Mean-risk models have been widely used in portfolio optimisation. However, such models may
produce portfolios that are dominated with respect to second order stochastic dominance and therefore not
optimal for rational and risk-averse investors. This paper considers the problem of constructing a portfolio
which is nondominated with respect to second order stochastic dominance and whose return distribution
has specified desirable properties. The problem is multi-objective and is transformed into a single
objective problem by using the reference point method, in which target levels, known as aspiration points,
are specified for the objective function values. A model is proposed in which the aspiration points relate to
ordered return outcomes of the portfolio return. The model is extended by additionally specifying
reservation points, which act pre-emptively in the optimisation. The theoretical properties of the models
are studied. The performance of the models on real data drawn from the Hang Seng index is also
investigated
