Optimal prediction under LINLIN loss: Empirical evidence

I compare the forecasts of returns from the mean predictor (optimal under MSE), with the pseudo-optimal and optimal predictor for an asymmetric loss function under the assumption that agents have an asymmetric LINLIN loss function. The results strongly suggest not using the conditional mean predictor under conditions of asymmetry. In general, forecasts can be improved by the use of optimal predictor rather than the pseudo-optimal predictor, suggesting that the loss reduction from using the optimal predictor can actually be important for practitioners as well.