IDEAS home Printed from https://ideas.repec.org/a/sae/ausman/v11y1986i1p67-85.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/031289628601100105
    Download Restriction: no
    File URL: https://libkey.io/10.1177/031289628601100105?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access 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. 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)

    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. Erdinc Altay, 2003. "The Effect of Macroeconomic Factors on Asset Returns: A Comparative Analysis of the German and the Turkish Stock Markets in an APT Framework," Finance 0307006, University Library of Munich, Germany.
    2. Bruce N. Lehmann & David M. Modest, 1985. "Mutual Fund Performance Evaluation: A Comparison of Benchmarks and Benchmark Comparisons," NBER Working Papers 1721, National Bureau of Economic Research, Inc.
    3. 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).
    4. Moon K. Kim & Chunchi Wu, 1987. "Macro-Economic Factors And Stock Returns," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 10(2), pages 87-98, June.
    5. Suat Teker & Oscar Varela, 1998. "A comparative analysis of security pricing using factor, macrovariable and arbitrage pricing models," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 22(2), pages 21-41, June.
    6. Geweke, John & Zhou, Guofu, 1996. "Measuring the Pricing Error of the Arbitrage Pricing Theory," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 557-587.
    7. Chadwick, Meltem, 2010. "Performance of Bayesian Latent Factor Models in Measuring Pricing Errors," MPRA Paper 79060, University Library of Munich, Germany.
    8. Gur Huberman & Zhenyu Wang, 2005. "Arbitrage pricing theory," Staff Reports 216, Federal Reserve Bank of New York.
    9. Clare, Andrew D. & Priestley, Richard, 1998. "Risk factors in the Malaysian stock market," Pacific-Basin Finance Journal, Elsevier, vol. 6(1-2), pages 103-114, May.
    10. Ladrón de Guevara Cortés Rogelio & Torra Porras Salvador, 2014. "Estimation of the underlying structure of systematic risk with the use of principal component analysis and factor analysis," Contaduría y Administración, Accounting and Management, vol. 59(3), pages 197-234, julio-sep.
    11. Robert W. Faff, 1993. "A Multivariate Test of an Equilibrium APT with Time Varying Risk Premia in the Australian Equity Market," Australian Journal of Management, Australian School of Business, vol. 17(2), pages 233-258, December.
    12. Jack S. K. Chang & Latha Shanker, 1987. "Option Pricing And The Arbitrage Pricing Theory," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 10(1), pages 1-16, March.
    13. Attiya Y. Javed, 2000. "Alternative Capital Asset Pricing Models: A Review of Theory and Evidence," PIDE-Working Papers 2000:179, Pakistan Institute of Development Economics.
    14. repec:gnv:wpaper:unige:76321 is not listed on IDEAS
    15. Michael C. Ehrhardt, 1987. "Arbitrage Pricing Models: The Sufficient Number Of Factors And Equilibrium Conditions," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 10(2), pages 111-120, June.
    16. Attiya Yasmeen Javid, 2000. "Alternative Capital Asset Pricing Models: A Review of Theory and Evidence," PIDE Research Report 2000:3, Pakistan Institute of Development Economics.
    17. Trabelsi, Mohamed Ali, 2010. "Choix de portefeuille: comparaison des différentes stratégies [Portfolio selection: comparison of different strategies]," MPRA Paper 82946, University Library of Munich, Germany, revised 01 Dec 2010.
    18. 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.
    19. Sentana, Enrique, 2004. "Factor representing portfolios in large asset markets," Journal of Econometrics, Elsevier, vol. 119(2), pages 257-289, April.
    20. Laurence Carassus & Miklos Rasonyi, 2019. "Risk-neutral pricing for APT," Papers 1904.11252, arXiv.org, revised Oct 2020.
    21. Lam, Keith S. K., 2002. "The relationship between size, book-to-market equity ratio, earnings-price ratio, and return for the Hong Kong stock market," Global Finance Journal, Elsevier, vol. 13(2), pages 163-179.

    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:sae:ausman:v:11:y:1986:i:1:p:67-85. 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: SAGE Publications (email available below). General contact details of provider: http://www.agsm.edu.au .

    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.