Journal of Corporate Finance

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1 Journal of Corporate Finance 9 (23) 9 39 Contents lists available at civerse ciencedirect Journal of Corporate Finance journal omepage: Production and edging implications of executive compensation scemes agi Akron a,, imon Benninga b a Te Graduate cool of Management, University of Haifa, Mount Carmel, Haifa 395, Israel b Te Faculty of Management, Tel Aviv University, Tel Aviv 69978, Israel article info abstract Article istory: Received 9 December 2 Received in revised form 3 October 22 Accepted 3 October 22 Available online 9 October 22 JEL classification: G G3 G3 G3 G32 Keywords: Optimal managerial compensation sceme Corporate edging devices Executive equity-linked compensation Frictions Regulation eparation teorems Tis paper connects executive compensation wit edging and analyzes a crucial sareolders and managers agency source tat evolves from te pricing of te edging device. Te sareolders are risk-neutral, wile te risk-averse manager edges te price risk of te manufactured quantity, and is compensation package includes equity-linked compensationstock grants. Only wen te edging instrument's pricing includes a risk premium, edging is costly to te sareolders, wile it is costless to te manager. Ten from te owners' point of view, we observe managerial over-edging, increasing in te equity-linked compensation level. Tis result leads to a violation of te classical production and edging separation teorem. We conclude tat, in te case were te edging device's pricing bears a risk premium, sareolders can regulate te corporate value diversion to managers troug diminising te managerial equity-linked compensation sceme or by putting restrictions on te extent of edging activities of executives. 22 Elsevier B.V. All rigts reserved.. Introduction Following te sub-prime crisis, criticism against excessive managerial compensation as frequently emerged. candals, suc as te taxpayers' financing of AIG managerial bonus compensations, ave recently enanced te conviction tat te core of managerial compensation scemes sould switc from options-based to a long-term vesting period of stock grants. Te aim of tis suggested cange is to diminis managers' excessive risk-taking and increase managers' interest coesiveness wit te sareolders (Denis et al., 26). However, no attention was given to te potential agency problem of managerial edging opportunities, in ligt of te equity-linked compensation sceme. Tis study considers te interaction between equity-linked managerial compensation scemes and various managerial decisions, suc as effort, production, and edging. Using tis framework, we demonstrate a crucial principal-agent agency source tat evolves from a specific pricing span of te edging device. Tis pricing span results in excessive managerial edging operations. In tis case we sow tat regulation, on te level of equity-linked compensation scemes or te edging activities, is essential in order to alleviate te corporate value diversion from sareolders to managers. Corresponding autor. Tel.: ; fax: addresses: sagiakron@univ.aifa.ac.il, sagiakron@gsb.aifa.ac.il (. Akron), benninga@post.tau.ac.il (. Benninga) /$ see front matter 22 Elsevier B.V. All rigts reserved. ttp://dx.doi.org/.6/j.jcorpfin.22..4

2 2. Akron,. Benninga / Journal of Corporate Finance 9 (23) 9 39 Te seminal papers of Baron (97) and andmo (97) were te first to consider te impact of future contracts on managerial decision-making. However, neiter tese papers nor later papers considered several important sareolders manager conflict of interest issues simultaneously. 2 More specifically, prior studies ave rarely considered te interaction between equity-linked compensation scemes and corporate edging operations wile controlling for managerial sacrifice towards te firm and production decisions. In addition, tis classical literature derived its separation teorem results, regarding te independence of production and edging decisions, under a specific bencmark pricing of te edging devices, wic does not necessarily old. Terefore, an analysis tat incorporates bot te edging compensation interaction and a wide pricing span of te edging devices, i.e., commodity future contracts, is vital to better understanding of optimal managerial compensation scemes, in ligt of te possibility of costly edging for te sareolders. We sow tat in cases like tis, increased equity-linked compensation migt result in excessive managerial corporate edging, wic furter diverts corporate value from te sareolders to te manager. Hence, in suc scenarios corporations sould consider diminising te equity-linked component in te managerial compensation package, in order to moderate tis acute agency problem. In te framework of tis paper, we assume tat as te firm manager absorbs most of is wealt from te corporate value, e is more risk-averse tan te diversified owners of te firm. 3 As in reality, corporations do not activate robots to manage firms. Hence, te asymptotically risk-neutral company owners ire a risk-averse manager, under te assumption tat e is well qualified to increase te corporate value troug te performance of observable and latent activities. We assume tat control of production and edging decisions is vested in te manager, wo determines is sacrifice level towards te firm, i.e., te unobservable managerial perks e consumes and/or te level of efforts e exerts. Bot managerial latent effects are quantified into one personal sacrifice variable, wic positively impacts te corporate cas flows. In addition, te manager suffers a subjective disutility from is sacrifice, i.e., effort exertion or diminised perks consumption, as in Holmstrom and Tirole (993). To overcome tis ambiguity regarding te managerial sacrifice parameter, te manager is granted equity-linked compensation, i.e., stock grants, wic induces im to work in te sareolders' best interests. 4 Terefore, we observe an incentive friction, as in Bebcuk and Jolls (998) and Bebcuk and Fried (23), wic ultimately results in an incentive ownersip dilution tradeoff. Te above studies, owever, as well as tose of Core and Guay (2) and Meulbroek (2), ordemsetz and Villalonga (2), do not incorporate te manager's opportunities to control risks, and terefore to impact te corporate sareolders' value, wenever tey bear a cost for edging activities. Te 97s classical production and edging separation teorems derive complete independence between production and edging decisions in a situation were managers and owners are assumed to be a single entity. Furtermore, witin tis conventional outline, tis classical solution is found to be invariant to te level of managerial risk aversion. 