The entropy rate of a dynamic process measures the uncertainty that remains in the next information produced by the process given complete knowledge of the past. It is thus a natural measure of the difficulty faced in predicting the evolution of the process. The first question investigated here is whether stock price time series exhibit temporal dependencies that can be measured through entropy estimates. Then we study the extent to which the return of GP-induced financial trading rules is correlated with the entropy rates of the price time series. Experiments are conducted on EOD data of the stocks making up the NYSE US 100 index during the period 2000-2006, with genetic programming being use to induce the trading rules.