Bankruptcy Prediction

Accurate bankruptcy prediction has value in a number of contexts. Creditors and credit analysts want to know the whether a borrower is likely to file for bankruptcy. Shareholders, from long-term investors to high-frequency traders, and from longs to shorts, also want to understand bankruptcy risk. Public accountants want to avoid giving a public company a "clean opinion" when the company is at high risk of bankruptcy within the following year. Vendors, tort claimants, and employees, as well as local communities and their taxing authorities also have good reasons to want early and accurate warnings of company bankruptcies that would impact them.

Unfortunately, no reliable and easy-to-calculate measure has been available for bankruptcy prediction. While the Altman (1968) Z Score ("AZS") enjoys a reputation as a bankruptcy predictor, we have shown that the AZS does not classify firms accurately into those that will and will not file for bankruptcy.  The false positive rate of the AZS is 99% at a one-year horizon and 98% at a two-year horizon. This makes the AZS unreliable for bankruptcy prediction.


Fortunately, we have discovered a remarkably simple but powerful bankruptcy predictor involving only the face value of debt and the market value of equity:

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When this ratio is calculated for publicly-traded firms with negative returns in the prior year, the incidence of bankruptcy filing within one year rises dramatically as Ps approaches 1.0:


Here's an example. On August 16, 2019, six months before Dean Foods Company filed for bankruptcy, its Ps was 0.94, calculated as



We can compare Dean Foods' Ps of 0.94 with the following chart of bankruptcy frequencies:

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Dean Foods filed for bankruptcy six months later. 

You can download the full paper for free at