Over the last decade, numerous papers have investigated the use of GP for creating financial trading strategies. Typically in the literature results are inconclusive but the investigators always suggest the possibility of further improvements, leaving the conclusion regarding the effectiveness of GP undecided. In this paper, we discuss a series of pretests, based on several variants of random search, aiming at giving more clearcut answers on whether a GP scheme, or any other machine-learning technique, can be effective with the training data at hand. The analysis is illustrated with GP-evolved strategies for three stock exchanges exhibiting different trends.