The heuristic $1/N$ (i.e., equally weighted) portfolio and heuristic quintile portfolio are both popular simple strategies in financial investment. In the $1/N$ portfolio, a fraction of $1/N$ of the wealth is allocated to each of the $N$ available assets. In the quintile portfolio, first the assets are sorted according to some characteristics, e.g., expected returns, and then the strategy equally longs the top 20% (i.e., top quintile) and perhaps shorts the bottom 20% (i.e., bottom quintile). Although they have been criticized for their lack of mathematical justification when proposed by practitioners, they have shown great advantage over more sophisticated portfolios in terms of stable performance and easy deployment. In this paper, we reinterpret the $1/N$ and quintile portfolios as solutions to a mathematically sound robust portfolio optimization under different levels of robustness level in the stocks’ characteristics. A variance-adjusted robustness uncertainty set is also proposed, leading to the inverse-volatility portfolios, whose nonzero weights are inversely proportional to their standard deviation.

中文翻译：

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了解 Quintile 投资组合

启发式 $1/N$（即等权重）投资组合和启发式五分之一投资组合都是金融投资中流行的简单策略。在里面$1/N$ 投资组合，一小部分 $1/N$ 的财富分配给每个人 $N$可用资产。在五分位数投资组合中，首先根据一些特征（例如预期收益）对资产进行排序，然后该策略同样做多顶部 20%（即顶部五分之一）并可能做空底部 20%（即底部五分之一）。尽管它们在被从业者提出时因缺乏数学论证而受到批评，但它们在性能稳定和易于部署方面表现出比更复杂的投资组合更大的优势。在本文中，我们重新解释了$1/N$和五分位数投资组合作为在股票特征的不同稳健性水平下数学上合理的稳健投资组合优化的解决方案。还提出了一个方差调整的稳健性不确定性集，导致反波动性投资组合，其非零权重与其标准偏差成反比。