dittmann, yu (2010) how important are risk-taking incentives in executive compensation 1 how...

Dittmann, Yu (2010)How Important are Risk-Taking

Incentives in Executive Compensation

1

How Important Are Risk-Taking Incentives

in Executive Compensation?

Ingolf Dittmann Ko-Chia YuErasmus University Shanghai University of

Rotterdam Finance and Economics

Motivation:Relation between risk and incentives

• Informativeness principle (standard agency theory):– More risk less incentive pay– Mixed empirical evidence (Prendergast, 2002)



2

Firm Risk CEO incentives

Motivation:Relation between risk and 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)



3

Firm Risk CEO incentives



4

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?

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?

How Important are Risk-Taking Incentives in Executive

Compensation5Dittmann, Yu (2010)

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.



6



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Results (1)Consistence with compensation practice

Results (2)Application: In-the-money options are optimal


Compensation8

P

W

observed

optimal

Replace stock & ATM options by ITM options

Small savings

Dittmann, Yu (2010)

•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

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).



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 How Important are Risk-Taking


10

Dittmann, Yu (2010)

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



The principal‘s problem

TT T T

W ,e,

T

T

maxE P W (P ) | e,

s.t. E V(W(P ),e ) | e, C(e) U

{ e, } arg max E V(W(P ),e ) | e, C(e)


Compensation12

Assume that first-order approach holds, so that the incentive compatibility constraint can be written as:

0

0

dTde

dTd

E V(W(P ),e ) | e, C'(e )

E V(W(P ),e ) | e,

Dittmann, Yu (2010)

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.



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



Dataset: Descriptive Statistics

Table 1How Important are Risk-Taking


15Dittmann, Yu (2010)

Variable Mean Std. Dev. 10% Quantile Median 90% Quantile

Stock (%) nS 1.83% 4.94% 0.04% 0.32% 4.68%Options (%) nO 1.37% 1.62% 0.14% 0.92% 3.17%Fixed Salary ($m) phi 1.64 4.47 0.51 1.04 2.43Value of contract ($m) pi 159.63 1,700.06 4.58 24.97 172.74Non-firm Wealth ($m) W0 62.8 667.0 2.5 12.0 72.2Firm Value ($m) P0 9,294 22,777 377 2,387 20,880Moneyness (%) K/P0 70.1% 21.7% 41.2% 72.0% 100.0%Maturity T 4.6 1.4 2.8 4.4 6.4Stock Volatility (%) sigma 30.0% 13.4% 16.4% 28.3% 45.5%Dividend Rate (%) d 1.24% 2.25% 0.00% 0.63% 3.30%Age 56.0 6.8 47 56 64Return 2001-2005 (%) 　 11.8% 15.6% -5.7% 11.4% 28.7%

Optimal Contracts with Risk-Taking Incentives



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Table 3

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



Optimal Contracts that Consist of Salary, Stock, and Options

Table 6



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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.



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.



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Optimal Contracts with Loss-Aversion



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Loss Aversion with Risk-Taking Incentives



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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 1 how...

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