Employee Sentiment and Stock Option Compensation

Transcription

1 Employee Sentiment and Stock Option Compenation ittai K. Bergman Dirk Jenter MIT Sloan School of Management Thi Draft: February Abtract The ue of equity-baed compenation for employee in the lower rank of an organization i a puzzle for tandard economic theory: undiverified employee hould dicount company equity heavily, and any poitive incentive effect hould be diminihed by free rider problem. We develop a model of optimal compenation policy for a firm faced with employee with poitive or negative entiment. We etablih the condition neceary for the firm to compenate it employee with equity in equilibrium, while explicitly taking into account that current and potential employee are able to purchae equity in the firm through the tock market. We how that equity compenation i ued in equilibrium only when employee are willing to overpay for it. Thi occur if employee prefer the non-traded equity compenation intrument offered by the firm to the traded equity offered by the market, or if the traded equity i overvalued. We then provide empirical evidence confirming that firm ue broad-baed option compenation when boundedly rational employee are likely to be exceively optimitic about company tock, and when employee are likely to have a trict preference for option over tock. We alo provide evidence that manager grant more option to rank-and-file employee when management believe it tock to be overvalued, again conitent with our model. MIT Sloan, E5-40, Cambridge, MA nbergman@mit.edu MIT Sloan, E5-446, Cambridge, MA djenter@mit.edu 3 We are grateful for comment from eminar participant at the AFA Meeting in San Diego, the Harvard Law, Economic, and Organization Seminar, the Frank Batten Young Scholar Conference, the Financial Management Aociation Meeting in ew Orlean, the BER Behavioral Finance Program Meeting, MIT Sloan, the Univerity of Minneota, HEC Pari, ISEAD, and epecially from Andrei Shleifer, Jeremy Stein, Malcolm Baker, Rajeh Aggarwal, Gordon Alexander, Lucian Bebchuk, Luca Benzoni, John Boyd, Marku Brunnermeier, Henrik Cronqvit, Loui Kaplow, Rakeh Khurana, Ro Levine, Paul Oyer, Valery Polkovnichenko, Paul Povel, Michael Robert, Scott Schaefer, Paul Sengmueller, Aamer Sheikh, Rajdeep Singh, Eric Van den Steen, Wanda Wallace, Martin Weber, Andrew Winton, and Peter Wyocki. We thank John Core and Wayne Guay for making their employee option data available to u. All remaining error are our own.

2 . Introduction The ue of equity-baed compenation for employee below the executive rank ha been growing rapidly during the lat decade, with broad tock option plan a the mot common method. The ational Center for Employee Ownerhip (00) etimate that between 7 and 0 million US employee held option in 000. The popularity of equity-baed compenation for employee in the lower rank of an organization i a puzzle for tandard economic theory: any poitive incentive effect hould be diminihed by free rider problem and overhadowed by the cot of impoing rik on employee. 4 Holding tock option in their employer expoe employee to price rik which i highly correlated with the rik in their human capital. 5 Hence employee hould be an inefficient ource of capital, at leat compared to well-diverified outide invetor. Several tudie how, however, that employee do not value company tock and option a precribed by extant theory. For example, employee purchae company tock (at market price) for their 40(k) and ESOP plan on a large cale, and epecially o after company tock ha performed well. 6 In any portfolio election framework, thi obervation trongly ugget that employee valuation of company tock i higher than the prevailing market price. With regard to tock option, urvey evidence ugget that many employee have unrealitic expectation about future tock price and frequently value their option ubtantially above Black-Schole value. 7 Motivated by thee obervation, we analyze the role of employee optimim in option compenation for rank and file employee. 8 We develop a model of optimal compenation policy for a firm faced with employee that exhibit either poitive or negative entiment toward it, and ae whether employee optimim lead to equitybaed compenation. The omewhat urpriing anwer i that employee optimim by itelf i inufficient to make equity compenation optimal for the firm. The crucial inight i that firm compete with financial market a upplier of equity to employee; the ability of employee to purchae equity on their own retrict firm capacity to profit off employee optimim, and hence retrict or even eliminate firm incentive to compenate with equity. Indeed, employee optimim about traded firm equity i ufficient to make firm indifferent between paying their employee in equity or cah, but it i inufficient, by itelf, to 4 See Core and Guay (00) and Oyer and Schaefer (004), a well a Lazear (999). 5 In the remainder of the paper we ue the term employee a equivalent to non-executive employee. 6 See Benartzi (00), Liang and Weibenner (00), and Huberman and Sengmüller (004). 7 See Lambert and Larcker (00). 8 The behavioral finance literature provide further evidence uggeting that employee are more likely to be optimitic about their firm than other invetor in the equity market: Employee may root for the home team and

