Work hard, not smart: Stock options as compensation

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1 Wok had, not smat: Stock options as compensation John M. Baon a len R. Waddell b, * a Depatment of conomics, Pudue Univesity, W. Lafayette, IN , USA b Depatment of conomics, Univesity of egon, ugene, R , USA June 2003 This pape examines the optimal compensation package fo executives, in paticula the optimal mix of stock options and stock gants, fo an agent deciding whethe to adopt o eject a plan of uncetain value. The compensation stuctue in such a setting affects not only an executive's effots to impove the pecision of signals egading the tue value of poposed plans but also the choice of a esevation signal that detemines the likelihood a poposed plan is adopted. While stock options can bias an executive s decision citeia away fom fist-best, we show that the leveage they povide to motivate an executive to undetake moe extensive plan evaluation makes options the pefeed fom of equity compensation if the execise pice is feely chosen. Howeve, thee is a ole fo esticted stock in ealigning the inteests of the executive with shaeholdes if the fim is constained in the choice of the execise pice, which we ague may sometimes be the case. Using extensive data on top-executive compensation, we epot evidence on this tadeoff that is consistent with the theoetical pedictions. We also find that the extent of option compensation among top executives at a fim is associated with an incease in the likelihood of exteme etuns in subsequent peiods. JL classification: J33; J41; 3. Keywods: executive compensation; agency theoy; incentive pay We thank Kevin J. Muphy, Lay Singell, and Dan Kovenock fo helpful comments as well as semina paticipants at the 2003 IZA/SL Tansatlantic Meeting of Labo conomists, emany, and the 2003 conometic Society Noth Ameican Summe Meetings. We also thank Rajesh Aggawal and paticipants in seveal seminas fo comments on an ealie vesion. We gatefully acknowledge the financial suppot of the Pudue Reseach Foundation. * Coesponding autho, -mail: waddell@oegon.uoegon.edu.

2 Wok had, not smat: Stock options as compensation Abstact: This pape examines the optimal compensation package fo executives, in paticula the optimal mix of stock options and stock gants, fo an agent deciding whethe to adopt o eject a plan of uncetain value. The compensation stuctue in such a setting affects not only an executive's effots to impove the pecision of signals egading the tue value of poposed plans but also the choice of a esevation signal that detemines the likelihood a poposed plan is adopted. While stock options can bias an executive s decision citeia away fom fist-best, we show that the leveage they povide to motivate an executive to undetake moe extensive plan evaluation makes options the pefeed fom of equity compensation if the execise pice is feely chosen. Howeve, thee is a ole fo esticted stock in ealigning the inteests of the executive with shaeholdes if the fim is constained in the choice of the execise pice, which we ague may sometimes be the case. Using extensive data on top-executive compensation, we epot evidence on this tadeoff that is consistent with the theoetical pedictions. We also find that the extent of option compensation among top executives at a fim is associated with an incease in the likelihood of exteme etuns in subsequent peiods. A cental thesis of the extensive pincipal-agent liteatue is the incentive effect on an agent's effot that deives fom linking compensation to a measue of the agent's output, albeit at the expense of exposing a isk-avese agent to uncetain compensation. 1 Moe ecently, the liteatue has consideed multiple dimensions to the actions taken by agents depending on the cicumstances. 2 When agents ae executives, expanding the chaacteization of the activities of the agent is paticulaly impotant. Fo instance, Muphy (1999) wites that although the [executive s] action space is typically defined as one-dimensional effot, it is widely acknowledged that the fundamental shaeholde-manage agency poblem is not getting the [executive] to wok hade, but athe getting him to choose actions that incease athe than decease shaeholde value. [In pat], inceasing shaeholde wealth involves investing in positive net pesent value plans (p.28). 1 aen (1994) is one of the fist papes to develop and test pedictions of the standad pincipal-agent model with espect to executive compensation. 2 The classic pape intoducing multiple activities of agents is Holmstöm and Milgom (1991), whee the additional activity can be actions such as quality contol o maintenance of capital assets. the examples include Milgom (1988), whee the additional activity involves actions to influence task assignments; Lazea (1989), whee the additional activity involves the sabotage cowokes contibution to output; Dago and avey (1998), whee the additional activity is helping othes pefom thei tasks; and Wulf (1999, 2001), whee additional activities ae influence actions and the distotion of subjective infomation about investment oppotunities. 1

3 The pape is oganized as follows. Section 1 intoduces a model in which a isk-neutal executive must choose to adopt o eject a poposed plan of uncetain outcome based on an impefect signal of the plan s value. The executive also chooses a level of effot to invest in the pocess of evaluation an investment that affects the infomativeness of the signal of the plan's value. 3 The pupose of the model is to evaluate the use in executive compensation packages of two foms of equity-based compensation: esticted stock gants and stock options, as well as to exploe the potential link between the use of stock options and the pefomance of fims. In the model, option-based equity compensation moves effot towad fist best, but distots executive decision making away fom fist best. Thus, in contast to the common adage fo manages to wok smat, not had, we find that stock options encouage a wok had, not smat appoach elative to esticted stock. To illustate the potential effect of stock gants vesus stock options on executives actions, Section 2 consides how the substitution between stock gants and stock options influences the behavio of executives and shows that if the fim is unconstained in its choice of the execise pice on options awaded to an executive, the optimal equity compensation package consists only of options. In othe wods, the optimal execise pice allows the pincipal to limit the decisiondistotion consequences associated with options while taking advantage of the capacity of options to encouage effot though leveage. Thee ae two impotant featues of ou theoy. Fist, unlike Hall and Muphy (2000), isk avesion on the pat of executives is not necessay fo a finite optimal execise value in ou model. 4 This esult aises fom an expansion of the executive s poblem to a poject-selection setting in which options can distot executive decision making, and inceasingly so as the execise pice 3 This view follows Baon and Waddell (2003) the papes that conside a poject-selection decision include: Lambet (1986), Holmstöm and Ricat-i-Costa (1986), Campbell, Chan and Maino (1989), Smith and Watts (1992), Hishliefe and Suh (1992), and Bizjak, Bickley and Coles (1993). 4 Hall and Muphy (2000) suggest that if [isk neutal] manages valued stock options at thei Black-Scholes value, the optimal ganting policy would be to gant an infinite numbe of options at an infinite execise pice. 2

