How do you create a Z-Score?

Given I use Z-Scores heavily in my analysis I thought I would write a quick tutorial on how to create a Z-Score (and answer the question “What is a Z-Score?” at the same time!).

Why use a Z-Score in financial market analysis?

I have a confession to make. I was never any good at maths in high school, learning formulae and working on vague and seemingly irrelevant problems didn’t interest me, but if I knew what I was trying to do and the purpose behind it then usually I could just figure it out. Point I’m trying to make is that if you know *why* or the purpose of what you are trying to do then that solves half the problem.

The reason you use a z-score is to “standardize” a series. There are a few different ways you can standardize a time series such as percentage change across time periods (e.g. rolling annual % change [t252/t0-1], expressing one series as a percentage of another (e.g. dividend yield [dividend per share/share price]), deviation from trend, ranking, etc.

You can even standardize a standardized series. For example you could take a z-score of the rolling percentage change of two series, particularly if it helps put them on a more comparable scale (e.g. compare and contrast the percentage change in commodities vs GDP growth).

So the purpose of using a z-score to standardize a time series is *comparability*, or stating different series in common terms. This can be particularly useful in building composite indicators. For example you might take a z-score of futures positioning, implied volatility, fund flows, etc to build a composite view of sentiment. Taking a z-score of the individual components allows them to be stated in common terms to combine the signal.

To that end it’s really all about the signal. The reason I use z-scores in financial market time series analysis is to present the signal from the series either for use by itself or in combination with other factors.

What is a Z-Score?,,,

The Z-score is the number of standard deviations away from the mean a particular observation is.

How do you calculate a Z-score?

( data point – mean ) / standard deviation

In excel this would be (e.g. if you are looking at column B, and expressing the z-score with reference to the entire time series): =(B2-AVERAGE(B:B))/STDEV(B:B)

So there you go. It’s pretty straightforward really, but its simplicity belies its power in presenting and combining signals. And when you’re studying financial markets and economics to make better investment decisions developing and expressing signals is key, and building up your analytical toolkit is essential.

Hope you found this useful.