3 force firm away from cah wage. Firm could imply pay employee a cah amount equal to the market value of the deired equity, and leave the deciion whether to purchae equity up to the employee. For equity compenation to become optimal in the model, employee mut overpay for the compenation intrument offered. The model allow for two channel through which firm can extract uch rent from overoptimitic employee. The firt channel i operative if employee, for behavioral or rational reaon, value a non-traded compenation intrument more highly than poition in traded equity of imilar fundamental value. In thi cae, a the monopoly upplier of the compenation intrument, firm are able to profitably extract thi valuation premium from their employee. We how that the feaibility and magnitude of the rent extraction i determined by employee willingne to pay for the non-traded compenation intrument (rather than by employee optimitic valuation of the intrument). Thi willingne to pay i, in turn, determined by what employee can purchae in the equity market on their own. If employee recognize that the tock market offer an equivalent bet on the firm, then they refue to pay more than the market value for the equity offered by their firm. Recognizing that the market offer equivalent or uperior bet on the firm i much harder for employee when firm offer option a compenation intrument a compared to when they offer tock. The reaon i that rational option valuation on the bai of oberved tock price and volatilitie i difficult and likely beyond the capabilitie of almot all employee. Intead, they are likely to rely on heuritic and to value option on the bai of their own or their peer pat experience with option payoff. When looking for poible alternative method for inveting in their employer, employee are likely to imply compare the option offered by the firm to traded hare, which are the mot alient alternative offered by the market, and then ue their valuation heuritic to decide which of the two aet they prefer. 9 Evidence conitent with thi hypothei i provided by Lambert and Larcker (00) who conduct a mall urvey and report that many employee value their option ubtantially above Black- Schole value. Thee exceive option valuation are likely caued by naive extrapolation from the high payoff many employee experienced during the late feel loyalty toward their employer (Baker, Jenen, and Murphy (988), Cohen (004)), and employee familiarity with their employer may increae their valuation for employer equity (Huberman (00)). 9 Exchange-traded hort-term option are available for a ubet of firm, but mot employee are unlikely to be aware of thi. 0 Beide bounded rationality, there may be other reaon for employee to trictly prefer the option offered by the firm to traded hare. Employee may prefer a levered, option-like poition in their employer and may face borrowing contraint. Alternatively, tranaction cot of trading in the tock market may make the proviion of option by the firm more efficient than purchae of equity by employee in the market. Tranaction cot can give an advantage to firm paying with equity, even though thi advantage i arguably too mall to explain the maive increae in alary required in non-entiment firm to retain their employee (Snider, 000). 3

4 The econd reaon for paying optimitic employee with equity, in either traded or non-traded form, come into effect when the equity i overvalued by the market. If equity i overvalued, and optimitic employee private valuation are even higher, then firm are able to profit by effectively elling overvalued equity to their employee. In fact, firm are on the margin indifferent between paying their employee with equity, and iuing equity directly into the market. Due to the overvaluation, thi i profitable even if the price the firm i able to charge i no higher than the market price. ext, the model allow u to analyze the effect of entiment-induced equity compenation on firm profitability and labor market outcome. Perhap omewhat urpriingly, poitive employee entiment i not alway beneficial to the firm ubject to it. Becaue employee human capital covarie poitively with tock return, optimitic employee may decide to work at a different firm while till inveting in the one they are optimitic about, thereby avoiding the poitive correlation between labor income and financial wealth. If firm-pecific human capital rik i a eriou problem, and if the equity market i highly efficient, thi mechanim can make firm without poitive entiment the beneficiarie of poitive entiment toward other firm, both in term of profitability and in term of firm ize. On the other hand, the model how that firm ubject to poitive entiment are the net beneficiarie of equity compenation if there i a ignificant preference for the non-traded compenation intrument over traded tock combined with moderate level of firm-pecific human capital rik, or when equity market are inefficient. The tock option boom of the late 990 can thu be interpreted a a ituation in which firm ubject to both poitive employee entiment and overvalued equity benefited through lower compenation cot, a larger number of employee, and higher profit. Having etablihed a theoretical foundation for the ue of equity compenation, we empirically tet whether the obervable cro-ectional and time-erie pattern of broad-baed option grant are conitent with the hypothei that option compenation i driven by employee entiment. Our model predict that option compenation i ued when employee are optimitic about option, and when employee trictly prefer (non-traded) option to the equity intrument available in the market. Prior literature ugget that employee entiment improve with prior tock price performance. In addition, we If firm face downward-loping demand curve for their hare in the market, and employee are ubject to an endowment effect (o that once granted hare they do not ell them, even though they would not have gone out and purchaed any by themelve), then paying optimitic employee with hare may be cheaper than iuing equity into the market (Baker, Coval, and Stein (004)). Alternatively, tranaction cot aociated with eaoned equity iue (Smith 986, Lee, Lochhead, Ritter and Zhao 996, and Altinkiliç and Hanen 000) may make paying optimitic employee with equity cheaper than iuing equity into the market (Core and Guay 00, Fama and French 003). 4

5 expect boundedly rational employee to extrapolate more trongly from pat return when valuing option than when valuing retricted tock becaue of the amplified nature of option payoff. Thu, our model predict that better tock price performance i aociated with greater ue of tock option compenation. We make ue of the pychology literature on expectation formation and exceive extrapolation to develop additional tetable hypothee relating tock return pattern and firm characteritic to employee entiment and tock option compenation. All hypothee are developed in detail in Section 4. Diagram give a firt graphical impreion of the evolution of employee option grant in our ample of,7 publicly traded firm from 99 to 003. The graph provide ome prima facie evidence in upport of the entiment hypothei: in cloe parallel with tock market valuation, per employee option grant tarted to rie rapidly in the mid 990, peaked in 000, and dropped by approximately 60% over the ubequent three year. Uing regreion analyi, we how that the prediction of the employee entiment hypothei are trongly confirmed by both the cro-ectional and the time erie evidence. Option compenation for non-executive employee i mot common among firm with excellent prior tock price performance: the average prior two-year return for companie with granting activity in the bottom quintile i 7% per annum compared to 30% p.a. for firm in the top quintile. Sorting firm by prior year return yield average (median) grant of $,55 ($,838) among firm in the top return quintile compared to only $7,850 ($,6) among firm in the bottom return quintile. Conitent with Griffin and Tverky (99), the effect of pat return on granting activity i non-linear, with granting activity concentrated among the very bet prior performer. Conitent with Benartzi (00), the poitive relationhip between tock return and option grant become tronger when we enlarge the window over which pat return are meaured. Ditreed firm which are about to delit for performance reaon ue fewer option, uggeting that bad entiment prevent thee firm from uing option compenation to conerve on cah. Finally, firm which grant more option have fater employment growth than firm which ue fewer or no option, conitent with the prediction of our model. Finally, we tet the model prediction that firm are more likely to pay with option when manager view their own tock a overvalued. We identify ituation in which manager are likely to view their firm tock price a too high by looking at firm in which manager have manipulated earning and at firm in which manager ell large amount of company equity. We meaure earning manipulation uing everal verion of the modified Jone model and find that firm likely to have manipulated earning upward grant between 3 and 3% more option than firm with no manipulation. The inider trading 5