5 Tis classical framework analysis is based upon a crucial assumption made regarding te price of te future contract. It is assumed tat te current price of te future contract equals te market consensus expectation of te spot price on te delivery date. uc bencmark pricing of te future contract is referred to as unbiased pricing of te future contract, since tere is no upward or downward drift on te average delivery spot price. 6 According to te alternative approac to te unbiased pricing of futures, in a market were edgers use futures (i.e., sort position of futures) to eliminate price risks, tey pay substantial risk premiums to speculators wo supply tis insurance (i.e., long futures). 7 Indeed, it is plausible to assume tat for eac case in wic te insured product as a positive systematic risk correlation wit te market, te insurers demand a risk premium. Hence, we sould expect tat in tis case te speculators buy (long) future contracts from te edgers only if te latter are willing to sell (sort) futures at a price below tat wic te future price is expected to reac. Tat is wy one sould actually expect a deviation from te unbiased future price. For example, in te above described case, we expect to ave a downward bias of te future contract's price. Tis expresses te positive risk premium speculators demand and edgers are willing to pay. Empirical evidence supporting eac of te approaces as been documented. 8 However, according te later empirical analysis conducted by Cang (985), te pro unbiased future pricings neiter convincingly confirm nor deny te normal backwardation Oter extensions appear in Holtausen (979) and Anderson and Dantine (98, 98). 2 For example, tulz (984), Benninga et al. (985), Adam-Muller (997), Adam-Muller and Wong (23), Macnes (25), mit and tulz (985), Froot et al. (993), Nance et al. (993), DeMarzo and Duffie (995), Mian (996), Graam and mit (999), Graam and Rogers (22), Tufano (996), Battermann et al. (2), Bartram (26), Bartram et al. (29) Adam et al. (27), Mackay and Moeller (27) and Campello et al. (2). We rarely see a model tat simultaneously integrates all te following: managers owners distinction of risk aversion and incentives, equity-linked compensation as an incentive mecanism, i.e., Grossman and Hart (983), te determination of output, and te conduction of risk management activities. Different from production and edging literature, in Gao (2) te manager edges er equity compensation sceme. 3 Graam and Harvey (2) Kim et al. (26) Lins et al. (29) and Disatnik et al. (29) mention tat managers and sareowners tend to be concerned about cas flow realizations and teir potential impact on corporate value. As Gao (2) we use te standard way to differentiate teir risk attitudes by assuming a risk-averse manager and asymptotically (or in fact), risk-indifferent owners. Canging tis standard risk neutrality assumption of te owners into risk aversion, in a lower level tan tat of te manager, doesn't cange te essence of analysis but complicates te implicit functions calculations. 4 To illustrate te paper's main idea, we concentrate in stock grants compensation. Hence we are less exposed to utility function sensitivities to convex compensation scemes suc as executive stock options as Ross (24) sows. We don't consider board-management considerations suc as in Hallock (977). 5 Tis literature originally deals wit product price risk, as examined by Jin and Jorion (26), but includes oter risk sources extensions, suc as excange rate risk or quantity risk, as discussed by Brown and Toft (22). 6 For example, see amuelson (965). 7 Tis idea is already expressed in te Normal Backwardation Teory of Keynes (93). 8 Wile a few empirical studies, suc as tose of Telser (958) and Dusak (973) find support in future unbiased pricing, oter researces, suc as Houtakker (957) and Cang (985), document a downward bias of te futures price.

3 . Akron,. Benninga / Journal of Corporate Finance 9 (23) teory, nor do tey persuasively rule out future contract pricing bias. In is paper, Cang uses a nonparametric statistical approac to confirm te existence of an evolving positive risk premium for speculators, wic as tended towards increased prominence in recent years as compared to earlier years. Cang's findings raise doubts regarding te classical analysis, wic lacks our entities' distinction and te frictions between managers and sareolders. More recent literature specifies anoter possible source of future contracts' risk premiums. Gorton et al. (28) find evidence tat commodities' risk premiums evolve from market inventories' cyclical beavior. Following te Teory of torage, tey find empirical evidence for negative relations between inventory levels and te risk premium of commodity futures. Regardless of wic is te correct explanation, tere is strong evidence for risk premiums in future contract prices. Te implication of future contracts' risk premiums is te acknowledgement tat te cost of edging for owners is different from its cost for te (more) risk-averse manager, as tey ave different certainty equivalents. Hence, biased future pricing migt result in a negative sareolders' corporate value impact. Te iger te level of managerial equity-linked compensation, te greater excessive managerial edging will be. Our model also generalizes te classical production and edging literature into its framework. We first sow tat te classical separation results could not exist in te absence of equity-linked compensation. Furtermore, we sow tat te classical results are obtained only under a specific unbiased bencmark pricing of te future contracts. Only under suc unbiased pricing, we observe tat production and edging decisions are insensitive to eiter te managerial level of equity-linked compensation or te manager's risk aversion. Ten, te risk-averse manager cooses a costless risk elimination edging strategy, wic is also optimal for risk-indifferent owners. 