Abstract

Three Dimensions of Shortfall Risk: Transformation and Extension of Sen's Poverty Index

Frank Eggers
Andreas Pfingsten
Sven Rieso

Westfälische Wilhelms-Universität Münster

Incidence, intensity, and inequality of possible shortfalls relative to a target are features of shortfall risk. They are all integrated in a single measure by transfering an index known from the theory of poverty measurement, the Sen-Index. The index is reformulated to be used as a downside-risk measure for yield distributions in general. The resulting new Sen-Index provides a complete ranking of yield distributions with respect to the three aggregated dimensions of shortfall risk named above. Additionally, displaying the individual components separately makes the structure of a distribution's shortfall risk more transparent. Following, a discussion of selected axioms highlights a specific weakness of the new Sen-Index with respect to a certain degree of sensitivity to inequality in the distribution of downside yields. To overcome the detected shortcoming, a further modification is presented.

Despite remaining disadvantages, the new concepts provide improved performance in several respects, compared to indices that are popular at present.