4 inceases. 5 A second impotant featue of ou analysis is that the model yields a knife-edge esult wheeby optimal equity-based compensation package switches fom almost all esticted stock to all stock options if the execise pice falls below a citical level. As all-options equity awads ae common in pactice, identifying conditions unde which all-option equity awads ae optimal is an appealing aspect of the theoy. 6 Section 3 povides a systematic examination of the composition of equity-based compensation among top executives. Although the use of options athe than esticted stock is widespead, thee emain instances when the compensation packages of top executives include esticted stock. To explain the use of esticted stock ove options in ou setting, we exploe the implications of estictions on the setting of the execise value. We stat by noting that ou evidence fo topexecutive stock-option compensation confims Hall and Muphy s (2000) obsevation that the execise pice is nealy always set equal to the cuent stock pice (p. 209). We exploe easons why fims may follow a simple ule of thumb in setting the execise pice equal to the gant-date maket pice (i.e., at the money ) and the consequences of such a ule. Simulations ae used to show that the fim will intoduce esticted stock into the executive s compensation if such a ule of thumb esults in the execise pice being too high. In such cases, the esticted stock component of equity compensation acts to incease the executive s concen fo accepting bad pojects and moves the agent s decision ule towad fist-best, although typically at the expense of less effot. Section 4 develops hypotheses based on the simulations pesented in Section 3 and epots the esults of empiical tests of these hypotheses using an extensive collection of data ecoded diectly fom the poxy statements of ove 1,400 publicly taded US companies ove The 5 Note also that in ou setting, options can be the pefeed means of compensation. This contasts with Jente (2001), who finds options to be an infeio means of inducing manageial effot incentives. Jente's esult elies on a isk-avese manage's undevaluation of option awads elative to the maket and a downplaying of the leveage ole fo options in inducing effot. 6 u focus is on stock option compensation fo top executives. Fo discussions of vaious ationales suppoting a moe boad-based use of options, see Hall and Muphy (2003) and ye and Schaefe (2003). Hall and Muphy focus on the mispeception of boads and manages egading the cost of options, while ye and Schaefe focus on the oles of etention and soting. 3

5 analysis identifies vaiables that can incease the likelihood an at-the-money execise pice is highe than optimal fo the alignment of incentives, and thus should lead to a educed use of options as a popotion of an executive s equity-based compensation. Consistent with the pedictions of the model, we find a systematic tendency to use stock options ove esticted stock in eseach-intensive envionments, in smalle fims, and in fims that do not have a policy of paying dividends. Inteestingly, we also find evidence that, fo both pooled and fixed-effect specifications, higheanking executives ae less likely to have a given dolla of equity compensation awaded in the fom of stock options. This povides stong suppot fo the idea that as one moves up the anks of top executives, the distotion effects of stock options become moe impotant, and thus options play a less impotant ole in equity compensation. Section 5 exploes the link between the use of option-based compensation among the top executives of a fim and the subsequent patten of fim etuns. u analysis indicates that executives ae moe likely to choose an uncetain plan that is eithe bette o wose than the status quo if options ae substituted fo esticted stock. This suggests that, othe things equal, etuns should be moe exteme when compensation is weighted towad options. The empiical analysis finds suppot fo this pediction. Namely, a fim s subsequent thee-yea etun is moe likely to be exteme (in the top o bottom 20 pecent of etuns) if the option popotion of total compensation among top executives at the fim is highe. Section 6 contains concluding emaks and potential extensions. It is impotant to note at the outset that ou focus is on stock option vesus stock gant compensation in lieu of a moe geneal analysis of the optimal compensation package. 7 The ationale fo doing so is theefold: the obseved impotance of equity-based compensation in the 7 See Baon and Waddell (2003) fo futhe discussion of such issues as well as evidence on the use of incentive-based pay in geneal. 4

6 compensation packages of top executives; 8 a desie to distinguish the diffeent incentive effects of these two types of equity-based awads that ae ovelooked in many models of executive compensation; 9 and the peception in the popula pess that the main pupose of options is to geneate atificially high pofits as such compensation need not be expensed. 10 With egad to this final point, the model intoduces a positive featue of options in encouaging effot that can esult in the extensive use of options in spite of thei potential to enich executives as well as to induce executives to take unwaanted isks fom the pespective of shaeholdes. 1. A model of plan selection Conside n executive positions at a fim odeed accoding to ank, = 1,, n, with the mostsenio position having a ank of = 1. At this point, it is sufficient fo one to egad moe senio positions as positions in which moe impotant decisions ae made; below we make specific what we mean by moe impotant decisions Plan chaacteistics and executive decision vaiables Following Baon and Waddell (2003), and in the spiit of Lambet (1986), the ole of the executive in each of these n positions is to detemine whethe to accept o eject a single poposed B plan that is one of only two types (good o bad) with expected futue goss values, and, B o espectively. The values fo all plans ae bounded on the left by zeo and that < < o that a good plan has an expected value above the status quo,, while the bad plan s expected, so 8 See, fo instance, Yemack (1995), Hall and Liebman (1998), Coe and uay (1999), Muphy (1999), and Baon and Waddell (2003). 9 Fo examples of analysis that does not distinguish types of equity-based compensation, see Baon and Waddell (2003) and the liteatue cited in this pape. 10 Fo example, conside the following quote taken fom the aticle What W. Didn t Lean Fom non by John B. Judis that appeaed in the May 6, 2002, issue of The New Republic. What is poblematic (egading stock options) is the way companies count them on thei financial ecods and tax etuns. As the law now stands, companies don't have to deduct stock options fom the pofit totals on thei financial statements even though, like wages, the options ae a fom of compensation. This omission played a key ole in ceating the wildly inflated pofits and consequent euphoia that fueled the '90s stock maket bubble." 5

