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Hyperfinite Asset Pricing Theory

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Author Info

  • M. Ali Khan

    (Johns Hopkins University)

  • Yeneng Sun

    (Cowles Foundation & Nat. University of Singapore)

Abstract

We present a model of a financial market which unifies the capital-asset-pricing model (CAPM) of Sharpe-Lintner, and the arbitrage pricing theory (APT) of Ross. The model is based on a recent theory of hyperfinite processes, and it uncovers asset pricing phenomena which cannot be treated by classical methods, and whose asymptotic counterparts are not already, or even readily, apparent in the setting of a large but finite number of assets. In the model, an asset's unexpected return can be decomposed into a systematic and an unsystematic part, as in the APT, and the systematic part further decomposed leads to a pricing formula expressed in terms of a beta that is based on a specific index portfolio identifying essential risk, and constructed from factors and factor loadings that are endogenously extracted from the process of asset returns. Furthermore, the valuation formulas of the two individual theories imply, and are implied by, the pervasive economic principle of no arbitrage. Explicit formulas for the characterization, as well as conditions for the existence, of important portfolios are furnished. The hyperfinite factor model possesses an optimality property which justifies the use of a relatively small number of factors to describe the relevant correlational structures. The asymptotic implementability of the idealized limit model is illustrated by an interpretation of selected results for the large but finite setting.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1139.

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Length: 60 pages
Date of creation: Nov 1996
Date of revision:
Handle: RePEc:cwl:cwldpp:1139

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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
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Web page: http://cowles.econ.yale.edu/
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References

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  1. Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February.
  2. Edward J. Green, 1994. "Individual Level Randomness in a Nonatomic Population," GE, Growth, Math methods 9402001, EconWPA.
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  6. C. Gilles & S.F. Leroy, 1989. "On the Arbitrage Pricing Theory," Carleton Economic Papers 89-09, Carleton University, Department of Economics, revised Jul 1991.
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  8. Gary Chamberlain & Michael Rothschild, 1982. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," NBER Working Papers 0996, National Bureau of Economic Research, Inc.
  9. Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, vol. 51(5), pages 1305-23, September.
  10. Hal Varian, 1993. "A Portfolio of Nobel Laureates: Markowitz, Miller and Sharpe," Journal of Economic Perspectives, American Economic Association, vol. 7(1), pages 159-169, Winter.
  11. Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February.
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  13. Huberman, Gur, 1982. "A simple approach to arbitrage pricing theory," Journal of Economic Theory, Elsevier, vol. 28(1), pages 183-191, October.
  14. James Tobin, 1956. "Liquidity Preference as Behavior Towards Risk," Cowles Foundation Discussion Papers 14, Cowles Foundation for Research in Economics, Yale University.
  15. Anderson, Robert M., 1991. "Non-standard analysis with applications to economics," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 39, pages 2145-2208 Elsevier.
  16. Brown, Stephen J, 1989. " The Number of Factors in Security Returns," Journal of Finance, American Finance Association, vol. 44(5), pages 1247-62, December.
  17. Samuelson, Paul A., 1967. "General Proof that Diversification Pays," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(01), pages 1-13, March.
  18. Reisman, Haim, 1988. "A General Approach to the Arbitrage Pricing Theory (APT)," Econometrica, Econometric Society, vol. 56(2), pages 473-76, March.
  19. Samuelson, Paul A, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances, and Higher Moments," Review of Economic Studies, Wiley Blackwell, vol. 37(4), pages 537-42, October.
  20. Admati, Anat R. & Pfleiderer, Paul, 1985. "Interpreting the factor risk premia in the arbitrage pricing theory," Journal of Economic Theory, Elsevier, vol. 35(1), pages 191-195, February.
  21. Gur Huberman & Zhenyu Wang, 2005. "Arbitrage pricing theory," Staff Reports 216, Federal Reserve Bank of New York.
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Cited by:
  1. M Ali Khan & Yeneng Sun, 2002. "Exact Arbitrage Well-Diversified Potfolios and Asset Pricing in Large Markets," Economics Working Paper Archive 483, The Johns Hopkins University,Department of Economics.
  2. Khan, A. & Sun, Y., 2000. "Asymptotic Arbitrage and the APT with or Without Measure-Theoretic Structures," Papiers d'Economie Mathématique et Applications 2000.81, Université Panthéon-Sorbonne (Paris 1).

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