Existence of Equilibrium and Zero-Beta Pricing Formula in the Capital Asset Pricing Model with Heterogeneous Beliefs
AbstractWe study a mean-variance capital asset pricing model (CAPM) in which investors have different probability beliefs about assets returns and different attitudes towards risk, all assets are risky, short-selling is allowed and satiation is possible. First, we prove that there exists a competitive equilibrium in the model under a rather general condition. This condition indicates a simple relationship among initial endowment vectors, risk aversion ratio functions, perceived mean vectors and covariance matrices of all investors. Secondly, we derive a zero-beta pricing formula for the model which generalizes the well known Black¡¯s zero-beta pricing formula. In addition, we find in closed form an equilibrium price vector expressed in terms of perceived mean vectors, covariance matrices, and initial endowments of all investors.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Society for AEF in its journal Annals of Economics and Finance.
Volume (Year): 4 (2003)
Issue (Month): 1 (May)
Capital asset pricing model; Heterogeneity; Equilibrium theorem; Pricing formula;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
- D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
- D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
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.:
- Owen, Joel & Rabinovitch, Ramon, 1983. " On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-52, June.
- Berk, Jonathan B., 1997. "Necessary Conditions for the CAPM," Journal of Economic Theory, Elsevier, vol. 73(1), pages 245-257, March.
- Duffie, Darrell, 1987. "Stochastic equilibria with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 41(2), pages 405-416, April.
- Duffie, Darrell & Shafer, Wayne, 1985. "Equilibrium in incomplete markets: I : A basic model of generic existence," Journal of Mathematical Economics, Elsevier, vol. 14(3), pages 285-300, June.
- Williams, Joseph T., 1977. "Capital asset prices with heterogeneous beliefs," Journal of Financial Economics, Elsevier, vol. 5(2), pages 219-239, November.
- Gonedes, Nicholas J, 1976. "Capital Market Equilibrium for a Class of Heterogeneous Expectations in a Two-Parameter World," Journal of Finance, American Finance Association, vol. 31(1), pages 1-15, March.
- Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, vol. 9(3), pages 293-311, November.
- Werner, Jan, 1985. "Equilibrium in economies with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 36(1), pages 110-119, June.
- Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-55, July.
- Nielsen, Lars Tyge, 1989. "Asset Market Equilibrium with Short-Selling," Review of Economic Studies, Wiley Blackwell, vol. 56(3), pages 467-73, July.
- Nielsen, Lars Tyge, 1990. "Existence of equilibrium in CAPM," Journal of Economic Theory, Elsevier, vol. 52(1), pages 223-231, October.
- Allingham, Michael, 1991. "Existence Theorems in the Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 59(4), pages 1169-74, July.
- Hiroshi Konno & Hiroshi Shirakawa, 1995. "Existence Of A Nonnegative Equilibrium Price Vector In The Mean-Variance Capital Market," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 233-246.
- Nielsen, Lars Tyge, 1990. "Equilibrium in CAPM without a Riskless Asset," Review of Economic Studies, Wiley Blackwell, vol. 57(2), pages 315-24, April.
- Lei Shi, 2010. "Analysis and Equilibrium Asset Pricing with Heterogeneous Beliefs," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 9.
- D. Won & G. Hahn & N. Yannelis, 2008. "Capital market equilibrium without riskless assets: heterogeneous expectations," Annals of Finance, Springer, vol. 4(2), pages 183-195, March.
- repec:wyi:wpaper:001969 is not listed on IDEAS
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Qiang Gao).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.