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On the Arbitrage Pricing Theory

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  • C. Gilles
  • S.F. Leroy

Abstract

The Arbitrage Pricing Theory relates the expected rates of return on a sequence of primitive securities to their factor exposures, suggesting that factor risk is of critical importance in asset pricing. However, we show that if the sequence of primitive returns is replaced by a sequence of returns on portfolios formed from the primitive securities, then the factor subspace is arbitrary. The implication is that the theorems relating expected returns to factor risk require substantial reinterpretation. Our reinterpretation consists of a demonstration that exact and approximate factor pricing do not constitute substantive characterizations of asset pricing. Instead, they are implications of the characterization of the returns space as a Hilbert space (exact factor pricing corresponds to the Riesz representation theorem and approximate factor pricing is a consequence of Bessel's inequality).
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Suggested Citation

  • C. Gilles & S.F. Leroy, 1989. "On the Arbitrage Pricing Theory," Carleton Economic Papers 89-09, Carleton University, Department of Economics, revised Jul 1991.
    • Handle: RePEc:car:carecp:89-09
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    Cited by:

    1. Tarak Nath Sahu & Krishna Dayal Pandey, 2020. "Money Supply and Equity Price Movements During the Liberalized Period in India," Global Business Review, International Management Institute, vol. 21(1), pages 108-123, February.
    2. Frère, Eric & Schyra, Andreas, 2011. "Ausgewählte steuerliche Einflussfaktoren der Unternehmensbewertung," Arbeitspapiere der FOM 19, FOM Hochschule für Oekonomie & Management.
    3. Rajnish Mehra & Sunil Wahal & Daruo Xie, 2021. "Is idiosyncratic risk conditionally priced?," Quantitative Economics, Econometric Society, vol. 12(2), pages 625-646, May.
    4. Nawalkha, Sanjay K., 1997. "A multibeta representation theorem for linear asset pricing theories," Journal of Financial Economics, Elsevier, vol. 46(3), pages 357-381, December.
    5. M. Ali Khan & Yeneng Sun, 1996. "Hyperfinite Asset Pricing Theory," Cowles Foundation Discussion Papers 1139, Cowles Foundation for Research in Economics, Yale University.
    6. HEIFETZ, Aviad & MINELLI, Enrico & POLEMARCHAKIS, Heracles, 1999. "Arbitrage and equilibrium with exchangeable risks," LIDAM Discussion Papers CORE 1999046, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. Werner, Jan, 1997. "Diversification and Equilibrium in Securities Markets," Journal of Economic Theory, Elsevier, vol. 75(1), pages 89-103, July.
    9. Al-Najjar, Nabil I., 1999. "On the robustness of factor structures to asset repackaging," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 309-320, April.
    10. Roßbach, Peter, 2001. "Behavioral finance: eine Alternative zur vorherrschenden Kapitalmarkttheorie?," Frankfurt School - Working Paper Series 31, Frankfurt School of Finance and Management.
    11. To, Minh Chau & Assoé, Kodjovi Gakpo, 1995. "Performance et commission de souscription des fonds mutuels canadiens," L'Actualité Economique, Société Canadienne de Science Economique, vol. 71(1), pages 27-52, mars.
    12. Thomas A. Severini, 2022. "Some properties of portfolios constructed from principal components of asset returns," Annals of Finance, Springer, vol. 18(4), pages 457-483, December.

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