Standing Out from the Mean: Assessing Stock Risk with the Z-Score

If you’ve ever heard someone say a stock’s price is “three standard deviations away from the mean,” they’re talking about Z-Scores. In Chapter 11 of Data Analytics for Finance Using Python, we explore how to use this tool to find the “weird” data points that might actually be opportunities.

The Basics

A Z-score tells you how far a data point is from the average.

• Z = 0: You’re exactly at the average.
• Z > 0: You’re above the average.
• Z < 0: You’re below the average.

In finance, a high positive Z-score often indicates a good investment opportunity, while a very low negative score might mean the value is tanking.

The Findings

The authors calculated Z-scores for MRF stock’s opening, closing, high, and low prices. Here’s what they found:

• Most variables (High, Low, Close) had “poor” Z-scores, meaning they stayed pretty close to their expected values.
• The Opening Price was the outlier. It had a mean Z-score of 7.86.

What does a 7.86 mean?

That is a massive score. It means the opening price was consistently way above the expected mean return. The authors concluded that, for this specific stock and time period, the best investment opportunity was actually tied to the opening price.

Why it matters

Z-scores are like a spotlight. They help you ignore the “normal” noise of the market and focus on the things that are genuinely unusual. When you see a Z-score of 7+, you know something interesting is happening.

But here’s the thing: high Z-scores often come with high risk. Being “far from the mean” is great when you’re winning, but it’s a long way to fall if things turn around.

And that’s why it matters. Z-scores give you a mathematical way to define “unusual,” but they don’t tell you why it’s happening. You still need to do the homework.

Next: Predicting Stocks with Support Vector Machines | Previous: Assessing Stock Risk with the T-Test