7 value is below the status quo. 11 The exogenous and known pobability that the plan to be evaluated by executive is good is denoted by α. Unlike Baon and Waddell (2003), we intoduce non-degeneate distibutions h B and h fo B the ealized values of good and bad plans, espectively, with standad eos σ and σ. As will become appaent, given ou focus on stock options, this modification is necessay to eliminate a bias towads the use of options that othewise could exist fo positive execise pices; without this modification, the distoting effect of options on decision making that we identify below would not exist fo a ange of positive execise pices. Let o h o and σ epesent the density function and standad eo of the status quo plan. If the objective is to maximize the expected futue value of the plan, the stochastic natue of the signal geneating pocess leads the executive to e in plan selection in one of two ways. Adopting the teminology of Sah and Stiglitz (1988), the ejection of a good plan by the executive is a Type I eo and the adoption of a bad plan is a Type II eo. In evaluating a plan, assume that an executive in a position of ank who incus unobsevable effot e eceives an impefect signal s of the plan's undelying value to the fim. If the plan is good, the signal is dawn fom a nomal distibution with cumulative density function F ( e, s) with mean µ and pecision P( e, υ ), 2 2 whee P / e > 0, P / e 0 and υ is a paamete affecting the pecision of the signal fo a given level of effot. 12 If the plan is bad, the signal is dawn fom nomal distibution F (e, s) B with mean µ B < µ and pecision P( e, υ ). 11 Fo simplicity, we assume that the pincipal anks plans solely on the basis of thei expected value. This need not be the case. Fo instance, the simple capital asset picing model suggests that isk-avese shaeholdes value stocks in thei potfolio based on consideations beyond thei expected etun. 12 Fo discussion puposes we talk of signal pecision and not signal vaiance; pecision is simply the ecipocal of the vaiance of the signal. 6

8 The executive decides to accept o eject a poject based on the executive s choice of esevation signal ŝ. If the signal obtained fo the poposed plan is above the chosen esevation signal, the executive adopts the plan. If the signal obtained is less than s, the executive ejects the plan in favo of the status quo. 13 Fo a given evaluation effot e and esevation signal ŝ, the ˆ executive theefoe ejects a poposed plan that is good with pobability F e, sˆ ). Likewise, the ( executive adopts a poposed plan that is bad with pobability 1 F B ( e, sˆ ). Thus, an incease in ŝ inceases the likelihood of Type I eo but educes the likelihood of Type II eo The fist-best solution The expected futue goss value to the pincipal of the plan-selection decision of an executive in position of ank is given by: (1) e sˆ = F e sˆ k F e sˆ k, * I II [ (, )] (, ) (1 B(, )) I I II II whee k = α L and k = (1 α ) L denote the expected losses fom Type I and Type II eos fo I o II o B shaeholdes, with L = and L =. Accoding to q. (1), the best possible outcome * o I ( = α + (1 α ) ) is educed by losses associated with Type I eos ( ) and Type II eos II ( ). L 14 Whee etuns ae additively sepaable acoss executives and effot costs ae quadatic 2 ( ce ( ) e /2), the fist-best e and s that maximize shaeholde etun satisfy the poblem: = ˆ 2 max ρ[ (, ˆ e s)] e / 2 (2), e, sˆ whee the discount facto ρ [0,1] convets the goss futue value into cuent values. The fist- L 13 Note that we keep mattes simple by assuming the executive evaluates a single poposed plan. ne could instead conside the executive as engaged in sampling plans fom a pool of potential plans. In this case, one would eintepet the status quo as the value to continued seach (i.e., dawing anothe poposed plan to evaluate). 14 In the analysis to follow, we assume that the costs of these eos ae sufficiently lage that it is not optimal fo the pincipal to adopt the simple ule of eithe always ejecting o always accepting poposals. 7

9 best esevation signal, * sˆ, is given by: (3) whee s ˆ* ( ) ln Φ µ + µ B = + P( e ) ( µ µ ) 2 B, I II (4) Φ =k / k denotes the atio of expected losses fom Type I and Type II eos made by an executive in the position of ank. 15 iven the optimal esevation signal, * sˆ, the fist-ode condition that defines the fist-best evaluation effot, * e, is: (5) * * * * * F (, ˆ ) I (1 (, ˆ e s FB e s)) e = ρ k e e II k. The optimal evaluation effot fom the shaeholdes pespective equates the maginal cost of effot with the maginal benefit aising fom the effect of effot on educing the expected costs of making * Type I and Type II eos given s. ˆ 2. A Stylized xecutive Compensation Package In ode to undestand the advantages and disadvantages of stock gants vesus stock options, we contast the fist-best decision-making choices above with those of a isk-neutal executive when compensation takes the fom of options and esticted stock. In doing so, we demonstate that the ganting of stock options in place of esticted stock povides leveage to the fim in inducing executive effot, but comes at a potential cost of distoting the agent s decision citeia towad toofequent Type II eos (adopting a bad plan). 15 Note that if symmety exists in the expected gain and loss fom plan selection, such that k I (1 α)( o B ) k I 1 I o α ( ) = and Φ =, then the decision citeion is independent of the specific level of evaluation effot. 8

