How Important Are
Risk-Taking Incentives
in Executive Compensation?
Ingolf Dittmann
Erasmus University
Rotterdam
Dittmann, Yu (2010)
Ko-Chia Yu
Shanghai University of
Finance and Economics
How Important are Risk-Taking
Incentives in Executive Compensation
1
Motivation:
Relation between risk and incentives
Firm Risk
CEO incentives
• Informativeness principle (standard agency theory):
– More risk  less incentive pay
– Mixed empirical evidence (Prendergast, 2002)
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
2
Motivation:
Relation between risk and incentives
Firm Risk
CEO incentives
• Solid evidence that CEOs respond to risk-taking incentives
– Hedging: Tufano (1996); Knopf et al. (2002)
– Investments: Rajgopal and Shevlin (2002)
– Leverage: Coles et al. (2006), Tchistyi et al. (2007)
– Acquisitions: May (1995), Smith and Swan (2007)
• Stock and bond holders anticipate CEO risk-taking: DeFusco et
al. (1990), Billett et al. (2006)
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
3
Research question
• Do shareholders provide risk-taking incentives
on purpose?
– Or are risk-taking incentives just an unimportant
side effect of effort incentives?
• Is it important to take into account risk-taking
incentives when designing a CEO
compensation package?
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
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Approach
• We model the endogeneity between risk and incentives
• Principal-agent model
– Effort-averse agent chooses effort and firm strategy.
– Firm strategy affects firm value and volatility.
– Incorporate informativeness and risk-taking incentives
• Calibrate the model to individual CEO data.
• Model predicts
– Optimal compensation structure for each CEO
– Savings firms could realize by switching
• Compare model predictions with observed contracts
• Better than a model without risk-taking incentives?
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
5
Results (1)
Consistence with compensation practice
• Savings from recontracting are small (mean: 10.4%)
• Average distance between the observed contract and
the predicted contract is small. (mean: 8.0%)
• Much better fit than models with effort aversion alone
– Dittmann & Maug (2007) find up to 54% savings and
28.8% difference in distances
• Conclusion: Risk-taking incentives play an important
role in executive compensation practice.
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
6
Results (1)
Consistence with compensation practice
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
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Results (2)
Application: In-the-money options are optimal

Replace stock & ATM options by ITM options
W

observed

optimal
Small savings


P
•If U.S. taxes are taken into account:
–Observed contract is optimal for 93% of the CEOs
–Results consistent with the universal use of at-the-money options
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
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The model:
Standard assumptions
• Time t = 0: Contract is signed.
• Time T: End-of-period stock price PT is realized
and wage w(PT) is paid.
• Immediately after t = 0, the agent chooses effort
e.
– Firm value E(PT) is increasing and concave in e.
– Agent incurs costs of effort C(e) that are increasing
and convex in e.
• Stock price is lognormally distributed.
• Agent is risk-averse (CRRA-parameter γ).
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
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The model:
Additional assumptions
• In addition to effort, CEO chooses firm strategy s.
– Combination of many different actions (e.g., project
choice, M&A, financial transactions)
– Affects firm value E(PT) and firm risk σ.
• Risk-averse CEO with monotonic wage contract will
choose a strategy (s) that maximizes E(PT) given σ.
– Choice of s is equivalent to choice of σ.
•
•
•
•
Reduced form: assume that CEO chooses σ.
First-best strategy is associated with risk 
E(PT) is increasing and concave in σ if
E(PT) is weakly decreasing in σ if
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
10
Principal-agent models
with effort and risk-taking incentives
• Agent gathers information and makes project
choice
– Lambert (1986), Core & Qian (2002)
• Agent‘s effort affects mean and variance of stock
price
– Feltham & Wu (2001), Lambert & Larcker (2004)
• Continuous effort and volatility choice
– Hirshleifer & Suh (1992), Flor, Frimor & Munk (2006)
• Models in continuous time
– Hellwig (2008) assumes risk-neutral agent
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
11
The principal‘s problem
max E PT  WT ( PT ) | e,  
WT ,e,
s.t. E V (W ( PT ),e ) | e,    C( e )  U
{ e,  }  arg max E V (W ( PT ),e ) | e,    C( e )

