Asymptotic Arbitrage and the APT with or without Measure-Theoretic Structures
AbstractWe 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 InfoArticle provided by Elsevier in its journal Journal of Economic Theory.
Volume (Year): 101 (2001)
Issue (Month): 1 (November)
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Web page: http://www.elsevier.com/locate/inca/622869
Other versions of this item:
- Khan, A. & Sun, Y., 2000. "Asymptotic Arbitrage and the APT with or Without Measure-Theoretic Structures," Papiers d'Economie MathÃÂ©matique et Applications 2000.81, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- 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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- Huberman, Gur, 1982. "A simple approach to arbitrage pricing theory," Journal of Economic Theory, Elsevier, vol. 28(1), pages 183-191, October.
- Chamberlain, Gary & Rothschild, Michael, 1982.
"Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets,"
3230355, Harvard University Department of Economics.
- Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-304, September.
- Gary Chamberlain & Michael Rothschild, 1984. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," NBER Working Papers 0996, National Bureau of Economic Research, Inc.
- 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.
- M. Ali Khan & Yeneng Sun, 1999. "Weak measurability and characterizations of risk," Economic Theory, Springer, vol. 13(3), pages 541-560.
- 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.
- 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.
- 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.
- 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.
- 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.
- M. Ali Khan & Yeneng Sun, 1996. "Hyperfinite Asset Pricing Theory," Cowles Foundation Discussion Papers 1139, Cowles Foundation for Research in Economics, Yale University.
- Reisman, Haim, 1988. "A General Approach to the Arbitrage Pricing Theory (APT)," Econometrica, Econometric Society, vol. 56(2), pages 473-76, March.
- 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.
- Werner, Jan, 1997. "Diversification and Equilibrium in Securities Markets," Journal of Economic Theory, Elsevier, vol. 75(1), pages 89-103, July.
- Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
- 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).
- 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.
- 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.
- 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.
- 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.
- 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).
- 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.
- 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.
- M. Ali Khan & Yeneng Sun, 2003. "Exact arbitrage and portfolio analysis in large asset markets," Economic Theory, Springer, vol. 22(3), pages 495-528, October.
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