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Nonparametric portfolio efficiency measurement with higher moments

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  • Krüger, Jens J.

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

  • Krüger, Jens J., 2021. "Nonparametric portfolio efficiency measurement with higher moments," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 130825, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    • Handle: RePEc:dar:wpaper:130825
    Note: for complete metadata visit http://tubiblio.ulb.tu-darmstadt.de/130825/
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    File URL: https://link.springer.com/article/10.1007/s00181-020-01917-0
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    File URL: https://tuprints.ulb.tu-darmstadt.de/23869
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    References listed on IDEAS

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    1. Krüger, Jens & Hampf, Benjamin, 2015. "Optimal Directions for Directional Distance Functions: An Exploration of Potential Reductions of Greenhouse Gases," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 77007, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    2. 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.
    3. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1683, August.
    4. R. Färe & S. Grosskopf & G. Whittaker, 2013. "Directional output distance functions: endogenous directions based on exogenous normalization constraints," Journal of Productivity Analysis, Springer, vol. 40(3), pages 267-269, December.
    5. 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.
    6. 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.
    7. 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.
    8. Paul A. Samuelson, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances and Higher Moments," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(4), pages 537-542.
    9. Briec, Walter & Kerstens, Kristiaan, 2010. "Portfolio selection in multidimensional general and partial moment space," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 636-656, April.
    10. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    11. Murthi, B. P. S. & Choi, Yoon K. & Desai, Preyas, 1997. "Efficiency of mutual funds and portfolio performance measurement: A non-parametric approach," European Journal of Operational Research, Elsevier, vol. 98(2), pages 408-418, April.
    12. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    13. 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.
    14. repec:bla:jfinan:v:58:y:2003:i:4:p:1651-1684 is not listed on IDEAS
    15. 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.
    16. Campbell Harvey & John Liechty & Merrill Liechty & Peter Muller, 2010. "Portfolio selection with higher moments," Quantitative Finance, Taylor & Francis Journals, vol. 10(5), pages 469-485.
    17. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    18. Joro, Tarja & Na, Paul, 2006. "Portfolio performance evaluation in a mean-variance-skewness framework," European Journal of Operational Research, Elsevier, vol. 175(1), pages 446-461, November.
    19. Benjamin Hampf & Jens J. Krüger, 2015. "Optimal Directions for Directional Distance Functions: An Exploration of Potential Reductions of Greenhouse Gases," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 97(3), pages 920-938.
    20. Gourieroux, C. & Monfort, A., 2005. "The econometrics of efficient portfolios," Journal of Empirical Finance, Elsevier, vol. 12(1), pages 1-41, January.
    21. Lionel Martellini & Volker Ziemann, 2010. "Improved Estimates of Higher-Order Comoments and Implications for Portfolio Selection," The Review of Financial Studies, Society for Financial Studies, vol. 23(4), pages 1467-1502, April.
    22. 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.
    23. 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.
    24. 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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