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Asymptotic Arbitrage and the APT with or without Measure-Theoretic Structures

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  • Khan, M. Ali
  • Sun, Yeneng

Abstract

We present a version of the APT based on an asset index set of an arbitrary infinite cardinality. Under assumptions due to Ross and Chamberlain-Rothschild, we shhow that in the absence of gains from asymptotic arbitrage, the square of the deviations of the individual rates of return from a factor-pricing formula sum to a finite number ; and that this absence, while sufficient, is not necessary for the formula to hold. We relate these results to recent work, and explain, in particular, how a version of the APT exhibits several inconsistencies when the index set is the Lebesgue unit interval.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 101 (2001)
Issue (Month): 1 (November)
Pages: 222-251

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Handle: RePEc:eee:jetheo:v:101:y:2001:i:1:p:222-251

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Web page: http://www.elsevier.com/locate/inca/622869

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  1. Bewley, Truman F, 1973. "The Equality of the Core and the Set of Equilibria in Economies with Infinitely Many Commodities and a Continuum of Agents," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(2), pages 383-94, June.
  2. M. Ali Khan & Yeneng Sun, 1996. "Hyperfinite Asset Pricing Theory," Cowles Foundation Discussion Papers 1139, Cowles Foundation for Research in Economics, Yale University.
  3. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  4. 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.
  5. M. Ali Khan & Yeneng Sun, 1999. "Weak measurability and characterizations of risk," Economic Theory, Springer, vol. 13(3), pages 541-560.
  6. Huberman, Gur, 1982. "A simple approach to arbitrage pricing theory," Journal of Economic Theory, Elsevier, vol. 28(1), pages 183-191, October.
  7. Werner, Jan, 1997. "Diversification and Equilibrium in Securities Markets," Journal of Economic Theory, Elsevier, vol. 75(1), pages 89-103, July.
  8. 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.
  9. 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.
  10. 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.
  11. Kurz, Mordecai & Majumdar, Mukul, 1972. "Efficiency Prices in Infinite Dimensional Spaces: A Synthesis," Review of Economic Studies, Wiley Blackwell, vol. 39(2), pages 147-58, April.
  12. Al-Najjar, Nabil I., 1998. "Factor Analysis and Arbitrage Pricing in Large Asset Economies," Journal of Economic Theory, Elsevier, vol. 78(2), pages 231-262, February.
  13. Reisman, Haim, 1988. "A General Approach to the Arbitrage Pricing Theory (APT)," Econometrica, Econometric Society, vol. 56(2), pages 473-76, March.
  14. 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.
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Cited by:
  1. Michailidis, G., 2009. "Multivariate methods in examining macroeconomic variables effect on Greek stock market returns, 1997-2004," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 9(1).
  2. M Ali Khan & Yeneng Sun, 2002. "Exact Arbitrage and Portfolio Analysis in Large Asset Markets," Economics Working Paper Archive 484, The Johns Hopkins University,Department of Economics.
  3. Frederik Herzberg, 2008. "On the foundations of Lévy finance: Equilibrium for a single-agent financial market with jumps," Working Papers 406, Bielefeld University, Center for Mathematical Economics.
  4. Birge, John R. & Yang, Song, 2007. "A model for tax advantages of portfolios with many assets," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3269-3290, November.
  5. Kim Sawyer & André Gygax & Matthew Hazledine, 2010. "Pricing errors and estimates of risk premia in factor models," Annals of Finance, Springer, vol. 6(3), pages 391-403, July.
  6. Khan, M. Ali & Sun, Yeneng, 2001. "Exact Arbitrage, Well-Diversified Portfolios and Asset Pricing in Large Markets," Economics Working Papers (Ensaios Economicos da EPGE) 420, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).

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