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doi: 10.3934/jimo.2022083
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Optimal contracts and asset prices in a continuous-time delegated portfolio management problem

1. 

School of Economics, Xihua University, 611139, Chengdu, China

2. 

School of Economic Mathematics, Southwestern University of Finance and Economics, 611130, Chengdu, China

*Corresponding author: Zheng Dou

Received  October 2019 Revised  January 2022 Early access May 2022

We study optimal contracts and asset prices in a financial market in which an investor delegates a portfolio manager to manage her wealth. The agency frictions are caused by the manager's "shirking" action and hidden effort. The shirking action converts part of the return of the managed portfolio into the manager's income without reducing his utility. The manager's effort improves the return of the portfolio but reduces the manager's utility. We illustrate this dynamic principal-agent problem under hidden effort and observable effort, respectively. When the effort is hidden, to alleviate the impact of moral hazard, the investor pays more for the manager's performance and always keeps the optimal contract related to the returns of the manager's portfolio and market portfolio, and their quadratic (co)variations. When the manager's effort is observable, the optimal contract is related to the return of the market portfolio if the agency friction caused by the shirking action is serious, but is only related to the return of the manager's portfolio if shirking is not serious. Analysing the expected utility of the manager, we find that he has a disposition to hide information about effort to pursue a higher expected utility.

Citation: Zheng Dou, Shaoyong Lai. Optimal contracts and asset prices in a continuous-time delegated portfolio management problem. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022083
References:
[1]

S. Basak and A. Pavlova, Asset prices and institutional investors, American Economic Review, 103 (2013), 1728-1758. 

[2]

M. Brennan, Agency and asset pricing, working paper, 2008. Avialiable from: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1104546. doi: 10.2139/ssrn.1104546.

[3]

A. Buffa, D. Vayanos and P. Wooley, Asset management contracts and equilibrium prices, Working paper, 2019. Available from: https://www.nber.org/system/files/working_papers/w20480/w20480.pdf. doi: 10.3386/w20480.

[4]

A. CadenillasJ. Cvitanić and F. Zapatero, Optimal risk-sharing with effort and project choice, Journal of Economic Theory, 133 (2007), 403-440.  doi: 10.1016/j.jet.2005.12.007.

[5]

K. ChenX. WangM. Huang and W. Ching, Compensation plan, pricing and production decisions with inventory-dependent salvage value, and asymmetric risk-averse sales agent, Journal of Industrial and Management Optimization, 14 (2018), 873-899.  doi: 10.3934/jimo.2018013.

[6]

D. Cuoco and R. Kaniel, Equilibrium prices in the presence of delegated portfolio management, Journal of Financial Economics, 101 (2011), 264-296.  doi: 10.1016/j.jfineco.2011.02.012.

[7]

J. Cvitanić and H. Xing, Asset pricing under optimal contracts, Journal of Economic Theory, 173 (2018), 142-180.  doi: 10.1016/j.jet.2017.10.005.

[8]

J. CvitanićD. Possamaï and N. Touzi, Dynamic programming approach to principal-agent problems, Finance and Stochastics, 22 (2018), 1-37.  doi: 10.1007/s00780-017-0344-4.

[9]

A. CapponiJ. Cvitanić and T. Yolcu, Optimal contracting with effort and misvaluation, Mathematics and Financial Economics, 7 (2013), 93-128.  doi: 10.1007/s11579-012-0088-z.

[10]

G. Carroll and D. Meng, Locally robust contracts for moral hazard, Journal of Mathematical Economics, 62 (2016), 36-51.  doi: 10.1016/j.jmateco.2015.11.001.

[11]

M. Fagart and C. Fluet, The first-order approach when the cost of effort is money, Journal of Mathematical Economics, 49 (2013), 7-16.  doi: 10.1016/j.jmateco.2012.09.002.

[12]

B. Holmstrom and P. Milgrom, Aggregation and linearity in the provision of intertemporal incentives, Econometrica, 55 (1987), 303-328.  doi: 10.2307/1913238.

[13]

R. C. Leung, Dynamic contracts and the Sharpe ratio: Theory and evidence, Working paper, 2017.

[14]

A. Lioui and P. Poncet, Optimal benchmarking for active portfolio managers, European Journal of Operational Research, 226 (2013), 268-276.  doi: 10.1016/j.ejor.2012.10.043.

[15]

H. Ou-Yang, Optimal contracts in a continuous-time delegated portfolio management problem, Review of Financial Studies, 16 (2003), 173-208.  doi: 10.1093/rfs/16.1.0173.

[16]

Y. Sannikov, A continuous-time version of the principal-agent problem, Review of Economic Studies, 75 (2008), 957-984.  doi: 10.1111/j.1467-937X.2008.00486.x.

