Long-History PCA in a Dynamic Factor Model with Weak Loadings

Estimated covariance and precision matrices of asset returns significantly influence the set of portfolios compliant with risk budgets and their potential losses. Statistical risk modeling approaches often assume temporal stability for consistency with a static factor structure, typically estimated within TM ∼ 250 days of data history, resulting in finite-sample estimation error when the dimension of the population exceeds the number of observations. Our study introduces Long-History PCA (LH-PCA), utilizing extended data histories (e.g., TL ∼ 1500 trading days) to forecast the daily risk profile based on dynamic factor structures with heterogeneous factor strengths. The use of a longer data history mitigates excess dispersion bias in the estimated factor loadings, particularly in the presence of weak factors. As shown in simulations and empirical data from the United States and European stock markets, our approach substantially mitigates second-order risk bias compared to traditional methods using medium horizons (TM), both with and without the augmentation of Responsive Covariance Adjustment (RCA) using a short half-life (TS) of 40 days.