SØK460 Finance Theory, Diderik Lund, 4 April Options to employees

Transcription

1 Options to employees ² Hall and Murphy: Options as (part of) salaries? ² Call options on shares in company for which one works ² Widespread in practice: In particular to top management, CEOs, executives May also be given to any other employees To many employees when everyone s e ort is important U.S.A., 1998: 40 percent of total pay to CEOs Norway, 1998: 22 percent of CEOs receive options ² Purpose: Give incentives for (share-price-enhancing) e ort Give incentives to stay with employer for several years Save taxes compared to other arrangements (or vice versa)? Perhaps share owners risk with employees? ² Similar arrangements: Pro t sharing, bonuses Employee s share ownership 1

2 Typical arrangements ² Some number of call options given as part of total pay ² How many? What exercise price? What expiration date? ² Various limitations on trading of option or shares: Personal option: Cannot be resold European option, must hold until expiration Or limited American, must rst hold some time, then may exercise during window Sometimes: Obligation to keep shares some period after exercise ( not topic in Hall and Murphy) (In that case: Exercise worth less than monetary S K) ² Complicated rules for taxation of receiving employee Di erent in di erent countries Option may be taxable when received or when exercised May be viewed as capital income or labor income No more details in this course 2

3 Hall and Murphy s analysis ² Two main topics: Value to employee, and optimal design ² Value to employee: Option values generally found by Black and Scholes Validforeveryonewhoisfreetobuyandsell Employees, however: Restricted diversi cation If accept options, forced to hold disproportionately much Too many eggs in the same basket Reduces value of options for these employees More precisely: If only one personal option: B-S value But the more personal options one gets, the lower value at margin Would have been the same with shares with similar restriction Underlying assumption: Cannot circumvent the restriction Possible circumvention: Sell similar option in market Or approximate, short sell share, or something correlated ² Optimal design: How many options? What exercise price? What expiration date? Hall and Murphy s attention only on e ort incentive Optimal incentive means strongest interest in high S 3

4 Valuation of option for employee ² Value de ned as certainty equivalent in E[U] framework ² Speci cally, compare two situations: ² In both, the employee has some wealth w at risk free rate r f ² In both, a number s of shares (price P t ) in the company ² If in addition one option with exercise price X, ends up with W T = w(1 + r f ) T + sp T +max(0;p T X) ² (Could have had investment in market portfolio also, but simplify) ² If instead some additional wealth V at r f, ends up with W V T =(w + V )(1 + r f ) T + sp T ² The certainty equivalent V for the option is de ned by E[U(W T )] = E[U(WT V )] ² E[U] is the expected utility function of the employee ² Certainty equivalent, V, will depend on utility function ² V thus di erent for di erent managers, even with same w; s 4

5 Solution for V ² Need assumption on probability distribution of P T ² One equation in one unknown, V,whenU function known ² Cannot solve analytically (formula), but numerically ² Hall and Murphy nd (numerically) the following: ² V decreasing in coe cient of relative risk aversion, ½ (Reasonable: Cash ow from option is uncertain) ² V decreasing in s (Higher s means less diversi cation) ² V increasing in w (Higher w means the option restriction counts for less) ² V also depends on B-S variables P 0 ;X;r f ;¾;T ² No detailed discussion of these ¾ e ect not obvious ² Di erence C V is deadweight loss 5

6 Designing options for maximum incentives? ² Incentive from one option de ned by slope, ² Incentive from n options ² Hall and Murphy split company s decision in two parts: 1. For any amount k which is given as options to an employee: Maximize the 2. Decide on how large k should be (for each employee) ² Only rst of these two decisions is analyzed ² Assume owners are well diversi ed ( not always true) ² Thus assume cost per option to company is B-S C max subject to nc = k ² From diagram: X = P is close to maximum, but at ² Shares instead of options, as if X =0, not good for incentives 6

7 Conclusions in Hall and Murphy ² Common practice, X equals today s P, is not bad ² Value to employees V can be substantially below cost to company, C ² Thus a lot of value is lost in order to provide incentives ² Support for employees claims that V is low compared with C Relation to material in other courses ² Limited diversi cation known from Lund paper, andre avdeling ² Special case here: Can solve for V numerically ² Incentive problem known from micro theory of moral hazard ² Root of problem: Cannot pay according to unobserved e ort ² More detailed, exact model of incentives here 7

8 Application, Norway 2000 ² Relevance for Norwegian discussion: Value received by Åge Korsvold ² Mr. Korsvold was CEO of largest insurance company ² Had bought options in the company at below-b-s prices ² Options bought from outsiders with unknown motive ² Illegal for CEO to receive bene ts from anyone other than company ² Did cheap call options in company represent a gift to Mr. Korsvold? ² Korsvold claimed (basically) that he paid V ² This claim is disputed ² Anyhow: Value (opportunity cost) to seller was B-S value ² Thus a gift element from seller s point of view 8

9 Other issues ² Incentives during period until expiration? Hall and Murphy consider incentives when options are received Often two or three years until expiration Incentives during that period will di er, P t varies, T falls More complicated problem to solve: Dynamically optimal design Do not know solution In particular, incentives very weak if P t becomes much lower than X Some companies then renegotiate, or reset X, orgive new options Incentive e ect of these practices, if known, are very bad ² Indexed options Employees with options subject to unnecessary risk Ideally: Should be remunerated according to own e ort Future share price result of e ort and lots of other e ects Among the others: General economic situation, R ~ m Could try to separate in uence of general economy Indexed options let exercise price uctuate with R ~ m 9

10 Incentive e ects not covered in Hall and Murphy (Apart from their footnote 8) ² Incentive to stay with company Some employee personal options linked to continued employment If leave company, option cannot be used any longer Strong incentive to stay with company as long as P t >X Useful for company, since training new employees is costly Also useful for society, internalizing bene ts from training ² Incentive to take more risk Well known that B-S call option value increases with ¾ Whether this holds for V depends on degree of risk aversion When yes: Employee with call option will promote risktaking ² Incentive not to distribute dividends Option owners normally not protected against dividend payouts Will try to promote low dividends E ect of such promotion depends on management s strength Shareholders may have other interests 10