Portfolio Optimization with Other Real Features

Real features are all the additional characteristics an investor is interested to consider when selecting a real portfolio, because they reflect preferences or information not captured by the model otherwise, or he/she is obliged to include as restrictions imposed by market conditions. Besides transaction costs, real features include, transaction lots, thresholds on investment, restriction on the number of assets (cardinality constraint), and decision dependency constraints among assets or classes of assets. In this chapter, we focus on all real features different from transaction costs. We analyze their practical relevance and show how to model them in a portfolio optimization problem. The modeling of some real features is possible by using as decision variables the asset shares. In several cases, however, the introduction of real features implies the need of variables that represent the amount of capital invested in each asset. When discussing each real feature, and the way to treat it in a portfolio optimization model, we specify if the use of amounts instead of shares is required. Finally, we show how the modeling of some real features may require the introduction of binary or integer variables giving rise to mixed integer linear programming problems.