Portfolio Selection Under Various Risk Measures

Portfolio selection has been a major area of study after Markowitz\u27s ground-breaking paper. Risk quantification for portfolio selection is studied in the literature extensively and many risk measures have been proposed. In this dissertation we study portfolio selection under various risk measures. After exploring important risk measures currently available we propose a new risk measure, Unequal Prioritized Downside Risk (UPDR). We illustrate the formulation of UPDR for portfolio selection as a mixed-integer program. We establish conditions under which UPDR can be formulated as a linear program. We study single-period portfolio selection using two risk measures simultaneously. We propose four alternate models for single-period portfolio selection and elucidate their formulation. We discuss a procedure to obtain a set of solutions for the four models and illustrate this procedure with a numerical example. We study these models when chance constraint is included and also examine sensitivity analysis. Multi-period portfolio selection strives to build an optimal portfolio by doing multiple investment decisions during the investment period. We introduce four alternate models for multi-period portfolio selection under a two-risk measure context. A procedure to solve these four models is outlined with a numerical illustration. We also propose a new two-step process for portfolio selection. A sample of securities from the NYSE and BSE are taken and an empirical study is conducted to illustrate the two-step process for portfolio selection. Finally, we discuss conclusions based on the models we propose and directions for future research