Noise Trader Models and Concave Market Impact
Summary
The document explains a behavioral account of concave market impact using a simple model with informed and uninformed traders. In this account, informed traders tend to submit smaller orders and their trades contain more information about future prices. Other market participants respond to that information, so a small order can move prices more per share than a larger order associated with a noise trader. A noise trader is characterized as an unsophisticated agent whose trading has little predictive power.
The response describes these models as simple agent-based constructions used to build a mechanical explanation for observed market behavior. It also raises a qualification: the explanation need not depend on traders knowing who submitted a particular order. They might instead learn statistically that small orders have carried more information per share, allowing reactions to persist anonymously. This is a conceptual mechanism, not empirical proof that informed traders always trade smaller or that this mechanism alone causes concavity. The answer briefly notes that the referenced authors make a different anonymity-related argument, but does not develop or assess it.
Key ideas
- Noise trader models use simple agents to explain observed market behavior.
- The model distinguishes traders with little predictive power from better-informed traders.
- If informed traders tend to submit smaller orders, small orders may move prices more per share.
- Historical associations between order size and information can shape reactions even when orders are anonymous.
- The proposed mechanism is explanatory and does not establish that it is the sole cause of concave impact.
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Full text
# The noise trader explanation of concave market impact # The noise trader explanation of concave market impact In "How markets slowly digest changes in supply and demand" by JP Bouchaud, JD Farmer and F Lilo the authors asserts: > Noise trader models have been proposed to explain why market impact is a concave function of trading volume. and then they provide some more details: > The standard explanation for this is that it is due to a mixture of informed and uninformed trading. If more informed traders use small trade sizes and less informed traders use large trade sizes, then small trades will cause larger price movement per share than large trades. What "models" do they refer to? ## Answer by Pontus Hultkrantz (score 2) https://quant.stackexchange.com/a/71232 Generally any simple agent-based model where one assumes that one agent is a noise trader, an unsophisticated trader that generally has little predictive power in their trading behaviour, is a "noise trader model". Often these models are rather simple and backward engineered in order to derive a mechanical and behavioral understanding for what is observed in the market, e.g. market impact. For instance, assume that there are two kinds of agents trading, one unsophisticated noise trader, and one sophisticated informed trader. Furthermore, assume that we observe that the market impact is a concave function of market order size, hence a small market order cause a larger impact per share than does large a size. If orders made by informed traders tend to be smaller, and better predict the future price (as per definition of being an informed trader) than orders from noise traders, then a concave impact function will follow since other informed agents will react. Note that the authors in the article you reference argue that this assumes that orders are not anonymous, but I would claim that this is not necessarily the case. I would argue that it is simply enough that informed agents know that historically, small sizes carries more information per share (relatively more likely to have an informed trader behind), and thereafter a positive feedback effect will occur when a small order is observed.
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