Risk aversion

Risk aversion is a concept in psychology, economics and finance theory explaining the behaviour of consumers and investors under uncertainty. Risk aversion occurs when a person is willing to accept a lower expected payoff if it means they can have a more predictable outcome. For a more general discussion see the main article risk.

Measures of risk aversion

The higher the curvature of u(c), the higher the risk aversion. However, since utility functions are not uniquely defined (only up to linear transformations), a measure that stays constant is needed. This measure is the Arrow-Pratt measure of absolute risk-aversion (ARA, after the economists Kenneth Arrow and John W. Pratt) or coefficient of absolute risk aversion, defined as

Related Topics:
Linear transformations - Kenneth Arrow - John W. Pratt

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

r_u(c)=-u(c)/u'(c).

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The following expressions relate to this term:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

• Constant absolute risk aversion (CARA) if $r\_u(c)$ is constant with respect to $c$
• Decreasing/increasing absolute risk aversion (DARA/IARA) if $r\_u(c)$ is decreasing/increasing.

Also used is the Arrow-Pratt measure of relative risk-aversion (RRA) or coefficient of relative risk aversion, which is defined as R_u(c) = c*r_u(c)=-cu(c)/u'(c). As above, the corresponding terms constant relative risk aversion (CRRA) and decreasing/increasing relative risk aversion (DRRA/IRRA) are used. This measure has the advantage that it is still a valid measure of risk aversion, even if it changes from risk-averse to risk-loving, i.e. is not strictly convex/concave over all c.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~