What is a Z-score?

Z-score is the measurement of a number’s relationship to the mean of a group of numbers.

Let’s discuss in further detail what Z-score means and how to calculate a Z-score.

In finance, investors use Z-scores to determine a company’s overall health. A Z-score is the measure of standard deviation from the mean of a set of numbers. Z-scores will range from -3 standard deviation to +3 standard deviation. If a Z-score of a value is 0, it indicates that the value is identical to a set of numbers it is compared against. A Z-score of 1.0 indicates the value is one standard deviation from the mean. 

How Z-scores works

Z-scores are often referred to as the Altman Z-score, after New York University professor Edward Altman who developed the Z-score formula in the late 1960s to determine a company’s risk of bankruptcy. In 2012, he released an updated version of the formula called the Altman Z-score Plus, which is used to evaluate public and private companies worldwide.

The Z-score also provides investors with clues in order to evaluate a company’s financial health. Today, Z-score formulas are also used to determine a stock’s volatility relative to its historic mean, the broader market mean and counterparts.

How is Z-score calculated

In simple terms, Z-score gives us an idea how far a value is from its mean. Let’s look at the basic Z-score formula before moving on to Altman’s Z-score formula.

Z-score = (x - mean) / standard deviation

To provide a Z-score example, consider a company that has reported average full-year revenue of $100m over the last decade with a standard deviation of 10. Let’s say the company reports full-year revenue of $120m in the current financial year. The Z-score using the formula will be:

Z-score = (120 - 100) / 10 = +2. 

A Z-score of +2 is indicative that the value under consideration is higher than the mean.

The Altman Z-score formula is more complex:

1.2A + 1.4B +3.3C +0.6D +1.0 E

A = Working capital of company / total assets of company

B = Retained earnings of company / total assets of company 

C = Earnings before interest and taxes (EBIT) of company / total assets of company 

D = Market value of equity of company / book value of total liabilities of company

E = Sales of company / total assets of company 

An Altman Z-score of below 1.8 indicates that a company may be at risk of bankruptcy. A score close to 3 indicates a financially sound company. The five financial ratios required to calculate an Altman Z-score can be retrieved from the company's annual 10-K report.

Z-score explained: Criticism 

Z-scores are not always accurate. They can misrepresent a company’s financials. Z-scores can swing between different quarters. It varies when accounting exceptional, one-time profits, losses and write-offs. Furthermore, Z-scores are not effective for new companies with little public history of their finances. It is also not effective with companies making little or zero earnings.