Fat tails in financial time series and increase of stocks cross-correlations in high volatility periods are puzzling facts that ask for new paradigms. Both points are of key importance in fundamental research as well as in Risk Management (where extreme losses play a key role). In this paper we present a new model for an ensemble of stocks that aims to encompass in a unitary picture both these features. Equities are modelled as quasi random walk variables, where the non-Brownian components of stocks movements are leaded by the market trend, according to typical trader strategies. Our model suggests that collective effects may play a very important role in the characterization of some significantly statistical properties of financial time series.