Robust portfolio optimization under epistemic uncertainty

Abstract

This thesis proposes formulations and algorithms for robust portfolio optimization under both aleatory uncertainty (i.e., natural variability) and epistemic uncertainty (i.e., imprecise probabilistic information) arising from interval data. In this research, epistemic uncertainty is represented using two approaches: (i) moment bounding approach and (ii) likelihood-based approach. The moment bounding approach requires that the uncertainty analysis for the epistemic variables be performed inside the robust portfolio optimization framework. This thesis first proposes a nested robustness-based portfolio optimization formulation using the moment bounding approach-based representation of epistemic uncertainty. The nested robust portfolio formulation is simple to implement, however, the computational cost is often high due to the epistemic analysis performed inside the optimization loop. A decoupled approach is then proposed to un-nest the robustness-based portfolio optimization from the analysis of epistemic variables to achieve computational efficiency. This study also proposes a single-loop robust portfolio optimization formulation using the likelihood-based representation of epistemic uncertainty that completely separates the epistemic analysis from the portfolio optimization framework and thereby achieves further computational efficiency. This research considers four portfolio selection models such as classical mean-variance, meandownside risk (i.e., lower semi variance), median-variance, and median-downside risk models. The proposed robust portfolio optimization formulations are tested on real market data and performance of the robust optimization models is discussed empirically based on portfolio return and risk. Two groups of data (both single and multiple interval data) from five S&P 500 companies are used to examine the proposed models. The portfolio return levels in the four models do not decrease at the same rate with the change of the risk factor. The median-variance model and median-downside risk model provide the higher return values than mean-variance model and mean-downside risk model, respectively. Also, the mean-variance model and medianvariance model provide lower risk values than mean-downside risk model and median-downside risk model, respectively. The single-loop robust portfolio optimization formulation generates better optimal solutions than the decoupled approach in terms of both portfolio return and risk. The proposed robust portfolio formulations are also compared with a nominal mean-variance model, and it is seen that the proposed decoupled formulation generates conservative solutions in the presence of epistemic uncertainty.