Abstract
We utilize the joint elliptical distribution to model a multi-factor return generating process and derive an equilibrium multi-beta capital asset pricing model (CAPM) in which the market portfolio and a set of nonelliptical factors are sufficient to price all financial assets. Most important, it is shown that the market portfolio, while generally nonelliptical, can proxy all elliptical factors and hence: including elliptical factors in addition to the market portfolio in the pricing equation contribute nothing to asset pricing. While the representative investor prices the exposure of aggregate wealth to various nonelliptical systematic risk factors, individual securities are priced in accordance to their contributions to different aspects of the risk of aggregate wealth. The present model collapses to the Sharpe-Lintner CAPM when either the market investor is neutral to nonelliptical risk factors or when all risk factors follow a joint spherical distribution. When residuals cancel out of the market portfolio, the present model collapses to Conner (1984) pricing model.
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References
Brown, Stephen, “The Number of Factors in Security Returns.”Journal of Finance, 44, 1247–1262 (December 1989).
Burmeister, E., and M.B. McElroy, “Joint Estimation of Factor Sensitivity and Risk Premia for the Arbitrage Pricing Theory.”Journal of Finance, 43, 721–735, (July 1988).
Burmeister, F., and M.B. McElroy, “The Residual Market Factor, the APT and Mean Variance Efficiency.” Working paper, University of Virginia, Charlottesville, 1989.
Burmeister E., and K. Wall, “The Arbitrage Pricing Theory and Macroeconomic Factor Measures.”The Financial Review, 21, (February 1986).
Chamberlain, G., “A Characteristic of the Distributions That Imply Mean-Variance Utility Functions.”Journal of Economic Theory, 29, 185–201, (Month 1983).
Chamberlain, G., and M. Rotschild, “Arbitrage Factor Structure, and Mean-Variance Analysis on Large Asset Markets.”Econometrics, 51, 1281–1304 (1983).
Chen, N.F., and J. Ingersoll, “Exact Pricing in Linear Factor Models with Finitely Many Assets: A Note.”Journal of Finance, 38, 985–988, (July 1983).
Connor, G., “Asset Pricing in Factor Economics.” Unpublished Doctoral Dissertation.
Connor, G. “A Unified Beta Theory.”Journal of Economic Theory, 34, 13–31, (1984).
Dybvig, P. “An Explicit Bound on Individual Asset Deviation from APT Pricing in a Finite Economy.”Journal of Financial Economics, 12, 483–496, (December 1983).
Hanoch, G., and H. Levy, “The Efficiency Analysis of Choices Involving Risk.”The Review of Economic Studies, 36, 335–346 (1969).
Grinblatt, M., and S. Titman, “Factor Pricing in a Finite Economy.”Journal of Financial Economics, 12, 497–507, (December 1983).
Huberman, G., “A Simple Approach to Arbitrage Pricing Theory.”Journal of Economic Theory, 28, 183–191, (1982).
Kelker, D., “Distribution Theory of Spherical Distributions and a Location Scale Parameter Generalization.” Sankhya Ser. A32, 419–430, (1970).
Kraus, A., and R. Litzenberger, “Skewness Preference and the Valuation of Risky Assets.”The Journal of Finance, 30, 1213–1227, (Sepbember 1975).
Kraus, A., and R. Litzenberger, “On the Distributional Conditions for a Consumption-Oriented Three-Moment CAPM.”Journal of Finance, 38, 1381–1391, (December 1983).
Latham, M., “The Arbitrage Pricing Theory and Supershares.“Journal of Finance, 44, 263–282, (June 1989).
Lee, C.F., “Investment Horizon and the Functional Form of the Capital Asset Pricing Model.”The Review of Economics and Statistics, 356–363, (August 1976).
Lintner, J., “The Valuation of Risky Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.”The Review of Economics and Statistics, 47, 13–37, (1965).
Markowitz, H., “Portfolio Selection.”Journal of Finance, 6, 77–91, (March 1952).
Markowitz, H.,Mean-Variance Analysis in Portfolio Choice and Capital Markets. Blackwell, 1987.
McElroy, M.B., and E. Burmeister, “Arbitrage Pricing Theory as a Restricted Nonlinear Multivariate Regression Model: INTSUR Estimates.”Journal of Business and Economic Statistics, 6, 29–42, (January 1988).
Owen, J., and R. Rabinowitz, “On, the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice.”Journal of Finance, 38, 745–752, (June 1983).
Roll, R., “A Critique of the Asset Pricing Theory's Tests.”Journal ofFinancial Economics, 4, 129–176, (March 1977).
Roll, R., and S. Ross, “An Empirical Investigation of the Arbitrage Pricing Theory.”Journal of Finance, 35, 1037–1103, (1986).
Ross, S., “Mutual Fund Separation in Financial Theory-The Separating Distributions.”Journal of Economic Theory, 17, 254–286, (1978).
Ross, S., “The Arbitrage Theory of Capital Asset Pricing.”Journal of Economic Theory, 13, 341–360, (1976).
Shanken, J., “The Arbitrage Pricing Theory: Is It Testable?”Journal of Finance, 37, 1129–1140, (December 1982).
Simaan, Y., “Portfolio Selection and Capital Asset Pricing for a Class of Non-spherical Distributions.” Dissertation, Baruch College (CUNY), (1987).
Simaan, Y., “Portfolio Selection and Asset Three Parameter Framework:” Forthcoming inManagement Science.
Simaan, Y., and C.F. Lee, “A Note on Generalized Multi-beta CAPM.” Unpublished.
Stapleton, R., and M. Subrahmanyam, “The Market Model and Capital Asset Pricing Theory: A Note.”Journal of Finance, (December 1983).
Wei, J., “An Asset Pricing Theory Unifying CAPM and APT.”Journal of Finance, 43, 511–527, (September 1988).
Zeimba, WT., “Choosing Investment Portfolios When Returns Have Stable Distributions.” In Hammer-Zoutendijk (ed.),Mathematical Programming in Theory and Practice. North Holland.
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Simaan, Y., Lee, CF. Alternate approach to unify CAPM and APT. Rev Quant Finan Acc 2, 391–408 (1992). https://doi.org/10.1007/BF00939019
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DOI: https://doi.org/10.1007/BF00939019