9 Tis unbiased future pricing guarantees an alignment of interests between owners and management, at any level of equity-linked compensation. Tis friction mitigation results in a separation between production and edging decisions in te classical framework, as te manager fully edges te entire production. Terefore, in tis classical case, te optimal equity-linked compensation is solely determined by te mentioned incentive ownersip dilution tradeoff. Neverteless, wen te prices of te edging devices are biased, te separation teorems deviate from teir traditional forms. For instance, given a risk premium for te future contract (a downward bias in te future price), we observe a managerial tendency to increase edging positions along wit iger equity-linked compensation level. By doing so, managers decrease teir own risk exposure at te expense of te sare owner's corporate value. Tis outcome occurs because wen edging devices prices are biased, edging activities are no longer costless to te risk-indifferent owners. For example, consider te case in wic te future is downward biased. In suc a case, te risk-indifferent sareolders prefer tat te manager will under-edge as muc as possible, as te expected commodity price is greater tan te certain equivalent proceeds from te future contract. Consider te case of relatively low levels of equity-linked compensation. Ten te agent is exposed to rater negligible level of cas flow dispersion and aligns interests wit te desired under-edging strategy for te owners. Neverteless, as te equity-linked compensation level rises, te increased risk exposure induces te manager to demand a iger risk premium and generates a iger need for managerial edging position at te expense of te owners. Tus, we sow tat te separation teorems deviate from teir classical form under biased pricing span of te future contracts. We conclude tat tis outcome as an important governance impact on managerial compensation scemes. In cases were edging devices prices are biased, te executive compensation plan sould be designed to include a rater moderate level of equity-linked compensation. Finally, we deduce tat, given te edging compensation interaction, it is more appropriate to take risk management implications into account wen we solve executive compensation scemes models. In oter words, we acknowledge tat under certain conditions managerial edging opportunities are, in fact, part of te managerial compensation scemes. Tis paper proceeds as follows. In ection 2, we define our model and assumptions. ections 3 and 4 present te model under equity-linked managerial compensation scemes and corporate edging interaction. We generalize te separation teorems into our edging compensation setting, and caracterize te conditions for a deviation from te classical separation. ection 5 illustrates te classical separation and te deviation from te traditional form, given different pricing of future contracts using numerical simulations. pecifically, it demonstrates te value diversion of te owners, troug excessive edging, in te biased pricing for future contracts. Finally, ection 6 concludes te paper. 2. Te model Our model considers an all-equity firm in a two-date framework. Tere is one commodity, wic is used for bot consumption and production. In correspondence wit tis core literature we consider a price taker firm. However, we can extend te fundamental analysis into non-competitive environment witout any significant cange in te essence (Diagram ). At date, as soon as te manager learns about te composition of is compensation contract, i.e., cas and equity components, e decides on te fundamental firm's date- parameters. Terefore, e cooses te output level y, is individual sacrifice parameter or effort-perks level e, 2 and te corporate edging policy, i.e., te number of commodity futures contracts e 9 In suc a case, te future price equals te expected spot price. As regards risk-indifferent agents, expected utility from te stocastic spot price equals utility from certain future contract prices; tus in tis case, edging is costless in te eyes of te sareolders. In te production-edging literature, te concept of under-edge is used to indicate a edging allocation of less tan te entire produced output. For instance, an extreme under-edging preference of te owners migt result in teir preference towards a long position of te futures. Te framework is easily extended to te case of riskless firm debt. 2 Note tat iger values of managerial sacrifice parameter e migt be considered as a diminised impact on costs.

4 22. Akron,. Benninga / Journal of Corporate Finance 9 (23) 9 39 Date A firm is establised tocks are issued A compensation contract is offered to CEO CEO cooses output, effortperks parameter and edging policy Date Output is sold Costs are paid Futures and/or options are exercised CEO compensation Contract is paid Te firm is liquidated Diagram. Te model timeline. purcases to eliminate te price risk of te manufactured output. At eac of te N=, j J states of date, te firm's revenue is j y, were j is te state-dependent commodity price. Te firm's date costs are not state-dependent and are given by Cy; ð eþ ¼ C C ðyþc 2 ðþ; e ðþ were C > is a fixed cost, C (y) is a convex cost function of te production level, and C 2 (e) is a convex function, wic expresses te impact of te manager's effort on costs. 3 Wereas C " (y)> C " (y)>, we assume tat te effort function as te opposite properties C 2 ðþ< e C} 2 ðþ> e ; C 2ðe ¼ Þ > lim e C C 2 ðþ¼c e. Tis means tat exerted managerial efforts decreasingly diminis costs up to a certain unavoidable level C. Te diversified owners of te firm are assumed to be risk-neutral, and terefore value te firm according to te discounted expected profits. On te oter and, as te manager absorbs most of is wealt from working witin te firm, e is more sensitive to is wealt realizations; tus, e is considered to be a risk-averse agent wo values is end-of-period state dependent consumption, c, by te expected utility E U c. To old tis, we assume tat te agent can neiter sell nor completely edge is equity compensation a crucial assumption for an effective contract tat aspires to attain alignments of interests. A practical way to cope wit tis requirement is to impose a long vesting period on te equity compensation sceme, witout including opportunities to edge against tem as, for instance, in Bettis et al. (2). 2.. Te firm's value and te owner's problem Te state-dependent end of period firm value, V, for all stakeolders (for a firm tat issues E stock capital, at date wen te risk-free rate r f ) is given by 4 : V j ¼ E r f j yc y; e ð Þη F F j W : ð2þ were: j Te state-dependent commodity price, wit respective state probabilities π j. η F Te number of sort futures positions on te commodity. We assume tat all futures contracts ave a settlement price F. Te last part of Eq. (2) defines te manager's compensation sceme: W η v j Lump-sum managerial compensation tat also represent is reservation wage, Te number of stock grants in te manager's compensation contract, Te state-dependent stock price. Te firm's sareolders split tis value wit te managers, wo are granted stocks. Denoting te number of sares granted to managers by η, and te per-sare value of te company in state j by v j, ten te firm's net-of-stock-grant value to te original sareolders is ^V, were: ^V j ¼ E r f j ycðy; eþη F F j W η v j : ð3þ 3 Adding a simple wite noise factor (wit zero covariance wit te spot price, ) to te effort parameter makes it non-verifiable. Hence, te entire cost function or te end of period corporate value is non-verifiable. 4 We avoid te consideration of capital structure implications at tis stage suc as in Meran (992).

