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Estimating the Square-Root Market Impact Coefficient

Article Quant Q&A · Author: confused
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Summary

The note asks how to estimate the coefficient in the square-root market impact relationship when planning an order, using a hypothetical order of 100 lots. The response explains that much of the supporting literature estimates impact from large institutional metaorders: parent orders split into child trades and executed over time.

Such order-level data is often proprietary, making it difficult to reproduce the estimates or obtain a historical coefficient from ordinary trade records alone. The response points to published work describing a dataset and methodology, as well as earlier studies of the concave impact function. It offers no calculation for the hypothetical order and no universal coefficient; estimation depends on access to large-order data and details of execution. The discussion is brief and emphasizes the data limitations rather than a practical calibration recipe.

Key ideas

  • The square-root impact coefficient is commonly estimated using large parent orders split into child trades.
  • Institutional metaorder records provide the kind of data used in much of the research.
  • Proprietary execution data makes independent historical estimation difficult.
  • A small order example alone does not supply enough information to determine the coefficient.

Tags

Market microstructureExecutionStatistics
Full text
# Can someone explain to me the square root law of market impact?


# Can someone explain to me the square root law of market impact?












The square root law is shown here: Market impact, why square root?

Let's say I want to execute 100 lots. But I have never executed before so I have no idea what n is historically. How would I determine what C is? Or is there a way to get a historical n?

## Answer by TxsHdgr (score 1)

https://quant.stackexchange.com/a/58202

A lot of the literature relies on estimating impacts of large orders (n), typically from major funds, that are split into child orders and executed over some period. Usually this data is proprietary and difficult to replicate. The metaorders used in this paper https://arxiv.org/pdf/1412.2152.pdf are one example (see footnote 3). This paper explains their methodology and cites many older papers [5,6,7,8] which explain the concave function and how they captured it. Unfortunately, this makes it very difficult to get a historical C without having more information about large orders and how they are split.

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.