10 Resticted stock gants awad a fixed numbe of equity shaes to the executive with estictions on the eselling of the asset. Such contacts specify a time schedule fo elaxation of such maketability-estictions, with the typical vesting peiod being less than 50 months (Muphy, 1999). Stock options, on the othe hand, give the executive the ight to buy shaes of fim stock at a pe-specified execise pice ove a pe-specified tem, often vested ove time. Fo example, one thid of the options specified in the gant might become execisable in each of the thee yeas following the gant. ptions that ae awaded to executives ae non-tadable and ae typically fofeited if the executive leaves the fim befoe vesting. While many diffeences can be identified between stock gants and options, fo ou puposes the fundamental diffeence between the two types of equity awads is thei implied execise pices: zeo fo stocks and stictly positive fo options. To simplify ou analysis, we focus on this key distinction by assuming away all othe diffeences. 16 Fo tactability, we also assume that the time peiod to vesting fo stock gants and options equals the time peiod until the ealization of the plan s value. To maintain a simple chaacteization of the value at the time of vesting fo option gants, we also assume that options ae execised when vested. iven these simplifying assumptions, the cuent value of executive s compensation package, a value that depends on the discounted futue ealized value of the fim,, takes the fom: R δ + ρ( β + β ( )) if 0< (6) C =. R δ + ρ( β) if < In q. (6), δ is the salay component of the executive s emuneation. The paametes and β can be intepeted as the popotion of the fim s value and the popotion of the fim s value in excess of the execise value that the executive will acquie though stock holdings R β 16 Fo a discussion of the diffeences in vesting schedules between stock gants and option gants, see Kole (1997) and Muphy (1999). 9

11 and stock options, espectively. We adopt a common discount facto of ρ < 1. q. (6) illustates that fo stock options, unlike esticted stock, the executive ealizes inceased wealth only if the fim s futue value exceeds the execise value,. While we cast the option as having an execise value, this value is analogous to the execise pice on the option gant and is set pio to the executive choosing evaluation effot and the citeion fo adopting o ejecting the poposed plan. Befoe defining the agent s optimization poblem, it is helpful to chaacteize the expected compensation that is implied by (6). To simplify the pesentation to follow, we assume a single executive (n = 1). 17 Assume the ealized value fo the decision made by the executive has common lowe and uppe bounds of zeo and, espectively. Then, the expected futue value of the fim fom (1) is given by: (7) II k, 0 0 o I [ ] = α xh ( x) dx+ (1 α) xh ( x) dx Fk (1 FB) whee the expected losses to fim value fom ejecting a good poposal o accepting a bad poposal ae, espectively: (8) I o k = α x( h ( x) h ( x)) dx 0 and (9) II o B k = (1 α) x( h ( x) h ( x)) dx. 0 When equity is awaded to the executive in the fom of esticted stock, it is this chaacteization of fim value that is of ultimate inteest to the executive. 17 A fomal statement of the moe geneal poblem when n > 1 is available fom the authos upon equest. Note that the insights obtained fom the single executive case cay ove to the case of moe than one executive given ou pio assumption that fim value is simply the sum of the value of individual executive pojects. ne aea fo futue analysis is to conside the moe geneal case when actions by one executive can affect the poject values faced by othes. 10

12 In contast, the option holde is inteested in the expected value of the fim as it elates to an exogenous execise value,. 18 Recall that unless options ae in the money when execisable ( < ), the executive ealizes no incease in income fom having the option to puchase fim stock. That is, (10) [ ] = [ ]P( ) o I I II II B φ = α ( x ) h ( x) dx + (1 α ) ( x ) h ( x) dx F φ k (1 F ) k. To make the compaison between equity and options moe tanspaent, in (10) we expess the losses fom Type I and Type II eos fo an option holde as factions of the losses fom such eos I II fo one who holds stock gants, defined ealie as and, espectively. In paticula, the loss L L fom a Type I eo fo an option holde is denoted by I I φ k and the loss fom a Type II eo fo an II option holde is denoted by φ k II, such that: I I o (11) φ k = α ( x )( h ( x) h ( x)) dx and II II o B (12) φ k = (1 α ) ( x )( h ( x) h ( x)) dx. Recall that the non-zeo execise value is the single diffeence in ou model between a stock gant and an option gant, such that I lim φ = 1, 0 II lim φ = 1 and lim ( ) = ( ) Most fims almost univesally set the execise pice equal to the cuent stock pice (Muphy, 1985; Smith and Zimmeman, 1976). Fo a discussion of optimal stike pices see Hall and Muphy (2000). 11

13 2.1 ffot and plan selection of a isk-neutal agent When compensation can include both fim stock and stock options, the poblem fo a iskneutal agent is to choose effot and esevation signal to maximize expected compensation as given by (6). That is, the executive s poblem is: R max δ + ρ( β [ ] + β [ ]) c( e (13) ), e, sˆ whee (7) and (10) define ( ) and ( ), espectively. The fist-ode conditions fo the executive s esevation signal and effot ae: (14) sˆ ** ( ) ln Φ µ + µ = + P e B * ( ) ( µ µ B) 2 and (15) ** e F e sˆ F e sˆ ** ** ** ** ρ (, ) R I I B(, ) R II ( ) k ( e β φ β ρ = + + e β + φ ) II k β, whee the atio of expected losses fom Type I and Type II eos fo the executive is given by: (16) ( β + φ β ) k Φ = ( β + φ β ) k R I I. R II II R Note that the elative impotance of Type I and Type II eos is detemined by β and β (the I II weights fo these two types of compensation) and by φ and φ (the atio of losses fom Type I eo fo option ecipients vesus stock ecipients and the atio of losses fom Type II eo fo option vesus stock ecipients, espectively). As in the fist-best solution above, if symmety exists in the expected gain and loss fom plan selection, then the decision citeion is independent of the specific level of evaluation effot. 2.2 The Pincipal's poblem ven fo the single-agent case, chaacteizing the optimal compensation package that can include both options and stock emains analytically difficult. ne eason is that involved in the 12

