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.

最佳的恒定再平衡投资组合代表对数最优投资组合的标准估计量。结果表明，对数回报的二次逼近在每天的工作中都非常好，并且提出了均方差估算器作为最佳恒定再平衡投资组合的替代方案。即使维数很多，也可以很容易地计算出来，并且数值算法非常快。推导了估计量的一些小样本和基本的大样本属性。渐近结果可用于构建假设检验和计算置信区间。为此，应该应用有限样本校正，这将大大改善大样本近似值。然而，事实表明，估计误差对预期资产收益的影响是严重的。