It is shown in this paper that when the true mean return vector is replaced by the inferred mean vector obtained indirectly from factor model and arbitrage pricing theory, its impact on the resulting optimal portfolio is insignificant. To achieve this goal, several assumptions are imposed: (i) the asset returns are generated from a factor model, (ii) the number of assets goes to infinity, and (iii) there is no asymptotic arbitrage opportunities. Issues related to the efficiency of the estimated optimal portfolio for high-frequency data are discussed. The portfolio constructed using the sample mean vector and using the inferred mean vector from arbitrage pricing theory are compared.

中文翻译：

---

马科维茨投资组合和历史的模糊

本文表明，当真实的平均收益向量被从因子模型和套利定价理论中间接获得的推断平均向量代替时，其对得到的最优投资组合的影响是微不足道的。为了实现这一目标，强加了几个假设：（i）资产收益是从因子模型产生的，（ii）资产数量趋于无穷大，以及（iii）没有渐近套利机会。讨论了与高频数据估计最优组合的效率有关的问题。比较了使用样本均值向量和使用套利定价理论推断出的均值向量构建的投资组合。