The Dynamics of Optimal Risk Sharing
AbstractWe study a dynamic-contracting problem involving risk sharing between two parties — the Proposer and the Responder — who invest in a risky asset until an exogenous but random termination time. In any time period they must invest all their wealth in the risky asset, but they can share the underlying investment and termination risk. When the project ends they consume their final accumulated wealth. The Proposer and the Responder have constant relative risk aversion R and r respectively, with R>r>0. We show that the optimal contract has three components: a non-contingent flow payment, a share in investment risk and a termination payment. We derive approximations for the optimal share in investment risk and the optimal termination payment, and we use numerical simulations to show that these approximations offer a close fit to the exact rules. The approximations take the form of a myopic benchmark plus a dynamic correction. In the case of the approximation for the optimal share in investment risk, the myopic benchmark is simply the classical formula for optimal risk sharing. This benchmark is endogenous because it depends on the wealths of the two parties. The dynamic correction is driven by counterparty risk. If both parties are fairly risk tolerant, in the sense that 2>R>r, then the Proposer takes on more risk than she would under the myopic benchmark. If both parties are fairly risk averse, in the sense that R>r>2, then the Proposer takes on less risk than she would under the myopic benchmark. In the mixed case, in which R>2>r, the Proposer takes on more risk when the Responder's share in total wealth is low and less risk when the Responder's share in total wealth is high. In the case of the approximation for the optimal termination payment, the myopic benchmark is zero. The dynamic correction tells us, among other things, that: (i) if the asset has a high return then, following termination, the Responder compensates the Proposer for the loss of a valuable investment opportunity; and (ii) if the asset has a low return then, prior to termination, the Responder compensates the Proposer for the low returns obtained. Finally, we exploit our representation of the optimal contract to derive simple and easily interpretable sufficient conditions for the existence of an optimal contract.
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Date of creation: Jun 2010
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Other versions of this item:
- D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
- G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-06-26 (All new papers)
- NEP-BAN-2010-06-26 (Banking)
- NEP-DGE-2010-06-26 (Dynamic General Equilibrium)
- NEP-PPM-2010-06-26 (Project, Program & Portfolio Management)
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- Pierre‐André Chiappori & Monica Paiella, 2011.
"Relative Risk Aversion Is Constant: Evidence From Panel Data,"
Journal of the European Economic Association,
European Economic Association, vol. 9(6), pages 1021-1052, December.
- Pierre-André Chiappori & Monica Paiella, 2008. "Relative Risk Aversion Is Constant: Evidence from Panel Data," Discussion Papers 5_2008, D.E.S. (Department of Economic Studies), University of Naples "Parthenope", Italy.
- Monica Paiella & Luigi Guiso, 2004.
"Risk Aversion, Wealth and Background Risk,"
2004 Meeting Papers
525, Society for Economic Dynamics.
- Guiso, Luigi & Paiella, Monica, 2001. "Risk Aversion, Wealth and Background Risk," CEPR Discussion Papers 2728, C.E.P.R. Discussion Papers.
- Luigi Guiso & Monica Paiella, 2007. "Risk Aversion, Wealth, and Background Risk," Economics Working Papers ECO2007/47, European University Institute.
- Luigi Guiso & Monica Paiella, 2003. "Risk Aversion, Wealth and Background Risk," Temi di discussione (Economic working papers) 483, Bank of Italy, Economic Research and International Relations Area.
- Dumas, Bernard, 1989. "Two-Person Dynamic Equilibrium in the Capital Market," Review of Financial Studies, Society for Financial Studies, vol. 2(2), pages 157-88.
- Daniel Paravisini & Veronica Rappoport & Enrichetta Ravina, 2010. "Risk Aversion and Wealth: Evidence from Person-to-Person Lending Portfolios," NBER Working Papers 16063, National Bureau of Economic Research, Inc.
- Cvitanic Jaksa & Wan Xuhu & Zhang Jianfeng, 2008. "Principal-Agent Problems with Exit Options," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-43, October.
- Barsky, Robert B, et al, 1997. "Preference Parameters and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement Study," The Quarterly Journal of Economics, MIT Press, vol. 112(2), pages 537-79, May.
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