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Bootstrap estimation of the efficient frontier

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  • Begoña Font

    (University of Valencia)

Abstract

In this paper, we propose a bootstrap resampling methodology to obtain the confidence intervals for efficient portfolios weights and the sample characteristics of the mean-variance efficient frontier. We provide an estimate of efficient portfolios, compute the confidence region of the efficient frontier and get the prediction densities of the future efficient portfolio returns without distributional assumptions on returns. An extensive simulation study evaluates the finite-sample performance of these bootstrap intervals and stresses the advantages of such approach. Interestingly, the methodology can be easily modified to make inferences that incorporate our modelling of returns in the predictive efficient frontier estimation with or without additional managerial restrictions.

Suggested Citation

  • Begoña Font, 2016. "Bootstrap estimation of the efficient frontier," Computational Management Science, Springer, vol. 13(4), pages 541-570, October.
  • Handle: RePEc:spr:comgts:v:13:y:2016:i:4:d:10.1007_s10287-016-0257-2
    DOI: 10.1007/s10287-016-0257-2
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    References listed on IDEAS

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    1. MacKinlay, A Craig & Pastor, Lubos, 2000. "Asset Pricing Models: Implications for Expected Returns and Portfolio Selection," The Review of Financial Studies, Society for Financial Studies, vol. 13(4), pages 883-916.
    2. Taras Bodnar & Wolfgang Schmid, 2009. "Econometrical analysis of the sample efficient frontier," The European Journal of Finance, Taylor & Francis Journals, vol. 15(3), pages 317-335.
    3. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    4. Lorenzo Pascual & Juan Romo & Esther Ruiz, 2004. "Bootstrap predictive inference for ARIMA processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 449-465, July.
    5. Okhrin, Yarema & Schmid, Wolfgang, 2006. "Distributional properties of portfolio weights," Journal of Econometrics, Elsevier, vol. 134(1), pages 235-256, September.
    6. Huifu Xu & Dali Zhang, 2012. "Monte Carlo methods for mean-risk optimization and portfolio selection," Computational Management Science, Springer, vol. 9(1), pages 3-29, February.
    7. J. Knight & S. E. Satchell, 2010. "Exact properties of measures of optimal investment for benchmarked portfolios," Quantitative Finance, Taylor & Francis Journals, vol. 10(5), pages 495-502.
    8. Mark Britten‐Jones, 1999. "The Sampling Error in Estimates of Mean‐Variance Efficient Portfolio Weights," Journal of Finance, American Finance Association, vol. 54(2), pages 655-671, April.
    9. Ľuboš Pástor, 2000. "Portfolio Selection and Asset Pricing Models," Journal of Finance, American Finance Association, vol. 55(1), pages 179-223, February.
    10. Leung, Pui-Lam & Ng, Hon-Yip & Wong, Wing-Keung, 2012. "An improved estimation to make Markowitz’s portfolio optimization theory users friendly and estimation accurate with application on the US stock market investment," European Journal of Operational Research, Elsevier, vol. 222(1), pages 85-95.
    11. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
    12. 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.
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    Cited by:

    1. Taras Bodnar & Yarema Okhrin & Valdemar Vitlinskyy & Taras Zabolotskyy, 2018. "Determination and estimation of risk aversion coefficients," Computational Management Science, Springer, vol. 15(2), pages 297-317, June.
    2. Taras Bodnar & Mathias Lindholm & Erik Thorsén & Joanna Tyrcha, 2021. "Quantile-based optimal portfolio selection," Computational Management Science, Springer, vol. 18(3), pages 299-324, July.

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