Assume that first-order approach holds, so that the
incentive compatibility constraint can be written as:
d
de
E V (W ( PT ),e ) | e,    C'( e )  0
d
d
E V (W ( PT ),e ) | e,    0
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
12
Calibration method
• The full model cannot be calibrated to data,
because P0(e,σ) and C(e) are unknown.
• Solve a simpler problem (first stage of Grossman
and Hart, 1983): Search for a new contract with a
given shape that
–
–
–
–
provides the same utility to the agent,
generates the same effort incentives,
provides the same risk-taking incentives, and
is as cheap as possible.
• If the model is correct, the new contract must be
equal to the observed contract.
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
13
Dataset Construction
• Use CompuStat ExecuComp
– Require 5 years of continuous history
– Estimate wealth from previous years‘ income
– Construct approximate option portfolios
• Aggregate into “representative option“ with
same value, same option delta and same
option vega
• We are left with 727 CEOs (for the year 2006).
• Estimate volatility from daily CRSP returns
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
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Dataset: Descriptive Statistics
Variable
Stock (%)
Options (%)
Fixed Salary ($m)
Value of contract ($m)
Non-firm Wealth ($m)
Firm Value ($m)
Moneyness (%)
Maturity
Stock Volatility (%)
Dividend Rate (%)
Age
Return 2001-2005 (%)
Mean
nS
nO
phi
pi
W0
P0
K/P0
T
sigma
d
1.83%
1.37%
1.64
159.63
62.8
9,294
70.1%
4.6
30.0%
1.24%
56.0
11.8%
Std. Dev.
4.94%
1.62%
4.47
1,700.06
667.0
22,777
21.7%
1.4
13.4%
2.25%
6.8
15.6%
10% Quantile
0.04%
0.14%
0.51
4.58
2.5
377
41.2%
2.8
16.4%
0.00%
47
-5.7%
Median
0.32%
0.92%
1.04
24.97
12.0
2,387
72.0%
4.4
28.3%
0.63%
56
11.4%
90% Quantile
4.68%
3.17%
2.43
172.74
72.2
20,880
100.0%
6.4
45.5%
3.30%
64
28.7%
Table 1
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
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Table 3
Optimal Contracts with Risk-Taking
Incentives
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
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Optimal Contracts that Consist of Salary,
Stock, and Options
• Consider contracts that consist of base salary,
stock and one option grant.
• Principal minimizes contracting costs over
– Base salary
– Number of shares
– Number of options
– Option strike price
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
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Optimal Contracts that Consist of Salary,
Stock, and Options
Table 6
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
18
In-the-money options and the
U.S. tax system
• IRC 409A: Executives must pay a 20% penalty
tax on the intrinsic value of the option when it
becomes exercisable.
– Neglect other rules like IRC 162(m).
• Repeat analysis with this tax penalty
– Observed contract is optimal for 76% to 93% of all
CEOs (depending on assumptions)
– US tax system prohibits in-the-money options.
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
19
Robustness test: Loss-Aversion Utility
Function
• Dittmann, Maug, Spalt (2010) showed that if CEOs
are loss-averse, the principal agent model is able to
explain current compensation practices.
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
20
Optimal Contracts with Loss-Aversion
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
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Loss Aversion with Risk-Taking Incentives
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
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Conclusions
• Optimal compensation structure from a principal-agent model
where the agent chooses effort and firm-volatility
• Model performs much better than a model w/o risk-taking
incentives.
– Small savings (10.4% vs. 54% w/o risk-taking incentives)
– Small distance from observed contract (8% vs. 28.8% w/o
risk-taking incentives)
– Optimal contract is convex over some regions
• Risk-taking incentives are not a issue in LA models, but the RTI
explanation is less susceptive to parameter choices.
• Risk-taking incentives are a major objective in executive
compensation practice.
Dittmann, Yu (2010)
How Important are Risk-Taking
Incentives in Executive Compensation
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