Trading portfolios at Financial institutions are typically driven by a large number of financial variables. These variables are often correlated with each other and exhibit by time-varying volatilities. We propose a computationally efficient Value-at-Risk (VaR) methodology based on Dynamic Factor Models (DFM) that can be applied to portfolios with time-varying weights, and that, unlike the popular Historical Simulation (HS) and Filtered Historical Simulation (FHS) methodologies, can handle time-varying volatilities and correlations for a large set of financial variables. We test the DFM-VaR on three stock portfolios that cover the 2007-2009 financial crisis, and find that it reduces the number and average size of back-testing breaches relative to HS-VaR and FHS-VaR. DFM-VaR also outperforms HS-VaR when applied risk measurement of individual stocks that are exposed to systematic risk.