5 . Akron,. Benninga / Journal of Corporate Finance 9 (23) Denoted by, te original number of outstanding sares in te firm; ten according to te law of one price, te statedependent stock price: ^V j v j ¼ : ð4þ Te risk-neutral owners ave to coose te optimal managerial compensation package in order to maximize firm value. Denoting te end of period net-of-dilution percentage of te firm owned by te sareolders is ðαþ ¼ η η ¼ η ;te problem of te initial sareolders is to coose te optimal manager compensation contract wic maximizes: 8 n io < Max f W ;η g ðαþ E Ṽ ¼ ðα : Þ XN j¼ 9 = π j V j ; : ð5þ Because te manager determines te firm's policies, te above expression requires us to first consider te impact of te compensation sceme on te manager's decisions for te firm. Given te manager optimization solution, we can solve te sareolders' problem by implementing backward induction Te manager's problem Te manager maximizes an increasing concave utility function of consumption: 8 Max < X N fy;e;η F g fδ E U c De ðþ ¼ δ : j¼ π j U c j DðÞ e 9 = ; s:t: ð6þ c ¼ W η ṽ δ E½UðÞ cšdðþ δ U e c alternative ¼ W were: δ c D(e) Te subjective discount factor of te manager, Te manager's end of period state-dependent consumption, A strictly convex function in effort-perks parameter, wic expresses te manager's disutility from is exerted efforts level e. After defining eac player's problem, we can solve te manager problem and imply te optimal compensation for te owners. 3. Te effects of te managerial compensation plan on firm outputs In tis section, we consider te implications of managerial compensation scemes on te manager's decisions tat eventually determine corporate value. We first examine te condition for effective sacrifice incentive using te equity-linked compensation sceme. We continue by extending te literature to our equity-linked compensation environment. After allowing for edging opportunities using commodity futures, we examine te optimal edging policy and generalize te separation teorems to our compensation framework. Te analysis considers te classical bencmark case of unbiased pricing of future contracts. Under tis specification, we assume tat te edging device price does not include any risk premium. Later on, in ection 4, given te vast literature on te premium issue, we allow a deviation from tat pricing and examine te respective cange in te classical separation teorems. 3.. Lump-sum compensation We start wit te base case, were te managerial compensation contract is not tied to te stock value. Ten, we face te basic agency problem, in wic te manager's problem becomes: Max fy;η F ;η P ;eg fδ E U c De ðþ s:t: c j ¼ W : ð7þ It is clear tat te following lemma describes tis situation:

6 24. Akron,. Benninga / Journal of Corporate Finance 9 (23) 9 39 Basic Lemma. Te manager minimizes is efforts to zero and is indifferent as regards is production and edging decision variables, if is compensation package is based on purely lump-sum cas tock grants and cas compensation Next, we consider te case were te manager's compensation package is composed of bot stock grants and wages. In tis case, we sow tat te equity-linked compensation plan affects te manager's decisions. In te absence of corporate edging, i.e., substituting η F = in Eq. (3), te net-of-stock-grant firm value for te original sareolders in state j is: ^V j ¼ ðe Þ r f j yc y; e ð Þ W η v j : ð8þ From te definition of v j in Eq. (4): ^V j ¼ ðe Þ r f j yc y; e! ð Þ W ^V j η : ð9þ olving tis equation for ^V j gives: η ^V j ¼ V ðe η Þ r f j ycðy; eþw i ; ðþ and dividing by te original number of outstanding sares, we get: v j ¼ ðe η Þ r f j ycðy; e Þ W i : ðþ ubstituting tis into te manager's maximization problem gives: Max fy;e;η F ¼g fδ E U c De ðþ s:t: : ð2þ c ¼ W η ðe η Þ r f ycðy; eþw i Te first order conditions of Eq. (2) wit respect to exerted effort and output are: fg e ¼ δ η ii E U ðþ C 2ðÞ e D ðþ¼ e η fg y ¼ δ η E U ðþ η C ii ðyþ ¼ : ð3þ ð4þ Lemma. Te equity-linked compensation contract induces te manager to exert greater efforts tan te lump-sum compensation contract. ubject to te manager's risk aversion, a greater number of stock grants induces te manager to exert greater efforts. Proof. Te FOC from Eq. (3) requires tat η ii δ E U ðþ C 2ðÞ e η ¼ D ðþ: e ð5þ Te rigt-and side (RH) of tis equation, representing marginal disutility of effort, is clearly positive and increasing in e. Wewill sow tat te left-and side (LH) of Eq. (5), representing marginal disutility of effort, is decreasing and positive in effort e and depending on te manager's risk aversion sifts upward and to te rigt, wen te number of stock grants η increases. Te results are illustrated in Diagram 2; te tecnical proof follows te diagram:

