Hard work versus good intentions: Stock options as compensation

Transcription

1 Had wok vesus good intentions: Stock options as compensation John M. aon 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 Mach 2003 In this pape we contast the use 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. These decision vaiables eveal a tadeoff in the use of options. Stock options ae attactive in that, fo the same expected value as stock gants, they can povide the pincipal leveage to motivate an executive to undetake moe extensive plan evaluation. In shot, stock options encouage had wok. Howeve, stock options also bias an executive s decision citeia away fom fist-best. u analysis establishes stock options ae the pefeed fom of equity compensation if the execise pice is feely chosen, but also shows that 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 gatefully acknowledge the financial suppot of the Pudue Reseach Foundation. * Coesponding autho contact infomation: Univesity of egon, ugene, R mail: waddell@oegon.uoegon.edu

2 Had wok vesus good intentions: Stock options as compensation Abstact: In this pape we contast the use 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. These decision vaiables eveal a tadeoff in the use of options. Stock options ae attactive in that, fo the same expected value as stock gants, they can povide the pincipal leveage to motivate an executive to undetake moe extensive plan evaluation. In shot, stock options encouage had wok. Howeve, stock options also bias an executive s decision citeia away fom fist-best. u analysis establishes stock options ae the pefeed fom of equity compensation if the execise pice is feely chosen, but also shows that 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. The Wall Steet Jounal ecently an an aticle titled High Pofiles in Hot Wate, poviding a list of nine companies, and twelve executives in paticula, who ae in hot wate. 1 Fom this list of companies, five appea in the S&P 500, S&P Midcap 400 o S&P Smallcap 600, and thus ae in Standad & Poo s xecucomp dataset, which details the compensation of the top five executives at these companies as epoted on company poxy statements. Inteestingly, between 1992 and 2000, the top five executives in these companies eceived significantly moe equity compensation in the fom of stock options than did executives at compaable companies. The pupose of this pape is to contast the use of two foms of equity-based compensation in executive compensation packages, esticted stock gants and stock options, and to exploe the potential link between the use of options and the pefomance of fims. To do so, we adopt the standad appoach of pincipal-agent theoy. 2 Howeve, we divege fom the typical model in 1 Fiday June 28, 2002, page 1. 2 Although standad, the simple pincipal-agent appoach has ecently been challenged by etand and Mullainathan (2000, 2001), who also find suppot fo a skimming view of executive compensation, with executives manipulating the pay pocess itself. 1

3 that we cast the executive s ole as two-fold, involving an effot choice and a decision citeion choice. In ou setting, option-based compensation moves effot towad fist-best, but also distots executive decision-making, inceasing the pobability of adopting new uncetain plans above fist-best. Thus, in contast to the common advice fo manages to wok smat, not had, we find that stock options encouage a wok had, not smat appoach among executives. The pape is oganized as follows. To illustate the potential effects of stock gants vesus stock options on executives actions, 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 Section 2 consides how the substitution between stock gants and stock options influences the behavio of executives in the context of the plan-selection model. A key finding developed in Section 2 is that, if the fim is unconstained in its choice of the execise pice on options awaded to an executive, an equity-compensation package consisting only of options is the pefeed fom. Specifically, being able to choose the optimal execise pice allows the pincipal to limit the decision-distotion consequences associated with options while taking advantage of the tendency of options to encouage effot though leveage, thus making options pefeed to the ganting of esticted stock. Thee ae two impotant featues of 3 This view follows aon and Waddell (2003) and, in paticula, Muphy (1999) who 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). the papes that have consideed the association between investment behavio and executive compensation include: Lambet (1986), who analyzes isk-avese executives plan choices showing that the executive and pincipal will not always agee egading which plan is best but do not conside the methods of compensation that we conside hee; Campbell, Chan and Maino (1989), who suggest a pe-commitment of pefomance level by manages to emedy advese selection poblems that aise when manages have pivate infomation about thei own ability and about the value of plans; Smith and Watts (1992), who undetake an empiical explanation of copoate financing, dividend and compensation policies; Hishliefe and Suh (1992), who analyze the effects of desiable isky gowth oppotunities and effective monitoing institutions; and izjak, ickley and Coles (1993), who analyze the impact of gowth oppotunities on the method of C compensation. 2

