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Diversification and the Optimal Construction of Basis Portfolios

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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
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    File URL: http://dx.doi.org/10.1287/mnsc.1040.0316
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    References listed on IDEAS

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    1. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
    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. 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. 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.
    8. 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.
    9. 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.
    10. 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.
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    Cited by:

    1. repec:bla:eufman:v:16:y:2010:i:1:p:27-42 is not listed on IDEAS
    2. 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.
    3. Gregory Connor & Lisa R. Goldberg & Robert A. Korajczyk, 2010. "Portfolio Risk Analysis," Economics Books, Princeton University Press, edition 1, number 9224.

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