6 reult indicate that firm in which the top five manager cah out grant to 9% more option to their employee than comparable firm, while firm in which top manager purchae equity for their own account grant 7 to 9% le. The lat reult, however, i not robut to the incluion of firm fixed effect, leaving u with mixed evidence for the overvaluation reaon behind option compenation. Finally, our empirical reult provide evidence againt the hypothei that firm with cah contraint ue option compenation in order to minimize cah payout. 3 Core and Guay (00) argue that equity compenation i efficient if firm need to raie cah and if the information aymmetrie between firm and their employee are maller than thoe between firm and outide invetor. We therefore control for everal meaure of cah contraint in our empirical analyi. We find that option grant are trongly poitively aociated with corporate cah balance and contemporaneou cah flow, and negatively related to cah outflow for debt ervice (interet burden, leverage). Thee finding cat doubt on the hypothee that option grant are motivated by aymmetric information and cah contraint. Intead, the reult are again upportive of the idea that employee entiment determine the ability of firm to compenate their employee with equity: employee are likely to diplay more poitive entiment toward firm with higher cah balance, higher level of invetment, and better invetment opportunitie, and wore entiment toward firm with higher level of debt and higher interet payment. Thi interpretation alo help to explain Fama and French (005) obervation that many fat-growing and highly profitable firm iue equity to employee every year, in apparent contradiction to the Myer- Majluf (984) pecking order theory. We propoe that equity baed compenation i not driven by firm intention to raie fund, but intead by exuberant employee who want to be paid with option. Thi explanation i alo conitent with Kahle (00) finding that many firm repurchae (rather than iue) hare to fund option exercie by employee. 4 Beyond our own empirical reult, our model can explain the urvey evidence of Ittner, Lambert, and Larcker (003) that firm need to compenate with option in order to attract and retain employee. Anecdotal evidence from the dot-com era upport the model prediction that an improvement in employee entiment toward a firm can lead to a reduction in employment and an increae in compenation in it competitor: Snider (000) report that top law firm were forced to maively increae the alarie for aociate to prevent them from leaving to internet tart-up offering equity-baed compenation. In We define non-executive employee a all employee except the five mot highly paid executive identified in the proxy tatement. Thi definition i ued by everal tudie (Core and Guay, 00; Deai 00) and i impoed by the available data. 3 See, for example, Yermack (995), Dechow et al. (996), and Core and Guay (00). 6

7 addition, our model i conitent with the empirical dominance of option over retricted tock a employee are more likely to overpay for option given that a cloe ubtitute to retricted tock i traded in the market. 5 Our paper i not the firt to conider employee entiment a a factor in option compenation. The paper cloet to our model i by Oyer and Schaefer (004), who perform a calibration exercie to ae the effect of optimim about future return on employee relative valuation of tock and option. In addition to the novel empirical evidence preented here, the main difference in our approach i that their analyi doe not conider employee ability to purchae equity in the market. Our model how that financial market put a crucial contraint on firm ability to extract rent from employee, and that employee relative valuation for tock and option are of only econdary importance. Our analyi differ further from Oyer and Schaefer in that we explicitly model the effect of employee entiment on labor market equilibria, taking into account firm-pecific human capital rik and allowing for equity to be mipriced by the market. Another related paper i that by Liang and Weibenner (00), in which option are viewed a a reward for pat performance, leading to a poitive relationhip between firm tock price and option grant. Liang and Weibenner alo dicu the poibility that employee demand for option may be a function of pat performance. In the next ection we preent a imple model of optimal employee compenation when employee diplay entiment toward firm. We defer a detailed review of the prior literature on employee option plan and on employee pychological biae until ection 3. Section 4 tranlate the model and the prior literature on the formation of employee entiment into tetable prediction. Section 5 decribe the data and variable definition, and Section 6 preent the empirical reult. The final ection ummarize and conclude.. A Simple Model of Optimal Compenation We develop a imple one-period model in which two firm compete in the labor market and compenate their employee uing cah and equity intrument. The two firm, indexed by and, have identical production function uing labor and l a ole input to produce output G and G, with G i = f(l i ), and l 4 There are many example of firm which broadly grant option and repurchae hare in the ame year, even though the repurchae occur when option are exercied, often everal year after their granting. 7

