Altman Z-Score

Real World Example

Using the accounting data made available prior to later restatements, they found WorldCom's Z-score to be 2.697 in 1999, 1.274 in 2000, and 0.798 in 2001.

Source: Wesley R. Gray and Tobias E. Carlisle. Quantitative Value: A Practitioner's Guide to Automating Intelligent Investment and Eliminating Behavioral Errors. John Wiley & Sons, 2012. [B102]

Straight From The Source

[For the z-score,] a list of 22 potentially helpful variables (ratios) was compiled for evaluation. From the original list, five were selected as doing the best overall job together in the prediction of corporate bankruptcy. [...] Note that the model does not contain a constant term. […] As such, [the coefficients or weights] will be different if the sample changes or if new variables are utilized.

We found that the Z-Score model, using a cut-off score of 2.675, was between 82 percent and 94 percent accurate. […] The Type II error (classifying the firm as distressed when it does not go bankrupt or default on its obligations), however, has increased substantially with as much as 25 percent of all firms having Z-Scores below 1.81. […] While the Type I accuracy continues to be quite acceptable (i.e., greater than 80 percent prediction of default within one year of the default date), the Type II error has become quite high. As noted earlier, perhaps as many as 25 percent of U.S. firms have a financial profile more similar to bankrupt companies than to healthy entities. The main reason for this high error rate is that U.S. firms, in general, are far more risky than in the past.

One observes that in the period 1996–2001, triple-A bonds had an average Z-Score of 6.2, while single-B bonds have an average score of 1.8.

Regarding the actual parameters:

Retained earnings (RE) is the total amount of reinvested earnings and/or losses of a firm over its entire life. The account is also referred to as earned surplus. This is a measure of cumulative profitability over the life of the company. […] In addition, the RE/TA ratio measures the leverage of a firm. Those firms with high RE relative to TA have financed their assets through retention of profits and have not utilized as much debt. This ratio highlights the use of either internally generated funds for growth (low-risk capital) or OPM (other people’s money)—higher-risk capital. This variable has shown a marked deterioration in the average values of nondistressed firms in the past 20 years.

This ratio [Market Value of Equity/Book Value of Total Liabilities] adds a market value dimension that most other failure studies did not consider. [Note that] liabilities include both current and long-term obligations.

The capital turnover ratio is a standard financial ratio illustrating the sales-generating ability of the firm’s assets. This final ratio is unique because it is the least significant ratio, and on a univariate statistical significance test basis it would not be selected at all. However, because of its relationship to other variables in the model, the sales/total assets (S/TA) ratio ranks high in its contribution to the overall discriminating ability of the model.

By specifying log transformations on [retained earnings/total assets and equity/debt ratios], we have both increased the Type I accuracy and reduced the Type II error.

Source: Edward Altman and Edith Hotchkiss. Corporate financial distress and bankruptcy: Predict and avoid bankruptcy, analyze and invest in distressed debt. Vol. 289. John Wiley & Sons, 2010. [B064]

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