7 . Akron,. Benninga / Journal of Corporate Finance 9 (23) Marginal expected utility from (e) Marginal disutility from (e) e * e * e Diagram 2. Te optimal effort (e). Tis diagram describes te optimal effort first order condition for te case of lump-sum cas and stock grants compensation. Wen te manager's risk aversion is relatively low, or alternatively, in te case wen te ratio between te cas compensation and te equity-linked compensation is relatively ig, granting more stocks to te manager induces im to exert greater efforts. Te expression E[U () [C ' 2 (e)]] is clearly positive (Diagram 2). To sow tat it is decreasing in effort e, we differentiate and obtain: 8 9 zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{ 2 3 i zfflfflfflfflfflfflfflffl} fflfflfflfflfflfflfflffl{ du ðþ ½C 2ðÞŠ e >< ¼ U ðþ ½C >= 2ðÞ e Š de C 2ðÞ e U ðþ C 2ðÞ e <: ð6þ ffl{zffl} fflfflfflffl{zfflfflfflffl} ffl{zffl} {z} ffl{zffl} fflfflfflffl{zfflfflfflffl} >: >; Tis sows tat te LH of Eq. (5) is decreasing and positive in e. Next, we sow tat te LH of Eq. (5) siftsupwards andiito te rigt wen η increases, depending on te manager's risk aversion. To do tis, we differentiate δ η η EU ðþ C 2 e by te granted amount of stocks η. For convenience, let's define: Z Z ðy; eþ ¼ ðe Þ r f yc ðy; eþw : ð7þ Tis means tat te state-dependent consumption from te constraint in Eq. (2) is: c ¼ W η Z : η fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} α Terefore: 8 zfflfflfflfflfflfflfflffl} fflfflfflfflfflfflfflffl{ 9 >< i δ C η 2ðÞ e E U W η >= η η Z >: >; ¼ η η E U W η η η Z ¼ "" # η " # # η E V η 2 U η ðþ U η ðþ V η η 2 Z ð8þ ð9þ

8 26. Akron,. Benninga / Journal of Corporate Finance 9 (23) 9 39 A sufficient condition for Eq. (9) to increase for every y* and e*, is tat te expression inside te expectance be positive. In tis case, we get a condition for te coefficient of absolute risk aversion (CARA): CARA ¼ U ðþ U ðþ < : ð2þ η i Z η Multiplying Eq. (2) by c definition in Eq. (8), we get a condition for te manager's coefficient of relative risk aversion (CRRA): CRRA ¼ U c c< U η W c η η V η Z η Z CRRA ¼ U c W c< U : c η η Z fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl} ð2þ Wen Condition (2) olds, iger equity-linked compensation leads to iger exerted effort. 5 Tus, as long as te manager is not too risk-averse, or alternatively wen te equity-linked compensation is low enoug in comparison to te cas part, an increased equity-linked compensation plan effectively induces managers to exert efforts, i.e., e *>e *. Next, we examine te impact of te stock price linked compensation on te output level decision. In tis context, we generalize te literature from te 97s into our edging compensation model. Lemma 2. Increasing te number of te manager's stock grants diminises te manager's optimal output level. Proof. Te manager's coice for optimal output is determined by Eq. (4), from wic it follows tat at te manager's optimal y, EU ðþ i i ¼ EU ðþ C ðyþ: ð22þ From te definition of covariance: COV U ðþ; i EU ðþ E i ¼ EU ðþ C ðyþ: ð23þ Rewriting Eq. (23), we obtain 6 : 2 E COV U ðþ; 3 ¼ C ðyþ 4 5 : EU ð24þ ðþ fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Bias > To estimate te bias direction, recall tat E[U ()]>, and tat te marginal utility is decreasing in consumption. Wen te commodity price increases, te state-dependent consumption increases (since te firm's profit increases) and, consequently, te marginal utility decreases. Hence, te covariance between te decreasing marginal utility and te commodity price is negative, i.e. COV U ðþ; <, and te bias on te expected commodity price is positive. As a result, te manager observes a iger marginal cost for a given production level, y, and ence cooses an under optimal production level for te firm's owners. ince U ( ) is decreasing in te equity compensation level, tis proves te result. As noted by Baron (97), te bias increases in te manager's risk aversion, but it also intensifies in te level of stock grants compensation for a given managerial risk aversion. Grapically, te results of Lemma 2 are illustrated in Diagram 3 below. Te intuition of Lemma 2 is somewat less obvious tan tat of Lemma. We obtain te following: excluding edging opportunities, increased managerial equity-linked compensation deviates downwards from te optimal production to te sareolders, at teir expense. Tis is because witout edging opportunities, te risk-averse manager wises to diminis te variance of is compensation, wic is tied to te corporate value troug is stock grants compensation plan. Te way to acieve tis is to lower te support of te stocastic 5 It is easy to see tat Eq. (2) olds wen we assume tat te agent as eiter a power utility (i.e., constant relative risk aversion) or a log utility function. In a typical case of large U companies, cas pay/equity-based pay is rougly 4/6, in wic case te manager's RRA coefficient needs to be smaller tan.667 for Lemma to old. We tank te anonymous Referee for providing tis example. 6 Tis result was first sown by Baron (97), could not, in fact, exist unless we are in an equity-linked compensation world. Hence we also incorporate te impact of equity linked compensation level on tis bias.