8 f(0) = 0, f >0, f (0) =, and f < 0. The two firm hire employee in a competitive labor market by each offering a compenation contract coniting of Wi M i unit of a non-traded equity compenation intrument. in cah wage, i unit of traded company equity, and The ole, but crucial, difference between the two equity intrument offered by firm i that one i traded in the equity market and can be purchaed by employee, while the other i not traded and offered by the firm only. We call the former imply traded equity and the latter the non-traded equity compenation intrument. The aumption that each firm compete with the market in offering traded equity, while being, in eence, a monopoly upplier of it own compenation intrument, will drive much of the model reult. To emphaize the fundamental equivalence of the two form of equity in our model, aide from their differing tradability, we aume that for each firm, the payoff of a unit of the traded and of the non-traded equity i identical and given by the random variable X ~ (i {,}), with mean i normalized to and variance σ. Thu, our reult are not driven by different payoff tructure of the two intrument. We aume for implicity that the equity payoff of the two firm are independent of each other, and that the number of equity intrument to be iued i mall relative to the number of equity intrument outtanding o that the expected payoff to an intrument doe not change when more intrument are iued. 6 The equity market i rik neutral with a rikle interet rate of zero, which implie that the fair market value of a unit of traded or non-traded equity of either firm i equal to. There i a homogeneou ma of potential employee which we normalize to. Employee are rikavere with mean-variance preference and have a reervation wage of zero. We aume that potential employee diplay entiment with regard to the expected payoff to the equity intrument of firm. Parameterizing employee entiment by, employee believe the payoff of a unit of traded equity to ~ ~ be X +, and the payoff of a unit of the non-traded compenation intrument to be X + z( ), with z () > 0. Thu, we aume that employee do not recognize the fundamental equivalence in payoff between the non-traded compenation intrument and traded equity, and allow employee to exhibit differing entiment toward each. Whether employee prefer the non-traded compenation intrument to traded equity, and the determinant of any preference for one over the other, are ultimately empirical quetion, and we conider 5 The greater popularity of option compared to tock i uually attributed to their favorable accounting treatment (Murphy (00)). 8

9 both poibilitie (i.e. z and < z) in the analyi below. We motivate the aumption that employee do not recognize the equivalence between traded equity and the non-traded compenation intrument by the obervation that mot employee are completely unfamiliar with aet pricing technique. Deriving the value of a non-traded compenation intrument from the oberved price and volatilitie of traded equity i potentially difficult and beyond the abilitie of employee. They may therefore diregard the cloe ubtitutability of the traded and non-traded equity, and value the non-traded compenation intrument uing imple heuritic baed on, ay, experienced pat payoff. Thi may lead employee to prefer, for example, non-traded employee option to traded hare after a period with high tock (and even higher option) return. In contrat to firm, potential employee do not diplay entiment toward firm. We think of firm a operating in a new economy indutry ubject to entiment and fad, and of firm a operating in an old economy indutry for which entiment play no role. Modeling two firm with non-zero entiment doe not change the reult, but greatly complicate the expoition. Similarly, the modeling aumption that the traded and non-traded equity intrument are identical and linear claim i a convenient implification; auming intead that the non-traded compenation intrument i, for example, an optionlike claim and replacing the traded equity by employee preferred trading trategy would deliver imilar reult. In thi context, the difference in entiment between traded equity and the non-traded compenation intrument would meaure whether employee prefer the compenation intrument to the bet aet or trading trategy the employee are able to identify in the market. 7 The model take into account that employee bear rik aociated with firm-pecific human capital correlated with the equity value of their employer. We model thi rik in a reduced form manner, auming that when working for firm i, employee obtain implicit random compenationy ~ i, with mean 0, ~ ~ varianceσ Yi, and Cov( Y i, X i ) φ i 0. To implify notation, the level of firm-pecific human capital rik i the ame in both firm, o that σ Y = σ Y = σ Y and φ = φ = φ. Finally, we allow for the market price of a unit of traded equity of firm to deviate from fundamental value becaue of noie trader entiment and limited arbitrage. For implicity, employee entiment and noie trader entiment are identical, although allowing thee to differ doe not materially change the reult. Formally, a unit of traded firm equity can be purchaed in the market for p(), where p(0) =, and 0 p (). In thi 6 Thi aumption of infiniteimal dilution i imilar in pirit to the infiniteimal new loan aumption in Stein (998). 7 Borrowing contraint and tranaction cot may be reaon different from bounded rationality for why employee are unable to ue traded equity to create claim that they prefer to the compenation intrument offered by the firm. 9

10 formulation, p () i a meaure of the effectivene of arbitrage. With p () = 0 for all, there are no limit to arbitrage and capital market are perfectly efficient. When p () =, arbitrage ha no effect and price move one for one with entiment. 8 A there i no entiment toward firm equity, it market price equal it fundamental value of. Potential employee evaluate compenation contract offered by each firm (W i, i, M i ) uing their ubjective belief about firm value, taking into account their ability to purchae traded equity on their own. For empirical realim, we aume that employee cannot ell the equity they receive a compenation, though our reult are unchanged without thi aumption. We begin olving the model by calculating the equity purchae of employee with a given compenation package. Since employee are rik avere and ince they value firm equity correctly, it i eay to ee that employee never purchae firm equity on their own. In contrat, traded firm equity may appear cheap to optimitic employee of either of the two firm. The optimal purchae of firm equity by an employee of firm with compenation package (W,, M ) i the maximizing the following expected, ubjective utility: ˆ [ ] [ ] [ ] ] ) ˆ ( ) ˆ [( )) ( ( ˆ ) ( ) ( ) ˆ ( ˆ ) ( ~ ~ ~ ) ˆ ( ~ ~ ~ ) ˆ ( ˆ ),, ; ˆ ( ˆ φ σ σ M Y M z M p W p Y X M X Var W Y X M X E W W E U = = () Solving the maximization problem of firm employee, and the correponding problem of firm employee, yield the following reult: Lemma The olution of the portfolio choice problem i given by: (a) for firm employee: } ) ( {0, ˆ M p Max + = σ φ (3) (b) for firm employee: } ) ( {0, ˆ σ p Max + = (4) 8 Thi price tructure i the outcome of tandard model of financial market with noie trader and limited arbitrage (ee, for example, Shleifer (000)). 0

