Executive Compensation - gess.uni-mannheim.de

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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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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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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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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!

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0

expT fUPPS E U W r TP

Generate incentives with options

How does CEO utility change with firm value?


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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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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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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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


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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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


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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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


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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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?


Theoretical Solution – Which Option Contract is Optimal?

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p(PT)

PT

-W0exp(rfT)

> 1

< 1

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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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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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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


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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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


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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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


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

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Executive Compensation - gess.uni-mannheim.de