14 optimal compensation package is not only the choice of the weights fo options and stock, but also the choice of the optimal execise value. In paticula, the pincipal s poblem is: max ρ[ ] [ C ] (17), R δ, β, β,, e, sˆ subject to the agent s optimal choices of esevation signal and effot (the incentive compatibility 2 constaints (14) and (15)), the agent s ationality constaint ( C ( ) e /2= u ), and non-negativity constaints on δ, R β, β and. Ultimately, we esot to simulations to povide insight into the natue of the solution. Howeve, we stat by focusing on two special cases in ode to highlight the potential positive ole options can play in encouaging had wok (Section 2.3) and the negative ole of options in distoting executive decision making (Section 2.4). Section 2.5 then illustates the optimal choice of the execise value, noting the fact that in ou setup, if a positive execise value is optimal and the pincipal is unconstained in this choice, only options will be used in the compensation package. 2.3 ptions encouage had wok Recall that the single featue that distinguishes stock options fom esticted stock gants in ou model is the execise value. Inceasing the execise value can encouage agents to wok had. To isolate this featue of option gants, assume that vey low ealizations of fim value (i.e. fim values appoaching zeo) ae unlikely egadless of the executive s decision. In this case, as shown in Supplement A, fo any given β > 0, an incease in the execise value fom zeo povides a leveage gain. This leveaging aises as an incease in lowes the agent s expected value of a given numbe of options and theefoe allows moe options to be included in the contact subject to the agent s individual ationality constaint. An incease in the numbe of options induces the agent to choose an effot level close to fist-best as the maginal etun to effot is highe. 13

15 As Supplement A demonstates, we can genealize this esult if we assume symmety in the undelying costs to the Pincipal of Type I and Type II eos. Unde such an assumption, if the diffeence in the likelihood of bankuptcy (i.e. zeo fim value) fom a bad poject and the likelihood of bankuptcy fom a good plan is sufficiently small, we can again establish a stictly positive effect on effot fom the leveage that is coincident with inceasing the execise value fom zeo. 2.4 ptions distot decisions u twofold chaacteization of the executive s poblem eveals that the benefit fom substituting esticted stock fo options, the encouagement of effot though leveaging, is tempeed by a negative effect on the chosen esevation signal. This negative effect aises because options educe the decision-make s costs of adopting the poposed plan. Recall that the option ecipient ealizes an incease in income only when the ealized value of the fim s stock exceeds the pe-detemined execise value, and then only eceives the diffeence between the ealized stock value and the execise value. Thus, fom the pespective of the executive, an incease in the execise value fom zeo initially eplaces what would be elatively low-value outcomes with zeovalue outcomes. Howeve, key to the distotion is that this eplacement is asymmetic with espect to plan type. Fo any execise value, thee is lage mass below unde the distibution of outcomes fom the adoption of a bad plan then thee is below unde the distibution of outcomes fom the status quo and, in tun, fom the adoption of a good plan. This asymmety leads the agent to choose a esevation signal that is stictly biased downwad if options ae included in the compensation package. This bias can be significant, and acts to limit the magnitude of the optimal execise value on options awaded to the agent. To illustate the downside to the use of options on the chosen esevation signal, assume fo the moment that the agent s effot choice is fist best. It follows fom 14

16 (3), (4), (14), and (16), that the fist best esevation signal is chosen if the executive faces the same atio of losses as the pincipal. That is, if Φ =Φ, o R I β + φβ (18) = 1 R II β + φ β. I Fo a positive, φ > φ and q. (18) does not hold; fo an option ecipient (i.e. fo β > 0 ), II a Type II eo (appoving a bad plan) is now elatively less impotant than it is fo the pincipal o stock ecipient. 19 Compaing (3) and (14), this asymmety in losses acoss types of compensation means that s < s *. In othe wods, with options the expected cost of a Type II eo falls elative ** ˆ ˆ to that of a Type I eo, motivating the agent to choose a esevation signal that inceases the likelihood of making a Type II eo. 2.5 The optimal execise value: the tade-off of leveage and distotions The peceding two sections outline the tadeoff that is coincident with an incease in the execise value of stock options. Highe execise values tend to encouage evaluation effot but at the expense of a lowe standad fo plan adoption being chosen by the agent. Figue 1 eveals the tadeoffs implied by an inceasing execise value. The panels depicted in Figue 1 ae obtained fom simulations of the model assuming the pincipal optimally chooses the mix of stock options and stock at each execise value. 20 In each of the five panels in Figue 1, the tiangle on the axis indicates the optimal execise value. This execise value maximizes the value of the fim net of compensation, as illustated by Panel. Panel A documents the leveage effect of options, showing the incease in the agent s level of effot that accompanies an incease in the execise value. Fo low levels of, this leveage effect leads to an optimal compensation package that consists of only stock options, as 19 Supplement A povides the specific assumptions that suppot this statement. 20 Supplement B identifies the undelying paamete values used to obtain the simulated esults pesented in Figue 1. The esults discussed ae obust to paamete changes. 15

