Forecasting the stock risk premium: A new statistical constraint

We develop a new statistical constraint to improve the stock return forecasting performance of predictive models. This constraint uses a new objective function that combines the Huber loss function with the Ridge penalty. Out‐of‐sample results indicate that our constraint improves the predictive ability of the univariate models. The constrained univariate models significantly outperform the historical average benchmark model assuming no predictability. The forecast improvement based on the new constraint is also evident for multivariate information methods including forecast combination and diffusion index. The model is capable of capturing time‐varying risk which serves as the potential economic explanation of the improved return predictability. Our results are robust to different evaluation subsamples, validation sample lengths, and different risk aversion coefficients.