9 . Akron,. Benninga / Journal of Corporate Finance 9 (23) Costs/Price C '(y) + Positive Bias Marginal cost of production: C '(y) E(s) Y * Y * Y Diagram 3. Te optimal production (Y). Tis diagram describes te manager's first order condition for optimal production. In an equity-linked compensation world, te manager's risk aversion causes a iger marginal cost. Hence, te production cosen by te manager decreases, and te gap between te manager's cosen output and tat desired by sareolders increases (tis is one representation of te agency costs in our model). Tis outcome is a result of equity-linked compensation. Te agency cost increases te level of equity-linked compensation, as iger equity-linked compensation increases actual managerial risk aversion. Te manager responds by decreasing te output level, in order to decrease te dispersion of te firm's operating profit realizations. profit distribution function by coosing a lower level of optimal output for te firm. Prior studies ave noted tat tis agency problem intensifies managerial risk aversion. Furtermore, we sow tat it also increases in te equity-linked compensation level, wic amplifies te manager's demand for risk premium Optimal equity-linked compensation for te sareolders Next, we sow te optimal compensation sceme in te absence of edging opportunities for te manager. Tis solution is derived from te tradeoff effects tat equity-linked compensation causes. Lemma 3. Tere exists an optimal equity compensation level η *> for te sareolders. Te optimum is acieved wen te marginal benefit to te owners, from granting te additional stock grant to te manager, equals te expected stock price. Proof. Te proof for tis lemma is presented in Appendix B. Lemma 3 sows tat tere exists a finite positive optimal stock grant level. Tis is because as te stock grant compensation increases, tere is a cost benefit tradeoff of te corporate value. Te offsetting effects caused by te η increase are: i) an increase in te effort-perks parameter causes an increase in te end of period firm value (Lemma ); ii) a decrease in te optimal production bias from te optimal output for te original firm owners causes a decrease in te end of period corporate value (Lemma 2); iii) te dilution effect of te original sareolders' ownersip causes a decrease in teir end of period firm value. Incorporating tese tree effects gives an optimum ex-ante amount of stock grants, η, as te optimum is reaced wen te marginal benefit to te owners (revenue minus cost) from te marginal stock grants η equals te expected sare price. We support tis analytical result wit numerical simulations, wic are presented in ection 5. Next, we incorporate edging opportunities into te equity-linked compensation setting and generalize te separation teorems to our model. We consider a commodity futures edging strategy. First, we examine te classical bencmark unbiased pricing for te future contracts. In suc a case, we assume no-risk premiums for te edging device. Later, in ection 4, we examine te manager and sareolders solution, and te derived cange in te separation teorems wen te future price is biased Lump-sum wage and stock grants wit unbiased future edging An extensively examined edging device mentioned in te literature is te unbiased futures contract. In tis case, it is implicitly assumed tat te speculators supplying te insurance to te edgers do not require a risk premium, or tere are storage costs tat account for futures risk premium. Neverteless, tis classical literature does not consider a well defined setting of effort-perks incentive and production-edging under te equity-linked compensation framework. According to te classical production and edging separation teorems, te optimal production decision is independent of te manager's risk preferences and expectations. Likewise, it can be differentiated from te optimal edging decision (see Benninga and Oosterof, 24). We next generalize tis result to fit our model's compensation framework. Teorem. uppose te manager is compensated by cas and stock grants, and suppose se can use unbiased commodity futures to edge. In suc a case, te manager cooses full edging and tere is a separation between output and edging decisions. Tis result olds, regardless of te manager's risk-aversion or te level of equity-linked compensation. Te optimal managerial compensation contract suggested by te owners does not cange, since tey do not bear any cost for te edging operations conducted by te manager.

10 28. Akron,. Benninga / Journal of Corporate Finance 9 (23) 9 39 Proof. Te proof for tis teorem is presented in Appendix B. Note tat te manager cooses a edging policy tat eliminates production uncertainty. At te optimum level, te marginal utility becomes non-stocastic, and tus te left covariance term equals zero: U W η ðe η Þ r f yc y; e Hence, te optimal edging policy is one of full edging: ð Þη F F W i ¼ Constant: ð25þ η F ¼ y : Finally, given optimal production and te optimal edging decision Eq. (26), Eq. (B.6) becomes non-stocastic: Z Z y ; e; η F ¼ ðe Þ r f y Cy ; e ηf F W ; ð26þ ðb:6þ and te manager solves Eq. (26) for a positive optimal effort-perks parameter e*>. Tus, in te case were te manager is compensated wit a combination of cas and stock grants, te possibility to manage risks using unbiased futures solves production and incentive deficiencies. 7 Notice tat, in te specific case were te future pricing is defined to be unbiased, we get te classical results of te separation teorems. ince te edging is costless to te owners te manager edges until te full elimination of risk as been acieved. Terefore, in tis case, neiter is production decision nor is edging decision is influenced by eiter is risk aversion or te equity-linked compensation level. Finally, in te case of no edging costs for te owners, edging does not cange te optimal equity-linked compensation contract. Following Teorem, we also notice te existence of a potential positive impact of edging on te corporate value, even wen te owners are risk-indifferent. imultaneous offsetting effects of managerial sacrifice and coice of production determine weter te edging impact on te corporate value is eventually positive. 4. Lump-sum wage and stock grants compensation wen te edging device prices are biased Tus far, we ave examined te case of unbiased edging instruments. In tis section, we look at te case were tis assumption does not old. 8 Te unbiased case will serve as a useful bencmark. However, it is essential to also consider te plausible cases in wic future pricing includes risk premium, i.e., speculators demand risk premium from edgers, or storage risk premium exists. We can even tink about contracting costs. Terefore, witout loss of generality, we examine te manager's problem in te case of downwards biased pure future edging contracts. 