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Diversification and the Optimal Construction of Basis Portfolios

Author

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  • Bruce N. Lehmann

    (Graduate School of International Relations and Pacific Studies, 9500 Gilman Drive, University of California at San Diego, La Jolla, California 92092-0519)

  • David M. Modest

    (Azimuth Trust, 162 Fifth Street, 8th Floor, New York, New York 10010)

Abstract

Nontrivial diversification possibilities arise when a factor model describes security returns. This paper catalogs the merits of alternative strategies for constructing basis portfolios to mimic the common factors. We show how to use the \chi 2 statistic for the joint significance of mean basis portfolio returns to rank alternative procedures and the bootstrap to perform inferences on the disparity between \chi 2 statistics across portfolio formation procedure, estimation method, cross-section size, and number of factors. Our main conclusion is that maximum likelihood factor analysis coupled with minimum idiosyncratic risk portfolio formation yields economically and statistically superior basis portfolios compared with those derived from asymptotic principal components.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:51:y:2005:i:4:p:581-598
    DOI: 10.1287/mnsc.1040.0316
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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. Lehmann, Bruce N & Modest, David M, 1987. "Mutual Fund Performance Evaluation: A Comparison of Benchmarks and Benchmark Comparisons," Journal of Finance, American Finance Association, vol. 42(2), pages 233-265, June.
    3. Lehmann, Bruce N. & Modest, David M., 1988. "The empirical foundations of the arbitrage pricing theory," Journal of Financial Economics, Elsevier, vol. 21(2), pages 213-254, September.
    4. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    5. Jobson, J. D. & Korkie, Bob, 1982. "Potential performance and tests of portfolio efficiency," Journal of Financial Economics, Elsevier, vol. 10(4), pages 433-466, December.
    6. Connor, Gregory & Korajczyk, Robert A., 1986. "Performance measurement with the arbitrage pricing theory : A new framework for analysis," Journal of Financial Economics, Elsevier, vol. 15(3), pages 373-394, March.
    7. 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.
    8. 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.
    9. Bruce N. Lehmann & David M. Modest, 2003. "Diversification and the Optimal Construction of Basis Portfolios," NBER Working Papers 9461, National Bureau of Economic Research, Inc.
    10. 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.
    11. Connor, Gregory & Korajczyk, Robert A., 1988. "Risk and return in an equilibrium APT : Application of a new test methodology," Journal of Financial Economics, Elsevier, vol. 21(2), pages 255-289, September.
    12. Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-636, May-June.
    13. Jones, Christopher S., 2001. "Extracting factors from heteroskedastic asset returns," Journal of Financial Economics, Elsevier, vol. 62(2), pages 293-325, November.
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    3. Steven L. Heston & Robert A. Korajczyk & Ronnie Sadka, 2010. "Intraday Patterns in the Cross‐section of Stock Returns," Journal of Finance, American Finance Association, vol. 65(4), pages 1369-1407, August.
    4. M. Hashem Pesaran & Ron P. Smith, 2019. "The Role of Factor Strength and Pricing Errors for Estimation and Inference in Asset Pricing Models," CESifo Working Paper Series 7919, CESifo.
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    6. Avanidhar Subrahmanyam, 2010. "The Cross†Section of Expected Stock Returns: What Have We Learnt from the Past Twenty†Five Years of Research?," European Financial Management, European Financial Management Association, vol. 16(1), pages 27-42, January.
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    9. Lambert, Marie & Fays, Boris & Hübner, Georges, 2020. "Factoring characteristics into returns: A clinical study on the SMB and HML portfolio construction methods," Journal of Banking & Finance, Elsevier, vol. 114(C).

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