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We analyze the demand for hedging and insurance by a firm facing cash-flow risks. We study how the firm's liquidity management policy interacts with two types of risk: a Brownian risk that can be hedged through a financial derivative, and a Poisson risk that can be insured by an insurance contract. We find that the patterns of insurance and hedging decisions are pole apart: cash-poor firms should hedge but not insure, whereas the opposite is true for cash-rich firms. We also find non-monotonic effects of profitability. This may explain the mixed findings of empirical studies on corporate demand for hedging and insurance.