4 ou theoy. Fist, unlike the findings of Hall and Muphy (2000), isk avesion on the pat of executives is not necessay fo a finite optimal execise value in ou model. 4 The eason fo this is that we have expanded the natue of the executive s poblem to a poject-selection setting in which options distot executive decision making. Second, we identify a knife-edge type esult, with the optimal equity-based compensation package switching fom all stock options to almost all stock gants if the execise pice wee set above a citical level. It is impotant to note at the outset that ou focus is on stock gant vesus option compensation in lieu of a moe geneal analysis of the optimal compensation package. 5 u ationale fo doing so is theefold: the obseved impotance of equity-based compensation in the compensation packages of top executives; 6 a desie to highlight the key diffeences between these two types of equity-based awads that ae often ovelooked in pincipal agent models of executive compensation; and the peception in the popula pess that option compensation has in pat contibuted to executives making decisions that have lead to substantial losses of shaeholde wealth. 7 4 Hall and Muphy (2000) suggest that if [isk neutal] manages valued stock options at thei lack-scholes value, the optimal ganting policy would be to gant an infinite numbe of options at an infinite execise pice. They go on to indicate that The absudity of this esult undescoes the need to intoduce manageial isk avesion into any analysis of executive stock option valuations and incentives (p.213). 5 See aon and Waddell (2003) fo futhe discussion of such issues as well as evidence on the use of incentivebased pay in geneal. 6 See, fo instance, Yemack (1995), Hall and Liebman (1998), Coe and uay (1999), Muphy (1999), and aon and Waddell (2003). 7 Fo example, conside the following quote taken fom the aticle What W. Didn t Lean Fom non by John. Judis that appeaed in the May 6, 2002, issue of The New Republic. Now, thee's nothing intinsically wong with stock options; they can motivate employees by ganting them a stake in thei company's success. What is poblematic 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. Accoding to the Fedeal Reseve, if stock options had been counted fom 1995 to 2000, Fotune 500 companies would have seen thei annual pofit magins dop fom 12 pecent to 9.4 pecent. Among some high flyes the deflation would have been lage still: Counting stock options, Cisco Systems' pofits in 2000 would have been 40 pecent lowe and Lucent Technologies' 32 pecent lowe. In the following analysis, it is impotant to ecognize that we conside the ole of options ganted to the top five executives in the company. Such options ae public knowledge to the investment community, and thus we do not focus on the cost-accounting featue of options mentioned in the quote, fo the public can discen the 3

5 Section 3 examines the evidence on the use of equity-based compensation among top executives. We find the use of options athe than esticted stock widespead, yet thee emain instances when the compensation packages of top executives include esticted stock. We also find evidence acoss top-executive anks that confims Hall and Muphy s (2000) obsevation that the execise pice is nealy always set equal to the cuent stock pice (p. 209). This leads us to exploe the optimal use of esticted stock gants when fims follow a simple ule of thumb in setting the execise pice equal to the gant-date maket pice (i.e., at the money ). Though simulations, we 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 set too high fom an incentive stand point. 8 The esticted stock component of compensation acts to incease the executive s concen fo accepting bad pojects and moves the agent s decision ule towad fistbest, 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. In paticula, we identify vaiables that we ague incease the likelihood that an at-the-money execise pice is highe than optimal fo the alignment of incentives, and thus lead to a educed use of options as a popotion of an executive s equity-based compensation. u findings ae lagely consistent with the model s pedictions. 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 substituting options fo esticted induces executives to be moe likely to choose an uncetain plan that is eithe bette o wose than the status quo. This suggests that, othe things equal, exta expected cost of such options to the fim. Instead, we focus on two othe incentive-oles that options play, namely a positive one of encouaging effot and a negative one of inducing top executives to take unwaanted isks. 8 Note that, unlike Hall and Muphy (2000), in this section ou focus is not on why an execise pice is set at the money, but athe the implications of such a ule on the optimal use of esticted stock gants vesus options. 4

