We investigate the temporal aggregation of the Aumann–Serrano (AS) and Foster–Hart (FH) performance indexes considered by Kadan and Liu (2014). We provide sufficient conditions for the two indexes to be closed under temporal aggregation, that is, for the two indexes to have the same values when the observations are aggregated. Here, we present empirical examples using U.S. stock data and the four anomalies studied by Fama and French (1993) and Carhart (1997), where the two indexes have nearly identical values in some stocks and one anomaly when the observations are aggregated. Unlike the Sharpe ratio, the AS and FH performance indexes have more stable properties with respect to temporal aggregation.

我们研究了 Kadan 和 Liu (2014) 考虑的 Aumann-Serrano (AS) 和 Foster-Hart (FH) 性能指标的时间聚合。我们为两个索引在时间聚合下闭合提供了充分条件，即两个索引在观察聚合时具有相同的值。在这里，我们使用美国股票数据以及 Fama 和 French (1993) 和 Carhart (1997) 研究的四个异常情况提供经验示例，其中这两个指数在某些股票中具有几乎相同的值，而当汇总观察结果时，出现一个异常情况。与夏普比率不同，AS 和 FH 性能指标在时间聚合方面具有更稳定的特性。