11 Lemma tate that upon receiving (W,, M ) from firm, employee of firm purchae traded + p( ) φ equity in their employer until they reach their optimal portfolio of unit of equity, taking σ into account the traded equity and non-traded compenation intrument received from the firm. If an employee ha received more than her deired allocation of firm equity a compenation, he would prefer to ell unit of the traded equity intrument, but i by aumption precluded from doing o. An increae in entiment increae the demand for equity in firm by both et of employee, depite the fact that an increae in entiment alo tend to increae the price of traded firm equity. Thi i becaue arbitrageur caue the increae in price to be maller than the increae in entiment (p () ). Alo, a would be expected, purchae by firm employee are decreaing in firm-pecific human capital rik, φ. Since employee of firm do not bear firm firm-pecific human capital rik, their purchae of firm equity are independent of φ. Firm maximize hareholder value by hiring the optimal number of worker and minimizing compenation cot. In doing o, firm take into account the fact that employee may purchae equity on their own, and that employee will work for the competing firm if it contract i more attractive: Max E l, W, i i i ~ ~ [ f ( l ) l ( W + X + M X )] = f ( l ) l ( W + + M ) i i i i i i i i i i i i. t. [ ˆ i ( W,,, M ;, z( ), φ, p( )) ] Eˆ U [ ˆ i ] ˆ[ ˆ j ( W,,, M ;, z( ), φ, p( )) E U ( W,,, M ;, z( ), φ, p( )) ] for i j. Eˆ U i i i i i i 0 j j j (5) The firm valuation of the compenation contract differ from employee valuation becaue firm are rik neutral while employee are rik avere, and becaue employee (may) feel entiment toward equity compenation. The difference in rik averion by itelf would make equity-baed compenation inefficient ince rik i tranferred to the party le able to bear it. However, a will be hown, thi concluion may be revered by ufficiently poitive employee entiment. The equilibrium in thi model, decribed in the following theorem, i given by a pair of * * * * * * compenation contract ( W,, ) and ( W,, ) offered by the two firm and by the reulting * * allocation of labor ( l, l ). M M

12 Theorem The equilibrium compenation contract and labor allocation are uch that: (a) The perceived expected utility from working for each firm i equalized: [ ] [ ], )) (, ), (, ;, ˆ,, ( ˆ )) (, ), (, ;, ˆ,, ( ˆ * * * * * * p z M W E U p z M W U E φ φ = where and are the optimal portfolio purchae of traded firm equity by firm and firm employee repectively given in equation (3) and (4). ˆ ˆ (b) The allocation of labor between the two firm i uch that marginal product of labor equal actual compenation cot, and the labor market clear. ( ) ( ) ) ( ' ) ( ' ) ( * * * * * * * * = + = + + = l l iii W l f ii M W l f i (c) The optimal compenation contract offered by firm involve only cah:. 0 * * = = M (d) The optimal compenation contract offered by firm i decribed by: φ φ φ σ φ φ σ φ φ σ φ = = > > = = > > = = = > = ) ( 0 0 ) ( ) ( ) ( ) ( 0 ) ( 0 ) '( ) ( 0 ) ( 0 ) '( ) ( 0 ] [0, ) ( * * * * * * * * z and if and M iv z and z if z and M iii p and z and if and M ii p and z and if and M i Proof See Appendix A. The equilibrium compenation package offered by both firm are perceived to be of equal value by potential employee, which i the only way both firm can imultaneouly attract employee (part a). 9 Alo, a i tandard, firm hire employee up to the point where their marginal product equal the cot of

13 their employment (part b). Becaue employee are rik avere and do not exhibit entiment toward firm, firm never offer equity in it compenation package (part c). In contrat, firm offer either traded or non-traded equity whenever the employee willingne-to-pay for equity exceed it fundamental value (part d). When doing o, the firm offer the equity claim toward which employee exhibit higher poitive entiment. The number of unit of the equity claim provided equal the number of unit the employee would purchae herelf if offered to her at a price of per unit. Thi i becaue the firm i effectively iuing equity to employee at a cot equal to the fundamental value of per unit. Undertanding employee willingne-to-pay for the offered equity i the key to undertanding equity compenation. Part (d) of Theorem how that employee optimim i, by itelf, inufficient to make equity compenation profitable and to force firm away from cah wage. The eential inight i that the firm i directly competing with the tock market a upplier of traded equity to employee. A a reult, employee willingne-to-pay for traded equity i capped by the market price of equity, independently of their degree of optimim. The implication can be mot eaily een in the cae in which market are efficient and optimitic employee prefer traded equity to the compenation intrument (cae (d.i)), o that, following Theorem, the firm i conidering whether to pay it employee with traded equity or cah. In equilibrium, ince employee can purchae traded equity on their own, they never give up more than the market price p for each unit with which they are compenated. With perfectly efficient market, the cot to the firm of providing a unit of traded equity it fundamental value exactly equal the price which employee are willing to pay. Firm i therefore indifferent between paying with cah and paying with traded equity of the ame market value. 0 Thi reult ha been largely overlooked by the prior literature, which ha focued on employee valuation of equity claim rather than their willingne to pay for equity. When market are not perfectly efficient, in the ene that entiment doe affect equity price (cae (d.ii)), then firm i no longer indifferent to the amount of traded equity it iue to it employee. Becaue optimitic employee willingne to pay for traded equity goe a high a the (overvalued) market price, compenating employee with traded equity become profitable for the firm, a it i, in 9 Equilibria in which one firm attract all the potential employee and the other firm hut down are ruled out by the aumption that f ' (0) =. 0 To be more precie, firm i indifferent between paying with cah and paying with tock of the ame market φ value up to hare, at which point the employee marginal willingne to pay exactly equal the fundamental σ value of per hare. 3

