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Risk Aversion and Optimal Portfolio Policies in Partial and General Equilibrium Economies

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  • Leonid Kogan
  • Raman Uppal

Abstract

In this article, we show how to analyze 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 statics 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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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 8609.

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Date of creation: Nov 2001
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Handle: RePEc:nbr:nberwo:8609

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Cited by:
  1. 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. Antonio Mele, 2004. "General Properties of Rational Stock-Market Fluctuations," FMG Discussion Papers dp489, Financial Markets Group.
  3. 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.
  4. Gollier, Christian, 2005. "Optimal Portfolio Management for Individual Pension Plans," IDEI Working Papers 298, Institut d'Économie Industrielle (IDEI), Toulouse.
  5. Gollier, Christian, 2007. "Understanding Saving and Portfolio Choices with Predictable Changes in Assets Returns," IDEI Working Papers 430, Institut d'Économie Industrielle (IDEI), Toulouse.
  6. 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.
  7. Paolo Porchia & Pedro Gete, 2011. "Fertility and Consumption when Having a Child is a Risky Investment," 2011 Meeting Papers 563, Society for Economic Dynamics.
  8. Das, Sanjiv Ranjan & Uppal, Raman, 2002. "Systemic Risk and International Portfolio Choice," CEPR Discussion Papers 3305, C.E.P.R. Discussion Papers.
  9. 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.
  10. Sbuelz, A. & Trojani, F., 2002. "Equilibrium Asset Pricing with Time-Varying Pessimism," Discussion Paper 2002-102, Tilburg University, Center for Economic Research.
  11. Weinbaum, David, 2010. "Preference heterogeneity and asset prices: An exact solution," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2238-2246, September.
  12. 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.
  13. 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.

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