Incomplete risk-preference information in portfolio decision analysis

Portfolio decision analysis models support decisions on the allocation of resources among assets with uncertain outcomes (e.g., investments, projects or stocks). These models require information on the decision maker’s risk-preferences which can be difficult to obtain in practice. Stochastic dominance criteria show promise in this regard as they can compare portfolios without exact specification of risk-preferences, but the current literature lacks practical approaches for generating the efficient frontier, i.e., the set of those portfolios that are not stochastically dominated by any other portfolio. We address this gap by developing models to identify sets of portfolios that are efficient in the sense of second- or third-order stochastic dominance (SSD, TSD). These models provide novel insights into the composition of portfolios belonging to the efficient frontier by, e.g., identifying those assets that are included in all efficient portfolios. Moreover, the identification of the efficient frontier makes it possible to utilize additional information on the decision maker’s risk-preferences to further reduce the set of admissible portfolio alternatives, and to analyze the implications this information has on the amount of capital that should be allocated to each individual asset. We illustrate the usefulness of these models with applications in project portfolio selection and financial portfolio diversification.