Predicting Financial Asset Returns with Factor and Lead-Lag Relationships: Ridge Regression with Lagged Penalty

The traditional finance theory, efficient market hypothesis (EMH), claims that asset returns fully reflect all available information, making it impossible to consistently beat the market on a risk-adjusted basis. However, several anomalies, such as the value and momentum factor, and lead-lag effect, have been observed that cannot be explained by the EMH. In this study, we propose a new linear predictive regression model that incorporates factor information as well as lead-lag information from other assets to increase the predictive power. Our proposed method extends the Ridge regression model by introducing a lagged penalty, which avoids multicollinearity and overfitting. The regularization term of the proposed method is a linear combination of the squared penalty of the coefficient and the squared penalty of the deviation from the coefficient of the previous estimation result. We prove that our proposed method can yield superior profitability compared to other linear models. Additionally, we identify the effective factors for predicting future returns of the U.S. stocks such as the Reversal factor of commodities.