The paper investigates the portfolio allocation effects of increased asset co-movements during extreme market downturns. We develop a model for the state variables underlying the stock price process that allows for increased and asymmetric dependence between extreme return realizations. We isolate the portfolio hedging demands that arise due to extreme co-movements and find a substantial shift of the portfolio holdings toward the risk-free asset. Ignoring the dependence between extreme events gives rise to sizeable economic losses. It penalizes investors for holding levered positions, and reduces the gains from diversification. These findings are robust along different specifications of the utility function, varying levels of risk aversion, and alternative modeling assumptions of extreme co-movements and conditional correlation.