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A generalized pivotal quantity approach to portfolio selection

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  • Philip L.H. Yu
  • Thomas Mathew
  • Yuanyuan Zhu

Abstract

The major problem of mean–variance portfolio optimization is parameter uncertainty. Many methods have been proposed to tackle this problem, including shrinkage methods, resampling techniques, and imposing constraints on the portfolio weights, etc. This paper suggests a new estimation method for mean–variance portfolio weights based on the concept of generalized pivotal quantity (GPQ) in the case when asset returns are multivariate normally distributed and serially independent. Both point and interval estimations of the portfolio weights are considered. Comparing with Markowitz's mean–variance model, resampling and shrinkage methods, we find that the proposed GPQ method typically yields the smallest mean-squared error for the point estimate of the portfolio weights and obtains a satisfactory coverage rate for their simultaneous confidence intervals. Finally, we apply the proposed methodology to address a portfolio rebalancing problem.

Suggested Citation

  • Philip L.H. Yu & Thomas Mathew & Yuanyuan Zhu, 2017. "A generalized pivotal quantity approach to portfolio selection," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(8), pages 1402-1420, June.
    • Handle: RePEc:taf:japsta:v:44:y:2017:i:8:p:1402-1420
    DOI: 10.1080/02664763.2016.1214241
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    References listed on IDEAS

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    1. Konstantin Glombek, 2014. "Statistical Inference for High-Dimensional Global Minimum Variance Portfolios," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 845-865, December.
    2. 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.
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    5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    6. Wei-Hwa Wu & Hsin-Neng Hsieh, 2014. "Generalized confidence interval estimation for the mean of delta-lognormal distribution: an application to New Zealand trawl survey data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(7), pages 1471-1485, July.
    7. Best, Michael J & Grauer, Robert R, 1991. "On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results," The Review of Financial Studies, Society for Financial Studies, vol. 4(2), pages 315-342.
    8. Okhrin, Yarema & Schmid, Wolfgang, 2006. "Distributional properties of portfolio weights," Journal of Econometrics, Elsevier, vol. 134(1), pages 235-256, September.
    9. Vasyl Golosnoy & Yarema Okhrin, 2007. "Multivariate Shrinkage for Optimal Portfolio Weights," The European Journal of Finance, Taylor & Francis Journals, vol. 13(5), pages 441-458.
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