Sign prediction and sign regression

Intuitively, the model prediction signs matter a lot in finance, especially for investment strategy constructions. This paper proposes an approach in which the loss function regularizes the errors in prediction in different ways. In particular, the loss function considers simultaneously errors in prediction signs and the sizes and signs of the residuals in the model prediction. Less weight is given to the residuals with correct prediction signs but more weight is assigned to the residuals with wrong prediction signs. This is important because agents make decisions according to model predictions, especially the signs of the predictions. Simultaneously, the residuals of larger size are also penalized more and the ones of smaller size are penalized less. Also, the signs of the residuals are considered in the loss function because they also affect decision making processes. For these reasons, training models by weights varying with the correctness of the prediction signs and the sizes and signs of the residuals is significant for decision making. This paper proposes a new approach termed as Sign regression which takes into account of these considerations. The simulation results show that Sign regression consistently performs better than the ordinary least squares method and least absolute deviations method out-of-sample. An application on Fama and French three factor model also shows good performance of Sign regression.