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Nonparametric portfolio efficiency measurement with higher moments

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  • Jens J. Krüger

    (Technical University of Darmstadt)

Abstract

The paper considers a nonparametric approach to determine portfolio efficiency using specific directions toward the portfolio frontier function. This approach allows for a straightforward incorporation of higher moments of the returns distribution beyond mean and variance. The nonparametric approach is extended by the computation of optimal directions endogenously by maximizing the distance toward the portfolio frontier as a novel methodological feature. An empirical application to Fama–French portfolios demonstrates the applicability of the nonparametric approach. The results show that the optimal directions to the frontier depend on the portfolio considered as well as on the period for which the moments are estimated. Skewness in particular plays a role in determining the optimal direction, whereas kurtosis seems to be less crucial.

Suggested Citation

  • Jens J. Krüger, 2021. "Nonparametric portfolio efficiency measurement with higher moments," Empirical Economics, Springer, vol. 61(3), pages 1435-1459, September.
    • Handle: RePEc:spr:empeco:v:61:y:2021:i:3:d:10.1007_s00181-020-01917-0
    DOI: 10.1007/s00181-020-01917-0
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    References listed on IDEAS

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    1. Walter Briec & Kristiaan Kerstens & Octave Jokung, 2007. "Mean-Variance-Skewness Portfolio Performance Gauging: A General Shortage Function and Dual Approach," Management Science, INFORMS, vol. 53(1), pages 135-149, January.
    2. Branda, Martin, 2015. "Diversification-consistent data envelopment analysis based on directional-distance measures," Omega, Elsevier, vol. 52(C), pages 65-76.
    3. Eric Jondeau & Michael Rockinger, 2006. "Optimal Portfolio Allocation under Higher Moments," European Financial Management, European Financial Management Association, vol. 12(1), pages 29-55, January.
    4. Brandouy, Olivier & Briec, Walter & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2010. "Portfolio performance gauging in discrete time using a Luenberger productivity indicator," Journal of Banking & Finance, Elsevier, vol. 34(8), pages 1899-1910, August.
    5. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    6. Kerstens, Kristiaan & Mounir, Amine & Van de Woestyne, Ignace, 2011. "Geometric representation of the mean-variance-skewness portfolio frontier based upon the shortage function," European Journal of Operational Research, Elsevier, vol. 210(1), pages 81-94, April.
    7. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    8. Edirisinghe, N.C.P. & Zhang, X., 2007. "Generalized DEA model of fundamental analysis and its application to portfolio optimization," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3311-3335, November.
    9. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    10. Fama, Eugene F & French, Kenneth R, 1996. "Multifactor Explanations of Asset Pricing Anomalies," Journal of Finance, American Finance Association, vol. 51(1), pages 55-84, March.
    11. Scott, Robert C & Horvath, Philip A, 1980. "On the Direction of Preference for Moments of Higher Order Than the Variance," Journal of Finance, American Finance Association, vol. 35(4), pages 915-919, September.
    12. Fama, Eugene F & French, Kenneth R, 1995. "Size and Book-to-Market Factors in Earnings and Returns," Journal of Finance, American Finance Association, vol. 50(1), pages 131-155, March.
    13. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    14. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-1123, September.
    15. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    16. Morey, Matthew R. & Morey, Richard C., 1999. "Mutual fund performance appraisals: a multi-horizon perspective with endogenous benchmarking," Omega, Elsevier, vol. 27(2), pages 241-258, April.
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    More about this item

    Keywords

    Finance; Portfolio choice; Directional distance functions; Skewness and kurtosis;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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