A practical guide to robust portfolio optimization

Abstract

Robust optimization takes into account the uncertainty in expected returns to address the shortcomings of portfolio mean-variance optimization, namely the sensitivity of the optimal portfolio to inputs. We investigate the mechanisms by which robust optimization achieves its goal and give practical guidance when it comes to the choice of uncertainty in form and level. We explain why the quadratic uncertainty set should be preferred to box uncertainty based on the literature review, we show that a diagonal uncertainty matrix with only variances should be used, and that the level of uncertainty can be chosen as a function of the asset Sharpe ratios. Finally, we use practical examples to show that, with the proposed parametrization, robust optimization does overcome the weaknesses of mean-variance optimization and can be applied in real investment problems such as the management of multi-asset portfolios or in robo-advising.

Listed Infrastructure Assets as a Tool for Diversification

“…is equal to 𝛿 2 . (Yin et al, 2019) follows the spirit of Bayesian covariance matrix shrinkage factor and chooses Σ 𝜇 ≡ 𝑑𝑖𝑎𝑔(Σ) and determines 𝛿 2 by heuristics in the data. In this study, we adopt the diagonal of covariance matrix as the uncertainty matrix because the errors in small covariances can be mitigated by weighting them down.…”

Robust and Sparse Portfolio: Optimization Models and Algorithms

“…Assume that asset returns are independent and identically distributed and µ − µ follows a normal distribution with mean value 0 and covariance matrix Ω, where Ω is the covariance matrix of errors in the expected asset return. In Yin et al [35], they discussed the choice of uncertainty matrix Ω in the quadratic uncertainty set and proposed the selection criteria. In the quadratic uncertainty case, min µ∈U w T µ in problem ( 5) is equivalent to the following problem:…”

Can Zakat and Purification Be Employed in Portfolio Modelling?

“…In addition, the MV model is also said to be sensitive because of the input parameters used. Various kinds of optimal robust portfolio methods have been developed (Supandi, Rosadi, & Abdurakhman, 2017;Yin, Perchet, & Soupé, 2021). However, the MV model is still used as a reference in the framework of development and modification for optimal portfolio modelling.…”