How Trading Volume Relates to Price Impact
Summary
The document separates two reasons trading activity can coincide with price moves. Informational impact occurs when a trader’s order reflects insight about future value; the price may move because the information is correct, without volume itself explaining the change. Mechanical impact occurs when one-sided buying or selling pressure moves the market.
For mechanical impact, it gives a square-root relation: price change scales with instrument volatility and the square root of order quantity relative to traded volume, with an additional term involving the bid-ask spread. This offers a framework for thinking about volume and impact, rather than a simple correlation that applies in every case. The discussion does not provide an empirical estimate or explain how to fit the relation to data. It also leaves open how wash trading affects the inputs and how to distinguish informational from mechanical impact in practice.
Key ideas
- Price impact can arise from information revealed by trading or from mechanical order pressure.
- The square-root model relates impact to volatility and order size relative to traded volume.
- The proposed relation also includes a term tied to the bid-ask spread.
- Volume alone does not explain price moves when informed trading drives the change.
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# To what degree is volume correlated with price impact?
# To what degree is volume correlated with price impact?
There is question from 2017 here but the answer given doesn't really go into any detail.
How correlated is volume with price impact? Especially with regard to wash trading; For example, wash trading is extremely prevalent in crypto markets and yet, despite this, one can still a clear correlation between volume and price impact.
Is there a nice formula that can break down the relationship?
## Answer by lehalle (score 3)
https://quant.stackexchange.com/a/77835
Market impact corresponds to price moves due to the intensity of trading in one direction. As you mention: when a market participant trades in size in one direction, the price usually follows.
They are two reasons:
- the first one is informational: the trader is right to buy (or sell), he or she understood the price will go up (or down). Hence in this case, a relation with volume is not needed: the price will move.
- the second one is mechanical: it is the one you mention. The pressure of the buying flow moves the price. In such a case the relation between the traded quantity $Q$ and the price move $\Delta P$ is square root (Bacry, Emmanuel, Adrian Iuga, Matthieu Lasnier, and C-A L. "Market impacts and the life cycle of investors orders" Market Microstructure and Liquidity 1, no. 02 (2015)): $$\Delta P\propto \sigma\sqrt{Q\over V} + a\,\psi,$$ where $\sigma$ is the volatility of the specific instrument, $\psi$ its bid-ask spread, and $V$ its traded volume.
JP Bouchaud explains the two effects quite well in his Introduction to Part II. Price Impact: Information Revelation or Self- Fulfilling Prophecies? to Capponi, Agostino, and C-A L, eds. Machine Learning and Data Sciences for Financial Markets: A Guide to Contemporary Practices Cambridge University Press, 2023.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.