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Sequential Tests of the Arbitrage Pricing Theory: A Comparison of Principal Components and Maximum Likelihood Factors

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  • Shukla, Ravi
  • Trzcinka, Charles

Abstract

The authors examine the cross-sectional pricing equation of the arbitrage pricing theory using the elements of eigenvectors and the maximum likelihood factor loadings of the covariance matrix of returns as measures of risk. The results indicate that, for data assumed stationary over twenty years, the first vector is a surprisingly good measure of risk when compared with either a one-factor or a five-factor model or a five-vector model. The authors conclude that principal components analysis may be preferred to factor analysis in some circumstances. Copyright 1990 by American Finance Association.

Suggested Citation

  • Shukla, Ravi & Trzcinka, Charles, 1990. "Sequential Tests of the Arbitrage Pricing Theory: A Comparison of Principal Components and Maximum Likelihood Factors," Journal of Finance, American Finance Association, vol. 45(5), pages 1541-1564, December.
    • Handle: RePEc:bla:jfinan:v:45:y:1990:i:5:p:1541-64
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    Cited by:

    1. Astrid Eisenberg & Markus Rudolf, 2007. "Exchange Rates and the Conversion of Currency‐Specific Risk Premia," European Financial Management, European Financial Management Association, vol. 13(4), pages 672-701, September.
    2. Susana Iglesias Antelo & Jean-Pierre Levy Mangin, 2010. "An analysis of the risk-return relationship in the Spanish capital market using a structural equation model," Applied Economics Letters, Taylor & Francis Journals, vol. 17(14), pages 1397-1403.
    3. Mahsa Ghorbani & Edwin K. P. Chong, 2018. "Stock Price Prediction using Principle Components," Papers 1803.05075, arXiv.org.
    4. S. Saiful Bahri & Lawrence Leger, 2001. "The stability of risk factors in the UK stock market," Applied Financial Economics, Taylor & Francis Journals, vol. 11(4), pages 411-422.
    5. Freyaldenhoven, Simon, 2022. "Factor models with local factors — Determining the number of relevant factors," Journal of Econometrics, Elsevier, vol. 229(1), pages 80-102.
    6. Mahsa Ghorbani & Edwin K P Chong, 2020. "Stock price prediction using principal components," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-20, March.
    7. Colin T. Bowers & Chris Heaton, 2013. "What does high-dimensional factor analysis tell us about risk factors in the Australian stock market?," Applied Economics, Taylor & Francis Journals, vol. 45(11), pages 1395-1404, April.
    8. Simon Freyaldenhoven, 2017. "A Generalized Factor Model with Local Factors," 2017 Papers pfr361, Job Market Papers.
    9. Gallo, John G. & Swanson, Peggy E., 1996. "Comparative measures of performance for U.S.-based international equity mutual funds," Journal of Banking & Finance, Elsevier, vol. 20(10), pages 1635-1650, December.
    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. Masud Alam, 2021. "Time Varying Risk in U.S. Housing Sector and Real Estate Investment Trusts Equity Return," Papers 2107.10455, arXiv.org.
    12. Lawrence Leger & Vitor Leone, 2008. "Changes in the risk structure of stock returns: Consumer Confidence and the dotcom bubble," Review of Financial Economics, John Wiley & Sons, vol. 17(3), pages 228-244, August.
    13. Huang, Roger D. & Jo, Hoje, 1995. "Data frequency and the number of factors in stock returns," Journal of Banking & Finance, Elsevier, vol. 19(6), pages 987-1003, September.
    14. Civitarese, Jamil, 2016. "Volatility and correlation-based systemic risk measures in the US market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 459(C), pages 55-67.
    15. Mahsa Ghorbani & Edwin K. P. Chong, 2022. "A dimension reduction method for stock-price prediction using multiple predictors," Operational Research, Springer, vol. 22(3), pages 2859-2878, July.
    16. Peter Karlsson, 2011. "The Incompleteness Problem of the APT Model," Computational Economics, Springer;Society for Computational Economics, vol. 38(2), pages 129-151, August.

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