The main motivation for this paper is to introduce a novel hybrid method for the prediction of the directional movement of financial assets with an application to the ASE20 Greek stock index. Specifically, we use an alternative computational methodology named evolutionary support vector machine (ESVM) stock predictor for modeling and trading the ASE20 Greek stock index extending the universe of the examined inputs to include autoregressive inputs and moving averages of the ASE20 index and other four financial indices. The proposed hybrid method consists of a combination of genetic algorithms with support vector machines modified to uncover effective short-term trading models and overcome the limitations of existing methods. For comparison purposes, the trading performance of the ESVM stock predictor is benchmarked with four traditional strategies (a naïve strategy, a buy and hold strategy, a moving average convergence/divergence and an autoregressive moving average model), and a multilayer perceptron neural network model. As it turns out, the proposed methodology produces a higher trading performance, even during the financial crisis period, in terms of annualized return and information ratio, while providing information about the relationship between the ASE20 index and DAX30, NIKKEI225, FTSE100 and S&P500 indices