On a New Index Aimed at Comparing Risks

Marina Resta, Maria Erminia Marina

DIEC, University of Genova, Genova, Italy.

DOI: 10.4236/jmf.2015.52011                

Abstract

This paper fits into the research stream started by Aumann and Serrano (2008) with their index R_AS, and introduces a new index of riskiness called I_θ. In particular, our intuition moves from the observation that the R_AS index is defined over the set of gambles whose expected value of losses is lower than the one of gains. We then restrict the attention on investment opportunities in a proper relation with a benchmark value and we build the index I_θ. The mathematical features of the new index are discussed in deepest detail, providing evidence that I_θ can be used by the investor in comparing risks: θ plays the role of a threshold value such that once fixed in the range (0,1] , I_θ suggests to take into consideration a gamble (an investment, an asset) g only if the ratio between the expected value of its losses and the expected value of its gains is lower than such θ. Moreover, I_θ nests R_AS as special case when θ = 1, and it satisfies both homogeneity and duality properties. In the light of these features, I_θ seems to satisfy the common need among practitioners for flexible index of riskiness.

Keywords

Index of Riskiness, Threshold Value, Losses/Gains Ratio

Conflicts of Interest

The authors declare no conflicts of interest.

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