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Optimal portfolio delegation when parties have different coefficients of risk aversion

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  • Kasper Larsen

Abstract

We consider the problem of delegated portfolio management when the involved parties are risk-averse. The agent invests the principal's money in the financial market, and in return he receives a compensation which depends on the value that he generates over some period of time. We use a dual approach to explicitly solve the agent's problem analytically and subsequently we use this solution to solve the principal's problem numerically. The interaction between the principal's and the agent's risk aversion and the optimal compensation scheme is studied and, for example, in the case of the more risk averse agent according to common folklore the principal should optimally choose a fee schedule such that the agent's derived risk aversion decreases. We illustrate that this is not always the case.

Suggested Citation

  • Kasper Larsen, 2005. "Optimal portfolio delegation when parties have different coefficients of risk aversion," Quantitative Finance, Taylor & Francis Journals, vol. 5(5), pages 503-512.
    • Handle: RePEc:taf:quantf:v:5:y:2005:i:5:p:503-512
    DOI: 10.1080/14697680500305204
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    References listed on IDEAS

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    1. Jennifer N. Carpenter, 2000. "Does Option Compensation Increase Managerial Risk Appetite?," Journal of Finance, American Finance Association, vol. 55(5), pages 2311-2331, October.
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    Cited by:

    1. Basak, Suleyman & Makarov, Dmitry & Shapiro, Alex & Subrahmanyam, Marti, 2020. "Security design with status concerns," Journal of Economic Dynamics and Control, Elsevier, vol. 118(C).
    2. Felix Fie{ss}inger & Mitja Stadje, 2024. "Mean-Variance Optimization for Participating Life Insurance Contracts," Papers 2407.11761, arXiv.org, revised Dec 2024.
    3. Escobar-Anel, M. & Havrylenko, Y. & Zagst, R., 2020. "Optimal fees in hedge funds with first-loss compensation," Journal of Banking & Finance, Elsevier, vol. 118(C).
    4. Thai Nguyen & Mitja Stadje, 2018. "Optimal investment for participating insurance contracts under VaR-Regulation," Papers 1805.09068, arXiv.org, revised Jul 2019.
    5. Cadenillas, Abel & Cvitanic, Jaksa & Zapatero, Fernando, 2007. "Optimal risk-sharing with effort and project choice," Journal of Economic Theory, Elsevier, vol. 133(1), pages 403-440, March.
    6. Maxim Bichuch & Stephan Sturm, 2014. "Portfolio optimization under convex incentive schemes," Finance and Stochastics, Springer, vol. 18(4), pages 873-915, October.
    7. Chen, An & Hieber, Peter & Nguyen, Thai, 2019. "Constrained non-concave utility maximization: An application to life insurance contracts with guarantees," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1119-1135.
    8. Cuoco, Domenico & Kaniel, Ron, 2011. "Equilibrium prices in the presence of delegated portfolio management," Journal of Financial Economics, Elsevier, vol. 101(2), pages 264-296, August.
    9. Alain Bensoussan & Abel Cadenillas & Hyeng Keun Koo, 2015. "Entrepreneurial Decisions on Effort and Project with a Nonconcave Objective Function," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 902-914, October.
    10. Guasoni, Paolo & Muhle-Karbe, Johannes & Xing, Hao, 2017. "Robust portfolios and weak incentives in long-run investments," LSE Research Online Documents on Economics 60577, London School of Economics and Political Science, LSE Library.
    11. Sotes-Paladino, Juan & Zapatero, Fernando, 2022. "Carrot and stick: A role for benchmark-adjusted compensation in active fund management," Journal of Financial Intermediation, Elsevier, vol. 52(C).
    12. Maxim Bichuch & Stephan Sturm, 2011. "Portfolio Optimization under Convex Incentive Schemes," Papers 1109.2945, arXiv.org, revised Oct 2013.
    13. Anne MacKay & Adriana Ocejo, 2022. "Portfolio Optimization With a Guaranteed Minimum Maturity Benefit and Risk-Adjusted Fees," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1021-1049, June.
    14. Christian Dehm & Thai Nguyen & Mitja Stadje, 2020. "Non-concave expected utility optimization with uncertain time horizon," Papers 2005.13831, arXiv.org, revised Oct 2021.

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