17 illustated in Panel D. Howeve, as Panel B indicates, an inceasing execise value intoduces distotions in the esevation signal away fom fist-best levels ( s ˆ = 0 ), and eventually leads to a significant bias towad Type II eo (accepting a bad poject) as shown in Panel C. At that point, the distotion induced by options moe than offsets the gain fom effot enhancement, and the use of options is abuptly discontinued, as illustated in Panel D. Figue 2 illustates this knife-edge chaacteistic of the optimal compensation package, showing how a small incease in the execise value can esult in a jump in the optimal compensation package fom one that is options to one that is pedominately stock gants. 3. vidence on compensation packages Collectively, the panels in Figue 1 illustate an impotant featue of the pincipal s poblem. When unconstained in the choice of execise value, it is in the pincipal s best inteest to compensate the isk-neutal agent only with stock options. This is fomally demonstated in Supplement A, whee we show that at the optimal level of, the salay component is zeo R ( δ = 0) and the level of esticted stock gants is zeo ( β = 0 ), such that all compensation is in the fom of options. To detemine to what extent this holds fo actual compensation packages, we examine the S&P xecucomp dataset. Recoded diectly fom poxy statements, this dataset contains details on the compensation of the top five executives of publicly taded companies in the S&P 500, S&P Midcap 400 and S&P Smallcap 600 fo the yeas 1992 though Limiting ou attention to executives who eceive equity compensation yields a sample of ove 55,000 executive-yea obsevations, eflecting the compensation of the top 5 executives at appoximately 1,500 fims each yea. 21 The xecucomp dataset includes epots by some companies of compensation beyond the five highest paid mandated by SC disclosue equiements. We limit ou analysis to the top five to eliminate potential sample-selection bias diven by ove-epoting. Baon and Waddell (2003) povides futhe details on the identification of the top five executives at each fim. Note that since ou analysis focuses on option compensation, the sample diffes fom that in Baon and Waddell as 4,175 obsevations that have missing infomation egading the value of options ae dopped. 16

18 3.1 The pedominate use of options Table 1 indicates the beakdown of compensation by yea, fist with espect to the popotion of executives with equity-based compensation and then, fo those with equity-based compensation, with espect to the extent to which options ae used. Note that ove the 9-yea peiod, thee was an inceased use of equity-based compensation, with ove 85 pecent of top executives in 2000 eceiving some compensation that is equity based. Table 1 eveals that each yea ove 74 pecent of such equity-based compensation packages ely solely on options. This povides some suppot fo the clea advantage of options pedicted by the theoy when the execise pice is optimally chosen. Howeve, Table 1 also indicates instances when esticted stock is used, both in combination with options and by itself. Simulations of ou model when diffeent execise values ae specified highlight a eason why the ganting of esticted stock may supplement the ganting of options. In paticula, if the execise value of an option awad is set above what would be optimal, some compensation in the fom of esticted stock can be optimal. 3.2 The pactice of setting the execise value equal to maket value In the sample of executives in the xecucomp dataset between 1992 and 2000 thee ae 81,118 individual option awads made, with ove 95 pecent of these awads made at the money. 22 In the context of ou model, this suggests a nea-univesal ule fo setting the execise value,, equal to the gant-date maket value of the fim s stock. If such a ule of thumb wee to exist, then fom an incentive standpoint alone, the execise pice associated with some contacted options could be highe than optimal. At the vey least, it is unlikely to be the case that the incentive-optimal execise pices ae so commonly set equal to fims stock pices, both within and acoss fims. 22 This is consistent with the findings epoted in Hall and Muphy (2000), who advance an economic ationale fo the nea-unifom pactice of issuing options at the money within a famewok fo measuing the value and incentives povided by non-tadable stock options as opposed to taditional option picing mechanisms. Resting lagely on iskavesion, it is shown that thee is a faily wide ange of execise picing policies that yield close-to-optimal pay-topefomance incentives, and that this ange typically includes gant-date maket values (p. 209). Note that ou appoach assumes a isk-neutal agent, and so is not diectly compaable to the analysis of Hall and Muphy. 17

19 But, why would the execise pice of options not be set optimally fom the pespective of the ecipient s decision-making incentives? Conside two potential easons. The fist eflects the gowing evidence that individuals, in ou case executives, cae not only about thei own compensation package, but also with how it compaes with othes. Bolton and ckenfels (2000) povide stong aguments that elative teatment mattes to individuals, and in paticula that simila teatment is valued. In ou context, we intepet this as intoducing a social efeence point of execise pices being set at the money. The esult is to add a second component into the agent s utility function that is concave in the diffeence between the execise pice and the maket pice, eaching a maximum whee the execise pice equals the maket pice. As a consequence, to educe compensation costs, the pincipal can now find it less costly to set the execise pice equal to the maket pice even if doing so educes the goss value of the poject selection pocess. Note that this ationale fo teating executives the same with espect to the setting of the execise pice applies not only fo within-fim compaisons but also fo acoss-fim compaisons. A second potential eason fo an execise pice set diffeently fom that pedicted by ou simply theoy, at least with espect to the awading of options in the money, is that thee ae potential accounting disadvantages to deviating fom this ule-of-thumb that ae not explicitly modeled. 23 Hall and Muphy (2000) suggest this possibility, noting that U.S. accounting ules which equie some accounting chages fo discount options, help explain why execise pices ae seldom set below gant-date maket pices (p.213). In the next section, we take as given the paticula ationale fo an at-the-money constaint, be it fainess, accounting issues, o some othe eason. We then addess how such a constaint influences optimal equity-based compensation packages. 23 Howeve, in tems of the executive s incentives to invest in the evaluation of poposed plans of actions o to decide on a paticula standad against which such a poposal will be measued, the key issue is that the execise value is detemined befoe the decision is made. In this context, the paticula tax implications of awading options in the money fall outside of the agent s optimization poblem. Note that we have also abstacted fom the issues of the optimal timing by which the executive execises options, something to be consideed in subsequent eseach. 18

