Nº 21-09: A Penalized Two-Pass Regression to Predict Stock Returns with Time-Varying Risk Premia

We develop a penalized two-pass regression with time-varying factor loadings. The penalization in the first pass enforces sparsity for the time-variation drivers while also maintaining compatibility with the no arbitrage restrictions by regularizing appropriate groups of coefficients. The second pass delivers risk premia estimates to predict equity excess returns. Our Monte Carlo results and our empirical results on a large cross-sectional data set of US individual stocks show that penalization without grouping can yield to nearly all estimated time-varying models violating the no arbitrage restrictions. Moreover, our results demonstrate that the proposed method reduces the prediction errors compared to a penalized approach without appropriate grouping or a time-invariant factor model.