Tuesday, April 23rd @ 11:00-12:30 PM, 648 Evans Hall and Zoom
The accurate estimation of the covariance matrix and its inverse (= precision) matrix of asset returns significantly shapes the range of admissible portfolio compositions and the potential magnitude of associated losses, given the portfolio manager's predetermined risk budget. In this study, we propose Long-History PCA (LH-PCA), which uses longer data histories (T_L), such as 1500 trading days or six years, to predict daily portfolio risks. We show that LH-PCA consistently estimates dynamic factor models with essentially arbitrary variable volatility structures and time-varying loadings with heterogeneous strengths. By using a longer data history, the excess dispersion bias of minimum-variance optimized portfolios can be effectively mitigated by reducing the finite-sample correlations between factor returns and idiosyncratic returns, particularly in the presence of weaker factors. Combined with Responsive Covariance Adjustment (RCA) using a short half-life (T_S) of 40 days, our proposed approach offers substantial improvements in risk prediction for minimum-variance portfolios compared to alternative specifications, including traditional approaches using a medium horizon (T_M) of one or two years, in both simulations and empirical studies.