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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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  • 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.
  • Handle: RePEc:eee:jetheo:v:101:y:2001:i:1:p:222-251
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    1. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
    2. 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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    6. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    7. Werner, Jan, 1997. "Diversification and Equilibrium in Securities Markets," Journal of Economic Theory, Elsevier, vol. 75(1), pages 89-103, July.
    8. M. Ali Khan & Yeneng Sun, 1999. "Weak measurability and characterizations of risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(3), pages 541-560.
    9. M. Ali Khan & Yeneng Sun, 1996. "Hyperfinite Asset Pricing Theory," Cowles Foundation Discussion Papers 1139, Cowles Foundation for Research in Economics, Yale University.
    10. 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 383-394, June.
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    12. 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.
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    Cited by:

    1. Khan, M. Ali & Sun, Yeneng, 2003. "Exact arbitrage, well-diversified portfolios and asset pricing in large markets," Journal of Economic Theory, Elsevier, vol. 110(2), pages 337-373, June.
    2. M. Ali Khan & Yeneng Sun, 2003. "Exact arbitrage and portfolio analysis in large asset markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(3), pages 495-528, October.
    3. Herzberg, Frederik, 2011. "On the foundations of Lévy finance. Equilibrium for a single-agent financial market with jumps," Center for Mathematical Economics Working Papers 406, Center for Mathematical Economics, Bielefeld University.
    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. 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).

    More about this item

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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