6 etuns should be moe exteme when compensation is weighted towad options. We do find that an incease in the option popotion of total compensation among top executives at a fim inceases the likelihood the fim s subsequent thee-yea etun is in the extemes (top o bottom twenty pecent of aveage etuns). Section 6 contains concluding emaks and potential extensions. 1. A model of plan selection Conside n executive positions at a fim odeed accoding to ank, = 1,, n, with the most-senio 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 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 poposed plans fo the fim. Fo simplicity, we assume that each executive evaluates a single poposed plan and that the plan is one of only two types; good o bad. The executive eithe adopts the plan o emains with the status quo. If an executive in position adopts a good plan, the goss value of the plan afte T peiods is assumed to be dawn fom a distibution with density function and h, expected value and standad eo σ. Let epesent the density function and expected value, espectively, of a bad plan and let h o h and epesent the density function and expected value of the status quo plan. The o coesponding standad eos ae, likewise, σ and σ. We assume the values fo all plans ae bounded on the left by zeo and that < <, so that a good plan has an expected value above the status quo, while the bad plan s expected o 5

7 value is below the status quo. 9 Let α denote the exogenous and known pobability that the plan to be evaluated by executive is good. If the objective is to maximize the expected value of the plan T peiods fom now, an executive can e in plan selection in one of two ways. The executive can eject a poposed plan in favo of the status quo plan when the poposed plan is actually good and should have been adopted., the executive can adopt a poposed plan ove the status quo when the poposed plan is bad and should have been ejected. Adopting the teminology of Sah and Stiglitz (1988), the ejection of a good plan is a Type I eo and the adoption of a bad plan is a Type II eo. Note that a natual way of chaacteizing moe senio positions is to have these mistakes be moe costly fo executives in these positions. As such, all else equal, we think of moe senio positions as positions with a geate expected loss to the fim fom ejecting a good plan, o, o fom accepting a bad plan, 1.2. xecutives decision vaiables o. In evaluating a plan, we assume that an executive eceives an impefect signal, s, of the plan's undelying value to the fim. Fo an executive in position of ank, if the plan is good the signal is dawn fom a nomal distibution with cumulative density function F (s), mean µ and pecision P. 10 If the plan is bad, the signal is dawn fom nomal distibution F (s) with mean µ and pecision P. We assume that F (s) fist-ode stochastically dominates F (s), such that good plans tend to geneate highe signals on aveage, o µ > µ. The twodimensional action of the executive is intoduced with espect to this signal geneating pocess. 9 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. 10 Fo discussion puposes we talk of signal pecision and not signal vaiance, while it emains tue that pecision is simply the ecipocal of the vaiance of the signal. 6

8 Specifically, an executive who evaluates a poposed plan can affect the pecision of the signal of plan type by investing costly effot into the evaluation of the plan. To captue this we let P = f( e, υ), with f / e > 0 and 2 2 / 0, whee f e e denotes the choice of evaluation effot fo the executive assigned to position of ank and υ is a paamete affecting the pecision of the signal fo a given level of effot. iven this, we amend ou notation to account fo this effot choice; if the plan is good the signal is dawn fom F ( e, s), if the plan is bad the signal is dawn fom F ( e, s). nce a signal on a poposed plan is eceived, the executive must detemine whethe to accept o eject the plan based on the infomation evealed. This decision to accept o eject is captued by the executive s choice of esevation signal, ŝ. If the signal obtained fo the poposed plan is above the chosen esevation signal, ŝ, the executive adopts the plan. If the signal obtained is less than ŝ, the executive ejects the plan in favo of the status quo. 11 Fo a given evaluation effot, e, and esevation signal, ŝ, the executive theefoe ejects a poposed plan that is good with F e, sˆ ). Likewise, the executive adopts a poposed plan that is bad ( with pobability F ( e, sˆ ) 1 but educes the likelihood of Type II eo The pincipal s objective and the fist-best solution. Thus, an incease in ŝ inceases the likelihood of Type I eo The expected futue goss value to the pincipal of the plan-selection decision of an executive in position of ank is given by: (1) * I II ˆ ˆ ˆ [ ( e, s )] = F ( e, s ) k (1 F ( e, s )) k, 11 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). 7

