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Exact Arbitrage Well-Diversified Potfolios and Asset Pricing in Large Markets

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Author Info
M Ali Khan
Yeneng Sun

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Abstract

For market with an atomless continuum of assets, we formulate the intuitive idea of a "well-diversified" portfolio, and present a notion of "exact arbitrage", strictly weaker than the more conventional notion of "asymptotic arbitrage", and necessary and sufficient for the validity of an APT pricing formula. One formula involves "essential" risk based on a specific index portfolio constructed from factors and factor loadings that are endogenously extracted to satisfy an optimality property involving a finite number of factors. We illustrate how our results can be translated to markets with a large but finite number of assets.

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Paper provided by The Johns Hopkins University,Department of Economics in its series Economics Working Paper Archive with number 483.

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Date of creation: Oct 2002
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Handle: RePEc:jhu:papers:483

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  1. M. Ali Khan & Yeneng Sun, 1996. "Hyperfinite Asset Pricing Theory," Cowles Foundation Discussion Papers 1139, Cowles Foundation, Yale University. [Downloadable!]
  2. 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. [Downloadable!] (restricted)
  3. Khan, M. Ali & Sun, Yeneng, 2001. "Asymptotic Arbitrage and the APT with or without Measure-Theoretic Structures," Journal of Economic Theory, Elsevier, vol. 101(1), pages 222-251, November. [Downloadable!] (restricted)
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  4. 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. [Downloadable!] (restricted)
  5. Sun, Yeneng, 1998. "A theory of hyperfinite processes: the complete removal of individual uncertainty via exact LLN1," Journal of Mathematical Economics, Elsevier, vol. 29(4), pages 419-503, May. [Downloadable!] (restricted)
  6. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December. [Downloadable!] (restricted)
  7. Huberman, Gur, 1982. "A simple approach to arbitrage pricing theory," Journal of Economic Theory, Elsevier, vol. 28(1), pages 183-191, October. [Downloadable!] (restricted)
  8. Reisman, Haim, 1988. "A General Approach to the Arbitrage Pricing Theory (APT)," Econometrica, Econometric Society, vol. 56(2), pages 473-76, March. [Downloadable!] (restricted)
  9. Werner, Jan, 1997. "Diversification and Equilibrium in Securities Markets," Journal of Economic Theory, Elsevier, vol. 75(1), pages 89-103, July. [Downloadable!] (restricted)
  10. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  12. M. Ali Khan & Yeneng Sun, 1999. "Weak measurability and characterizations of risk," Economic Theory, Springer, vol. 13(3), pages 541-560. [Downloadable!] (restricted)
  13. Gur Huberman & Zhenyu Wang, 2005. "Arbitrage pricing theory," Staff Reports 216, Federal Reserve Bank of New York. [Downloadable!]
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