Introducing Anomalous Price Impact and Square-Root Liquidity for after-work quants

Large orders move prices. Empirically, impact often grows roughly like the square root of traded volume—not linearly. Why would liquidity behave that strangely near the current price?

Anomalous Price Impact and the Critical Nature of Liquidity in Financial Markets (Tóth, Lemperière, Deremble, de Lataillade, Kockelkoren, Bouchaud, 2011) offers a dynamical liquidity story: a V-shaped latent supply/demand profile that vanishes around the current price, under mild assumptions plus roughly diffusive prices.

This Hub note is a plain-language intro. Not investment advice.

The intuition (without the full theory)

• If available liquidity thins out near the touch, small child orders can have outsized local impact—linear response breaks.
• Large metaorders must be split to pass through that “funnel,” which helps explain long memory in order-flow signs.
• Together, these ideas organise the famous square-root impact stylised fact and add empirical support in the paper.

Read the PDF for assumptions, numerics, and figures. Do not treat the square-root rule as a trading edge by itself.

Why after-work learners should care

Execution and transaction-cost intuition shows up long before you build a fancy optimizer. If your after-work path includes any portfolio or backtest code, you need a mental model for why costs are nonlinear. This paper is a classic open-PDF route into that mindset.

Healthy practice later: plot impact-vs-size on a public or simulated series and label it “learning only.”

One-evening reading checklist

1. Read the abstract until the V-shape / vanishing liquidity sentence clicks.
2. Skim the section connecting metaorder fragmentation to order-flow memory.
3. Note how they argue for square-root impact.
4. Write a disclaimer you would paste above any personal impact plot.

Download the PDF

Download PDF

Landing: arXiv:1105.1694

Important disclaimer

Not investment advice. Impact laws are descriptive research tools. They are not instructions to trade, size, or time orders in a live account.

What this is not

• Not CEF / subsidy framing
• Not Quant or Macro course CTA
• Not broker TCA sales content

Next step

Single course CTA: SoloQuant Academy’s Introduction to Python Programming—get comfortable with arrays, files, and plots first; microstructure papers become much less scary afterward.