Portfolio Selection with Multiple Time Horizons: A Mean Variance ‐ Stochastic Goal Programming Approach

Standard approaches to portfolio selection from classical Markowitz mean‐variance model require using a time horizon of historical returns over a period that the investor defines in a conventional way. To avoid arbitrary choice of the time horizon, this paper proposes a satisfying compromise solution relying on mean variance ‐ stochastic goal programming (EV‐SGP), where the goals are defined from the different time horizons under consideration. As the information on returns provided by each horizon is of different quality and reliability, critical parameters in this method are Arrow's absolute risk aversion (ARA) coefficients and the investor's preferences for each horizon. After formulating the proposed method, a suitable technique to determine the ARA coefficients in our context is given in a strict way according to Arrow's risk theory. An actual numerical example is developed throughout the paper leading to consistent results. The sensitivity analysis shows robust solutions. A generalization of results requires further examples.