riskaverse

Risk-averse describes a preference pattern in decision making under uncertainty whereby a decision-maker prefers a sure outcome to a gamble with the same expected value. In economics and finance, risk-averse individuals accept smaller expected returns to avoid uncertainty. A risk-averse person prefers a certain amount of wealth to a lottery with the same expected wealth.

From a utility perspective, risk aversion corresponds to a concave utility function of wealth: as wealth increases, the marginal utility of wealth decreases. This concavity implies that the loss of utility from potential downside weighs more heavily than the potential upside of the same amount.

The degree of risk aversion can be summarized by the Arrow-Pratt coefficients: absolute risk aversion A(x) = -u''(x)/u'(x), and relative risk aversion R(x) = -x u''(x)/u'(x). A constant relative risk aversion (CRRA) utility function, u(x) = x^(1-ρ)/(1-ρ) for ρ ≠ 1, exhibits constant R equal to ρ. When ρ > 0 the agent is risk averse; ρ = 0 corresponds to risk neutrality; ρ < 0 to risk seeking.

Implications include demand for insurance, preference for diversification, and the requirement of a risk premium in expected returns. In finance, risk aversion shapes portfolio choice and asset prices, with more risk-averse investors demanding higher expected returns for bearing risk.

Risk aversion can vary across domains and individuals and may depend on wealth, time horizon, and framing. It is a foundational concept in models of choice under uncertainty, but empirical assessments show heterogeneity and context dependence.