Dynamic Moral Hazard and Executive Stock Options

• Author: Frank Yong Wang,Baomin Dong,Guixia Guo
• DOI: http://doi.org/10.1111/1468-0106.12017
• Published date: 01 May 2013
• Date: 01 May 2013

DYNAMIC MORAL HAZARD AND EXECUTIVE

STOCK OPTIONS

BAOMIN DONG Henan University

GUIXIA GUO University of International Business and Economics

FRANK YONG WANG*University of International Business and Economics

Abstract. This paper shows that the optimal executive compensation scheme in a dynamic moral

hazard environment is convex in the firm value. This implies that the optimal contract should include

stock options. This is because the private benefit of shirking is increasing in firm value and the

manager’s utility is concave. Therefore, in contrast to the previous literature that takes stock options

in the incentive contract exogenously, we rationalize the optimality of their use endogenously.

Moreover, we show that the optimal amount of stock options (restricted stocks) increases with

agency cost and the executive’s reservation utility, decreases with the degree of risk aversion of the

manager, and increases (decreases) with the firm size.

JEL Classification: C73, D86, G34

1. INTRODUCTION

Executive stock options, as a long-term incentive mechanism, give executives the

right to buy their firm’s shares at a prespecified strike price. Over the past two

decades, the use of stock options has represented a major change in the corpo-

rate governance structure (Holmstrom and Kaplan, 2001). Stock options are

also one of the most frequently used tools in executive compensation schemes

(Hall and Liebman, 1998; Murphy, 1999; Hall and Murphy, 2000, 2002, 2003).

However, with the increasingly extensive use of stock options and with the

rising proportion of option value in executives’ compensation, heated debate has

emerged over the ‘generosity’ of executive stock options, both in academia and

industry. After the global financial crisis in 2008, several financial institutions,

including those who received government bailouts, continued to provide fat

bonuses for their executives. Whether such huge bonuses are worthwhile has

been discussed extensively in the literature. For instance, Meulbroek (2001) and

*Address for Correspondence: School of International Trade and Economics, University of Inter-

national Business and Economics, Beijing 100029, China. E-mail: wangyong9110@gmail.com. The

authors are grateful to an anonymous referee for his insightful comments on an earlier version of the

paper. Guixia Guo is grateful for financial support from the 2011 National Social Science Founda-

tion Major Project (Grant no. 11&ZD007), the 2012 National Natural Science Funds of China for

Young Scholars (Grant no. 71203026), the Humanities and Social Science Research Projects of the

MOE in China (Grant no. 12YJC790047), Program for Innovative Research Team and the ‘211

Program’ in UIBE. Frank Yong Wang is grateful for financial support from the Program for

Innovative Research Team and from the ‘211 Program’ at the University of International Business

and Economics.

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Pacific Economic Review, 18: 2 (2013) pp. 259–279

doi: 10.1111/1468-0106.12017

© 2013 Wiley Publishing Asia Pty Ltd

Hall and Murphy (2000, 2002) claim that firms have to compensate their

risk-averse executives with more stock options, because the executives cannot

choose efficient investment portfolios and, thus, significantly undervalue the

stock options.1However, Lambert and Larcker (2004) point out that such

analysis is incomplete, because the incentive role of stock options is neglected.

The essence of the debate is whether executives should be granted stock

options and, if so, what is the optimal amount? No consensus has been reached.

Haugen and Senbet (1981) are among the first to propose stock options as an

instrument to alleviate the conflict between shareholders and managers, but

their focus is on executives’ excessive incentive of entrenchment due to the

issuance of new shares. Therefore, their discussion is more about the issue of

capital structure. In a setting with hyperbolic absolute risk aversion utility and

gamma distribution functions, Hemmer et al. (2000) show that stock options are

a component of the optimal compensation contract only if the executive’s abso-

lute coefficient of risk aversion is decreasing and his or her relative coefficient

of risk aversion is moderate. However, using constant relative risk aversion

(CRRA) utility and lognormal distribution functions, the simulation results of

Dittmann and Maug (2007) predict that the optimal compensation scheme that

does not include stock options can realize the same level of incentive and

executives’ utility at 20% less cost.

In our opinion, the long-run or dynamic nature of moral hazard of the

executives is key for executive stock options plans. Thus, in the current paper,

we use a dynamic or multi-period moral hazard framework to study the optimal

compensation contract. This is in contrast to the aforementioned papers, which

use a static setup in which before the output realization the manager can make

his or her effort decision only once. The dynamic model is better suited for

reality and tailored to address the incentive role of stock options in the long run.

Using a simple binomial output process, we show that the optimal compen-

sation scheme is convex in the firm value. This naturally implies that stock

options should be included in the optimal contract. There are two factors

contributing to the convexity result. The first is that the private benefit of

shirking is increasing in the firm value. Hence, the optimal contract should pay

higher at the margin for a given increase in output. In addition, because the

manager is risk averse, his or her marginal utility for a given increase in payment

is smaller, and, hence, the firm needs to pay more to offset a given amount of

private benefit derived from shirking. Note that the fixed payment plus a linear

piece rate contract prescribed by the traditional principal–agent theory only

yields a linear contract. Given that stock options are financial assets with a

convex payoff structure in reality, they should be included in the optimal com-

pensation contract.

In contrast to the previous literature that exogenously assumes that the com-

pensation contract consists of a base wage, restricted stocks and stock options

(e.g. Lambert and Larcker, 2004; Dittmann and Maug, 2007; Armstrong et al.,

1When granting stock options and restricted stock to executives, there is generally a vesting period

during which the options and stocks cannot be sold out.

B. DONG ET AL.

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© 2013 Wiley Publishing Asia Pty Ltd