Z-Score : How to Calculate Z-Score

What Is a Z-Score?

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values. Z-score is 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.

In finance, Z-scores are measures of an observation's variability and can be used by traders to help determine market volatility. The Z-score is also sometimes known as the Altman Z-score.

How Z-Scores Work

Z-scores reveal to statisticians and traders whether a score is typical for a specified data set or if it is atypical. 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 more accurately.

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 that Altman developed actually ended up providing investors with an idea of the overall financial health of a company.

Over the years, Altman continued to reevaluate his Z-score. From 1969 until 1975, Altman looked at 86 companies in distress. From 1976 to 1995, he observed 110 companies. Finally, from 1997 to 1999, he evaluated an additional 120 companies. From his findings, it was revealed that the Z-score had an accuracy of between 82% and 94%.

In 2012, Altman released an updated version of the Z-score, which is called the Altman Z-score Plus. It can be used to evaluate public and private companies, manufacturing and non-manufacturing companies, and U.S. and non-U.S. companies.

A Z-score is the output of a credit-strength test that helps gauge the likelihood of bankruptcy for a publicly traded 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:

ζ = 1 . 2 A + 1 . 4 B + 3 . 3 C + 0 . 6 D + 1 . 0 E where: Zeta ( ζ ) = The Altman  Z -score A = Working capital/total assets B = Retained earnings/total assets C = Earnings before interest and taxes (EBIT)/total assets D = Market value of equity/book value of total liabilities \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} ζ=1.2A+1.4B+3.3C+0.6D+1.0Ewhere:Zeta(ζ)=The Altman Z-scoreA=Working capital/total assetsB=Retained earnings/total assetsC=Earnings before interest and taxes (EBIT)/totalassetsD=Market value of equity/book value of total liabilities

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

Z-Scores vs. Standard Deviation

Standard deviation is essentially a reflection of the amount of variability within a given data set. Standard deviation is calculated by first determining the difference between each data point and the mean. The differences are then squared, summed, and averaged. This produces the variance. The standard deviation is the square root of the variance.

The Z-score, by contrast, is the number of standard deviations a given data point lies from the mean. 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.

Criticisms of Z-Scores

The Z-score should be calculated and interpreted with care. For example, the Z-score is not immune to false accounting practices. Since companies in trouble may sometimes misrepresent or cover up their financials, the Z-score is only as accurate as the data that goes into it.

Additionally, the Z-score isn't very effective for new companies with little to zero earnings. Regardless of their actual financial health, these companies will score low. Moreover, the Z-score doesn't address the cash flows of a company. Rather, it only hints at it through the use of the net working capital-to-asset ratio.

Finally, Z-scores can swing from quarter to quarter if a company records one-time write-offs. These events can change the final score and may falsely suggest a company is on the brink of bankruptcy.