14 effect, equivalent to iuing overvalued equity to the market. Viewing cae (d.i) and (d.ii) of Theorem together, we ee that compenating employee with the traded equity intrument cannot be motivated by employee entiment alone. A neceary additional ingredient for compenation with traded equity to be profitable i an overvalued equity price. In contrat, compenating employee with the non-traded equity intrument can be explained by employee entiment alone. The crucial difference i that employee willingne to pay for non-traded equity may exceed it fair market value. Becaue firm i a monopoly upplier of it non-traded compenation intrument, it i able to extract any entiment premium for the compenation intrument over the traded equity (given by z() ). The availability of traded equity continue to place a cap on the amount of rent the firm can extract: the maximum amount optimitic employee are willing to pay for the compenation intrument i the market price of a unit of traded equity plu the employee exce valuation of the compenation intrument over traded equity. For example, if the market price of traded firm equity i $5 per hare, and optimitic employee value the traded equity at $0 and the compenation intrument at $, then employee are willing to forgo at mot $6 (= $5 + ($ $0)) in cah wage for a unit of the compenation intrument (and only $5 in wage for a unit of traded equity). The entiment premium for the compenation intrument over traded equity (z() ) i equal to $ and i uccefully extracted by firm. A can be een from cae (d.iii) of Theorem, thi occur whenever entiment toward the non-traded compenation intrument i ufficiently high to overcome the cot of being expoed to both equity and firm pecific human capital rik (z() >φ ), and when entiment toward the compenation intrument i greater than toward traded equity (z() > ). Theorem identifie two channel through which entiment-induced equity compenation affect the profit and relative ize of the two firm. Firt, entiment directly affect employee valuation of the two equity claim, and econd, entiment may affect tock price. The following theorem demontrate formally how entiment affect the profit level of the two firm in equilibrium. It i traightforward to how that employment level (firm ize) and profit are trictly increaing function of each other in our model, and hence identical reult apply to employment level a well. See footnote 6 for reaon why firm may prefer either equity compenation or direct equity iuance in thi ituation. Recall that even though option are not traded, their fair market value can be deduced from the price of the fundamentally equivalent traded hare. 4

15 Theorem hence z() > 0. We have that: Aume that entiment for traded and non-traded equity of firm i poitive: > 0 and (a) If max(, z) > φ, o that firm pay with equity, firm make greater profit and hire more employee than firm if and only if: max(z, 0) + (p() ) > φ. (6) (b) If max(, z) φ, o that firm pay in cah, firm make maller profit and hire fewer employee than firm. Proof See Appendix A. There are two channel through which firm can profit from poitive entiment. Firt, the firm extract a entiment premium for the non-traded compenation intrument over the traded equity when uch a entiment premium exit, a repreented by the max(z, 0) term in (6). When traded equity i preferred to the compenation intrument ( > z), thi channel hut down becaue employee can buy their preferred equity intrument in the market with no need for the firm. The econd channel work through entiment effect on tock price a repreented by the (p() ) term in (6). Poitive entiment combined with imperfect arbitrage lead to overvalued price, allowing firm to profit by elling overvalued equity to it optimitic employee. When the equity market i perfectly efficient, p i equal to, and thi econd channel cloe. Firm benefit from poitive entiment, and enjoy higher profit and employment than firm, if the combined overvaluation (p() ) and option premium (z() ) exceed the level of firm-pecific human capital rik, φ. Firm pecific human capital enter into the calculation becaue firm mut compenate it employee for the correlation between their human capital and their equity holding in firm. 3 All ele equal, thi place firm at a diadvantage relative to firm ; indeed, a can be een from part (b) of the theorem, when employee are excited about traded firm equity, but not ufficiently excited to 3 Recall that, becaue employee exhibit entiment only toward firm, they hold firm but not firm equity in our model. In general, if employee exhibit poitive entiment toward both firm, the firm with greater poitive entiment i the one toward which, ceteri paribu, employee have more equity expoure, and therefore the one which mut compenate it employee more for their attendant firm pecific human capital rik. 5

