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Aggregation, Efficiency and Mutual Fund Separation in Incomplete Markets

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  • Jérôme B. Detemple

    ()

  • Piero Gottardi

Abstract

This paper studies the conditions for aggregation, portfolio separation and effective completeness of competitive allocations in general equilibrium models with incomplete markets in which 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. Cet article étudie les conditions requises pour l'aggrégation, la séparation de portefeuille et la complétude effective des allocations compétitives dans les modèles d'équilibre général avec marchés incomplets où les agents ont des préférences et des distributions de dotations initiales générales. Nous montrons que ces propriétés sont distinctes. Les demandes peuvent agréger sans pour autant satisfaire la propriété de séparation de portefeuille et inversement. La séparation de portefeuille implique la complétude effective, tandis que l'agrégation ne l'implique pas. Les conséquences de ces propriétés pour la structure des équilibres sont discutées, et des généralisations du CAPM, du CAPM de consommation et du CAPM avec richesse non négociée émergent de l'analyse.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 97s-11.

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Date of creation: 01 Mar 1997
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Handle: RePEc:cir:cirwor:97s-11

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Keywords: Aggregation; Efficiency; Mutual Fund Separation; Incomplete Markets; General Preferences; Nontraded Endowments; Agrégation; efficience; séparation de portefeuille; marchés incomplets; préférences générales; dotations non-marchandées;

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References

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  1. Michael Jerison, 1997. "Nonrepresentative Representative Consumers," Discussion Papers 97-01, University at Albany, SUNY, Department of Economics.
  2. Bottazzi, Jean-Marc & Hens, Thorsten, 1996. "Excess Demand Functions and Incomplete Markets," Journal of Economic Theory, Elsevier, vol. 68(1), pages 49-63, January.
  3. 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.
  4. Mossin, Jan, 1969. "Security Pricing and Investment Criteria in Competitive Markets," American Economic Review, American Economic Association, vol. 59(5), pages 749-56, December.
  5. Rubinstein, Mark, 1974. "An aggregation theorem for securities markets," Journal of Financial Economics, Elsevier, vol. 1(3), pages 225-244, September.
  6. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
  7. 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.
  8. 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.
  9. Mantel, Rolf R., 1976. "Homothetic preferences and community excess demand functions," Journal of Economic Theory, Elsevier, vol. 12(2), pages 197-201, April.
  10. 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.
  11. Chipman, John S., 1974. "Homothetic preferences and aggregation," Journal of Economic Theory, Elsevier, vol. 8(1), pages 26-38, May.
  12. 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.
  13. 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.
  14. 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.
  15. Lewbel, Arthur, 1989. "A Demand System Rank Theorem," Econometrica, Econometric Society, vol. 57(3), pages 701-05, May.
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Cited by:
  1. Hens, Thorsten, 2001. "An extension of Mantel (1976) to incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 36(2), pages 141-149, November.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  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. 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.
  8. 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.

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