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Arbitrage Pricing, Factor Structure, Eigenvectors and all That—An Exposition

Author

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  • Bernd P. Luedecke

    (Australian Graduate School of Management.)

Abstract

This paper re-presents the essentials of Ross' (1976) derivation of his Arbitrage Pricing Theory (APT) and explains the empirical implications of recent extensions to the APT due to Chamberlain & Rothschild (1983). The natural statistical methodology for empirically testing Ross' for Mulation is to factor-analyze a certain variance-covariance matrix. This factor analysis bears a close relationship to the natural empirical counterpart of Chamberlain & Rothschild's generalisations of the APT: computation of the eigenvalues and eigenvectors. An important implication is that this new method for testing the APT is simpler than factor analysis but perfor Ms as well, is much less of a computational burden, and includes a new way to count the factors.

Suggested Citation

  • Bernd P. Luedecke, 1986. "Arbitrage Pricing, Factor Structure, Eigenvectors and all That—An Exposition," Australian Journal of Management, Australian School of Business, vol. 11(1), pages 67-85, June.
    • Handle: RePEc:sae:ausman:v:11:y:1986:i:1:p:67-85
    DOI: 10.1177/031289628601100105
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    References listed on IDEAS

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    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. Roll, Richard & Ross, Stephen A, 1980. "An Empirical Investigation of the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 35(5), pages 1073-1103, December.
    3. Reinganum, Marc R, 1981. "The Arbitrage Pricing Theory: Some Empirical Results," Journal of Finance, American Finance Association, vol. 36(2), pages 313-321, May.
    4. Brown, Stephen J & Weinstein, Mark I, 1983. "A New Approach to Testing Asset Pricing Models: The Bilinear Paradigm," Journal of Finance, American Finance Association, vol. 38(3), pages 711-743, June.
    5. Shanken, Jay, 1982. "The Arbitrage Pricing Theory: Is It Testable?," Journal of Finance, American Finance Association, vol. 37(5), pages 1129-1140, December.
    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. Chen, Nai-fu, 1983. "Some Empirical Tests of the Theory of Arbitrage Pricing," Journal of Finance, American Finance Association, vol. 38(5), pages 1393-1414, December.
    8. Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, vol. 51(5), pages 1305-1323, September.
    Full references (including those not matched with items on IDEAS)

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