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

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  • M Ali Khan
  • Yeneng Sun
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.

Suggested Citation

  • 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.
    • Handle: RePEc:jhu:papers:483
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    References listed on IDEAS

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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. 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.
    3. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    4. Mordecai Kurz & Mukul Majumdar, 1972. "Efficiency Prices in Infinite Dimensional Spaces: a Synthesis," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 39(2), pages 147-158.
    5. Werner, Jan, 1997. "Diversification and Equilibrium in Securities Markets," Journal of Economic Theory, Elsevier, vol. 75(1), pages 89-103, July.
    6. Reisman, Haim, 1988. "A General Approach to the Arbitrage Pricing Theory (APT)," Econometrica, Econometric Society, vol. 56(2), pages 473-476, March.
    7. 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.
    8. 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.
    9. 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.
    10. Gur Huberman, 2005. "A Simple Approach to Arbitrage Pricing Theory," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 9, pages 289-308, World Scientific Publishing Co. Pte. Ltd..
    11. 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.
    12. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    13. 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.
    14. M. Ali Khan & Yeneng Sun, 1996. "Hyperfinite Asset Pricing Theory," Cowles Foundation Discussion Papers 1139, Cowles Foundation for Research in Economics, Yale University.
    15. Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, vol. 51(5), pages 1305-1323, September.
    16. 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.
    17. 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.
    18. Gur Huberman & Zhenyu Wang, 2005. "Arbitrage pricing theory," Staff Reports 216, Federal Reserve Bank of New York.
    19. BEWLEY, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," LIDAM Reprints CORE 122, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. 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.
    2. Chen Zhang & Wei Yan, 2019. "Spot Market Mechanism Design for the Electricity Market in China Considering the Impact of a Contract Market," Energies, MDPI, vol. 12(6), pages 1-23, March.
    3. Laurence Carassus & Miklos Rasonyi, 2019. "Risk-neutral pricing for APT," Papers 1904.11252, arXiv.org, revised Oct 2020.
    4. Laurence Carassus & Miklós Rásonyi, 2020. "Risk-Neutral Pricing for Arbitrage Pricing Theory," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 248-263, July.
    5. 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).

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