 Relative risk aversion coefficient

For positive wealth and increasing twice differentiable utility function, this dimensionless coefficient measures sensitivity to proportional wealth risk. If it is constant, integration gives $U^{\prime }(W)=c{W}^{-\alpha }$ with $c>0$, and hence $U(W)=c{W}^{1-\alpha }/(1-\alpha )+d$ for $\alpha \ne 1$ or $c\log W+d$ for $\alpha =1$. Positive, zero and negative coefficients correspond respectively to risk aversion, risk neutrality and risk seeking. The usual CRRA utility subclass takes $\alpha >0$.