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Executive Compensation
Ernst Maug
Universität Mannheim
E-mail: [email protected]
© 2016 Ernst Maug Executive Compensation
Should CEOs receive options?Some Practitioners are Skeptical
„We don't give options because it would be a lottery ticket.“
Warren Buffet, Berkshire Hathaway
„There will be no new stock option grants from Microsoft. Instead, we will award actual stock to our employees.“
Steve Ballmer, Microsoft
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© 2016 Ernst Maug Executive Compensation
Literature – The „conventional model“
CRRA-lognormal models are widely used in applications:
Lambert, Larcker, Verrecchia (1991)
Hall and Murphy (2001), (2002)
Hall and Knox (2002)
Jenter (2001)
Huddart (1994, binomial)
Carpenter (1998, binomial)
Tian (2001, geometric Brownian motion)
Johnson and Tian (2000a, 2000b, geom. Brown. m.)
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© 2016 Ernst Maug Executive Compensation
Are Options Cheap or Expensive?
Compensate CEOs with options
Compute certainty equivalent values of options
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Results (Lambert, Larcker und Verrecchia, 1991):
CEOs value options much less than market
Typically 60%-80% discount relative to Black-Scholes Price
Options are expensive!
0 0 max ,0O TU W V E U W n P K
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© 2016 Ernst Maug Executive Compensation
Options: Cheap or Expensive?
Results (Hall and Murphy, 2000):
CEOs get leveraged instrument
Dollar value of one unit of incentives less with options than with restricted stock
Options are cheap!
5
0
expT fUPPS E U W r TP
Generate incentives with options
How does CEO utility change with firm value?
© 2016 Ernst Maug Executive Compensation
Options: Cheap or Expensive?A Simple Example
Options are a „cheap“ form of providing incentives: ($100 > $95)
Relevant in model with rigid base salaries
Options are an „expensive“ form of compensation
$60 < $70: relevant if salaries can be reduced
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$70$60Risk Premium
$25$40Subjective Value
$95$100Market Value
OptionsStock
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© 2016 Ernst Maug Executive Compensation
Research Strategy
Formulate principal-agent model
CRRA-utility, lognormal prices
Contracts with base salary, stock, options
Calibrate model to actual data on 598 US CEOs
Estimate wealth, representative option, etc.
Grid on relative risk aversion
Evaluate optimal contract numerically
Analyze deviations from actual (observed) contracts
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© 2016 Ernst Maug Executive Compensation
Main Results
Optimal contracts almost never include options
But 96.5% of the sample CEOs have some options!
Use stock instead to provide incentives
Model implies lower base salaries
...and negative base salaries in many plausible cases
CEOs need to invest private wealth in their companies
What does this mean?
Either the world is inefficient
...or the model is incorrect
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© 2016 Ernst Maug Executive Compensation
The Model
Stock Prices are log-normal:
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Permissable contracts:
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0 exp , ~ 0,12
T fP P e r T u T u N
0 exp max ,0T f S T O TW W r T n P n P K
Separable preferences:
1
,1
TT
WU W e C e
© 2016 Ernst Maug Executive Compensation
Assume risk-neutral pricing
Model only allows for firm-specific risk
Market risk would require additional r.v.
Introduction of return m > rf would yield incoherent results (e. g. Tian, 2001)
- CEO cannot trade in the stock market!
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© 2016 Ernst Maug Executive Compensation
Two-stage solution (Grossman-Hart, 1983), minimize:
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0 0exp f T S Or T E n P n BSp p
s. t. :
IC constraint
PC constraint
We only need the first stage
© 2016 Ernst Maug Executive Compensation
Replace IC constraint with first-order condition
Need to check that this is ok later!
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*
* 0
0
, 0TT
T
C ePPUE U W e E
e P P e e
Define utility-adjusted pay for performance sensitivity:
* *
0
, expT fUPPS E U W e r T k eP
UPPS
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© 2016 Ernst Maug Executive Compensation
Using First-Order Conditions – The Problem
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Effort
Utility
Model
e* (Model) e* (Observed)
Observed
IC and PC-constraints holdunder both contracts
© 2016 Ernst Maug Executive Compensation
Using First-Order Conditions
Local maxima only if function not globally concave for all effort levels below e* (i. e. P<P0).
Check second order condition:
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2 22 2 20 0
2 2 2 20 0
,0
TE U W e E V E VP P C
e P e P e e
< 0< 0> 0???
Sufficient condition for second order condition to hold:
Contract p(PT) is non-convex
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© 2016 Ernst Maug Executive Compensation
Numerical Approach
Hence, we need to solve this program numerically:
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0 0, ,
0
Min exp
. . , , ; , , ;
, , ; , , ;
0 1, 0,
S Of T S O
n n
d d dT S O T S O
d d dT S O T S O
S O
r T E n P n BS
s t E V W n n E V W n n
UPPS W n n UPPS W n n
n n W
p p
Can we find a cheaper contract, that
provides the same incentives, and
provides the same utility to the CEO?
© 2016 Ernst Maug Executive Compensation
Theoretical Solution – Which Option Contract is Optimal?