9 Teorem 2. uppose te manager is compensated by cas and stock grants and as only futures contracts for edging. If te futures' price bears risk premium (meaning, it is downward-biased, FbE()), ten: Te optimal production will be less tan for te case of unbiased futures. Te optimal edging strategy is to under-edge production. Under-edging decreases at te level of stock compensation. Te level of production is determined only by te futures price F. Te optimal compensation contract for te sareolders decreases te level of stock grants' compensation. Tis is done to regulate te corporate value diversion to te manager, troug excessive edging. Proof. Te proof for tis teorem is presented in Appendix B. Wat is te intuition for tis outcome? Recall, tat in te case of unbiased futures contracts, te separation teorems old, suc tat te manager cooses full edging and tus, entirely eliminates uncertainty. Neverteless, in te case were te future price is downwards biased, separation teorems old somewat differently and reveal a dependency on te edging policy at te level of equity-linked compensation. At low levels of equity compensation, te agent is exposed to a rater negligible level of cas flow dispersion. A very small stocastic dispersion on te manager's concave utility function simulates a local convergence into an asymptotically linear utility function. Terefore, in te presence of costly edging for te owners, te manager aligns interests better wit te owners wen moderately compensated wit equity-linked compensation, i.e., te manager under-edges 7 Anoter way of expressing te result in Teorem is to note tat unbiased futures contracts align manager and sareolder preferences by elimination of production risk. 8 Tere are inconclusive findings in te literature regarding te pricing of te edging devices. Wile a few empirical studies, suc as tat of Dusak (973), find tat in te case of future contracts edging te future price is found to be unbiased, oter papers (for example, Cang (985)) contradict tese finding and document a downwards bias of te futures prices. 9 Te empirical findings regarding downwards bias of future price i.e., Cang (985), expresses a similar idea as a positive correlation between te product price and te systematic market risk. However, te analysis is similar for upwards biased pure future edging contracts. In case of upwards bias in te future price contract, te corporate value diversion analysis doesn't cange. Obviously, in tis case te optimal quantity of edging differs to an opposite direction.

11 . Akron,. Benninga / Journal of Corporate Finance 9 (23) aggressively. However, as te managerial equity-linked compensation increases, te increased risk exposure induces te manager to demand a iger risk premium, and generates a iger need for a managerial edging position at te expense of te owners. Here we conclude an important implication regarding te optimal compensation contract from te sareolders point of view. In order to alleviate tis edging agency in case of biased edging instruments pricing it may be wiser for te corporation's owners to diminis te equity-linked compensation to a relatively low level. Tat is since a iger level induces te manager to increase expendable edging activities from te owners' point of view. Wit respect to te deduction of te above analysis, we sould take into account a potential bias in te prices of te edging devices. A priori, it seems tat only rarely does tis bias equal zero, and only ten do we converge to te classical examined cases. Oterwise, wen speculators demand risk premium for supplying insurance for edgers or wen te storage cost of te commodity creates risk premium, we are exposed to an important value diversion opportunity troug te manager's risk-management operations. Next, we illustrate our lemmas and teorems using numerical simulations. 5. imulations of te model and discussion In tis section, we simulate our model. We use a binomial setting in wic te commodity price is eiter =2 or 2 =6 wit probabilities π =.5; π 2 =.5. Te manager as a constant-relative-risk-aversion utility function u(c)=c (γ) /(γ); were γ=.5. Te manager's disutility from effort-perks sacrifice is expressed by D(e)=e 2. Te manager is paid a lump-sum wage of W=, apart from is equity-linked based compensation. Wen te firm is establised, it raises an initial equity of E =, and te risk-free return is assumed to be r f =.5. Te number of outstanding sares at te beginning of te period is =,. Bot te futures price contract and te put option exercise price are taken as F=Xp=4. Finally, te costs function of bot, te effort-perks parameter and te produced quantity, is represented by te function: Cy; ð eþ ¼ y 2 C Ke ; were C ¼ 5; K ¼ :: Besides illustrating te analytical results proved above, te simulations allow us to observe te cange of te stockolders' corporate value, given te stock grants compensation level. Tus, te simulations illustrate grapically te optimal level of manager compensation, of wic we ave proven analytically using implicit functions. Figs. 4 illustrate te model setting before edging opportunities Lemma, Lemma 2, and Lemma 3. Given te sufficient condition for effort induced by te manager, we notice in Fig. te effectiveness of stock grants compensation in motivating te manager to exert efforts (Lemma results). Fig. 2 exemplifies te monotonic increasing under optimal production as te number of stock grants rises (Lemma 2 results). Fig. 3 illustrates Lemma 3's optimal stock grants quantity (or alternatively, post dilution managerial ownersip level α). In Figs. 5 8, we allow edging opportunities using unbiased (UB) future contracts (excluding oter edging instruments as puts). We clearly notice in Figs. 6 and 7 te classical separation teorems according to wic te level of production and (full) edging of te manufactured quantity is invariant to te level of equity-linked compensation. In tis bencmark pricing, were edging opportunities using futures are costless to te owners, we observe te convergence of owners manager risk interests. Terefore, te optimal compensation, wic maximizes corporate value, is solely determined by te effort-inducing versus ownersip-dilution tradeoff, and te optimal contract is similar to te non-edging opportunities case. However, wen we allow edging opportunities and te future contracts price is downwards biased (DWB), i.e., Figs. 9, we notice a conflict of interests between te manager and te owners. Tis tension increases in te level of stock grants compensation. Terefore, we detect a crucial deviation from te classical separation teorems. At low levels of stock grants compensation tere is a relative coesiveness of interests and actual risk preferences; ence, te manager under-edges e* Managerial Percentage Ownersip (α) Fig.. Optimal e canging α No futures no puts. Tis illustration of Lemma is te simulation results for te optimal effort-perks parameter (e ) tat te manager cooses, as te offered percentage post dilution ownersip (α) is canged using stock grants. We see tat, under a given manager's risk aversion, te equity-linked compensation contract induces te manager to monotonically exert effort (until a certain finite-asymptotic level of.233, wic does not appear in tis figure).