20 3.3. The optimal compensation package with a binding constaint on the execise value In ou simulation of a fim with a single executive, we define the cuent maket value of the C fim,, as the pincipal s pesent value of the fim, net of compensation costs, given fist-best effot and signal cut-off. We discount the expected fim value to eflect the time that elapses befoe the value fom chosen poject is ealized, such that: C (19) = ρ[ ( e *, sˆ * )] [ C ( e * )]. Fo ou benchmak case, we choose initial paamete values such that the optimal execise value equals the fist-best cuent maket value of the fim as defined by (19). Thus, ou benchmak simulation can be intepeted as one fo which it is optimal fo the pincipal to follow the simple ule of thumb of setting the execise value equal to the gant-date maket value of the fim. 24 We then conside the effect of changes in paamete values on the optimal agent s compensation package assuming the pincipal maintains the execise value at the money. We exploe, in paticula, paamete changes that esult in the execise value being set too high, leading to a mix of stocks and options in the optimal compensation package. The thee paamete changes we conside elate to the chaacteistics of the poposed plan, the quality of the signal that the executive eceives egading the plan s type, and the chaacteistics of the default plan that we efe to as the status quo. B Fist, conside an incease in and a decease in that ae equal in size. The esult is an incease in the diffeence between the expected values of good and bad poposed pojects, and B, espectively. This geate diffeence inceases the impotance of decisions being made in that the individual decision make has geate influence on the futue value of the fim when this o diffeence is lage. Holding constant, it is clea that these changes incease to the same degee 24 Supplement B povides details egading the benchmak paametes. 19

21 the undelying costs to the stock holde of a Type I eo ( o B ) and a Type II eo ( ). Howeve, fo the option holde the inceases in costs of eos ae asymmetic, as the stictly positive execise value esults in a elatively lage incease in the cost of Type I eo (ejecting a good poject). Ceteis paibus, this leads the option holde to lowe the chosen esevation signal. In esponse, the optimal execise value falls elative to the fim s cuent maket value in ode to maintain balance between the expected cost of decision-making bias and the leveaging gain to setting a highe execise value. If, howeve, we conside the case whee the pincipal is constained to set the execise value at o the money (i.e. = C ), then ou theoy suggests that the pincipal may find a substitution of esticted stock in place of stock options to be optimal, with a esulting decease in the popotion of equity-based compensation that is options. u simulations bea this out. When decisions cay the potential fo geate upside and downside consequences, stock options ae a potentially lessfavoable method of linking executive wealth to fim value, and we expect to see moe use of esticted stock. Now conside an incease in the infomativeness of the signal of plan type as eflected by a decease in the paamete υ, a paamete diectly elated to the vaiance in the signal, and thus invesely elated to the pecision of the signal, P. Assume such an incease in the quality of the signal fo a given evaluation effot also educes the maginal impact of inceased effot on signal pecision. 25 With such an incease in the infomativeness of the signal, the gain to the use of options to encouage effot is educed, and thus the optimal execise value falls. If the pincipal is constained to set the execise value at the money ( = C ), the fim can find it optimal to 25 That is, we assume P / υ < 0 and P e υ > 0. In ou simulations, we adopt the following specific fom fo 2 / the signal pecision function: P = 1/( γ + ( υ/(1 + λ) e )). Natually, given this fom, ou discussion in the text egading the effect of a decease in υ also holds fo an incease in the paamete λ. 20

22 accommodate such an incease in signal pecision by substituting esticted stock in place of stock options. u simulations again bea this out. Finally, conside the effect of a mean-peseving eduction in the spead of the density function o of the status quo outcome, h. Fo an option holde, such a decease in the vaiance of the status quo enhances the attactiveness of tying out the new, moe uncetain poject. To offset this tendency, thee would be a decease in the optimal execise value elative to the fim s maket value. If the pincipal is constained in the choice of execise value, not being able to lowe in esponse to such a change, then the pincipal may find the substitution of stock gants fo options optimal to tempe the inceased attactiveness of the uncetain poject ove the status quo fo the option holde. u simulations bea this out. A decease in the vaiability of the status-quo fim value with a fixed execise value can educe the optimal popotion of equity-based compensation that is stock options. 4. Hypotheses and Tests Regading the Use of Resticted Stock and Stock ptions The pio section consideed paamete changes that make it moe likely a simple ule of thumb that sets execise values equal to maket values yields highe-than-optimal execise values. In this section, we identify poxies fo such paamete changes that lead to testable hypotheses with espect to the use of esticted stock gants in place of options Hypotheses egading the use of options The fist compaative static esult above suggests that a elationship exists between the use of stock options and the impotance of the decision as measued in the theoy by the diffeence between the value of a good and a bad poject. We posit that executives who ae moe senio within thei espective fims make moe impotant decisions. In such cases, stock options, by downplaying vey bad outcomes, make the executive too willing to ty new, uncetain pojects. If the fim is constained in tems of educing the execise pice below an at-the-money value, the optimal 21

