Increases in skewness and three-moment preferences

We call an agent skewness affine if and only if his marginal willingness to accept a risk increases when the distribution of the risk becomes more skewed to the right. Skewness affinity is shown to be equivalent to the marginal rate of substitution between mean and variance of wealth being decreasing in the skewness. This property allows us to characterize the comparative static effect of increases in the skewness in quasi-linear decision problems. Over domains of skewness-comparable lotteries skewness affinity is equivalent to the von Neumann–Morgenstern utility index of relative temperance being smaller than three. ► We characterize skewness affinity for three-moment preferences. ► An agent is skewness affine if he accepts a higher risk when the risk’s distribution becomes more right-skewed. ► In quasi-linear decision models skewness affine agents increase risk taking upon an increase in the skewness.