9 whee k II II = α L and k = (1 α ) L denote the expected losses fom Type I and Type II eos I I fo shaeholdes, with L = and I o L =. Accoding to q. (1) the best possible II o * o outcome ( = α + (1 α) ) is educed by losses associated with Type I eos ( L ) and Type II eos ( L ). In the analysis to follow, we assume that the costs of these eos ae II sufficiently lage that it is not optimal fo the pincipal to adopt the simple ule of eithe always ejecting o always accepting poposals. Assuming independence in plan etuns acoss executives, the pincipal s expected futue goss value fom the n plans sepaately evaluated by the n executives can be expessed as: I (2) n ( e,s ˆ) = = [ (, ˆ e s)], 1 whee e { e 1,..., e n } is a vecto of effots and ŝ { ŝ 1,, ŝ n } is a vecto of esevation signals acoss the n executives. The fist-best evaluation effot and esevation signal fo an executive in position, = 1,, n, maximize the shaeholdes expected value of the plan, as defined by q. (2), net of the executive s effot costs. iven a simple quadatic cost function fo the executive s effot, ce 2 ( ) e /2 =, the fist-best e and s ˆ fo the executive in position satisfy the poblem: (3) max e, sˆ ρ e sˆ e 2 [ (, )] / 2. whee the discount facto ρ [0,1] convets the goss futue value to be eceived in T peiods into cuent values. The fist-best esevation signal, * s ˆ, is given by: (4) whee sˆ * ( ) ln Φ µ + µ = + P( e ) ( µ µ ) 2, 8

10 I (5) Φ = k / k II denotes the atio of expected losses fom Type I and Type II eos made by an executive in the position of ank. Note that if symmety exists in the expected gain and loss fom plan I o o II selection, such that k α ( ) = (1 α )( ) k, then the decision citeion is independent of the specific level of evaluation effot. iven the optimal esevation signal, evaluation effot, * e, is: * s ˆ, the fist-ode condition that defines the fist-best (6) * e ρ F e sˆ k F e sˆ k * * * * (, ) I (1 (, )) II = e e. 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 too-fequent Type II eos. 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 9

11 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 stocks 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. 12 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, that is, T peiods. 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: (7) C R δ + ρ( β + β ( )) if 0< = δ + ρ( β) if < R. In q. (7), 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 acquies in T peiods though stock holdings and stock options, espectively. We adopt a common discount facto of ρ < 1. q. (7) illustates that fo stock options, unlike esticted stock, the executive ealizes inceased wealth only if the fim s futue value exceeds the execise value, R β. While we cast the option as having an execise value, this value is analogous to the execise pice on the 12 Fo a discussion of the diffeences in vesting schedules between stock gants and option gants, see Kole (1997) and Muphy (1999). 10

