For increasing expected utility preferences, an investor is risk-averse when a sure mean is at least as desirable as the corresponding lottery. A concave utility function gives this preference by the Jensen inequality; a strictly concave utility gives strict preference for nondegenerate risks. Local risk aversion is measured by and its relative counterpart .
For positive wealth and increasing twice differentiable utility function, this dimensionless coefficient measures sensitivity to proportional wealth risk. If it is constant, integration gives with , and hence for or for . Positive, zero and negative coefficients correspond respectively to risk aversion, risk neutrality and risk seeking. The usual CRRA utility subclass takes .
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Risk aversion is a concept in economics and finance that refers to the preference of individuals or entities to avoid taking risks. It describes a behavior where people prefer outcomes with certainty over those with uncertain outcomes, even if the uncertain outcome could potentially yield a higher payoff. In practical terms, a risk-averse individual would choose a guaranteed, lower return over a higher return with some probability of loss.