Dynamic Factor Correlations

We introduce a dynamic factor correlation model whose core methodological innovation is a variation‐free parametrization of dynamic factor loadings, inspired by the generalized Fisher transformation. The model accommodates time‐varying correlations, heterogeneous heavy tails, and dependent idiosyncratic shocks. Applied to a Small Universe of 12 assets and a Large Universe of 323 stocks, the factor structure induces a sparse idiosyncratic correlation matrix with dependencies concentrated within subindustries, enabling scalability to high dimensions under a sparse block structure. Both factor loadings and correlations vary substantially. Allowing for heterogeneous heavy tails via convolution‐t$$ t $$ distributions yields sizable improvements relative to Gaussian and multivariate‐t$$ t $$ benchmarks.