16 overcome the firm pecific human capital rik (max(, z) φ ), then firm ha lower profit than firm ince employee prefer to work in firm and invet in firm. In ummary, the model ha identified two reaon why firm pay optimitic employee with a non-traded equity compenation intrument: the extraction of a entiment premium and the iuing of overvalued equity to employee. In both cae, firm pay with the compenation intrument becaue employee are willing to overpay for equity compenation. Beyond the motivation for paying employee with equity, the model illutrate the effect of entiment on profitability and labor market outcome. If firm-pecific human capital rik i a eriou problem when working for firm, and if the equity market i highly efficient, firm can be the beneficiary of poitive entiment toward firm. On the other hand, when the non-traded compenation intrument i preferred to traded equity and the level of firm-pecific human capital rik in firm i moderate, or when market are le efficient, it i firm which benefit from poitive entiment toward it equity through lower compenation cot, a larger number of employee, and higher profit. Firm react by increaing it wage offer, and till loe employee to firm in equilibrium. Thu, which firm benefit from employee entiment in reality depend on the level of firm pecific human capital rik and the level of tock price mivaluation. The prior empirical and experimental evidence (Benartzi (00), Degeorge et al. (004), Klo and Weber (004)) ugget that employee tend to ignore the correlation between human capital and tock return when evaluating invetment. If employee, rightly or wrongly, act a if firm-pecific human capital rik φ i low, then poitive entiment for firm i more likely to benefit firm. Market overvaluation of firm tock caued by poitive entiment and limit to arbitrage advantage firm further. 4 In light of our model, the tock option boom of the 990 technology bubble likely repreent a cae of poitive entiment toward option combined with overvalued tock price, which lead to an expanion of technology firm at the expene of other firm. With the theoretical foundation for the ue of equity compenation to optimitic employee etablihed, we next review the prior empirical and theoretical literature on broad-baed equity compenation. We pay particular attention to the behavioral literature on expectation formation and to the empirical literature on employee behavior toward company tock, in order to derive prediction about where and when employee entiment i likely to induce equity-baed compenation. 4 A natural extenion of our model would allow for employee entiment to affect alo employee perception of the value of their human capital. Poitive entiment toward firm then give employee a direct preference for 6

17 3. Literature Review The quetion a to why ome firm encourage or even mandate holding of company equity by nonexecutive employee ha attracted coniderable attention. Oyer and Schaefer (004) preent an extenive dicuion of the potential benefit of tock option uage in firm. They argue that the incentive effect from option for lower-level employee are likely to be inignificant and outweighed by the cot of expoing employee to rik. 5 They further argue that the veting tructure of option grant help firm retain employee. Lazear (999) and Murphy (00) have hown that other form of deferred compenation that do not expoe employee to tock price rik are a more efficient mean of providing retention incentive. 6 A large number of paper quantify the deadweight lo from elling company equity and option to employee, with a general conenu that employee rational valuation of company tock and option are ignificantly below fair market value. 7 Indert and Müller (004) how that option compenation can be beneficial becaue it lower a firm compenation bill in bad tate of nature in which owner hould have full cah flow right in order to induce efficient trategic deciion. Finally, Oyer and Schaefer (004) argue that option compenation allow firm to creen for optimitic employee. A we dicu in the introduction, Oyer and Schaefer focu on employee valuation rather than their willingne-to-pay for equity compenation, and they do not incorporate firm competition with the tock market a upplier of equity to employee into their analyi. The model in the previou ection demontrate the importance of the contraint thi competition impoe on the firm. Core and Guay (00) are the firt to perform a large-ample analyi of non-executive employee tock option holding, grant, and exercie. They document the widepread ue of tock option grant to non-executive employee in a ample of 756 firm during 994 to 997. They preent evidence that grant are poitively aociated with invetment opportunitie and with the difference between cah flow from invetment and cah flow from operation ( cah flow hortfall ). Anderon, Banker and Ravindran (000) a well a Ittner, Lambert and Larcker (00) document that tock option compenation i ued employment in firm over firm, allowing, once again, firm to lower it compenation cot and increae it ize and profit relative to firm. 5 Krue and Blai (997) and Krue (00) review the evidence on the hypothei that equity ownerhip by employee help to align takeholder interet and find mixed reult at bet. 6 Oyer and Schaefer (004) argue on the bai of Oyer (004) that unveted option erve to index employee' deferred compenation to their outide opportunitie and reduce tranaction cot aociated with the renegotiation of compenation. 7 See, for example, Lambert, Larcker, and Verecchia (99), Murphy (999), Hall and Murphy (00), Meulbroek (00 and 00), Ingeroll (00), Jenter (00), and Kahl, Liu, and Longtaff (003). 7

