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The Empirical Foundations of the Arbitrage Pricing Theory II: The Optimal Construction of Basis Portfolios


  • Bruce N. Lehmann
  • David M. Modest


The Arbitrage Pricing Theory (APT) of Ross (1976) presumes that a factor model describes security returns. In this paper, we provide a comprehensive examination of the merits of various strategies for constructing basis portfolios that are, in principle, highly correlated with the common factors affecting security returns. Three main conclusions emerge from our study. First, increasing the number of securities included in the analysis dramatically improves basis portfolio performance. Our results indicate that factor models involving 750 securities provide markedly superior performance to those involving 30 or 250 securities. Second, comparatively efficient estimation procedures such as maximum likelihood and restricted maximum likelihood factor analysis(which imposes the APT mean restriction) significantly outperform the less efficient instrumental variables and principal components procedures that have been proposed in the literature. Third, a variant of the usual Fame-MacBeth portfolio formation procedure, which we call the minimum idiosyncratic risk portfolio formation procedure, outperformed the Fama-MacBeth procedure and proved equal toor better than more expensive quadratic programming procedures.

Suggested Citation

  • Bruce N. Lehmann & David M. Modest, 1985. "The Empirical Foundations of the Arbitrage Pricing Theory II: The Optimal Construction of Basis Portfolios," NBER Working Papers 1726, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:1726
    Note: ME

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    References listed on IDEAS

    1. Grinblatt, Mark & Titman, Sheridan, 1983. "Factor pricing in a finite economy," Journal of Financial Economics, Elsevier, vol. 12(4), pages 497-507, December.
    2. Albert Madansky, 1964. "Instrumental variables in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 29(2), pages 105-113, June.
    3. Stambaugh, Robert F., 1983. "Arbitrage pricing with information," Journal of Financial Economics, Elsevier, vol. 12(3), pages 357-369, November.
    4. Gösta Hägglund, 1982. "Factor analysis by instrumental variables methods," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 209-222, June.
    5. 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.
    6. Ingersoll, Jonathan E, Jr, 1984. " Some Results in the Theory of Arbitrage Pricing," Journal of Finance, American Finance Association, vol. 39(4), pages 1021-1039, September.
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    Cited by:

    1. Miklós Koren & Silvana Tenreyro, 2007. "Volatility and Development," The Quarterly Journal of Economics, Oxford University Press, vol. 122(1), pages 243-287.
    2. Phylaktis, Kate & Xia, Lichuan, 2006. "Sources of firms' industry and country effects in emerging markets," Journal of International Money and Finance, Elsevier, vol. 25(3), pages 459-475, April.
    3. Miklos Koren & Silvana Tenreyro, 2003. "Diversification and development," Working Papers 03-3, Federal Reserve Bank of Boston.
    4. Gur Huberman & Zhenyu Wang, 2005. "Arbitrage pricing theory," Staff Reports 216, Federal Reserve Bank of New York.
    5. Robin Brooks & Marco Del Negro, 2006. "Firm-Level Evidence on International Stock Market Comovement," Review of Finance, European Finance Association, vol. 10(1), pages 69-98.
    6. Terry V. Grissom & David Hartzell & Crocker H. Liu, 1987. "An Approach to Industrial Real Estate Market Segmentation and Valuation Using the Arbitrage Pricing Paradigm," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 15(3), pages 199-219.
    7. Arnold Cheng, 1998. "International correlation structure of financial market movements - the evidence from the UK and the US," Applied Financial Economics, Taylor & Francis Journals, vol. 8(1), pages 1-12.
    8. Sentana, Enrique, 2004. "Factor representing portfolios in large asset markets," Journal of Econometrics, Elsevier, vol. 119(2), pages 257-289, April.
    9. Richard H. Pettway & Bradford D. Jordan, 1987. "Apt Vs. Capm Estimates Of The Return-Generating Function Parameters For Regulated Public Utilities," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 10(3), pages 227-238, September.
    10. Bruce N. Lehmann & David M. Modest, 2005. "Diversification and the Optimal Construction of Basis Portfolios," Management Science, INFORMS, vol. 51(4), pages 581-598, April.

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