12 option gant and is set befoe the executive chooses evaluation effot and the citeion fo adopting o ejecting the poposed plan. efoe defining the agent s optimization poblem, it is helpful to chaacteize the expected compensation that is implied by (7). To do so, we fist divide the value of the fim into two components, the value aising fom the decisions of the executive in position,, and the value aising fom the decisions of the othe n-1 executives employed at the fim in positions, Let g ( ) denote the density functions fo the value of the sum of the othe n-1 executives plans. Assume the ealized value fo the decision made by each executive has common lowe. and uppe bounds of zeo and, espectively. Then, fom (1) and (2), the expected futue value of the fim is given by: (8) ( n 1) o I II α α 0 0 0, [ ] = yg ( y) dy + xh ( x) dx + (1 ) xh ( x) dx F k (1 F ) k whee the expected losses to fim value fom ejecting a good poposal o accepting a bad poposal ae, espectively: (9) I o = α 0 k x( h ( x) h ( x)) dx and (10) II o = α 0 k (1 ) x( h ( x) h ( x)) dx. 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. 11

13 In contast, the option holde is inteested in the expected value of the fim as it elates to an exogenous execise value,. 13 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, (11) [ ] = [ ]P( ). To make the compaison between equity and options moe tanspaent, we expess the losses fom Type I and Type II eos fo an option holde as factions of the losses fom such eos fo one who holds stock gants, defined ealie as I L and II L, espectively. In paticula, let the loss I I fom a Type I eo fo an option holde be denoted by φ L and the loss fom a Type II eo fo II an option holde be denoted by φ L II. 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 0 lim ( ) = ( ) ffot and plan selection of isk-neutal agents 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 (7). That is, the executive s poblem is: (12) R max δ + ρ( β [ ] + β [ ]) c( e) e, sˆ, whee (8) and (11) define ( ) and ( ), espectively. The fist-ode conditions fo the executive s esevation signal and effot ae: 13 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). 12

14 (13) sˆ ** ( ) ln Φ µ + µ = + P e * ( ) ( µ µ ) 2 and (14) ** e F e sˆ k F e sˆ k ** ** ** ** (, ) R I I (, ) R II II = ρ ( β + φβ ) + ρ ( β + φ β ) e e, whee the atio of expected losses fom Type I and Type II eos fo the executive is given by: (15) ( 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 options vesus stock and the atio of losses fom Type II eo fo options vesus stock, 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. Fom the executive s maximization poblem, assuming the existence of unique solutions, we have the following implicit solutions fo the optimal evaluation effot and signal choices of the executive assigned to position : (16) e = g ( β, β,, k, k, φ, φ, ρ) ** R I II I II and (17) ** R I II I II sˆ j( β, β,, k, k, φ, φ, ρ) =. 2.2 The case of a single isk-neutal agent The complexity of the expessions undelying the expected value of compensation in the fom of options makes it difficult to clealy see the positive and negative oles that options can 13

15 play in compensation. To highlight these two distinct oles, we simplify by consideing a single agent. Setting n = 1 and omitting the subscipt indicating an executive in position, we can ewite the expected value of equity shaes as: o I II (18) ( ) = α + (1 α ) F k (1 F ) k. Recall that k I I II II = α L, k = (1 α) L, I o L = and II o L =. When n = 1, the expected value of options is: (19), o [ ] = α ( x ) h ( x) dx + (1 α ) ( x ) h ( x) dx F φ k (1 F ) φ k I I II II whee the expected losses fom Type I and Type II eos fo a holde of options ae: I I o (20) φ k = α ( x )( h ( x) h ( x)) dx and II II o (21) φ k = (1 α ) ( x )( h ( x) h ( x)) dx. Combining (18) though (21), the agent s expected compensation is given by: (22) R o [ C] = δ + ρβ ( α + (1 α) ) o + ρβ ( α ( x ) h ( x) dx+ (1 α) ( x ) h ( x) dx) ( ) R I II I I II II ρβ ( Fk + (1 F) k ) ρβ Fφ k + (1 F) φ k. 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 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: 14

16 (23) max ρ[ ] [ C] R δ, β, β,, e, sˆ, subject to the agent s optimal choices of esevation signal and effot (the incentive compatibility 2 constaints (13) and (14)), the agent s ationality constaint ( C ( ) e /2= u), and nonnegativity 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 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 15

