A novel interval optimisation approach is developed to include imprecise forecasts into the portfolio selection process for investors measuring upside potential and downside risk as deviations from a target return. Crisp scenarios are substituted by interval scenarios and the resulting interval optimisation problem is solved in a tractable manner by means of a bi-objective formulation exploiting a partial order relation between intervals. Four utility case studies involving assets from the F.T.S.E. M.I.B. Index are considered to illustrate how impreciseness can be efficiently handled in portfolio management.