A Note on the Two-fund Separation Theorem
This note contains two remarks on the traditional capital asset pricing model (CAPM) with one risk-free asset. Firstly, an elementary proof of the two-fund separation theorem is provided showing that asset-demand may become undefined if the limiting slope of the investor's indifference curves is finite. Secondly, it is shown that an additional limiting condition on the risk aversion is generally necessary to guarantee existence of an equilibrium in the CAPM with one risk-free asset. The role of these two limiting conditions seems to have been overlooked in the established literature. A generalized existence result is formulated which allows for the case in which in equilibrium not all investors participate in the market for risky assets.
|Date of creation:||08 Feb 2008|
|Date of revision:||31 Sep 2008|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- J. Tobin, 1958.
"Liquidity Preference as Behavior Towards Risk,"
Review of Economic Studies,
Oxford University Press, vol. 25(2), pages 65-86.
- Nielsen, Lars Tyge, 1990. "Existence of equilibrium in CAPM," Journal of Economic Theory, Elsevier, vol. 52(1), pages 223-231, October.
- Bohm, Volker & Wenzelburger, Jan, 2005.
"On the performance of efficient portfolios,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 29(4), pages 721-740, April.
- Dana, Rose Anne, 1993. "Existence and Uniqueness of Equilibria When Preferences Are Additively Separable," Econometrica, Econometric Society, vol. 61(4), pages 953-57, July.
- Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(04), pages 1851-1872, September.
- Lars Tyge Nielsen, 1990. "Equilibrium in CAPM Without a Riskless Asset," Review of Economic Studies, Oxford University Press, vol. 57(2), pages 315-324.
- Lars Tyge Nielsen & Fatma Lajeri, 2000.
"Parametric characterizations of risk aversion and prudence,"
Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 469-476.
- Lajeri, Fatma & Nielsen, Lars Tyge, 1997. "Parametric Characterizations of Risk Aversion and Prudence," CEPR Discussion Papers 1650, C.E.P.R. Discussion Papers.
- Volker Böhm & Nicole Deutscher & Jan Wenzelburger, 2000. "Endogenous Random Asset Prices in Overlapping Generations Economies," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 23-38.
- Volker Böhm & Carl Chiarella, 2005.
"Mean Variance Preferences, Expectations Formation, And The Dynamics Of Random Asset Prices,"
Wiley Blackwell, vol. 15(1), pages 61-97.
- Volker Bohm & Carl Chiarella, 2000. "Mean Variance Preferences, Expectations Formation, and the Dynamics of Random Asset Prices," Research Paper Series 46, Quantitative Finance Research Centre, University of Technology, Sydney.
- repec:dau:papers:123456789/6112 is not listed on IDEAS
- 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.
- Ulrich Horst & Jan Wenzelburger, 2008. "On non-ergodic asset prices," Economic Theory, Society for the Advancement of Economic Theory (SAET), vol. 34(2), pages 207-234, February.
- 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.
- 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(03), pages 329-336, September.
- Nielsen, Lars Tyge, 1987. " Portfolio Selection in the Mean-Variance Model: A Note," Journal of Finance, American Finance Association, vol. 42(5), pages 1371-76, December.
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:11014. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter)
If references are entirely missing, you can add them using this form.