Statistical properties of estimators for the log-optimal portfolio

Artikel

The best constant re-balanced portfolio represents the standard estimator for the log-optimal portfolio. It is shown that a quadratic approximation of log-returns works very well on a daily basis and a mean-variance estimator is proposed as an alternative to the best constant re-balanced portfolio. It can easily be computed and the numerical algorithm is very fast even if the number of dimensions is high. Some small-sample and the basic large-sample properties of the estimators are derived. The asymptotic results can be used for constructing hypothesis tests and for computing confidence regions. For this purpose, one should apply a finite-sample correction, which substantially improves the large-sample approximation. However, it is shown that the impact of estimation errors concerning the expected asset returns is serious. The given results confirm a general rule, which has become folklore during the last decades, namely that portfolio optimization typically fails on estimating expected asset returns.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Mathematical Methods of Operations Research ; ISSN: 1432-5217 ; Volume: 92 ; Year: 2020 ; Issue: 1 ; Pages: 1-32 ; Berlin, Heidelberg: Springer

Classification and Topics

• Classification: Wirtschaft ; Estimation: General ; Portfolio Choice; Investment Decisions
• Subject: Best constant re-balanced portfolio ; Estimation risk ; Growth-optimal portfolio ; Log-optimal portfolio ; Mean-variance optimization

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Frahm, Gabriel
• Event: Veröffentlichung
• (who): Springer
• (where): Berlin, Heidelberg
• (when): 2020

Further information

• DOI: doi:10.1007/s00186-020-00701-1
• Last update: 10.03.2025, 11:42 AM CET