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p(PT)
PT
-W0exp(rfT)
> 1
< 1
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© 2016 Ernst Maug Executive Compensation
Data
Use CompuStat ExecuComp
Generated from Proxy Statements
1.696 CEOs in 2000
Require 5 years of continuous history
Reconstruct approximate option portfolios
- Aggregate into „representative option“
Estimate wealth from previous years‘ income
We are left with 598 CEOs
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© 2016 Ernst Maug Executive Compensation
The Sample
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Variable Symbol Mean Median Std. Dev. Minimum Maximum
Base Salary ($ '000) 2,037 1,261 2,570 97 22,109
Stock (%) nS 2.29% 0.29% 6.00% 0.00% 46.34%
Options (%) nO 1.29% 0.84% 1.82% 0.00% 24.32%
Market Value ($ mil.) P 0 9,857 1,668 27,845 7 280,114
Wealth ($ '000) W 0 34.60 6.86 234.79 0.03 5,431.72
Option Delta N(d1) 0.834 0.856 0.126 0.001 1.000
Maturity (years) T 5.89 5.54 1.96 1.20 22.18
Stock Price Volatility σ 0.377 0.335 0.196 0.136 3.487
Age of CEO 57 57 7 36 84
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© 2016 Ernst Maug Executive Compensation
Result 1: Option Holdings in Optimal Contracts
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Risk
aversion
Mean option
holdings
Fraction with
options >0
Option holdings
as % of actual
holdings
t-statistic
for equal
means
0.5 0.054% 13.12% 5.05% -15.10
0.5 0.059% 13.64% 5.52% -15.12
1.0 0.041% 10.77% 4.01% -16.86
2.0 0.014% 5.25% 1.60% -17.17
3.0 0.003% 1.34% 0.27% -17.33
4.0 0.001% 0.34% 0.02% -17.36
5.0 0.000% 0.00% 0.00% -17.36
6.0 0.000% 0.00% 0.00% -17.33
8.0 0.000% 0.00% 0.00% -17.27
10.0 0.000% 0.00% 0.00% -16.69
© 2016 Ernst Maug Executive Compensation
Result 1: Stock Options in Optimal Contracts ( = 3)
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p(PT)
PT
-W0exp(rfT)
590 CEOs
8 CEOs
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© 2016 Ernst Maug Executive Compensation
Result 2: CEOs should hold more stock
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Mean Median Mean Median Mean Median
0.5 0.97% 0.55% 33,887 8,430 157.35% 0.710 0.726
1 0.83% 0.49% 32,023 8,705 158.64% 0.633 0.628
2 0.63% 0.38% 26,760 6,356 122.79% 0.485 0.468
3 0.47% 0.27% 21,476 4,667 95.04% 0.368 0.351
4 0.36% 0.20% 16,596 3,428 67.31% 0.284 0.262
5 0.28% 0.14% 12,908 2,590 53.13% 0.223 0.197
6 0.23% 0.11% 10,081 1,880 39.08% 0.178 0.147
8 0.17% 0.08% 6,811 1,062 23.67% 0.125 0.092
10 0.13% 0.05% 4,806 567 13.48% 0.089 0.053
Risk
aversion
Change in stock
holding
D value
($ '000)
Median
relative
change
Exchange
ratio
© 2016 Ernst Maug Executive Compensation
Result 3: CEOs should receive lower base salaries
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Mean Median Mean Median
0.5 -7,652 -3,046 -415.32% -239.66% 79.55% -54.11%
1 -6,888 -2,924 -356.83% -216.41% 75.04% -49.80%
2 -5,122 -1,961 -253.68% -137.91% 62.81% -44.51%
3 -3,821 -1,319 -182.17% -95.83% 48.70% -40.54%
4 -2,786 -888 -131.58% -64.75% 36.46% -37.90%
5 -2,066 -637 -97.71% -47.37% 26.34% -35.43%
6 -1,501 -478 -73.49% -31.61% 18.95% -34.19%
8 -874 -228 -45.91% -16.68% 10.20% -30.26%
10 -496 -110 -26.57% -8.56% 5.00% -25.21%
Risk
aversion
Change in base
salary ($ '000)
Fraction
with base
salary < 0
Relative change in
base salaryCorrelation
between D salary
and wealth
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© 2016 Ernst Maug Executive Compensation
Wealth to be invested in stock
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Risk
aversion
Mean Median Mean Median
0.5 5,844 1,746 33.46% 22.38%
1 5,094 1,505 31.49% 18.79%
2 3,481 450 19.12% 4.75%
3 2,338 0 10.88% 0.00%
4 1,485 0 5.62% 0.00%
5 960 0 3.02% 0.00%
6 594 0 1.60% 0.00%
8 269 0 0.48% 0.00%
10 113 0 0.15% 0.00%
Wealth that must be
invested ($ '000)
Investment relative
to wealth
© 2016 Ernst Maug Executive Compensation
Result 4: Potential Savings are significant
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Mean Median Mean Median Mean Median
0.5 690 179 1.71% 1.01% 0.04% 0.01%
1 2,292 606 5.09% 3.40% 0.10% 0.03%
2 7,387 1,583 13.20% 10.05% 0.24% 0.09%
3 12,722 2,648 20.29% 16.42% 0.35% 0.15%
4 16,764 3,585 25.40% 21.13% 0.44% 0.21%
5 19,704 4,154 29.14% 25.37% 0.49% 0.24%
6 21,842 4,595 31.92% 28.98% 0.54% 0.28%
8 24,998 5,373 35.54% 33.17% 0.67% 0.38%
10 27,721 5,799 37.49% 35.45% 0.77% 0.47%
Savings as
percentage of firm
value
Risk
aversion
Savings ($ '000) Savings as
percentage of
total pay