[17]

J. Sung and X. Wan, A general equilibrium model of a multifirm moral-hazard economy with financial markets, Mathematical Finance, 25 (2015), 827-868.  doi: 10.1111/mafi.12032.

[18]

X. WangY. Lan and W. Tang, An uncertain wage contract model for risk-averse worker under bilateral moral hazard, Journal of Industrial and Management Optimization, 13 (2017), 1815-1840.  doi: 10.3934/jimo.2017020.

show all references

References:
[1]

S. Basak and A. Pavlova, Asset prices and institutional investors, American Economic Review, 103 (2013), 1728-1758. 

[2]

M. Brennan, Agency and asset pricing, working paper, 2008. Avialiable from: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1104546. doi: 10.2139/ssrn.1104546.

[3]

A. Buffa, D. Vayanos and P. Wooley, Asset management contracts and equilibrium prices, Working paper, 2019. Available from: https://www.nber.org/system/files/working_papers/w20480/w20480.pdf. doi: 10.3386/w20480.

[4]

A. CadenillasJ. Cvitanić and F. Zapatero, Optimal risk-sharing with effort and project choice, Journal of Economic Theory, 133 (2007), 403-440.  doi: 10.1016/j.jet.2005.12.007.

[5]

K. ChenX. WangM. Huang and W. Ching, Compensation plan, pricing and production decisions with inventory-dependent salvage value, and asymmetric risk-averse sales agent, Journal of Industrial and Management Optimization, 14 (2018), 873-899.  doi: 10.3934/jimo.2018013.

[6]

D. Cuoco and R. Kaniel, Equilibrium prices in the presence of delegated portfolio management, Journal of Financial Economics, 101 (2011), 264-296.  doi: 10.1016/j.jfineco.2011.02.012.

[7]

J. Cvitanić and H. Xing, Asset pricing under optimal contracts, Journal of Economic Theory, 173 (2018), 142-180.  doi: 10.1016/j.jet.2017.10.005.

[8]

J. CvitanićD. Possamaï and N. Touzi, Dynamic programming approach to principal-agent problems, Finance and Stochastics, 22 (2018), 1-37.  doi: 10.1007/s00780-017-0344-4.

[9]

A. CapponiJ. Cvitanić and T. Yolcu, Optimal contracting with effort and misvaluation, Mathematics and Financial Economics, 7 (2013), 93-128.  doi: 10.1007/s11579-012-0088-z.

[10]

G. Carroll and D. Meng, Locally robust contracts for moral hazard, Journal of Mathematical Economics, 62 (2016), 36-51.  doi: 10.1016/j.jmateco.2015.11.001.

[11]

M. Fagart and C. Fluet, The first-order approach when the cost of effort is money, Journal of Mathematical Economics, 49 (2013), 7-16.  doi: 10.1016/j.jmateco.2012.09.002.

[12]

B. Holmstrom and P. Milgrom, Aggregation and linearity in the provision of intertemporal incentives, Econometrica, 55 (1987), 303-328.  doi: 10.2307/1913238.

[13]

R. C. Leung, Dynamic contracts and the Sharpe ratio: Theory and evidence, Working paper, 2017.

[14]

A. Lioui and P. Poncet, Optimal benchmarking for active portfolio managers, European Journal of Operational Research, 226 (2013), 268-276.  doi: 10.1016/j.ejor.2012.10.043.

[15]

H. Ou-Yang, Optimal contracts in a continuous-time delegated portfolio management problem, Review of Financial Studies, 16 (2003), 173-208.  doi: 10.1093/rfs/16.1.0173.

[16]

Y. Sannikov, A continuous-time version of the principal-agent problem, Review of Economic Studies, 75 (2008), 957-984.  doi: 10.1111/j.1467-937X.2008.00486.x.

[17]

J. Sung and X. Wan, A general equilibrium model of a multifirm moral-hazard economy with financial markets, Mathematical Finance, 25 (2015), 827-868.  doi: 10.1111/mafi.12032.

[18]

X. WangY. Lan and W. Tang, An uncertain wage contract model for risk-averse worker under bilateral moral hazard, Journal of Industrial and Management Optimization, 13 (2017), 1815-1840.  doi: 10.3934/jimo.2017020.

Figure 1.  $ \bar Z $ and $ \bar Z^{obs} $
Figure 2.  Sensitivity to the return of the market portfolio $ U $ and $ U^{obs} $
Figure 3.  Expected excess returns. The excess return of stocks in large supply is in the top half of the graph, and the excess return of stocks in small supply is in the bottom half of the graph
Figure 4.  The manager's expected utility
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