Robust Portfolio Optimization with Data-Driven Contextual Uncertainty Sets

This paper proposes a robust portfolio optimization model with data-driven contextual uncertainty sets. At each rebalancing, observed macroeconomic variables define the current context, and the historical returns associated with the k closest contexts, selected by the k-nearest neighbors method, compose a polyhedral set of plausible scenarios. The allocation decision is formulated as a max–min problem, later reformulated as linear programming through the variable θt, incorporating proportional transaction costs and non-short sale constraint. The model is evaluated in a backtest with five North American sectoral portfolios, between January 2006 and September 2025, for different values of k. The results show that k = 60 and 72 present a better balance between return and risk, outperforming the benchmarks in final wealth, accumulated return, Sharpe ratio, and maximum drawdown, in addition to exhibiting low violation of the robust quota in the analyzed context.