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Diversification and the Optimal Construction of Basis Portfolios

  • Bruce N. Lehmann
  • David M. Modest
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    Nontrivial diversification possibilities arise when 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 underlying 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 Fama-MacBeth portfolio formation procedure, which we call the minimum idiosyncratic risk portfolio formation procedure, outperformed the Fama-MacBeth procedure and proved equal to or better than more expensive quadratic programming procedures.

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    Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 9461.

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    Date of creation: Jan 2003
    Date of revision:
    Publication status: published as Lehmann, Bruce N. and David M. Modest. "Diversification and the Optimal Construction of Basis Portfolios." Management Science 51, 4 (2005): 581-598.
    Handle: RePEc:nbr:nberwo:9461
    Note: AP
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    1. Gary Chamberlain & Michael Rothschild, 1981. "Arbitrage and Mean-Variance Analysis on Large Asset Markets," NBER Technical Working Papers 0015, National Bureau of Economic Research, Inc.
    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. 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.
    4. Jones, Christopher S., 2001. "Extracting factors from heteroskedastic asset returns," Journal of Financial Economics, Elsevier, vol. 62(2), pages 293-325, November.
    5. Albert Madansky, 1964. "Instrumental variables in factor analysis," Psychometrika, Springer, vol. 29(2), pages 105-113, June.
    6. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    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 607-36, May-June.
    13. Gösta Hägglund, 1982. "Factor analysis by instrumental variables methods," Psychometrika, Springer, vol. 47(2), pages 209-222, June.
    14. Bruce N. Lehmann, 1991. "Notes on Dynamic Factor Pricing Models," NBER Working Papers 3677, National Bureau of Economic Research, Inc.
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