WELCOME to Infolib’s resource library!
This educational resource, pertaining to trading and investing, is a continual work in progress and intended for users who are interested in self-educating themselves. There are no fees or classes. For those interested in learning more about the website’s tools, the wiki will be more insightful.
Disclaimer: Nothing here is financial advice, and the examples provided are incidental.
Credit
Created by https://x.com/SargonDinkha1
Links: GitHub · YouTube · Trading View
Table of Contents
- Z-Score?
- The Formula (For Understanding, Not Memorizing)
- Market Structure & Risk Filters
- Choosing Z-Score Lookbacks by Timeframe
Z-Score?
A Z-score tells you how far today’s price is from its recent “normal” level.
More precisely, a Z-score measures how many standard deviations the current value is away from its recent average.
In trading terms, it answers one simple question:
Is the current price normal, stretched, or extreme compared to its recent history?
Intuition First: Z-Score Using Silver’s Real Behavior
Silver has a known historical range of roughly $18–$26.
Price would drift, trend, and revert, but the overall range remained stable. Over time, our brain adapts to that rhythm.
Occasionally, silver — like most asset classes — breaks its rhythm.
Our intuition notices things like:
- If it’s $20, it feels normal
- At $25, it feels high
- At $17, it feels low
This is not calculation — it is pattern recognition.
Now imagine the price today is $40.
Most people would instinctively think:
“Something unusual is going on — this is not just a normal price movement. It’s far outside where price normally lives.”
That intuitive reaction — “this is strange, not normal” — is exactly what a Z-score quantifies.
The Hunt Brothers Squeeze (Extreme Example)
Think about the famous Hunt Brothers silver squeeze:
- Silver didn’t just rise — it exploded
- It moved from “normal” pricing to $50+
- In futures markets, intraday spikes pushed toward $80
That kind of move is not just “up.”
Price moved outside the normal distribution of silver’s historical behavior.
What Z-Score Is Telling You in That Moment
When silver jumps from its usual $20–$25 range to $50–$80:
- The price isn’t just high
- It’s statistically extreme
- It is many standard deviations above its mean
- It is a rare event, not a typical trend
Z-score as an indicator helps quantify this extremity:
“Price is X standard deviations above its normal recent behavior.”
Because Z-score uses standard deviation, the scale is consistent:
- Z = 0 → price is at its recent average
- Z = +1 → above normal, but still common
- Z = +2 → quite unusual
- Z = +3 or more → very rare
With silver, if price sits at $40, the Z-score will be very high — because that price almost never occurs in normal history.
This is the mathematics behind an intuitive feeling.
The Formula (For Understanding, Not Memorizing)
You do not need to calculate Z-score manually — trading platforms handle this automatically.
However, understanding the components helps you know what is happening under the hood.
Definitions
- Pt → Current price (or spread, or ratio)
- MAₙ(P) → Average price over the last n periods
- SDₙ(P) → How much price typically fluctuates over that same period
Formula (Conceptual)
Z-score = (Current price − Recent average) ÷ Typical price movement
This converts price into a standardized scale, allowing comparison of extremes across time and assets.
Example
Assume:
- 20-day average price = $100
- Typical daily fluctuation (standard deviation) = $5
- Current price = $110
Calculation:
Z = (110 − 100) ÷ 5 = 2
Explanation:
- Z = 2
- Price is 2 standard deviations above normal
- Market is statistically stretched
Spread and Pairs Trading
Z-score is widely used in:
-
Pairs trading
Long one asset and short another when the spread’s Z-score is extreme. -
Statistical arbitrage
Normalizing spreads and baskets via Z-score to detect mispricing.
Because spreads and ratios are often more stationary than raw prices, applying Z-score to these series is more statistically sound.