Distributionally robust end-to-end portfolio construction

AbstractWe propose an end-to-end distributionally robust system for portfolio construction that integrates the asset return prediction model with a distributionally robust portfolio optimization model. We also show how to learn the risk-tolerance parameter and the degree of robustness directly from data. End-to-end systems have an advantage in that information can be communicated between the prediction and decision layers during training, allowing the parameters to be trained for the final task rather than solely for predictive performance. However, existing end-to-end systems are not able to quantify and correct for the impact of model risk on the decision layer. Our proposed distributionally robust end-to-end portfolio selection system explicitly accounts for the impact of model risk. The decision layer chooses portfolios by solving a minimax problem where the distribution of the asset returns is assumed to belong to an ambiguity set centered around a nominal distribution. Using convex duality, we recast the minimax problem in a form that allows for efficient training of the end-to-end system.Keywords: Portfolio optimizationAsset allocationMachine learningDistributionally robust optimizationStatistical ambiguity Disclosure statementNo potential conflict of interest was reported by the author(s).Data availabilityThe data that support the numerical experiments in this study are available online from the following two sources below. Feature data: These data are openly available through Kenneth French's Data Library at https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.Asset data: AlphaVantage at www.alphavantage.co. Restrictions apply to the availability of these data, which were used under a free academic license for this study.Correction StatementThis article has been corrected with minor changes. These changes do not impact the academic content of the article.Notes1 For a description of ϕ-divergence functions and their convex conjugates, please refer to Tables 2 and 4 in Ben-Tal et al. (Citation2013).2 If ϕ is the Hellinger distance, the DR layer reduces to a second-order cone program provided the function R(X) in Proposition 2.1 is quadratic or piecewise linear. If ϕ is the Variational distance, the DR layer reduces to a linear program provided the function R(X) is piecewise linear. Otherwise, the complexity of the problem is dictated by the choice of R(X).3 Note that we have defined the Sharpe ratio using the portfolio returns rather than the portfolio excess returns (i.e. the returns in excess of the risk-free rate).Additional informationFundingThis work was supported by Natural Sciences and Engineering Research Council of Canada [PDF - 557467 - 2021].