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Optimal CEO compensation and stock options


  • Arantxa Jarque

    () (Universidad Carlos III de Madrid)


We study the incentive problem between the owners of a firm and its CEO's due to the unobservability of the manager's actions. Our model departs from the literature in two ways. First, we acknowledge that, in contrast with standard repeated moral hazard models, actions taken by CEO's have a persistent effect in time. Second, we derive the effect of effort on stock prices from primitives; i.e., effort affects directly the conditional distribution of profits, and not the distribution of prices. The stock market determines the price of the stock of the firm using information about past profits. A complete characterization of the Second Best contract assuming limited liability is given as a benchmark. Allowing for an arbitrary number of option grants to be awarded, sufficient conditions are given for the implementation of the Second Best contract by an Options Scheme. For a stylized scheme with a unique option grant, the characteristics of the solution are analyzed. We find that the optimal time of exercise balances the increase in quality of information of waiting one extra period with the cost of the poorer smoothing of incentives of doing so. The number of options in the grant, the constant wage, and especially the exercise price are used to best exploit the correlation between the changes in prices and in the likelihood ratios of the histories of profits generating them. As an example, whenever low prices are poorly correlated with the likelihood ratios, the optimal option scheme implies a positive exercise price, which allows for a better use of a higher correlation over the high stock price range than a simple restricted stock scheme. Our results suggest caution regarding regulations that influence the setting of exercise prices. Este artículo estudia el problema de incentivos que surge entre los dueños de una empresa y el ejecutivo que la dirige, fruto de la imposibilidad de observar directamente las acciones del directivo. El modelo difiere del modelo estándar en la literatura en dos puntos clave. En primer lugar, tiene en cuenta que las acciones que toma el directivo tienen un efecto persistente en el tiempo; esta persistencia no la consideran los modelos estándar de riesgo moral repetido. En segundo lugar, el efecto del esfuerzo del directivo en el precio de las acciones de la empresa se deriva de los primitivos del modelo: el esfuerzo determina la distribución de probabilidad de los beneficios de la empresa, y no directamente la distribución de precios. Los compradores en el mercado de valores determinan el precio de las acciones basándose en la información disponible sobre los beneficios pasados. El artículo presenta, como marco de referencia, una caracterización del contrato óptimo asumiendo responsabilidad limitada por parte del directivo. Para el caso en que se pueden emitir múltiples paquetes de opciones, se presentan condiciones suficientes para la implementación del contrato óptimo. Para un caso simplificado en el que la compensación se realiza con un solo paquete de opciones, se analizan las características del mismo. Los resultados del análisis indican que la fecha de ejercicio óptima se determina balanceando los beneficios y los costes de esperar un periodo más: por un lado, aumenta la calidad de información; por el otro, aumenta el coste de proveer incentivos, por tener que estar estos concentrados en un horizonte temporal menor. El número de opciones en el paquete, el salario, y especialmente el precio de ejercicio se usan para explotar la correlación entre los cambios en precios y los cocientes de probabilidad relativa correspondientes a las historias de beneficios que generan esos precios. Por ejemplo, cuando los precios bajos están débilmente correlacionados con los correspondientes cocientes, el paquete óptimo de opciones tiene un precio de ejercicio positivo, que permite explotar la correlación existente en el rango de precios alto mejor que un paquete que incluyera simplemente acciones (i.e, acciones de venta restringida). Estos resultados sugieren cautela a la hora de aprobar regulación que pueda distorsionar la elección de los precios de ejercicio de las opciones en los paquetes de compensación de directivos de empresa.

Suggested Citation

  • Arantxa Jarque, 2008. "Optimal CEO compensation and stock options," Working Papers. Serie EC 2008-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  • Handle: RePEc:ivi:wpasec:2008-04

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    References listed on IDEAS

    1. Clementi, Gian Luca & Cooley, Thomas F. & Wang, Cheng, 2006. "Stock grants as a commitment device," Journal of Economic Dynamics and Control, Elsevier, vol. 30(11), pages 2191-2216, November.
    2. Ohad Kadan, 2008. "Stocks or Options? Moral Hazard, Firm Viability, and the Design of Compensation Contracts," Review of Financial Studies, Society for Financial Studies, vol. 21(1), pages 451-482, January.
    3. Wang, Cheng, 1997. "Incentives, CEO Compensation, and Shareholder Wealth in a Dynamic Agency Model," Journal of Economic Theory, Elsevier, vol. 76(1), pages 72-105, September.
    4. Patrick Bolton & José Scheinkman & Wei Xiong, 2006. "Executive Compensation and Short-Termist Behaviour in Speculative Markets," Review of Economic Studies, Oxford University Press, vol. 73(3), pages 577-610.
    5. Jorge Aseff & Manuel Santos, 2005. "Stock options and managerial optimal contracts," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 813-837, November.
    6. Jewitt, Ian & Kadan, Ohad & Swinkels, Jeroen M., 2008. "Moral hazard with bounded payments," Journal of Economic Theory, Elsevier, vol. 143(1), pages 59-82, November.
    7. Kevin J. Murphy & Brian J. Hall, 2000. "Optimal Exercise Prices for Executive Stock Options," American Economic Review, American Economic Association, vol. 90(2), pages 209-214, May.
    8. Marco Celentani & Rosa Loveira, 2006. "A Simple Explanation of the Relative Performance Evaluation Puzzle," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(3), pages 525-540, July.
    9. Yermack, David, 1995. "Do corporations award CEO stock options effectively?," Journal of Financial Economics, Elsevier, vol. 39(2-3), pages 237-269.
    10. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    11. Murphy, Kevin J., 1999. "Executive compensation," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.),Handbook of Labor Economics, edition 1, volume 3, chapter 38, pages 2485-2563, Elsevier.
    12. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
    13. Bengt Holmström, 1999. "Managerial Incentive Problems: A Dynamic Perspective," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 169-182.
    14. Bengt Holmstrom, 1999. "Managerial Incentive Problems: A Dynamic Perspective," NBER Working Papers 6875, National Bureau of Economic Research, Inc.
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    1. Clementi, Gian Luca & Cooley, Thomas F. & Wang, Cheng, 2006. "Stock grants as a commitment device," Journal of Economic Dynamics and Control, Elsevier, vol. 30(11), pages 2191-2216, November.

    More about this item


    Riesgo Moral; Contratos Óptimos; Persistencia; Compensación de Directivos; Opciones Moral Hazard; Optimal Contracts; Persistence; CEO Compensation; Stock;

    JEL classification:

    • D30 - Microeconomics - - Distribution - - - General
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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