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We propose a fast and flexible method to scale multivariate return volatilitypredictions up to high-dimensions using a dynamic risk factor model. Ourapproach increases parsimony via time-varying sparsity on factor loadings andis able to sequentially learn the use of constant or time-varying parametersand volatilities. We show in a dynamic portfolio allocation problem with 452stocks from the S&P 500 index that our dynamic risk factor model is able toproduce more stable and sparse predictions, achieving not just considerableportfolio performance improvements but also higher utility gains for themean-variance investor compared to the traditional Wishart benchmark and thepassive investment on the market index.

Dynamic Portfolio Allocation in High Dimensions using Sparse Risk Factors