In this paper, we develop a portfolio selection model which allocates financial assets by maximising expected return subject to the constraint that the expected maximum loss should meet the value-at-risk limits set by the risk manager. Similar to the mean–variance approach a performance index like the sharpe index is constructed. Furthermore when expected returns are assumed to be normally distributed we show that the model provides almost identical results to the mean–variance approach. We provide an empirical analysis using two risky assets: us stocks and bonds. The results highlight the influence of both non-normal characteristics of the expected return distribution and the length of investment time horizon on the optimal portfolio selection.