This paper fits into the research stream started by Aumann and Serrano (2008) with their index
RAS, and introduces a new index of riskiness called
Iθ. In particular, our intuition moves from the observation that the
RAS 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
Iθ. The mathematical features of the new index are discussed in deepest detail, providing evidence that
Iθ 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] ,
Iθ 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,
Iθ nests
RAS as special case when
θ = 1, and it satisfies both homogeneity and duality properties. In the light of these features,
Iθ seems to satisfy the common need among practitioners for flexible index of riskiness.