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We model systemic risk using a common factor that accounts for market-wide shocks and a tail dependence factor that accounts for linkages among extreme stock returns. Specifically, our theoretical model allows for firm-specific impacts of infrequent and extreme events. Using data on the four sectors of the US financial industry from 1996 to 2011, we uncover two key empirical findings. First, disregarding the effect of the tail dependence factor leads to a downward bias in the measurement of systemic risk, especially during weak economic times. Second, when these measures serve as leading indicators of the St. Louis Fed Financial Stress Index, measures that include a tail dependence factor offer better forecasting ability than measures based on a common factor only.