This work presents a novel application of the Stochastic Dual Dynamic Problem (SDDP) to large-scale asset allocation. We construct a model that delivers allocation policies based on how the portfolio performs with respect to user-defined (synthetic) indexes, and implement it in a SDDP open-source package. Based on US economic cycles and ETF data, we generate Markovian regime-dependent returns to solve an instance of multiple assets and 28 time periods. Results show our solution outperforms its benchmark, in both profitability and tracking error.