Portfolio Optimization Model with and without Options under Additional Constraints

In this paper, first, we study mean-absolute deviation (MAD) portfolio optimization model with cardinality constraints, short selling, and risk-neutral interest rate. Then, in order to insure the investment against unfavorable outcomes, an extension of MAD model that includes options is considered. Moreover, since the data in financial models usually involve uncertainties, we apply robust optimization to the MAD model with options. Finally, a data set of S&P index is used to compare the effectiveness of options in the models in terms of returns and Sharpe ratios.