Abstract
I study the relationship between trading volume and asset price fluctuations by developing a model of price formation with exogenous liquidity supply and demand. Competition imposes zero expected profits on liquidity providers. This condition implies that the expected future price equals the average execution price, thereby determining permanent price impact from the liquidity consumed by each trade. Aggregating price impacts across markets and time yields analytical relationships among trading volume, volatility, and liquidity at low frequency. I test these relationships using transaction-level data on U.S. common stocks from 2003 to 2024, aggregated into approximately one million stock-month observations. The predicted relationships provide an accurate description of the data. I estimate regression coefficients that are statistically indistinguishable from their predicted values under quadratic liquidity supply, and the results are qualitatively robust to alternative functional forms. Overall, the model reveals a simple structure linking trading volume to volatility under competitive liquidity provision.