12 3. Akron,. Benninga / Journal of Corporate Finance 9 (23) y* Managerial Percentage Ownersip (α) Fig. 2. Optimal y canging α No futures no puts. Tis illustration of Lemma 2 is te simulation results for te optimal production parameter (y ) tat te manager cooses, as te offered percentage post dilution ownersip (α) is canged using stock grants. We see tat, under a given manager's risk aversion, increase of ownersip percentage in te compensation contract induces te manager to a iger deviation from te optimal output cosen by te risk-neutral firm owners (equal to 2 units), as te offered ownersip percentage increases. Terefore, we observe underinvestment friction in te case were no edging is involved. 278 Original Owners EV* EV=278.6 * α [.37%,.4%] Managerial Percentage Ownersip (α) Fig. 3. Optimal EV canging α No futures no puts. Tis illustration of Lemma 3 presents te expected firm value for te original owners of te firm (EV ), as te offered percentage post dilution ownersip (α) to te manager. We evidence from tis simulation tat, under a given manager's risk aversion, te optimal equity-linked compensation contract part sould include about.4% of te end of period value Managerial EU* * EU [2.47, 2.5] Managerial Percentage Ownersip (α) Fig. 4. Optimal EU canging α No futures no puts. Tis figure is te simulation result for te manager's expected utility (EU ), as te offered percentage post dilution ownersip (α) to te manager. Not surprisingly, under a given manager's risk aversion, te manager's expected utility is monotonically increasing at te ownersip percentage level.

13 . Akron,. Benninga / Journal of Corporate Finance 9 (23) e* Managerial Percentage Ownersip (α) Fig. 5. Optimal e canging α UB futures no puts. Tis illustration of Teorem is te simulation results for te optimal effort-perks parameter (e ) tat te manager cooses, as te offered percentage post dilution ownersip (α) is canged using stock grants. We see tat, under a given manager's risk aversion, te equity-linked compensation contract induces te manager to monotonically exert effort, toug edging opportunities allow im to exert less effort tan before (until a certain finite-asymptotic level of.238, wic does not appear in te figure). y* Managerial Percentage Ownersip (α) Fig. 6. Optimal y canging α UB futures no puts. Tis illustration of Teorem is te simulation results for te optimal production parameter (y ) tat te manager cooses, as te offered percentage post dilution ownersip (α) is canged using stock grants. We can clearly see tat classical separation olds given costless edging to te owners (UB unbiased future pricing). Given te opportunity to edge price risks (using futures), te manager always cooses te optimal output for te risk-neutral firm owners (wic is also 2 units), regardless of te offered ownersip percentage cange. Terefore, we notice a mitigation of te underinvestment friction wen managers are exposed to edging opportunities. η F * Managerial Percentage Ownersip (α) Fig. 7. Optimal η F canging α UB futures no puts. Tis illustration of Teorem is te simulation results for te optimal edging parameter (η F ) tat te manager cooses, as te offered percentage post dilution ownersip (α) is canged using stock grants. We can clearly see tat classical separation olds given costless edging to te owners (UB unbiased future pricing). Te manager always cooses to fully edge te produced quantity to exclude uncertainty, regardless of te offered ownersip percentage. Terefore, regardless of te stock grant e gets, e fully edges (takes a sort position of 2 future contracts) te optimal output (wic is 2 units). Terefore, we see a mitigation of te underinvestment friction tat exists wen managers ave edging opportunities.

14 32. Akron,. Benninga / Journal of Corporate Finance 9 (23) Original Owners EV* EV=278.6 * α [.37%,.4%] Managerial Percentage Ownersip (α) Fig. 8. Optimal EV canging α UB future no puts. Tis illustration of Teorem is te simulation results for te optimal offered percentage post dilution ownersip (α), suc tat te corporate value for te original owners of te firm (EV ) is maximized. In tis simulation we see tat, given a manager's certain risk aversion, wen edging is costless to te owners (UB unbiased future pricing), we get te same optimal equity-linked compensation (about.4% of te post dilution ownersip) as in te case excluding edging opportunities y* Managerial Percentage Ownersip (α) Fig. 9. Optimal y canging α DWB futures no puts. Tis illustration of Teorem 2 is te simulation results for te optimal production parameter (y ) tat te manager cooses, as te offered percentage post dilution ownersip (α) is canged using stock grants. We can clearly see tat classical separation does not old, given costly edging to te owners (DWB downwards biased future pricing). Te manager cooses less tan te optimal output for te risk-neutral firm owners (less tan 2 units), regardless of ownersip percentage cange. Tus, tere exists separation regarding te production decision, even toug it is no longer optimal for te corporation's owners η F * Managerial Percentage Ownersip (α) Fig.. Optimal η F canging α DWB futures no puts. Tis illustration of Teorem 2 is te simulation results for te optimal edging parameter (η F ) tat te manager cooses, as te offered percentage post dilution ownersip (α) is canged using stock grants. We can clearly see tat classical separation does not old, given costly edging to te owners (DWB downwards biased future pricing). Te manager cooses to under-edge produced quantity. At a low level of stock grants, e under-edges as desired for te owners wo bear edging costs. However te iger is te equity compensation te iger is te managerial risk premium; ence, se edges more at te expense of te sareowners. In oter words, te edging policy is affected by te compensation sceme; tus, we deviate from te classical separation teorems, in te case were futures include risk premiums.