Putting the Aumann–Serrano Riskiness Index to work

Abstract

Purpose The purpose of this study is to estimate the convergence order of the Aumann–Serrano Riskiness Index. Design/methodology/approach This study uses the equivalent relation between the Aumann–Serrano Riskiness Index and the moment generating function and aggregately compares between each two statistical moments for statistical significance. Thus, this study enables to find the convergence order of the index to its stable value. Findings This study finds that the first-best estimation of the Aumann–Serrano Riskiness Index is reached in no less than its seventh statistical moment. However, this study also finds that its second-best approximation could be achieved with its second statistical moment. Research limitations/implications The implications of this research support the standard deviation as a statistically sufficient approximation of Aumann–Serrano Riskiness Index, thus strengthening the CAPM methodology for asset pricing in the financial markets. Originality/value This research sheds a new light, both in theory and in practice, on understanding of the risk’s structure, as it may improve accuracy of asset pricing.

On the General Deviation Measure and the Gini coefficient

“…Thus, for example, the Mean Absolute Deviation, the standard deviation, and the Value‐at‐Risk measurements cannot be considered a Coherent Risk Measure, but they are considered a General Deviation Measure. Conditional‐Value‐at‐Risk satisfies both the Coherent Risk Measure and the General Deviation Measure requirements, yet the Aumann–Serrano riskiness index still violates these two definitions (Nisani, 2018b; Nisani et al, 2023). However, these two definitions share a formal relation: $$\delta (X)=\rho (X-{\mu }_{X})$$ for strictly expectation‐bounded risk measures.…”