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Putting the Aumann–Serrano Riskiness Index to work

Doron Nisani (School of Business Administration, University of Haifa, Haifa, Israel)
Amit Shelef (Department of Industrial Management, Sapir Academic College, Sderot, Israel)
Or David (School of Business Administration, University of Haifa, Haifa, Israel)

Review of Accounting and Finance

ISSN: 1475-7702

Article publication date: 17 January 2023

Issue publication date: 25 January 2023




The purpose of this study is to estimate the convergence order of the Aumann–Serrano Riskiness Index.


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.


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.


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.



The authors thank Prof Haim Shalit from Ben Gurion University of the Negev, Prof Ralph Sonenshine from the American University, Prof Ender Demir from Reykjavik University, Prof Uchenna Tony-Okeke from Coventry University, Prof Conrado Diego García-Gómez from University of Valladolid and the two anonymous reviewers for their helpful comments.


Nisani, D., Shelef, A. and David, O. (2023), "Putting the Aumann–Serrano Riskiness Index to work", Review of Accounting and Finance, Vol. 22 No. 1, pp. 84-122.



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