23 popotion of popotion of equity-based compensation that is awaded in the fom of stock options falls. Thus we hypothesize the following: Hypothesis 1: xecutives who ae elatively moe impotant within thei espective fims ae less likely to have a given dolla of equity-compensation awaded in the fom stock options. We use the measue of the elative impotance of an executive within the fim intoduced in Baon and Waddell (2003), namely the log of the atio of the executive s total compensation to the highest total compensation at the executive s fim in the same yea. In the vast majoity of cases, the highest compensation in a given yea is that of the fim s C. In the same spiit as Hypothesis 1, we also contend that executives at lage fims ae likely to face lage consequences to adopting new pojects. Specifically, we maintain that executives employed at lage fims in ou sample likely make moe impotant decisions in tems of thei potential absolute influence on fim value than do executives at small fims in the sample. Shaing, then, the same motivation as Hypothesis 1, we have the following: Hypothesis 2: xecutives at lage fims ae less likely to have a given dolla of equitycompensation awaded in the fom stock options. We adopt as ou empiical measue of fim size the logaithm of the book value of the fim s assets. New poduct development often involves a lengthy time inteval until the poduct eaches the maket, and this can intoduce substantial uncetainty at the outset with egad to the value of a poposed plan. In the context of ou model, such an incease in uncetainty egading plan type can be intepeted as both inceasing the vaiance of the signal on poject type fo a given evaluation effot by the executive and aising the maginal gain fom inceased evaluation effot in tems of educing signal vaiance. u simulation esults suggest that in such a case, the advantage of options in inducing inceased evaluation effot by executives is enhanced. The Statement of Financial Accounting Standad No. 2 classification of eseach and development expenditues suggests that the magnitude of R&D expenditues can seve to indicate 22

24 the extent executive decisions involve new poduct development. Adopting the view that eseachintensive envionments ae envionments whee effots to impove the quality of the signal have a geate payoff, we have the following hypothesis: Hypothesis 3: xecutives at fims with highe eseach and development expenditues ae moe likely to have a given dolla of equity-based compensation awaded in the fom stock options. u empiical measue of eseach intensity is defined as the atio of eseach and development expenditues to the fim's book value of asset. u analysis pedicts a move away fom options when the execise pice is constained at too high a level. Fo a given futue etun to a poject, the likelihood this constaint binds will be highe if potential futue etuns ae paid out as dividends athe than etained, and thus eflected by an appeciation in the pice of the fim s stock. That is, an execise pice set equal to the cuent maket pice will be highe elative to the futue maket pice of the fim if the fim has a policy of paying dividends. This inceases the likelihood that the execise pice is set too high. We theefoe hypothesize the following: 26 Hypothesis 4: If dividends have been paid in the past, then executives at such fims ae less likely to have a given dolla of equity-based compensation awaded in the fom of stock options. The xecucomp dataset epots the past-payment of dividends of the fim. We assume that if dividends have been paid in the past, this is associated with a peceived inceased the likelihood of futue dividend payments being made. u measue fo futue dividend policy is thus a vaiable that equals one in the cuent peiod if the fim paid dividends in the peceding peiod, and zeo othewise. 26 u view is that a educed eliance in the past on dividends, by indicating a lowe futue popensity to pay dividends, helps explain an inceased use of options. This view contasts with Lambet, et al (1989) and, moe ecently, Fenn and Liang (2001). These authos evese the causation and suggest that the use of stock options today may help explain a educed eliance on dividends in the futue. 23

25 4.2. Tests of the hypotheses egading the use of stock options u theoy and the esulting fou hypotheses to test have focused on the optimal use of options as a popotion of total equity-based compensation. Using the measued popotion as the dependent vaiable intoduces potential econometic poblems as this vaiable is bounded in the unit inteval. Such boundedness implies that the assumption of a nomally distibuted eo tem is not tenable. Futhe, as indicated in Table 1, the option-popotion of equity compensation is fequently at the uppe o lowe bounds. Recognizing these issues, we adopt the technique of Baon and Waddell (2003). That is, we ephase ou question concening the popotion of equity awaded in a paticula fashion to take the following fom: What detemines the likelihood a given dolla of equity compensation is option-based? theeby handling both the unit inteval and the lumpiness of the popotional data. 27 Table 2 summaizes the vaiables used in the analysis. In addition to the vaiables discussed above, we include a numbe of contol vaiables. In paticula, we include in ou analysis the fim s pio-thee-yea total etun to shaeholdes, including the monthly einvestment of dividends. Fo appoximately 10 pecent of the obsevations in ou sample, this vaiable is missing. Fo these cases, we set the etun vaiable equal to the aveage acoss all fims. We then specify a dummy vaiable equal to one if the etun is missing to identify systematic diffeences in option use fo fims with missing values fo the pio-thee-yea etun vaiable. 27 Columns 1, 2 and 4 of Table 3 epot the esults of Pobit models that accommodate this issue. Fo this estimation pocedue, we ceate a binay vaiable equal to one fo the oiginal dataset and zeo fo a duplicate dataset. We then weight each oiginal obsevation by the obseved popotion of the executive s total equity compensation that is awaded as stock options and weight each duplicate obsevation with one minus this popotion. The fixed-effect esults epoted in Column (3) of Table 3 do not contol fo the boundedness of the dependent vaiable. Note, howeve, that the qualitative esults epoted in columns (1), (2) and (4) ae obust to seveal teatments. Specifically, we get qualitatively simila esults using simple popotions as the dependent vaiable, Logit-tansfomed popotions as the dependent vaiable o adopting a (simple o andom-effects) Tobit estimation pocedue whee the boundedness is teated as though the data ae both left- and ight-censoed. The esults ae also obust to an odeed Logit model whee the obseved popotions ae tansfomed into mutually exclusive intevals and theeby into an odinal appoximation of the undelying data. Finally, we note hee that the use of a Heckman specification to contol fo the use of stock options is not justified fo ou data by a likelihood atio test. 24