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.
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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
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- Nielsen, Lars Tyge, 1989. "Asset Market Equilibrium with Short-Selling," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 56(3), pages 467-73, July.
- Duffie, Darrell, 1987. "Stochastic equilibria with incomplete financial markets," Journal of Economic Theory, Elsevier, Elsevier, vol. 41(2), pages 405-416, April.
- Werner, Jan, 1985. "Equilibrium in economies with incomplete financial markets," Journal of Economic Theory, Elsevier, 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, University of Chicago Press, vol. 45(3), pages 444-55, July.
- Duffie, Darrell & Shafer, Wayne, 1985. "Equilibrium in incomplete markets: I : A basic model of generic existence," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 14(3), pages 285-300, June.
- Williams, Joseph T., 1977. "Capital asset prices with heterogeneous beliefs," Journal of Financial Economics, Elsevier, Elsevier, vol. 5(2), pages 219-239, November.
- 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, American Finance Association, vol. 38(3), pages 745-52, June.
- Berk, Jonathan B., 1997. "Necessary Conditions for the CAPM," Journal of Economic Theory, Elsevier, Elsevier, vol. 73(1), pages 245-257, March.
- Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, Elsevier, vol. 9(3), pages 293-311, November.
- Hiroshi Konno & Hiroshi Shirakawa, 1995. "Existence Of A Nonnegative Equilibrium Price Vector In The Mean-Variance Capital Market," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 5(3), pages 233-246.
- Gonedes, Nicholas J, 1976. "Capital Market Equilibrium for a Class of Heterogeneous Expectations in a Two-Parameter World," Journal of Finance, American Finance Association, American Finance Association, vol. 31(1), pages 1-15, March.
- Nielsen, Lars Tyge, 1990. "Existence of equilibrium in CAPM," Journal of Economic Theory, Elsevier, Elsevier, vol. 52(1), pages 223-231, October.
- Nielsen, Lars Tyge, 1990. "Equilibrium in CAPM without a Riskless Asset," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 57(2), pages 315-24, April.
- Allingham, Michael, 1991. "Existence Theorems in the Capital Asset Pricing Model," Econometrica, Econometric Society, Econometric Society, vol. 59(4), pages 1169-74, July.
- repec:wyi:wpaper:001969 is not listed on IDEAS
- Lei Shi, 2010. "Analysis and Equilibrium Asset Pricing with Heterogeneous Beliefs," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, 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, Springer, vol. 4(2), pages 183-195, March.
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