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.

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As of 2022, greenhouse gases (GHG) emissions reporting and auditing are not yet compulsory for all companies, and methodologies of measurement and estimation are not unified. We propose a machine learning-based model to estimate scope 1 and scope 2 GHG emissions of companies not reporting them yet. Our model, designed to be transparent and completely adapted to this use case, is able to estimate emissions for a large universe of companies. It shows good out-of-sample global performances as well as good out-of-sample granular performances when evaluating it by sectors, countries, or revenue buckets. We also compare the model results to those of other providers and find our estimates to be more accurate. Explainability tools based on Shapley values allow the constructed model to be fully interpretable, the user being able to understand which factors split explains the GHG emissions for each particular company.