We investigate the implications of non-normality for asset allocation and pricing. Asset returns non-normality is captured through a multivariate normal-exponential model; we develop an estimation procedure based on a generalized method of moments. Investors’ non-normality concerns are introduced by adding a linear non-normality constraint to an otherwise standard mean-variance framework. The optimal portfolio solution is obtained in closed form and can be reformulated as a three-fund separation strategy. Suboptimal portfolios that ignore non-normality or are naive in terms of diversification may result in important welfare costs as measured by the certainty equivalent, notably for the most risk-tolerant investors who target large non-normality ratios. In equilibrium, expected returns admit a two-beta representation in which the most important beta in explaining their cross-sectional variation is the one capturing non-normality (more than 60%) while the CAPM beta explains less than 12%.