## What Is a Z-Score?

A Z-score is a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score. A Z-score of 1.0 would indicate a value that is one standard deviation from the mean. Z-scores may be positive or negative, with a positive value indicating the score is above the mean and a negative score indicating it is below the mean.

Z-scores are measures of an observation's variability and can be put to use by traders in determining market volatility. The Z-score is more commonly known as the Altman Z-score.

- Z-scores are used in statistics to measure an observation's deviation from the group's mean value.
- Z-scores reveal to statisticians and traders whether a score is typical for a specified data set or if it is atypical.
- The Altman Z-Score is frequently used in testing credit strength.
- In general, a Z-score below 1.8 suggests a company might be headed for bankruptcy, while a score closer to 3 suggests a company is in solid financial positioning.

#### Z-Score

## The Altman Z-Score Formula

The Altman Z-score is the output of a credit-strength test that helps gauge the likelihood of bankruptcy for a publicly traded manufacturing company. The Z-score is based on five key financial ratios that can be found and calculated from a company's annual 10-K report. The calculation used to determine the Altman Z-score is as follows:

$\begin{aligned} &\zeta=1.2A+1.4B+3.3C+0.6D+1.0E\\ &\textbf{where:}\\ &\text{Zeta}(\zeta)=\text{The Altman }Z\text{-score}\\ &A=\text{Working capital/total assets}\\ &B= \text{Retained earnings/total assets}\\ &C=\text{Earnings before interest and taxes (EBIT)/total}\\ &\qquad\text{assets}\\ &D=\text{Market value of equity/book value of total liabilities}\\ &E=\text{Sales/total assets} \end{aligned}$

Typically, a score below 1.8 indicates that a company is likely heading for or is under the weight of bankruptcy. Conversely, companies that score above 3 are less likely to experience bankruptcy.

## What Do Z-Scores Tell You?

Z-scores reveal to statisticians and traders whether a score is typical for a specified data set or if it is atypical. In addition to this, Z-scores also make it possible for analysts to adapt scores from various data sets to make scores that can be compared to one another accurately. Usability testing is one example of a real-life application of Z-scores.

Edward Altman, a professor at New York University, developed and introduced the Z-score formula in the late 1960s as a solution to the time-consuming and somewhat confusing process investors had to undergo to determine how close to bankruptcy a company was. In reality, the Z-score formula Altman developed ended up providing investors with an idea of the overall financial health of a company.

## The Difference Between Z-Scores and Standard Deviation

Standard deviation is essentially a reflection of the amount of variability within a given data set. To calculate the standard deviation, first, calculate the difference between each data point and the mean. The differences are then squared, summed and averaged to produce the variance. The standard deviation is simply the square root of the variance, which brings it back to the original unit of measure.

The Z-score, by contrast, is the number of standard deviations a given data point lies from the mean. To calculate Z-score, simply subtract the mean from each data point and divide the result by the standard deviation.

For data points that are below the mean, the Z-score is negative. In most large data sets, 99% of values have a Z-score between -3 and 3, meaning they lie within three standard deviations above and below the mean.

## History of the Z-Score

NYU Stern Finance Professor Edward Altman developed the Z-score formula in 1967, and it was published in 1968. Over the years, Altman has continued to revaluate his Z-score over the years. From 1969 until 1975, Altman looked at 86 companies in distress, then 110 from 1976 to 1995, and finally 120 from 1996 to 1999, finding that the Z-score had an accuracy of between 82% and 94%.

In 2012, he released an updated version called the Altman Z-score Plus that one can use to evaluate public and private companies, manufacturing and non-manufacturing companies, and U.S. and non-U.S. companies. One can use Altman Z-score Plus to evaluate corporate credit risk. The Altman Z-score has become aa.

## Limitations of Z-Scores

Alas, the Z-score is not perfect and needs to be calculated and interpreted with care. For starters, the Z-score is not immune to false accounting practices. Since companies in trouble may be tempted to misrepresent financials, the Z-score is only as accurate as the data that goes into it.

The Z-score also isn't much use for new companies with little to no earnings. These companies, regardless of their financial health, will score low. Moreover, the Z-score doesn't address the issue of cash flows directly, only hinting at it through the use of the net working capital-to-asset ratio. After all, it takes cash to pay the bills.

Finally, Z-scores can swing from quarter to quarter when a company records one-time write-offs. These can change the final score, suggesting that a company that's really not at risk is on the brink of bankruptcy.