We provide new empirical evidence for the way in which financial markets process information. Our results rely critically on high-frequency intraday price and volume data for theS & P500 equity portfolio and U.S. Treasury bonds, along with new econometric techniques, for making inference on the relationship between trading intensity and spot volatility around public news announcements. Consistent with the predictions derived from a theoretical model in which investors agree to disagree, our estimates for the intraday volume-volatility elasticity around important news announcements are systematically belowunity. Our elasticity estimates also decrease significantly with measures of disagreements in beliefs, economic uncertainty, and textual-based sentiment, further highlighting the key role played by differences-of-opinion.