An integral index for measuring aversion to large‐scale risks

Joseph G. Eisenhauer (Department of Economics and Finance, Canisius College, Buffalo, New York, USA)

Studies in Economics and Finance

ISSN: 1086-7376

Publication date: 1 October 2006



Conventional measures of risk aversion based on first and second derivatives of utility are strictly local instruments, valid only for infinitesimally small changes in wealth. This paper to develop a global index suitable for assessing attitudes toward large‐scale risks.


Integral calculus is used to measure the geometric area between an individual's actual utility function and a linear function displaying risk neutrality, over the entire range of potential wealth outcomes for a given risk. The area is then converted to an index number.


Local and global measures of risk aversion yield similar interpersonal comparisons only for small risks; with larger risks, local measures distort interpersonal differences. The analysis also shows that individuals having exponential utility functions evaluate risk exclusively on the basis of wealth dispersion, whereas those with logarithmic or square‐root utilities consider both the mean and variance of wealth.


The global index is quantifiable if the functional form of utility is known; further research is needed to approximate the index when information about utility is limited.

Practical implications

The most important risks encountered in practice, such as the possibility of unemployment or disability, involve variations in wealth far larger than differential calculus is designed to accommodate. The integral index therefore provides a more appropriate basis for measuring and comparing risk preferences.


The paper provides an innovative geometric interpretation of global risk aversion, and in contrast to local measures, the integral index captures differences in the intensity of an individual's aversion toward risks of various magnitudes.



Eisenhauer, J.G. (2006), "An integral index for measuring aversion to large‐scale risks", Studies in Economics and Finance, Vol. 23 No. 3, pp. 202-210.

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