IDEAS home Printed from https://ideas.repec.org/p/ecm/wc2000/1503.html

Portfolio Delegation with Limited Liability

Author

Listed:
  • Uday Rajan

    (Carnegie Mellon University)

  • Sanjay Srivastava

    (Carnegie Mellon University)

Abstract

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, 2000. "Portfolio Delegation with Limited Liability," Econometric Society World Congress 2000 Contributed Papers 1503, Econometric Society.
    • Handle: RePEc:ecm:wc2000:1503
    as

    Download full text from publisher

    File URL: http://fmwww.bc.edu/RePEc/es2000/1503.pdf
    File Function: main text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Anthony W. Lynch & David K. Musto, 1997. "Understanding Fee Structures in the Asset Management Business," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-050, New York University, Leonard N. Stern School of Business-.
    2. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    3. Philip H. Dybvig & Heber K. Farnsworth & Jennifer N. Carpenter, 2010. "Portfolio Performance and Agency," The Review of Financial Studies, Society for Financial Studies, vol. 23(1), pages 1-23, January.
    4. Mark Grinblatt & Sheridan Titman, 1989. "Adverse Risk Incentives and the Design of Performance-Based Contracts," Management Science, INFORMS, vol. 35(7), pages 807-822, July.
    5. Heinkel, Robert & Stoughton, Neal M, 1994. "The Dynamics of Portfolio Management Contracts," The Review of Financial Studies, Society for Financial Studies, vol. 7(2), pages 351-387.
    6. Sanjiv Ranjan Das & Rangarajan K. Sundaram, 1998. "On the Regulation of Fee Structures in Mutual Funds," NBER Working Papers 6639, National Bureau of Economic Research, Inc.
    7. Innes, Robert D., 1990. "Limited liability and incentive contracting with ex-ante action choices," Journal of Economic Theory, Elsevier, vol. 52(1), pages 45-67, October.
    8. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Stefan W. Schmitz, 2005. "Die Governance-Struktur der Pensionskassen in Österreich und ihre politökonomischen Konsequenzen," Wirtschaft und Gesellschaft - WuG, Kammer für Arbeiter und Angestellte für Wien, Abteilung Wirtschaftswissenschaft und Statistik, vol. 31(3), pages 407-443.
    2. García, Diego & Vanden, Joel M., 2009. "Information acquisition and mutual funds," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1965-1995, September.
    3. Livio Stracca, 2006. "Delegated Portfolio Management: A Survey Of The Theoretical Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 20(5), pages 823-848, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Juan-Pedro Gómez & Tridib Sharma, 2006. "Portfolio delegation under short-selling constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(1), pages 173-196, May.
    2. Palomino, Frederic & Prat, Andrea, 2003. "Risk Taking and Optimal Contracts for Money Managers," RAND Journal of Economics, The RAND Corporation, vol. 34(1), pages 113-137, Spring.
    3. Agarwal, Vikas & Gómez, Juan-Pedro & Priestley, Richard, 2012. "Management compensation and market timing under portfolio constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 36(10), pages 1600-1625.
    4. Golec, Joseph & Starks, Laura, 2004. "Performance fee contract change and mutual fund risk," Journal of Financial Economics, Elsevier, vol. 73(1), pages 93-118, July.
    5. Ping Hu & Jayant Kale & Ajay Subramanian, 2003. "Compensation, Career Concerns, and Relative Risk Choices by Mutual Fund Managers: Theory and Evidence," Levine's Bibliography 666156000000000349, UCLA Department of Economics.
    6. Sheng, Jiliang & Wang, Xiaoting & Yang, Jun, 2012. "Incentive contracts in delegated portfolio management under VaR constraint," Economic Modelling, Elsevier, vol. 29(5), pages 1679-1685.
    7. Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, vol. 50(9), pages 1261-1273, September.
    8. Li, Xiao-Ming & Rose, Lawrence C., 2009. "The tail risk of emerging stock markets," Emerging Markets Review, Elsevier, vol. 10(4), pages 242-256, December.
    9. Farkas, Walter & Fringuellotti, Fulvia & Tunaru, Radu, 2020. "A cost-benefit analysis of capital requirements adjusted for model risk," Journal of Corporate Finance, Elsevier, vol. 65(C).
    10. Junhong Du & Zhiming Li & Lijun Wu, 2019. "Optimal Stop-Loss Reinsurance Under the VaR and CTE Risk Measures: Variable Transformation Method," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 1133-1151, March.
    11. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.
    12. Rostagno, Luciano Martin, 2005. "Empirical tests of parametric and non-parametric Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) measures for the Brazilian stock market index," ISU General Staff Papers 2005010108000021878, Iowa State University, Department of Economics.
    13. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2012. "When more is less: Using multiple constraints to reduce tail risk," Journal of Banking & Finance, Elsevier, vol. 36(10), pages 2693-2716.
    14. Sheng, Jiliang & Wang, Jian & Wang, Xiaoting & Yang, Jun, 2014. "Asymmetric contracts, cash flows and risk taking of mutual funds," Economic Modelling, Elsevier, vol. 38(C), pages 435-442.
    15. Fangyuan Zhang, 2023. "Non-concave portfolio optimization with average value-at-risk," Mathematics and Financial Economics, Springer, volume 17, number 3, June.
    16. Zhang, Qingye & Gao, Yan, 2016. "Optimal consumption—portfolio problem with CVaR constraints," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 516-521.
    17. José Santiago Fajardo Barbachan & Aquiles Rocha de Farias & José Renato Haas Ornelas, 2008. "A Goodness-of-Fit Test with Focus on Conditional Value at Risk," Brazilian Review of Finance, Brazilian Society of Finance, vol. 6(2), pages 139-155.
    18. Ana C. Díaz†Mendoza & Germán López†Espinosa & Miguel A. Martínez, 2014. "The Efficiency of Performance†Based Fee Funds," European Financial Management, European Financial Management Association, vol. 20(4), pages 825-855, September.
    19. Manganelli, Simone, 2007. "Asset allocation by penalized least squares," Working Paper Series 723, European Central Bank.
    20. Dingshi Tian & Zongwu Cai & Ying Fang, 2018. "Econometric Modeling of Risk Measures: A Selective Review of the Recent Literature," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201807, University of Kansas, Department of Economics, revised Oct 2018.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    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:ecm:wc2000:1503. See general information about how to correct material in RePEc.

    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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christopher F. Baum (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.