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square root law

2026-02-18 · 13:25 UTC ·Kris Abdelmessih from moontower: a stoner dad explains options trading to his kids ·5 min read

Brief

Abdelmessih uses a short appendix from a prior paid post to bridge two distinct questions in market microstructure: how much a levered ETF must rebalance at end of day, and how much that rebalance might actually move the market. Drawing on Bouchaud’s empirical “square-root law,” he highlights the stylized fact that market impact scales with the square root of total metaorder size Q rather than linearly, and is largely insensitive to how the order is split into N child orders or how long execution takes, provided participation is moderate. His practical workflow is to first compute the imbalance from levered ETF mechanics, then assume a share of daily volume transacts during the rebalance interval to infer likely impact. He is explicit that this is a coarse model: the more difficult forecasting challenge is estimating pre-positioning by other traders, which can absorb or anticipate part of the move before the official rebalance prints.

Why it matters

Kris Abdelmessih’s 2026-02-18 Moontower note applies the square-root law of market impact to estimate how levered-ETF rebalancing flows might move prices near the close.

Key details

  • Citing Jean-Philippe Bouchaud, the post states that a buy or sell metaorder of total size Q tends to move price by an amount proportional to sqrt(Q), with impact approximately independent of the number of child orders N and the execution time T, so long as participation rate is not too large.
  • Abdelmessih connects this to prior work on calculating end-of-day imbalances from levered ETFs: once the rebalance size is known, assuming what fraction of daily volume trades during the rebalance window allows a rough estimate of price impact.
  • He emphasizes the estimate is intentionally simple and “unconditioned”; the harder practical problem is pre-positioning—how much of the expected rebalance impact is already reflected in price through a Keynesian beauty-contest dynamic among traders.
  • The note also mentions he is using the square-root law as a slippage model in an Excel-based trading game prototype, with stock mechanics already playable and an options add-on planned later.
Cleaned source text

title: square root law

author: Kris Abdelmessih from moontower: a stoner dad explains options trading to his kids

content_type: newsletter

publication: substack.com

published: 2026-02-18T13:25:17+00:00

source_url: gmail://19c70edd36d33cd9

word_count: 1062

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square root law

Kris Abdelmessih

Feb 18

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Friends,

Since I’ve been discussing how to compute end-of-day flows from levered ETFs I figured I’ll share the appendix from last week’s paid post where I show how you could think about moving from _how much needs to be rebalanced_ to _how much it might move the market.

From the quant sensei Bouchaud:

The Square-Root Law of Market Impact

> _The square-root law for price impact is arguably one of the most fascinating robust empirical regularities discovered in the last 30 years. It states that when executing a buy (sell) “metaorder” of total size Q, sliced and diced into N child orders of size q=Q/N, the price on average moves up (down) by an amount proportional to sqrt(Q).

> _Price impact is, remarkably, found to be approximately independent of both N and of the total time T needed to achieve full execution.

> _In other words,provided the participation rate is not too large, average price impact only depends on the total volume traded Q, and barely on execution schedule.

> Such a square-root dependence, and its apparent universality across a wide variety of markets is surprising and non-intuitive.

In _levered silver flows_ , I showed how to compute the market imbalance. If we make an assumption about what percentage of the day’s volume will trade in the period of the rebalance, we can estimate a market impact.

I’m not an expert on this. I implemented a simple formula, but because it’s trivial to compute the imbalance, the real game is the Keynes Beauty contest of handicapping how much impact is already in the price because of pre-positioning. I do not address this, but the unconditioned impact estimate is at least interesting to derive a sense of proportion.

The simple model:

Implemented:

🧩Random fun bit…the square root law happens to do a fantastic job of handling “slippage” in the game I’m designing. Players will exactly what it’s like to get edge on a trade (or get hosed by negative edge!)

Screenshot of a playable prototype below. Just started playtesting. This version is really just the game’s stock engine. I have an option add-on but the prototype is in Excel but want to get the stock part dialed in before playtesting that.

Your regular reminder that focus is cleansing.

This is from Derek Sivers’ 2021 banger: _Here’s how to live: Master something.

> _Mastery is the best goal because the rich can ’t buy it, the impatient can’t rush it, the privileged can’t inherit it, and nobody can steal it.

> You can only earn it through hard work.

> Mastery is the ultimate status.

> _Striving makes you happy.

> Pursuit is the opposite of depression.

> People at the end of their life, who said they were the happiest with their life, were the ones who had spent the most time in the flow of fascinating work.

> _Concentrating all of your life ’s force on one thing gives you incredible power.

> Sunlight won’t catch a stick on fire.

> But if you use a magnifying glass to focus the sunlight on one spot, it will.

> Mastery needs your full focused attention.

Stay groovy

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