Relative risk aversion coefficient (source code)

= Relative risk aversion coefficient
{title2=$\alpha(W)=-WU''(W)/U'(W)$}

For positive wealth and increasing twice differentiable <utility function>, this dimensionless coefficient measures sensitivity to proportional wealth risk. If it is constant, integration gives $U'(W)=cW^{-\alpha}$ with $c>0$, and hence $U(W)=cW^{1-\alpha}/(1-\alpha)+d$ for $\alpha\ne1$ 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 $\alpha>0$.