We investigate the relationship between ownership structure of financial assets and non-fundamental risk. An asset is fragile if its owners collectively have to buy or sell. Such assets are susceptible to non-fundamental price movements. An asset can be fragile because of concentrated ownership, or because its owners face correlated liquidity shocks, ie., they must buy or sell at the same time. Two assets are "co-fragile" if their owners have correlated trading needs, even if the holdings of these owners do not directly overlap. We formalize this idea and apply it to the ownership of US stocks between 1990 and 2007. Consistent with our predictions, fragility strongly predicts future price volatility, and co-fragility predicts cross-stock return comovement.