In this paper, we introduce a novel observation-driven model for high-dimensional correlation matrices, wherein the largest conditional eigenvalues are modelled dynamically. We impose equal correlations for any pair of assets from the same sector(s), which facilitates the use of a highly efficient alternative expression of the likelihood of a tν-distributed random vector. This alternative expression utilises the canonical form for block correlation matrices by Archakov and Hansen (2020). The dynamics of the eigenvalues is obtained from the Generalised Autoregressive Score (GAS) framework by Creal et al. (2011). We provide an empirical application by constructing Global Minimum Variance (GMV) portfolios using daily returns of 200 assets. In its simplest form, where just a single eigenvalue is updated, our model is extremely fast to estimate. It surpasses the Dynamic Equicorrelation (DECO) model model by Engle and Kelly (2012) and rivals their Block DECO (BDECO) model’s performance in achieving low variance in GMV portfolio returns. Joint work with: Stan Thijssen and Andre Lucas.