A penalized two-pass regression to predict stock returns with time-varying risk premia

TL;DR

This paper introduces a penalized two-pass regression model with time-varying factor loadings to improve stock return predictions, ensuring no-arbitrage conditions and reducing prediction errors in empirical tests.

Contribution

It proposes a novel penalized regression approach that enforces sparsity and no-arbitrage constraints simultaneously in modeling time-varying risk premia.

Findings

Penalization without grouping often violates no-arbitrage restrictions.

The proposed method outperforms models without grouping or with time-invariant factors.

Empirical results show reduced prediction errors with the new approach.

Abstract

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.