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Aggregation, efficiency and mutual fund separation in incomplete markets

Author

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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.

Suggested Citation

  • JÊrÆme B. Detemple & Piero Gottardi, 1998. "Aggregation, efficiency and mutual fund separation in incomplete markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(2), pages 443-455.
    • 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. Lewbel, Arthur, 1989. "A Demand System Rank Theorem," Econometrica, Econometric Society, vol. 57(3), pages 701-705, May.
    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. Stephen A. Ross, 2005. "Mutual Fund Separation in Financial Theory—The Separating Distributions," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 10, pages 309-356, World Scientific Publishing Co. Pte. Ltd..
    4. 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.
    5. Geanakoplos, J. & Polemarchakis, H., 1985. "Existence,regularity, and constrained suboptimality of competitive allocations when the asset market is incomplete," LIDAM Discussion Papers CORE 1985037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. 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.
    7. Chipman, John S., 1974. "Homothetic preferences and aggregation," Journal of Economic Theory, Elsevier, vol. 8(1), pages 26-38, May.
    8. Mossin, Jan, 1969. "Security Pricing and Investment Criteria in Competitive Markets," American Economic Review, American Economic Association, vol. 59(5), pages 749-756, December.
    9. Michael Jerison, 1997. "Nonrepresentative Representative Consumers," Discussion Papers 97-01, University at Albany, SUNY, Department of Economics.
    10. Frank Milne, 1979. "Consumer Preferences, Linear Demand Functions and Aggregation in Competitive Asset Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(3), pages 407-417.
    11. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    12. Brennan, M. J. & Kraus, A., 1976. "The Geometry of Separation and Myopia," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 11(2), pages 171-193, June.
    13. Mantel, Rolf R., 1976. "Homothetic preferences and community excess demand functions," Journal of Economic Theory, Elsevier, vol. 12(2), pages 197-201, April.
    14. Thorsten Hens & Piero Gottardi, 1999. "Disaggregation of excess demand and comparative statics with incomplete markets and nominal assets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(2), pages 287-308.
    15. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    16. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
    17. Rubinstein, Mark, 1974. "An aggregation theorem for securities markets," Journal of Financial Economics, Elsevier, vol. 1(3), pages 225-244, September.
    18. 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.
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    2. 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.
    3. 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.
    4. 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.
    5. Hens, Thorsten, 2001. "An extension of Mantel (1976) to incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 36(2), pages 141-149, November.
    6. Chenghu Ma & Jiankang Zhang, 2013. "p-Weakly constrained Pareto efficiency and aggregation in incomplete markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 605-623, September.
    7. 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.
    8. Won, Dong Chul, 2018. "One-fund separation in incomplete markets with two assets," Finance Research Letters, Elsevier, vol. 24(C), pages 168-174.
    9. Gerber, Anke & Hens, Thorsten & Woehrmann, Peter, 2005. "Dynamic General Equilibrium and T-Period Fund Separation," Discussion Papers 2005/16, Norwegian School of Economics, Department of Business and Management Science.

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    More about this item

    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; Trading Volume; Bond Interest Rates

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