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Aggregation, efficiency and mutual fund separation in incomplete markets

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  • JÊrÆme B. Detemple

    (Faculty of Management, McGill University, 1001 Sherbrooke Street West, Montreal, H3A 1G5 and CIRANO, Montreal, H3A 2A5, CANADA)

  • Piero Gottardi

    (Dipartimento di Scienze Economiche, UniversitÁ CÁ Foscari di Venezia, I-30123 Venezia, ITALY)

Abstract

This paper studies the conditions for aggregation, portfolio separation and effective completeness of competitive allocations in general equilibrium models with incomplete markets where agents have general preference and endowment distributions. We show that these properties are distinct. Demands may aggregate yet may fail to exhibit fund separation and conversely. Fund separation implies effective completeness while aggregation does not. The implications of these properties for the structure of equilibria are discussed, and generalizations of the CAPM, the consumption CAPM and the CAPM with nonmarketed wealth emerge from the analysis.

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 11 (1998)
Issue (Month): 2 ()
Pages: 443-455

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Handle: RePEc:spr:joecth:v:11:y:1998:i:2:p:443-455

Note: Received: September 12, 1996; revised version: November 7, 1996
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  1. Bottazzi, Jean-Marc & Hens, Thorsten, 1996. "Excess Demand Functions and Incomplete Markets," Journal of Economic Theory, Elsevier, vol. 68(1), pages 49-63, January.
  2. Rubinstein, Mark, 1974. "An aggregation theorem for securities markets," Journal of Financial Economics, Elsevier, vol. 1(3), pages 225-244, September.
  3. Lewbel, A. & Perraudin, W.R.M., 1992. "Mutual Fund Separation with General Preferences," Cambridge Working Papers in Economics 9212, Faculty of Economics, University of Cambridge.
  4. Michael Jerison, 2006. "Nonrepresentative Representative Consumers," Discussion Papers 06-08, University at Albany, SUNY, Department of Economics.
  5. Ross, Stephen A., 1978. "Mutual fund separation in financial theory--The separating distributions," Journal of Economic Theory, Elsevier, vol. 17(2), pages 254-286, April.
  6. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
  7. Thorsten Hens & Piero Gottardi, 1999. "Disaggregation of excess demand and comparative statics with incomplete markets and nominal assets," Economic Theory, Springer, vol. 13(2), pages 287-308.
  8. Cass, David & Stiglitz, Joseph E., 1970. "The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds," Journal of Economic Theory, Elsevier, vol. 2(2), pages 122-160, June.
  9. Mossin, Jan, 1969. "Security Pricing and Investment Criteria in Competitive Markets," American Economic Review, American Economic Association, vol. 59(5), pages 749-56, December.
  10. Mantel, Rolf R., 1976. "Homothetic preferences and community excess demand functions," Journal of Economic Theory, Elsevier, vol. 12(2), pages 197-201, April.
  11. Milne, Frank, 1979. "Consumer Preferences, Linear Demand Functions and Aggregation in Competitive Asset Markets," Review of Economic Studies, Wiley Blackwell, vol. 46(3), pages 407-17, July.
  12. Chipman, John S., 1974. "Homothetic preferences and aggregation," Journal of Economic Theory, Elsevier, vol. 8(1), pages 26-38, May.
  13. Lewbel, Arthur, 1989. "A Demand System Rank Theorem," Econometrica, Econometric Society, vol. 57(3), pages 701-05, May.
  14. Breeden, Douglas T., 1979. "An intertemporal asset pricing model with stochastic consumption and investment opportunities," Journal of Financial Economics, Elsevier, vol. 7(3), pages 265-296, September.
  15. Brennan, M. J. & Kraus, A., 1976. "The Geometry of Separation and Myopia," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 11(02), pages 171-193, June.
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Cited by:
  1. Chenghu Ma & Jiankang Zhang, 2013. "p-Weakly constrained Pareto efficiency and aggregation in incomplete markets," Social Choice and Welfare, Springer, vol. 41(3), pages 605-623, September.
  2. Hens, Thorsten, 2001. "An extension of Mantel (1976) to incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 36(2), pages 141-149, November.
  3. Herings, P.J.J. & Kubler, F., 1999. "The Robustness of the CAPM - A Computational Approach," Discussion Paper 1999-54, Tilburg University, Center for Economic Research.
  4. Anil K Kashyap & Dimitrios P. Tsomocos & Alexandros P. Vardoulakis, 2014. "How does macroprudential regulation change bank credit supply?," NBER Working Papers 20165, National Bureau of Economic Research, Inc.
  5. Gerber, Anke & Hens, Thorsten & Woehrmann, Peter, 2005. "Dynamic General Equilibrium and T-Period Fund Separation," Discussion Papers 2005/16, Department of Business and Management Science, Norwegian School of Economics.
  6. Shen, Yang & Siu, Tak Kuen, 2013. "Stochastic differential game, Esscher transform and general equilibrium under a Markovian regime-switching Lévy model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 757-768.
  7. Hens, Thorsten & Reimann, Stefan & Vogt, Bodo, 2004. "Nash competitive equilibria and two-period fund separation," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 321-346, June.
  8. Pilgrim, Beate, 2002. "Non-equivalence of uniqueness of equilibria in complete and in incomplete market models," Research in Economics, Elsevier, vol. 56(2), pages 143-156, June.

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