well. Heterogeneou belief and peculative market would then give rie to another ine ciency: overinvetment in u. 0

23 and p 0 = ( )E A 0 [^u + maxf^v A ; ^v B g]. (5) Given a contract f; ; g; the manager then chooe her bet action by olving 5 : max ;! EA 0 ^u + maxf^v A ; ^v B g + e + (+!) V ara 0 ^u + maxf^v A ; ^v B g + e Initial hareholder, thu, chooe f; g to maximize the rm net expected value ubject to the manager incentive contraint in equation (6) and her participation contraint. Subtituting for ^u, ^v A and ^v B into equation (4), we obtain the following expreion for equilibrium hare price at t = : p = ( ) h + + ( h ) A +( )! max + A ; B + B Next, by ubtituting for p in the manager compenation formula W = ap + be + c we get the following expreion for the manager mean compenation and it variance. Lemma 3 Given the manager e ort choice (;!) and the choice, ; anticipated by invetor, the manager expected compenation i h + + h( ) + Kl! + h + with the coe cient K given in equation (). The variance of the manager compenation i : (6) ( + ) + " + l! with coe cient " = A B + A B + + A ( + A ) A A + A! A ( + A ) + B ( + B ) B # + B (7) Proof: See Appendix. 5 A the CEO i rik-avere he will alway ell all her non-veted hare at t =.

24 Uing thi lemma we can rewrite the manager optimization problem a follow: max ;! + + h + Kl! ( +!) l! : It i eay to ee from thi formulation that the manager marginal return to increaing the cale,!, of the catle-in-the-air project i increaing in the coe cient K. Moreover, K itelf i increaing in A + A B + B the di erence in invetor etimate of the ignal preciion. In other word, it i immediately apparent from thi expreion that the return to caling up the peculative project i increaing in the heterogeneou belief among invetor. To ee thi more explicitly, we olve the manager optimization problem under an arbitrary contract f; ; g and obtain the following characterization: Propoition 4 Given a compenation contract f; ; g, the manager bet-repone i decribed by the following three ituation: ) Fundamentalit:! = 0 and = h + + when Kl h + +, ) Short-termit:! = K l h l + + > 0 and = h + l + + when h + + < Kl h + l + +, 3) Purely peculative:! = Kl and = 0; + l K l 0 when Kl > h + l + +. Proof: See Appendix.

25 Becaue he i avere to rik, the CEO face a lower marginal cot of e ort on than on!. More explicitly, her marginal cot of action i only ( +!) while her marginal cot on! i [( +!) + l!]. Therefore, it only pay the manager to engage in hort-termit behavior (by raiing! above zero) if the marginal return on the catle-in-the-air project exceed that of the long-term project, or equivalently if Kl > h + +. A u cient condition for the manager not to engage in any catle-in-the-air activity i that Kl < h +, which hold when K or l are mall, or when h i large. That i, when there i either little peculative motive among invetor or it i di cult to cale up v, or it i eay to improve fundamental. In contrat, in a peculative bubble, when K i large (ay, Kl > h + ), the CEO would want to purue uch a hort-termit trategy provided that her hort-term tock holding i u cient large relative to her long-term holding. In the extreme cae when the marginal return on raiing! exceed that of, even after adjuting for the rik premium, the CEO would only purue the catle-in-the-air project. 4.3 The hareholder problem The general form of hareholder contrained optimization problem i the ame a before. They chooe f; ; g to maximize the market value of the rm at t = 0 ubject to the manager incentive and participation contraint: max p 0 = max f;;g f;;g ( )(h + Kl!) (8) ubject to: max ;! (h + Kl!) + h ( +!) V ar(w ) + W At the optimum the individual rationality contraint i binding and we can ubtitute for to obtain the following uncontrained problem: max ; h(; ) + ( )Kl!(; ) " # ( + ) + ((; ) +!(; )) l (!(; )) W, (9) 3

26 where (; ) and!(; ) atify the rt-order condition of the CEO optimization problem decribed in Propoition 4. Although the hareholder problem i conceptually identical to the previou one, it i more involved technically. In particular, due to the nonlinearity in the objective function, an analytical olution for the optimal contract f; ; g i not generally available. However, it i eay to ee that an optimal contract alway exit. Firt, the feaible et of contract f; g i bounded and cloed. Second, the objective in equation 9 i continuou over thi et of contract. Therefore, tandard conideration guarantee that: Propoition 5 There alway exit at leat one optimal contract that maximize the objective of initial hareholder in the et 0; 0 and +. We are only able to explicitly characterize the optimal contract in the pecial cae where the CEO i rik-neutral. In thi extreme cae the optimal contract i a follow: Propoition 6 When the manager i rik neutral ( = 0), the optimal contract induce either: a) Purely peculative behavior by the manager, when Kl > h. In that cae the optimal contract i uch that = and = 0, and the reulting managerial action are = 0 and! = Kl, or b) fundamentalit behavior, when Kl h. In that cae the optimal contract i uch that = 0 and =, and the reulting managerial action are = h and! = 0. Proof: ee Appendix. Thu, in accordance with tandard agency theory, when the manager i rik-neutral it i optimal to make her a reidual claimant on the rm cah- ow (ee Jenen and Meckling 976). Interetingly, however, in our et-up with peculative capital market thi i not the nal word on the optimal contract. It remain to determine whether the manager hould be encouraged to have an extreme peculative hort-termit perpective or a fundamentalit longterm one. When invetor have a high degree of potential heterogeneou belief o that the peculative option value at t = 0 i high (Kl > h) then it i optimal to induce the manager to focu on the hort-term trategy by allowing her to ell all her hare at t =. In contrat, when invetor are likely to be relatively le peculative, o that Kl h, the manager will chooe to 4

27 focu on the long-term fundamental value of the rm and will ell no hare at t = : Since the manager own the rm, the contract can be interpreted a a commitment device. Thi pecial cae with a rik-neutral CEO illutrate in a imple way one baic e ect of peculative trading generated by heterogeneou belief on the CEO incentive contract. However, in thi cae there i no real agency cot. 4.4 Rik avere CEO Even though a complete characterization of the optimal contract when the manager i rik avere i not available, it i poible to determine a u cient condition on the peculative coe cient K under which the manager engage in hort-termit behavior,! 6= 0. We give a u cient condition here for the pecial cae where only group-b invetor are overcon dent. The reaon why we focu on thi cae i to emphaize the obervation that: i) even under an incentive contract that i optimal given an e cient econdary market, the CEO may engage in horttermit behavior (by etting! > 0) when there i an epiode of overcon dence giving rie to a bubble; and ii) when uch an epiode arie it may be in the interet of hareholder to reinforce the manager incentive toward hort-termim by weighing her tock compenation more heavily toward hort-term compenation. When A =, the peculative coe cient K increae with the overcon dence level of group-b invetor: r + K = B + B +. Note that if B =, the optimal managerial contract i the one given in Propoition. Now, conider the following quetion: given that the manager and the incumbent hareholder are fully rational, how doe the preence of le ophiticated trader (group-b invetor) a ect the rm and the managerial contract? Although the rm could alway chooe to ignore thee invetor in the market, Propoition 7 below provide a u cient condition on the peculative coe cient K under which hareholder optimally adopt a managerial contract that induce ome hort-termit behavior from the manager. Propoition 7 Let ( y ; y ; y ) be a contract (a peci ed in Propoition ) that i optimal 5