We thoroughly analyze the asset allocation problem under exponential utility and generalized hyperbolic (GH) distribution of returns. We provide expressions to compute the optimal portfolio weights, as well as a formula to compute the optimal portfolio when the feasible set is a linear combination of pre-existing portfolios. We also dene more general measures of risk and return that allow the construction of an “efficient frontier” and are useful to assess the performance of investment alternatives and portfolio rules. Additionally, we relate our results with shrinkage estimators and three-fund rules, in the sense that they can be used to mitigate the eect of considering an elliptical distribution of returns when the true distribution is non-elliptical. Finally, we present an application to active portfolio management, and numerical results that assess the performance of several mean-variance portfolio rules under a particular case of GH distribution.