On a New Index Aimed at Comparing Risks

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.