Working Paper: CEPR ID: DP1650
Authors: Fatma Lajeri; Lars Tyge Nielsen
Abstract: We show that in order to determine whether one decision-maker is more risk averse than another, it is sufficient to consider their attitudes towards a given two-parameter family of risks. When all risks belong to this family, useful comparisons of risk aversion can be made even in situations of ?background risk?. Since expected utility becomes a function of mean and standard deviation, risk aversion can be measured by the marginal rate of substitution between mean and standard deviation. A utility function exhibits decreasing risk aversion if, and only if, this slope is a decreasing function of the mean. Second, we use the concept of prudence to solve a long-standing problem in mean-variance analysis: what is the economic interpretation of the concavity of a utility function which is a function of mean and variance? We show that in the case of normal distributions, utility is concave as a function of variance and mean if, and only if, it exhibits decreasing prudence.
Keywords: risk aversion; prudence
JEL Codes: 081
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| risk aversion (D81) | decision-making behavior (D91) |
| marginal rate of substitution between mean and standard deviation (C46) | risk aversion (D81) |
| wealth (D14) | risk aversion (D81) |
| utility function properties (D11) | prudence (D14) |