Risk aversion — the tendency to prefer a sure outcome to a gamble with the same expected value — is the most fundamental behavioral regularity in decision under risk. In expected utility theory, risk aversion corresponds to a concave utility function, and the degree of risk aversion is quantified by the Arrow-Pratt coefficient of absolute risk aversion.
Arrow-Pratt Measures
Relative risk aversion: R(x) = −x · u″(x) / u′(x)
CARA (constant absolute): u(x) = −e^(−αx)
CRRA (constant relative): u(x) = x^(1−ρ) / (1−ρ)
The risk premium π for a gamble with variance σ² is approximately π ≈ ½·r(x)·σ² for small risks. The certainty equivalent is the sure amount that is equally preferred to the gamble: CE = E[x] − π. These quantities connect the abstract curvature of the utility function to observable behavior in financial decisions.
Psychological Evidence
Laboratory studies find that risk aversion varies across domains (people are more risk averse for gains than for losses — the reflection effect), depends on the magnitude of stakes, and differs between experienced and described probabilities. Prospect theory accounts for these patterns through the value function's different curvatures for gains and losses, along with probability weighting that makes rare events loom larger than their probability warrants.