17 options induces the agent to choose an effot level close to fist-best as the maginal etun to effot is highe. 14 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 coincident with inceasing the execise value fom zeo. 2.4 ptions distot intentions u twofold chaacteization of the executive s poblem eveals that the benefit fom substituting esticted stock fo options, namely the encouagement of effot though leveaging, is tempeed by a negative effect on the chosen esevation signal. This negative effect aises due to the fact that 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 zeo-value 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 14 While ou focus is on the incentive stuctue of top-executive compensation, the model need not be limited to consideing the highest levels of oganization. Fo instance, one might expect boad-based stock options that ae awaded to lowe-level employees to simply act to extact additional effot. As lowe-level employees may only contibute effot, with decisions being made by supevisos, the downside to options would be discounted in contacting with such employees. Fo a discussion of poductivity changes elated to the ganting of boad-based stock options see Stock options, copoate pefomance, and oganizational change, The National Cente fo mployee wneship,

18 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. In othe wods, with options the expected cost of a Type II eo falls elative 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 (appoving a bad plan). 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 (4), (5), (13), and (15), 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 + φ β (24) = 1 R II β + φ β. Fo a positive I, φ II > φ and q. (24) does not hold; fo an option ecipient (i.e. fo β > 0 ), a Type II eo is now elatively less impotant than it is fo the pincipal o stock ecipient. 15 means that Compaing (4) and (13), this asymmety in losses acoss types of compensation sˆ < sˆ. ** * 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 15 Supplement A povides the specific assumptions that suppot this statement. 17

19 obtained fom simulations of the model assuming the pincipal optimally chooses the mix of stock options and stock at each execise value. 16 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 illustated in Panel D. Howeve, as Panel 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. The evidence on optimal 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. 16 Supplement identifies the undelying paamete values used to obtain the simulated esults pesented in Figue 1. The esults discussed ae obust to paamete changes. 18

20 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 55,763 executiveyea obsevations, eflecting the compensation of the top 5 executives at, on aveage, 1,478 fims each yea fo this 9-yea peiod. 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. 17 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 sampleselection bias diven by ove-epoting. aon 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 aon and Waddell as 4,175 obsevations that have missing infomation egading the value of options ae dopped. 19

21 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. 18 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. ut, 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. olton 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 could 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 18 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 isk-avesion, it is shown that thee is a faily wide ange of execise picing policies that yield close-to-optimal pay-to-pefomance 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. 20

22 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. 19 Muphy and Hall (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 following 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 The optimal compensation package with a binding constaint on the execise value fim, In ou simulation of a fim with a single executive, we define the cuent maket value of the C, 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: (25) C * * * = 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 (25). Thus, ou benchmak simulation can be intepeted as one fo which it is optimal fo the pincipal to follow the simple 19 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. 21

23 ule of thumb of setting the execise value equal to the gant-date maket value of the fim. 20 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. 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, 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 diffeence is lage. Holding o constant, it is clea that these changes incease to the same degee the undelying costs to the stock holde of a Type I eo ( ( o o ) 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. 20 Supplement povides details egading the benchmak paametes. 22

24 If, howeve, we conside the case whee the pincipal is constained to set the execise value at 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 less-favoable 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. 21 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 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 of the status quo outcome, o 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 21 That is, we assume P / υ < 0 and P 2 / e υ > 0. In ou simulations, we adopt the following specific fom fo the signal pecision function: = 1/( + ( /(1 + ) )). Natually, given this fom, ou discussion in the text P γ υ λ e egading the effect of a decease in υ also holds fo an incease in the paamete λ. 23

25 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 equitybased 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 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 aon and Waddell (2003), namely the log of the atio of the executive s total compensation to 24

26 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 the extent executive decisions involve new poduct development. Adopting the view that eseach-intensive 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 expenditue ae moe likely to have a given dolla of equity-based compensation awaded in the fom stock options. 25