Are asset prices unduly volatile and often detached from their fundamentals? Does the bursting of financial bubbles depress the real economy? This paper addresses these issues by constructing a DSGE model with speculative bubbles. We characterize conditions under which storable goods, regardless of their intrinsic values, can carry bubbles, and agents are willing to invest in such bubbles despite their positive probability of bursting. The results show that systemic risk, commonly perceived changes in the bubble's probability of bursting, can generate boom-bust cycles with hump-shaped output dynamics and produce asset price movements many times more volatile than the economy's fundamentals. (JEL E13, E23, E32, E44, G01, G12).