## Definition and Examples of Z-Scores

A Z-score uses standard deviation to indicate the difference between a data set’s mean and an individual observation. When the Z-score is 2.0, for example, the observed data is two standard deviations away from the mean.

Z-scores help you evaluate how normal an observation is for a given data set. You might see a result without knowing if it is high, low, or somewhere near the average. With a Z-score, you can quickly gain more insight.

Investors have adapted the Z-score to attempt to understand the financial health of a company. For example, the Altman Z-score is designed to predict how likely a company is to declare bankruptcy.

When you calculate a price-to-earnings ratio for a company, you don’t necessarily know if that number is high or low. But when you compare that ratio to other companies in the industry, you find out if it is above or below the average—and by how much.

## How Z-Scores Work

Z-scores compare individual observations to the average, and they can also help to standardize information, enabling comparisons between multiple data sets.

To calculate a Z-score, subtract the mean from the observation in question (data value), and divide the result by the dataset’s standard deviation:

Z-score = (Observation – Mean) / Standard Deviation

The Altman Z-score, developed in the late 1960s, modifies basic Z-scores to illustrate how financially healthy a business might be and to try to quantify its creditworthiness. The model is named after professor Edward Altman, who developed the concept at New York University. Ultimately, the Altman Z-score attempts to predict how likely a company is to declare bankruptcy, which could result in significant losses for investors.

You can calculate the Altman Z-score, by combining data from the company’s financial statements. In this calculation, assume:

- X1 = Working capital / total assets
- X2 = Retained earnings / total assets
- X3 = Earnings before interest and taxes / total assets
- X4 = Market value equity / book value of total liabilities
- X5 = Sales / total assets

Each metric is assigned its own weight. For example, X1 has a weighting factor of 1.2, so you would multiply it by 0.012. Here is the full calculation:

Altman Z-Score = 0.012X1 + 0.014X2 + 0.033X3 + 0.006X4 +0.999X5

If the result is below 1.81, Altman’s model suggests a relatively high likelihood of bankruptcy. For scores above 2.99, the company falls into the “safe” zone, although there is no guarantee that any company is a safe investment. Results between 1.81 and 2.99 are in a grey area.

Unlike a traditional Z-score, the Altman Z-score does not use standard deviation in the calculation.

Altman’s research showed that the Z-score model could identify roughly 80% to 90% of companies that were at risk of declaring bankruptcy (although the accuracy was best for periods of up to two years). However, that approach also produced false positives, flagging 15% to 20% of companies as “distressed” when they did not go bankrupt.

Altman’s original research focused on manufacturing firms based in the U.S. But the investment universe includes companies in various industries and countries, and Altman wanted to provide a method of evaluating other types of firms. The Z-score has evolved over time, and Altman’s Z-score Plus app is designed to accommodate a broader range of investments. Additionally, the Z-score aims to provide longer-range forecasts by predicting the probability of default for up to 10 years.

## What It Means for Individual Investors

Investing in a company that goes bankrupt can result in significant losses. The Z-score can help identify risks, but keep in mind that it’s just one tool. The calculation does include multiple data points from financial reports, but prudent investors will dig deeper before making a decision to buy or sell a stock. You may want to supplement Z-score analysis with other analysis techniques, including reviewing broader financial statement analysis, conducting industry and competitor research, and other strategies.

Just calculating numbers for a Z-score doesn’t tell you about a company’s potential strategy changes, which might affect its finances. With a big-picture understanding of an investment, you can be better prepared to make an informed decision to support your investing goals.

### Key Takeaways

- A traditional Z-score tells you how much an individual observation differs from the average.
- Z-scores can help put results into context so that a single number provides more meaning.
- The Altman Z-score can help investors determine if a company is likely to declare bankruptcy.
- Consider supplementing Z-score analysis with other investment research techniques before making investment decisions.