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.
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.
