Robustness-based portfolio optimization under epistemic uncertainty

Md Asadujjaman,Kais Zaman

doi:10.1007/s40092-018-0292-4

Abstract

In this paper, we propose 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. Epistemic uncertainty is represented using two approaches: (1) moment bounding approach and (2) likelihood-based approach. This paper 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 paper 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. The proposed robust portfolio optimization formulations are tested on real market data from five S&P 500 companies, and performance of the robust optimization models is discussed empirically based on portfolio return and risk.

Highlights

Portfolio optimization deals with the problems of how to allocate the total wealth among a number of assets
This paper 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
The proposed robust portfolio optimization formulations are tested on real market data from five S&P 500 companies, and performance of the robust optimization models is discussed empirically based on portfolio return and risk

Summary

Introduction

Portfolio optimization deals with the problems of how to allocate the total wealth among a number of assets. Unlike the nested and decoupled formulations discussed in “Nested-loop formulation” and “Decoupled approach” sections respectively, the proposed robustness-based portfolio optimization formulation is solved using the worst-case maximum likelihood estimates of the mean value ri∗ and covariance. It is assumed that the investor is biased to invest at least 20% of total money on the first asset Since this problem contains single-interval data, we cannot solve this problem using the robust portfolio optimization methods that use median and lower semi-variance. The assumptions for correlations between asset returns and the minimum amount to be invested on the first asset are the same as in Example 1 Since this problem does not contain any single-interval data, we solve this problem by the decoupled approach using four different risk–return measures: mean–variance, median–variance, mean–downside risk, and median–downside risk. The proposed single-loop robust optimization formulation generally outperforms the decoupled formulations in terms of both return and risk

Conclusions

Findings

Decoupled