IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v101y2001i1p222-251.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022-0531(00)92737-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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..
    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.
    3. 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.
    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. 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..
    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.
    11. Reisman, Haim, 1988. "A General Approach to the Arbitrage Pricing Theory (APT)," Econometrica, Econometric Society, vol. 56(2), pages 473-476, March.
    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.
    13. 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.
    14. 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).
    15. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Laurence Carassus & Miklos Rasonyi, 2019. "Risk-neutral pricing for APT," Papers 1904.11252, arXiv.org, revised Oct 2020.
    7. Anderson, Robert M. & Raimondo, Roberto C., 2007. "Equilibrium in Continuous-Time Financial Markets: Endogenously Dynamically Complete Markets," Department of Economics, Working Paper Series qt0zq6v5gd, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    8. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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, 1996. "Hyperfinite Asset Pricing Theory," Cowles Foundation Discussion Papers 1139, Cowles Foundation for Research in Economics, Yale University.
    3. Gabriel Frahm, 0. "Arbitrage Pricing Theory In Ergodic Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-28.
    4. Patrick Gagliardini & Elisa Ossola & Olivier Scaillet, 2016. "Time‐Varying Risk Premium in Large Cross‐Sectional Equity Data Sets," Econometrica, Econometric Society, vol. 84, pages 985-1046, May.
    5. A. El-Gamal, Mahmoud, 2001. "An Economic Explication of the Prohibition of Gharar in Classical Islamic Jurisprudence," Islamic Economic Studies, The Islamic Research and Training Institute (IRTI), vol. 8, pages 29-58.
    6. Darrell Duffie & Yeneng Sun, 2004. "The Exact Law of Large Numbers for Independent Random Matching," Levine's Bibliography 122247000000000328, UCLA Department of Economics.
    7. Khan, M. Ali, 2000. "Globalization Of Financial Markets And Islamic Financial Institutions," Islamic Economic Studies, The Islamic Research and Training Institute (IRTI), vol. 8, pages 20-66.
    8. repec:gnv:wpaper:unige:76321 is not listed on IDEAS
    9. 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.
    10. Rajnish Mehra & Sunil Wahal & Daruo Xie, 2021. "Is idiosyncratic risk conditionally priced?," Quantitative Economics, Econometric Society, vol. 12(2), pages 625-646, May.
    11. Duffie, Darrell & Sun, Yeneng, 2012. "The exact law of large numbers for independent random matching," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1105-1139.
    12. Al-Najjar, Nabil I., 2004. "Aggregation and the law of large numbers in large economies," Games and Economic Behavior, Elsevier, vol. 47(1), pages 1-35, April.
    13. Laurence Carassus & Miklos Rasonyi, 2019. "Risk-neutral pricing for APT," Papers 1904.11252, arXiv.org, revised Oct 2020.
    14. Khan, M. Ali & Qiao, Lei & Rath, Kali P. & Sun, Yeneng, 2020. "Modeling large societies: Why countable additivity is necessary," Journal of Economic Theory, Elsevier, vol. 189(C).
    15. Werner, Jan, 1997. "Diversification and Equilibrium in Securities Markets," Journal of Economic Theory, Elsevier, vol. 75(1), pages 89-103, July.
    16. Karavaev, Andrei, 2008. "A Theory of Continuum Economies with Idiosyncratic Shocks and Random Matchings," MPRA Paper 7445, University Library of Munich, Germany.
    17. Ferson, Wayne E. & Sarkissian, Sergei & Simin, Timothy, 1999. "The alpha factor asset pricing model: A parable," Journal of Financial Markets, Elsevier, vol. 2(1), pages 49-68, February.
    18. Sentana, Enrique, 2004. "Factor representing portfolios in large asset markets," Journal of Econometrics, Elsevier, vol. 119(2), pages 257-289, April.
    19. Aliprantis, Charalambos D. & Tourky, Rabee & Yannelis, Nicholas C., 2001. "A Theory of Value with Non-linear Prices: Equilibrium Analysis beyond Vector Lattices," Journal of Economic Theory, Elsevier, vol. 100(1), pages 22-72, September.
    20. Joao Gomes & Leonid Kogan & Lu Zhang, 2003. "Equilibrium Cross Section of Returns," Journal of Political Economy, University of Chicago Press, vol. 111(4), pages 693-732, August.
    21. repec:dau:papers:123456789/5374 is not listed on IDEAS
    22. M. Hashem Pesaran & Paolo Zaffaroni, 2008. "Optimal Asset Allocation with Factor Models for Large Portfolios," CESifo Working Paper Series 2326, CESifo.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:101:y:2001:i:1:p:222-251. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.