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Abstract

In this article, we show how to analyse analytically the equilibrium policies and prices in an economy with a stochastic investment opportunity set and incomplete financial markets, when agents have power utility over both intermediate consumption and terminal wealth, and face portfolio constraints. The exact local comparative statistics and approximate but analytical expression for the portfolio policy and asset prices are obtained by developing a method based on perturbation analysis to expand around the solution for an investor with log utility. We then use this method to study a general equilibrium exchange economy with multiple agents who differ in their degree of risk aversion and face borrowing constraints. We characterize explicitly the consumption and portfolio policies and also the properties of asset returns. We find that the volatility of stock returns increases with the cross-sectional dispersion of risk aversion, with the cross-sectional dispersion in portfolio holdings, and with the relaxation of the constraint on borrowing. Moreover, tightening the borrowing constraint lowers the risk-free interest rate and raises the equity premium in equilibrium.

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Paper provided by Wharton School Rodney L. White Center for Financial Research in its series Rodney L. White Center for Financial Research Working Papers with number 13-00.

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Handle: RePEc:fth:pennfi:13-00

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Find related papers by JEL classification:

• D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
• G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
• G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

This paper has been announced in the following NEP Reports:

• NEP-ALL-2000-10-23 (All new papers)
• NEP-DGE-2000-10-23 (Dynamic General Equilibrium)
• NEP-FIN-2000-10-23 (Finance)
• NEP-FMK-2000-10-23 (Financial Markets)
• NEP-IAS-2000-10-23 (Insurance Economics)

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Cited by:

1. Gromb, Denis & Vayanos, Dimitri, 2001. "Equilibrium and Welfare in Markets with Financially Constrained Arbitrageurs," CEPR Discussion Papers 3049, C.E.P.R. Discussion Papers.
   
   • Gromb, Denis & Vayanos, Dimitri, 2002. "Equilibrium and welfare in markets with financially constrained arbitrageurs," Journal of Financial Economics, Elsevier, vol. 66(2-3), pages 361-407.
2. Weinbaum, David, 2010. "Preference heterogeneity and asset prices: An exact solution," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2238-2246, September.
3. Sanjiv Ranjan Das & Raman Uppal, 2004. "Systemic Risk and International Portfolio Choice," Journal of Finance, American Finance Association, vol. 59(6), pages 2809-2834, December.
   
   • Das, Sanjiv Ranjan & Uppal, Raman, 2002. "Systemic Risk and International Portfolio Choice," CEPR Discussion Papers 3305, C.E.P.R. Discussion Papers.
4. Farhi, Emmanuel & Panageas, Stavros, 2007. "Saving and investing for early retirement: A theoretical analysis," Journal of Financial Economics, Elsevier, vol. 83(1), pages 87-121, January.
5. Judd, Kenneth L. & Leisen, Dietmar P.J., 2010. "Equilibrium open interest," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2578-2600, December.
6. Antonio Mele, 2004. "General Properties of Rational Stock-Market Fluctuations," Econometric Society 2004 North American Summer Meetings 223, Econometric Society.
   
   • Antonio Mele, 2004. "General Properties of Rational Stock-Market Fluctuations," FMG Discussion Papers dp489, Financial Markets Group.
   • Mele, Antonio, 2004. "General Properties of Rational Stock-Market Fluctuations," Economics Series 153, Institute for Advanced Studies.
7. Leippold, Markus & Trojani, Fabio & Vanini, Paolo, 2006. "Equilibrium impact of value-at-risk regulation," Journal of Economic Dynamics and Control, Elsevier, vol. 30(8), pages 1277-1313, August.
8. Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan Storud, 2004. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," NBER Working Papers 10934, National Bureau of Economic Research, Inc.
   
   • Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan R. Stroud, 2005. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 831-873.
9. Paolo Porchia & Pedro Gete, 2011. "Fertility and Consumption when Having a Child is a Risky Investment," 2011 Meeting Papers 563, Society for Economic Dynamics.
10. Martin D. D. Evans (Georgetown University) and Viktoria Hnatkovska (Georgetown University), 2005. "Solving General Equilibrium Models with Incomplete Markets and Many Assets," Working Papers gueconwpa~05-05-18, Georgetown University, Department of Economics.
    
    • Martin D. D. Evans & Viktoria Hnatkovska, 2005. "Solving General Equilibrium Models with Incomplete Markets and Many Assets," NBER Technical Working Papers 0318, National Bureau of Economic Research, Inc.
11. Christian Gollier, 2005. "Optimal Portfolio Management for Individual Pension Plans," CESifo Working Paper Series 1394, CESifo Group Munich.
    
    • Gollier, Christian, 2005. "Optimal Portfolio Management for Individual Pension Plans," IDEI Working Papers 298, Institut d'Économie Industrielle (IDEI), Toulouse.
12. Gollier, Christian, 2007. "Understanding Saving and Portfolio Choices with Predictable Changes in Assets Returns," IDEI Working Papers 430, Institut d'Économie Industrielle (IDEI), Toulouse.
    
    • Gollier, Christian, 2008. "Understanding saving and portfolio choices with predictable changes in assets returns," Journal of Mathematical Economics, Elsevier, vol. 44(5-6), pages 445-458, April.

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