IDEAS home Printed from
   My bibliography  Save this paper

Portfolio Delegation with Limited Liability


  • Uday Rajan
  • Sanjay Srivastava


We consider the portfolio delegation problem in a world with complete contingent claim markets. A principal hires an agent to manage a portfolio. When the agent has limited liability (that is, there is a lower bound on the compensation contract), she may have an incentive to take on excessive risk. With complete markets, the precise nature of the risk the agent may take on is a large short position in the state with lowest probability, and a long position in every other state. We impose an incentive constraint that prevents the agent from taking on risk in this form. We show that the optimal contract requires that the compensation function be bounded above, and that this prevents excessive risk taking. The size of the bound controls the degree of risk taken on by the agent. The upper bound alone is sufficient to prevent the deviation mentioned. Our main result is that, with limited liability and a large number of states, incentive compatibility alone restricts the feasible contract to be either a flat one or one with exactly two compensation levels (equal to the lower and upper bounds on compensation). Even a small positive slope to the compensation function over other regions of realized wealth will lead to the agent deviating in the prescribed manner. We then compare the outcome induced by the optimal contract to that induced by a Value at Risk compensation scheme. Value at Risk is a popular risk management tool currently used in the portfolio delegation context. An appropriately defined Value at Risk scheme can be effective in controlling excessive risk taking. A Value at Risk constraint is equivalent to a short-sale constraint in this case. However, it does not necessarily achieve the second best outcome. Our model highlights a potential downside to financial innovation. While it may lead to superior gains from risk sharing in an exchange economy, in our context, it lets the agent gamble on a finer set of states. This intensifies the agency problem.

Suggested Citation

  • Uday Rajan & Sanjay Srivastava, "undated". "Portfolio Delegation with Limited Liability," GSIA Working Papers 2000-E15, Carnegie Mellon University, Tepper School of Business.
  • Handle: RePEc:cmu:gsiawp:366

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Manuel A. Domínguez & Ignacio N. Lobato, 2004. "Consistent Estimation of Models Defined by Conditional Moment Restrictions," Econometrica, Econometric Society, vol. 72(5), pages 1601-1615, September.
    3. Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(03), pages 409-431, August.
    4. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    5. Gregory, Allan W. & Lamarche, Jean-Francois & Smith, Gregor W., 2002. "Information-theoretic estimation of preference parameters: macroeconomic applications and simulation evidence," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 213-233, March.
    6. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
    7. Guido W. Imbens & Richard H. Spady & Phillip Johnson, 1998. "Information Theoretic Approaches to Inference in Moment Condition Models," Econometrica, Econometric Society, vol. 66(2), pages 333-358, March.
    8. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
    9. repec:bla:restud:v:65:y:1998:i:3:p:361-93 is not listed on IDEAS
    10. Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 69(6), pages 1661-1672, November.
    11. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, January.
    Full references (including those not matched with items on IDEAS)

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cmu:gsiawp:366. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Steve Spear). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.