The coefficients of tail dependence, based on copulas, are proposed as a measure for portfolio risk management. Some aspects of the macro and microstructures of the Colombian stock market are described. Such features encourage the use of measures such as the one proposed herein. The application of the proposed methodology to the fourteen most liquid shares in the study period (2007-2012) derived in some diversification recommendations under extreme events. The main conclusion, based on the starting hypothesis, is related to the evidence of high vulnerability in the Colombian stock market to an event of systemic risk.