Z-Score

What Is a Z-Score?

A z-score is a standardized measure that shows how far a value sits from the average of its group, expressed in units of standard deviation. A z-score of 0 means the value equals the average. A positive z-score means the value is above average, and a negative one means it is below. Because the result has no unit of measurement, z-scores let investors compare numbers that were originally measured on different scales, such as returns, prices, or financial ratios.

How It Is Calculated

The formula subtracts the arithmetic mean from the observed value and divides the result by the standard deviation:

z = (x − μ) / σ

Here x is the observed value, μ is the mean of the group, and σ is its standard deviation.

For example, suppose a stock returned 3% in one month, while the average monthly return across a set of past months was 1% with a standard deviation of 2%. The z-score is (3 − 1) / 2 = 1.0, meaning that month's return was one standard deviation above the average. This example is purely illustrative and does not describe any real stock.

Interpreting z-scores as probabilities relies on the normal distribution, which market returns only approximate. Real returns often have fatter tails than that model predicts, so extreme readings can occur more often than a z-score alone would suggest.

The Altman Z-Score

The term also refers to a specific model. Developed by academic Edward Altman in 1968, the Altman Z-score combines several financial ratios, such as working capital, retained earnings, and profitability relative to total assets, into a single score intended to estimate a company's risk of bankruptcy. Higher scores generally indicate lower distress risk, and lower scores indicate higher risk. The original model was built on manufacturing companies, and later versions were adapted for other types of firms.

Why It Matters to Investors

Z-scores help investors spot unusual results. A stock whose recent return sits several standard deviations from its typical range stands out as an outlier worth examining, and analysts use z-scores to screen for companies showing signs of financial stress. However, z-scores describe past data, and their results depend on the inputs and assumptions chosen. They work best as one input among many rather than as a forecast.