square root law

Moontower Munchies #143

Feb 18, 2026

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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