A Bound on Price Impact and Disagreement

Asset prices are highly volatile, yet portfolio flows – changes in portfolio holdings – are relatively small. This reveals a fundamental tension between the price impact of portfolio flows and the agreement among investors: if price volatility is high while portfolio turnover is low, then either market participants largely agree with each other, or they are not sensitive to price changes (they are "inelastic"), resulting in large price impacts of portfolio flows. We formalize this trade-off and demonstrate that the ratio of return volatility to portfolio turnover provides a lower bound on price impact, conditional on the level of investor disagreement. Using several measures from survey data, we document substantial disagreement, implying meaningful lower bounds on price impacts. The bounds align closely with reduced-form estimates from a variety of quasi-experiments, such as price impacts from index reconstitutions. We demonstrate how these bounds vary across horizons, different assets, and at various levels of aggregation, including the aggregate stock market, and discuss their implications for asset pricing models. We argue that in such markets with high disagreement and price impact, observed trading activity is not peripheral but central to understanding asset price movements.