18 mot extenively in new economy firm. Interetingly, and conitent with the evidence we preent below, Ittner, Lambert and Larcker (00) how that new economy companie with greater cah flow ue employee option more extenively, contradicting the notion that option are ued to alleviate cah contraint. Murphy (00, 003) propoe that firm perceive the cot of option compenation a low and prefer it to cah compenation becaue option bear no accounting charge and incur no outlay of cah. We view thi hypothei a complimentary to the employee entiment hypothei, though we note that it doe not explain the cro-ectional and time erie pattern of option compenation preented in Section 6. Finally, Deai (00) and Graham, Lang, and Shackelford (00) conider the effect of employee tock option on corporate taxe. Thee tudie focu on how option compenation affect corporate taxe and capital tructure deciion, and do not attempt to find the determinant of option uage by firm. 8 There i coniderable evidence that employee thinking about company tock and employee tock option i ubject to behavioral biae. Benartzi (00) provide evidence that employee exceively extrapolate pat performance when deciding about company tock holding in their 40(k) plan. Employee of firm with the wort tock performance over the lat 0 year allocate 0% of their dicretionary contribution to company tock, wherea employee whoe firm experienced the bet tock performance allocate 40%. There i no evidence that allocation to company tock predict future performance. 9 Huberman and Sengmüller (004) analyze 40(k) allocation in a larger ample and find that employee chooe higher inflow allocation and tranfer to company tock baed on pat return over a three-year window, and to a much maller extent baed on volatility and buine performance. Liang and Weibenner (00) how that the average hare of participant dicretionary 40(k) allocation in company tock i almot 0%, and increaing in prior tock price performance. The pychology and behavioral finance literature provide poible explanation for the oberved biae in employee thinking about company equity: exceive extrapolation can be attributed to the repreentativene heuritic decribed by Tverky and Kahneman (974). They how that people expect that a equence of event generated by a random proce will reemble the eential characteritic of that proce even when the equence i hort. In an extenion, Griffin and Tverky (99) document that 8 Graham, Lang, and Shackelford (00) point out that, depite the maive ize of option-related tax deduction, the net effect of option compenation i mot likely a revenue gain for the U.S. Treaury becaue of the income taxe that employee pay at exercie. Therefore, option compenation cannot be explained a a tax-aving trategy. See alo Core and Guay (00). 9 Benartzi (00) alo conduct a urvey with Morningtar.com viitor aking them to rate the performance of their companie tock over the lat five year and the next five year. Depite the fact that individual tock return are largely unpredictable, the repondent pat and future rating where poitively correlated with a ρ of 0.5, conitent with exceive extrapolation. 8

19 people tend to focu on the trength or extremene of the evidence provided, while giving inufficient regard to it weight or predictive power. People tend to ee trend and pattern even in random equence, and expect epecially extreme equence to continue. In the context of company equity, the repreentativene heuritic may lead employee to expect extreme good and extreme bad price performance to continue into the future. Finally, there i ubtantial evidence that employee tend to underetimate, or even ignore, the correlation between their firm-pecific human capital and firm tock return when making invetment deciion. Benartzi (00), Huberman and Sengmüller (004), and Liang and Weibenner (00) document that employee invet ignificant portion of their retirement fund in 40(k) plan voluntarily into company tock. Degeorge et al. (004) how that during the partial privatization of France Telecom employee with high firm-pecific human capital rik inveted more in their employer equity. Conitent with thi, Klo and Weber (004) report evidence from laboratory experiment howing that invetor fail to take background rik into account when making invetment deciion. The empirical evidence, therefore, ugget that firm-pecific human capital rik i unlikely to play an important role in the deign of optimal employee compenation cheme, or in term of the notation of our model, φ i likely to be low Empirical Prediction The model in Section predict that equity-baed compenation i ued when employee are optimitic about the non-traded equity compenation intrument and value it above it fair market value (z() > 0), and when employee trictly prefer the non-traded compenation intrument to the equity available in the market (z() > ). Greater employee exuberance about firm equity hould therefore make equity compenation more likely and lead to a higher percentage of equity compenation in total pay. Empirically, tock option are the mot common form of equity compenation for rank and file employee, and correpond well to the non-traded compenation intrument in our model: for mot firm, employee option are not traded and hence employee are unable to directly oberve market price for them, and their valuation a a function of obervable price and volatilitie i ufficiently difficult to 30 An alternative interpretation uggeted by Huberman (00) i that concern about firm-pecific human capital rik are counterbalanced and outweighed by employee deire to invet into firm they are familiar with. 9

20 exceed the abilitie of almot all employee. 3 Mot employee are likely to imply compare the compenation intrument offered by their employer to traded hare, which are the implet alternative available in the market, and then ue valuation heuritic to decide which of the two aet they prefer. The reult in Benartzi (00) and Huberman and Sengmüller (00) ugget that prior tock return are a major determinant of employee willingne to invet in company tock, with entiment improving with prior tock price performance. We further conjecture that other meaure of high and increaing firm quality, like invetment, cah balance, and R&D, are poitively correlated with employee entiment, while any ign of ditre (high leverage, high interet burden) are aociated with worening entiment. Finally, we make ue of the pychology literature on expectation formation reviewed above to undertand the factor determining exceive extrapolation. Thee conideration lead to a number of tetable hypothee. Learning and extrapolating from pat option payoff i an obviou heuritic for employee with no knowledge of rational option valuation. Due to the amplified nature of option payoff, we conjecture that employee extrapolate more trongly from pat performance when valuing option than when valuing tock or any other imple traded equity poition which they recognize. After period with high tock return, employee are likely to view option a more deirable than the traded equity they ee in the market. On the other hand, employee are likely to aign low value to option after period with low tock return. In term of the notation of our model, we expect employee entiment for the non-traded compenation intrument (option) to react more trongly to pat performance than entiment for traded equity (z () > ), and thu the entiment premium of option over traded equity to increae in pat performance (z() larger after good performance). Finally, the empirical evidence that employee tend to ignore correlation between human capital and tock return ugget that firm-pecific human capital rik φ i unlikely to ignificantly dampen employee demand for equity compenation after period of high tock return (z() > φ ). The obervation that employee private valuation of company equity increae in pat performance (and for many rie above the market price), combined with the hypotheized increae in the entiment premium of option over tock in pat performance, lead to our firt tetable hypothei 3 : 3 Single-tock option for ome firm are traded. They are uually of much horter maturity than the option ued for compenation, and few employee are likely to be aware of their exitence. 3 A imilar hypothei appear in Liang and Weibenner (00). 0