Main gains

• A Z-score is a statistical measure of the relationship of a score within a set of scores to the mean.
• The Z-score can reveal to traders whether a value is typical, or atypical, for a given data set.
• Generally speaking, a Z-score of -3.0 to 3.0 indicates that a stock is trading within three standard deviations of its mean.
• Traders have developed many methods of using Z-scores to identify trades, correlations between trading positions, and evaluate trading strategies.

Understanding Z-scores

The Z-score is a statistical measure that quantifies the distance between a data point and the mean of a data set. It is expressed as standard deviation. It indicates how many standard deviations a data point differs from the mean of the distribution.

A Z-score of 0 means that the data point's score is the same as the mean score. A Z-score of 1.0 means that the value is one standard deviation away from the mean. Z-scores can be positive or negative, with positive values ​​indicating a score above the average and negative values ​​indicating a score below the average.

The Z-score is sometimes confused with the Altman Z-score, which is calculated using factors from a company's financial reports. The Altman Z-score is used to calculate the likelihood that a business will go bankrupt within the next two years, while the Z-score can be used to determine how different a stock's returns are from its average return - and more.

Note: Z-scores are also called standard scores.

Z fraction formula

The statistical formula for the Z-score of a value is calculated using the following formula:

Among them:

• z = Z score
• x = value being evaluated
• μ = average
• σ = standard deviation

How to calculate Z-score

Calculating a Z-score requires that you first determine the mean and standard deviation of your data. Once you have these numbers, you can calculate the Z-score. So let's say you have the following variables:

• x = 57
• μ = 52
• σ = 4

You will use these variables in the formula:

• z = ( 57 - 52 ) / 4
• z = 1.25

Therefore, the Z-score for the value you selected indicates that it is 1.25 standard deviations from the mean.

To determine a Z-score using a spreadsheet, you enter your values ​​and determine the mean and standard deviation of the range. Use the following formula:

You will find that the following values have a mean of 12.17 and a standard deviation of 6.4.

Using the Z-score formula, you can calculate the Z-score for each factor. Use the following formula in D2, then D3, and so on:

How to use Z score

In its most basic form, the Z-score allows you to determine how far away (measured as the standard deviation) the returns of a stock you are evaluating are from the mean of a sample of stocks. The average score you have can be the average of a stock's annual returns, the average return of its listed index, or the average return of a stock selection of your choice.

Some traders use Z-scores in more advanced valuation methods, such as weighting each stock's returns to use factor investing, where Z-scores and standard deviations are used to evaluate stocks based on specific attributes. In the Forex market, traders use Z-scores and confidence limits to test the ability of a trading system to generate winning and losing sequences.

Z score and standard deviation

In most large data sets (assuming the data is normally distributed), 99.7% of the values fall between -3 and 3 standard deviations, 95% fall between -2 and 2 standard deviations, and 68% fall between -1 and 1 standard deviation.

Standard deviation represents the amount of variation (or spread) within a given data set. For example, if one sample of normally distributed data has a standard deviation of 3.1 and another sample has a standard deviation of 6.3, then the model with a standard deviation (SD) of 6.3 is more spread out and plots lower peaks than the sample with an SD of 3.1.

Distribution curves have negative and positive sides, and therefore positive and negative standard deviations and Z-scores. However, this has nothing to do with the value itself, other than indicating which side of the mean it lies on. Negative values ​​mean it's to the left of the mean, positive values ​​mean it's to the right.

The Z-score shows how many standard deviations a given data point differs from the mean. Therefore, the standard deviation must be calculated first because the Z-score uses it to convey the variability of the data points.

What is a Z-score?

The Z-score is a method of determining the distance, measured in standard deviation, between data and the population mean. It tells us whether a data point is typical or unusual compared to the rest of the population, which is useful for discovering unusual values ​​and comparing data between different populations.

How to calculate Z-score?

The Z-score is calculated by finding the difference between a data point and the mean of the data set, then dividing that difference by the standard deviation to see how many standard deviations the data point is from the mean.

How are Z-scores used in real life?

Z-scores are used in many real-life applications such as medical assessment, test scoring, business decisions, and investment and trading opportunity measurement. Traders who use statistical indicators such as Z-scores to evaluate trading opportunities are called quantitative traders.

What is a good Z-score?

The higher (or lower) the Z-score, the farther away the point is from the mean. This isn't necessarily a good or bad thing; it just shows where the data falls within a sample from a normal distribution. This means that when evaluating an investment or opportunity, it comes down to preference. For example, some investors use a Z-score range of -3.0 to 3.0 because 99.7% of normally distributed data falls within this range, while others may use -1.5 to 1.5 because they prefer scores closer to the mean.

Why is the Z-score so important?

The Z-score is important because it tells you where your data lies in the data distribution. For example, if the Z-score is 1.5, it is 1.5 standard deviations from the mean. Since 68% of the data lies within one standard deviation (if it were normally distributed), 1.5 might be considered too far from the mean for your comfort.

Bottom line

The Z-score is a statistical measurement that tells you how far away your data is from the mean (or mean) in a normally distributed sample. At the most basic level, investors and traders use quantitative analysis methods like the Z-score to determine how a stock is performing compared to other stocks or to its own historical performance. In more advanced uses of Z-scores, traders weigh investments against ideal criteria, develop other indicators, or even attempt to predict the outcome of a trading strategy.

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