This paper provides a strategy for portfolio risk management by inferring extreme movements in financial markets. The core of the provided strategy is a statistical model for the joint tail distribution that attempts to capture accurately the data generating process through an extremal modelling for the univariate margins and the multivariate dependence structure. It takes into account the asymmetric behavior of extreme negative and positive returns, the heterogeneous temporal and cross-sectional lead-lag extremal dependencies among the portfolio constituents. The strategy facilitates scenario generation for future returns, estimation of portfolio profit-and-loss distribution and calculation of risk measures, and hence, enabling us to answer several questions of economic interest. We illustrate the usefulness of our proposal by an application to stock market returns for the G5 economies.