Statistical properties of estimators for the log-optimal portfolio

Gabriel Frahm ()
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Gabriel Frahm: Helmut Schmidt University

Mathematical Methods of Operations Research, 2020, vol. 92, issue 1, No 1, 32 pages

Abstract: Abstract 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.

Keywords: Best constant re-balanced portfolio; Estimation risk; Growth-optimal portfolio; Log-optimal portfolio; Mean-variance optimization (search for similar items in EconPapers)
JEL-codes: C13 G11 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s00186-020-00701-1

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