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Equilibria in the CAPM with non-tradeable endowments

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  • Koch-Medina, Pablo
  • Wenzelburger, Jan

Abstract

This paper establishes existence and uniqueness of equilibria in the capital asset pricing model (CAPM) in a setting with incomplete markets in which part of the endowments are non-tradeable. It is shown that in equilibrium, agents are willing to assume aggregate hedgeable risk of the market but will no longer hold fractions of the market portfolio. The paper studies the effects of non-traded endowments on equilibrium asset prices and allocations and establishes a linear pricing formula, a security market line, and conditions for the positivity of asset prices.

Suggested Citation

  • Koch-Medina, Pablo & Wenzelburger, Jan, 2018. "Equilibria in the CAPM with non-tradeable endowments," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 93-107.
    • Handle: RePEc:eee:mateco:v:75:y:2018:i:c:p:93-107
    DOI: 10.1016/j.jmateco.2017.12.004
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    References listed on IDEAS

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    1. Mayers, David, 1976. "Nonmarketable Assets, Market Segmentation, and the Level of Asset Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 11(1), pages 1-12, March.
    2. Nielsen, Lars Tyge, 1988. "Uniqueness of Equilibrium in the Classical Capital Asset Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(3), pages 329-336, September.
    3. Nielsen, Lars Tyge, 1990. "Existence of equilibrium in CAPM," Journal of Economic Theory, Elsevier, vol. 52(1), pages 223-231, October.
    4. Dana, Rose Anne, 1993. "Existence and Uniqueness of Equilibria When Preferences Are Additively Separable," Econometrica, Econometric Society, vol. 61(4), pages 953-957, July.
    5. Nielsen, Lars Tyge, 1992. "Positive Prices in CAPM," Journal of Finance, American Finance Association, vol. 47(2), pages 791-808, June.
    6. LeRoy,Stephen F. & Werner,Jan, 2014. "Principles of Financial Economics," Cambridge Books, Cambridge University Press, number 9781107024120, September.
    7. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    8. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, September.
    9. Nielsen, Lars Tyge, 1987. "Portfolio Selection in the Mean-Variance Model: A Note," Journal of Finance, American Finance Association, vol. 42(5), pages 1371-1376, December.
    10. Alberto Cambini & Laura Martein, 2009. "Generalized Convexity and Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-70876-6, October.
    11. Gyutaeg Oh, 1996. "Some Results in the CAPM with Nontraded Endowments," Management Science, INFORMS, vol. 42(2), pages 286-293, February.
    12. Jan Wenzelburger, 2010. "The two-fund separation theorem revisited," Annals of Finance, Springer, vol. 6(2), pages 221-239, March.
    13. Hens, Thorsten & Laitenberger, Jorg & Loffler, Andreas, 2002. "Two remarks on the uniqueness of equilibria in the CAPM," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 123-132, April.
    14. Levy, Moshe, 2007. "Conditions for a CAPM equilibrium with positive prices," Journal of Economic Theory, Elsevier, vol. 137(1), pages 404-415, November.
    15. 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.
    16. Dana, Rose-Anne, 1999. "Existence, uniqueness and determinacy of equilibrium in C.A.P.M. with a riskless asset," Journal of Mathematical Economics, Elsevier, vol. 32(2), pages 167-175, October.
    17. Lars Tyge Nielsen, 1990. "Equilibrium in CAPM Without a Riskless Asset," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(2), pages 315-324.
    18. repec:dau:papers:123456789/6112 is not listed on IDEAS
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    Cited by:

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