SØK460 Finance Theory, Diderik Lund, 4 April 2001
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
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SØK460 Finance Theory, Diderik Lund, 4 April 2001
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
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SØK460 Finance Theory, Diderik Lund, 4 April 2001
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
– Valid for everyone who is free to buy and sell
– 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
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SØK460 Finance Theory, Diderik Lund, 4 April 2001
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 rf
² In both, a number s of shares (price Pt ) in the company
² If in addition one option with exercise price X, ends up with
WT = w(1 + rf )T + sPT + max(0; PT ¡ X)
² (Could have had investment in market portfolio also, but simplify)
² If instead some additional wealth V at rf , ends up with
WTV = (w + V )(1 + rf )T + sPT
² The certainty equivalent V for the option is de…ned by
E[U(WT )] = E[U (WTV )]
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
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SØK460 Finance Theory, Diderik Lund, 4 April 2001
Solution for V
² Need assumption on probability distribution of PT
² One equation in one unknown, V , when U 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 P0; X; rf ; ¾; T
² No detailed discussion of these — ¾ e¤ect not obvious
² Di¤erence C ¡ V is deadweight loss
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SØK460 Finance Theory, Diderik Lund, 4 April 2001
Designing options for maximum incentives?
² Incentive from one option de…ned by slope, @V =@P
² Incentive from n options is @nV =@P
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 resulting @nV=@P
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 @nV=@P subject to nC = k
X
² From diagram: X = P is close to maximum, but ‡at
² Shares instead of options, as if X = 0, not good for incentives
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SØK460 Finance Theory, Diderik Lund, 4 April 2001
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
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SØK460 Finance Theory, Diderik Lund, 4 April 2001
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
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SØK460 Finance Theory, Diderik Lund, 4 April 2001
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, Pt varies, T falls
– More complicated problem to solve: Dynamically optimal
design
– Do not know solution
– In particular, incentives very weak if Pt becomes much
lower than X
– Some companies then renegotiate, or reset X, or give 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
~m
– Among the others: General economic situation, R
– Could try to separate in‡uence of general economy
~m
– Indexed options let exercise price ‡uctuate with R
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SØK460 Finance Theory, Diderik Lund, 4 April 2001
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 Pt > 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
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