High asset price volatility alongside low portfolio flows reveals a fundamental trade-off between investor disagreement and price impact: When volatility is high but flows are small, investors must either largely agree with each other or be insensitive to price changes, implying large price impacts of small flows. We formalize this relationship in a price impact bound based on price volatility, flow volatility, and investor agreement. Applying our bound to U.S. equities yields large price impacts, implying that flows are central to understanding price dynamics. Our bounds align with event-study estimates while revealing novel patterns across horizons, assets, and aggregation levels.