Sign prediction and sign regression

Intuitively, model-predicted signs matter a lot in finance, especially for investment strategy constructions. This paper proposes an approach whereby the loss function regularizes the errors in prediction in different ways. In particular, the loss function considers errors in predicted signs and the sizes and signs of the residuals in the model prediction simultaneously. Less weight is given to residuals with correctly predicted signs, while more weight is assigned to residuals with wrongly predicted signs. This is important because agents make decisions according to model predictions, especially the signs of the predictions. At the same time, larger residuals are penalized more and smaller residuals are penalized less. The signs of the residuals are considered in the loss function because they also affect decision-making processes. This paper proposes a new approach, termed “sign regression†, which takes these considerations into account. We show that ordinary least squares estimators generate better Sharpe ratios than sign regression does for most of the assets studied in this paper. However, sign regression can perform better for some assets.