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Bayesian estimation of the efficient frontier

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  • David Bauder
  • Rostyslav Bodnar
  • Taras Bodnar
  • Wolfgang Schmid

Abstract

In this paper, we consider the estimation of the three determining parameters of the efficient frontier, the expected return, and the variance of the global minimum variance portfolio and the slope parameter, from a Bayesian perspective. Their posterior distribution is derived by assigning the diffuse and the conjugate priors to the mean vector and the covariance matrix of the asset returns and is presented in terms of a stochastic representation. Furthermore, Bayesian estimates together with the standard uncertainties for all three parameters are provided, and their asymptotic distributions are established. All obtained findings are applied to real data, consisting of the returns on assets included into the S&P 500. The empirical properties of the efficient frontier are then examined in detail.

Suggested Citation

  • David Bauder & Rostyslav Bodnar & Taras Bodnar & Wolfgang Schmid, 2019. "Bayesian estimation of the efficient frontier," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(3), pages 802-830, September.
    • Handle: RePEc:bla:scjsta:v:46:y:2019:i:3:p:802-830
    DOI: 10.1111/sjos.12372
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    Cited by:

    1. Bodnar, Taras & Mazur, Stepan & Nguyen, Hoang, 2022. "Estimation of optimal portfolio compositions for small sampleand singular covariance matrix," Working Papers 2022:15, Örebro University, School of Business.
    2. Taras Bodnar & Holger Dette & Nestor Parolya & Erik Thors'en, 2019. "Sampling Distributions of Optimal Portfolio Weights and Characteristics in Low and Large Dimensions," Papers 1908.04243, arXiv.org, revised Apr 2023.
    3. Taras Bodnar & Mathias Lindholm & Vilhelm Niklasson & Erik Thors'en, 2020. "Bayesian Quantile-Based Portfolio Selection," Papers 2012.01819, arXiv.org.
    4. Taras Bodnar & Arjun K. Gupta & Valdemar Vitlinskyi & Taras Zabolotskyy, 2019. "Statistical Inference for the Beta Coefficient," Risks, MDPI, vol. 7(2), pages 1-14, May.
    5. Bauder, David & Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2020. "Bayesian inference of the multi-period optimal portfolio for an exponential utility," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    6. Bodnar, Taras & Lindholm, Mathias & Niklasson, Vilhelm & Thorsén, Erik, 2022. "Bayesian portfolio selection using VaR and CVaR," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    7. Restrepo, Hector & Zhang, Weiyi & Mei, Bin, 2020. "The time-varying role of timberland in long-term, mixed-asset portfolios under the mean conditional value-at-risk framework," Forest Policy and Economics, Elsevier, vol. 113(C).

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