Skip to main content

Some Critical Insights on the Unbiased Efficient Frontier à la Bodnar&Bodnar

  • 2156 Accesses

Abstract

In a couple of recent papers, Bodnar and Bodnar have tackled the estimation problem of the efficient frontier of a risky asset portfolio. The authors prove that the sample estimator of such a frontier is biased and provide, under proper but questionable hypotheses, an analytical expression for its unbiased estimator. In this contribution, first, we study the behavior of the unbiased estimator of the efficient frontier when the length of the return time series tends to infinity, then, we investigate a “strange” behavior of the unbiased estimator in correspondence of particular combinations of the means of the returns of the assets and of their variances and covariances with respect to the number of the assets and the length of the associated time series of returns; finally, we analyze the operational effectiveness of the proposed unbiased estimator by a bootstrap-based approach.

Keywords

  • Efficient frontier
  • Unbiased estimator
  • Asymptotic and “strange” behaviors
  • Bootstrap estimator

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-89824-7_44
  • Chapter length: 5 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   109.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-89824-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   149.99
Price excludes VAT (USA)
Hardcover Book
USD   249.99
Price excludes VAT (USA)
Fig. 1

References

  1. Bodnar, O., Bodnar, T.: Statistical inference procedure for the mean–variance efficient frontier with estimated parameters. Adv. Stat. Anal. 93, 295–306 (2009)

    MathSciNet  CrossRef  Google Scholar 

  2. Bodnar, O., Bodnar, T.: On the unbiased estimator of the efficient frontier. Int. J. Theor. Appl. Financ. 7, 1065–1073 (2010)

    MathSciNet  CrossRef  Google Scholar 

  3. Efron, B., Tibshirani, R.: Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Stat. Sci. 1, 54–75 (1986)

    MathSciNet  CrossRef  Google Scholar 

  4. Politis, D.N., Romano, J.P.: The stationary bootstrap. J. Am. Stat. Assoc. 89, 1303–1313 (1994)

    MathSciNet  CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Marco Corazza .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Verify currency and authenticity via CrossMark

Cite this chapter

Corazza, M., Pizzi, C. (2018). Some Critical Insights on the Unbiased Efficient Frontier à la Bodnar&Bodnar. In: Corazza, M., Durbán, M., Grané, A., Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-89824-7_44

Download citation