Here you will find:

1. The concept of Z-score, clear and simple so that everyone can understand it.

2. The theoretical mathematical foundation where it originates.

We’re going to use this metric a lot in the services we’re launching. It’s important that you understand it so we can move forward together.

Z-Score: A statistic every trader must understand

The Z-score is a metric we’re going to start using quite often. It’s important that you understand it because many of the decisions we make are based on this metric.

Don’t worry about the formulas you’ll see at the end of the article. They’re irrelevant in trading terms. What really matters is that you grasp the concept.

Z-Score: Step by step

1. The z-score is a metric on the asset you’re analyzing. It can be used to measure returns, volume, volatility, ratios, macro data—literally anything. It’s all the same.

2. The Z-score lets you compare completely different assets. That’s its key contribution. It lets you compare moves between apples and oranges. Not only that, you can compare any type of move—returns, volume, volatility, or any other metric you want to measure—between those apples and oranges.

Z-Score: Example

Let’s compare the return of two random assets from last week.

Asset A: could be City Bank

• In the week that just ended, A had a weekly return = X.

• We know, because we have the historical series, that A’s average weekly return = Y.

Z-Scores Numbers

Suppose A’s z-score is −2.5. In mathematical terms, the z-score tells you how many standard deviations (how far away) X is from Y.

Asset B: let’s say Bitcoin

• B’s z-score this week is 0. In other words, the weekly move was equal to its historical mean. 

• In Bitcoin’s case, that move can be huge due to its volatility; but when you convert it to a Z-score, that move is compared to its own mean and, therefore, it can be a normal move—even if it’s large compared with other assets.

Z-Score Levels

The wonderful thing about the Z-score is that it lets you compare moves—in this case, returns—of

Z-Score: How?

Step 1 – Weekly return
Rt = (Pt – Pt-1) / Pt-1

Step 2 – Annual average weekly return
R̄ = (1/52) × Σ Ri (i = 1 to 52)

Step 3 – Annual weekly volatility
σ = √[ (1/52) × Σ (Ri – R̄)² ] (i = 1 to 52)

Step 4 – Deviation
D = Rt – R̄

Step 5 – Z-score
Z = D / σ

Z-Score: Comparing Movements of any variable for any asset

In step 5 everything becomes comparable, because dividing by volatility removes each asset’s unit scale. No matter if it’s Citi, Bitcoin, or a Treasury bond, Z=2 always means “the move is two times larger than normal for that asset.”

Z-Score: Where do the levels come from?

 Well, as in every economic or mathematical model, you have to assume real-life conditions to move forward. In this particular case, we assume that returns, volume, volatility, etc., follow a normal distribution. The reality is that all those variables do follow a normal distribution—except when you face those big black swan events.

Z-Score: This is a normal distribution of a data series

It’s because of that assumption that we know 95.4% of the data falls between −2 and 2 standard deviations (𝛔), yellow+green zones.

 Any data point that falls outside that range, in the pink-red zone, is an extreme value which, as we’ve seen, lends itself to decision-making.

Z-Score: To sum up

• The Z-score tells you how big a return, a volume, or a volatility move was for any given asset. And since it’s standardized across all assets, it lets you compare moves between them.

• Likewise, Z-scores that get closer to ±2 become increasingly extreme. Those that fall in the green zone are normal.

Z-Score: Why is it important for trading?

1. A Z-score beyond ±2 is an extreme value. We’ve already seen that prices naturally tend to revert to their mean. Therefore, such a reading opens the door to a mean reversion trade.

2. If we’re trading a trend and the asset has moved out to 2 standard deviations, you need to wait for the pullback to enter. Ergo, buy the dip.

Good traders intuitively see these values on a chart. Still, quantifying them is better—it sets clear boundaries.

We’re adding to the service the tracking and quantification of practically every tradable asset. To make use of this enormous mass of information, we need to unify a single measure of comparison. That will allow us to identify and follow the assets where things are happening—whether in returns, volume, volatility, or anything else. It’s a powerful tool, and without understanding this, you won’t be able to take full advantage of it.

Keep in touch 

Martin