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Temporal aggregation of the Aumann–Serrano and Foster–Hart performance indexes

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  • Hodoshima, Jiro
  • Yamawake, Toshiyuki

Abstract

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.

Suggested Citation

  • Hodoshima, Jiro & Yamawake, Toshiyuki, 2022. "Temporal aggregation of the Aumann–Serrano and Foster–Hart performance indexes," International Review of Financial Analysis, Elsevier, vol. 83(C).
    • Handle: RePEc:eee:finana:v:83:y:2022:i:c:s1057521922001922
    DOI: 10.1016/j.irfa.2022.102232
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    References listed on IDEAS

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    1. Niu, Cuizhen & Guo, Xu & McAleer, Michael & Wong, Wing-Keung, 2018. "Theory and application of an economic performance measure of risk," International Review of Economics & Finance, Elsevier, vol. 56(C), pages 383-396.
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    More about this item

    Keywords

    Temporal aggregation; Performance index; Aumann–Serrano index; Foster–Hart index; Sharpe ratio;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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