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The Altman Z-Score: Is it possible to predict corporate bankruptcy using a formula?

April 15, 2011
Dave Brickell

Dave Brickell

2 followers
The Altman Z-score is a combination of five weighted business ratios that is used to estimate the likelihood of financial distress. If the credit crunch itself wasn’t lesson enough, respected fund manager Anthony Bolton has emphasised the importance of understanding credit risk when investing in equities: “When I analysed the stocks that have lost me the most money, about two-thirds of the time it was due to weak balance sheets. You have to have your eyes open to the fact that if you are buying a company with a weak balance sheet and something changes, then that’s when you are going to be most exposed as a shareholder.”

Background to the Z-Score

The Z-Score was developed in 1968 by Edward I. Altman, an Assistant Professor of Finance at New York University, as a quantitative balance-sheet method of determining a company’s financial health. A Z-score can be calculated for all non-financial companies and the lower the score, the greater the risk of the company falling into financial distress.

The original research was based on data from publicly held manufacturers (66 firms, half of which had filed for bankruptcy). Altman calculated 22 common financial ratios for all of them and then used multiple discriminant analysis to choose a small number of those ratios that could best distinguish between a bankrupt firm and a healthy one. To test the model, Altman then calculated the Z Scores for new groups of bankrupt and nonbankrupt but sick firms (i.e. with reported deficits) in order to discover how well the Z Score model could distinguish between sick firms and the terminally ill.

The results indicated that, if the Altman Z-Score is close to or below 3, it is wise to do some serious due diligence before considering investing. The Z-score results usually have the following "Zones" of interpretation:

  • Z Score below 2.99 -“Safe” Zones. The company is considered ‘Safe’ based on the financial figures only.
  • 1.8< Z< 2.99 -“Grey” Zones. There is a good chance of the company going bankrupt within the next 2 years of operations.
  • Z below 1.80 -“Distress” Zones. The score indicates a high probability of distress within this time period.
The Z-score has subsequently been re-estimated based on other datasets for private manufacturing companies, as well as non-manufacturing / service companies.

Does the Altman Z-Score Work?

In its initial test, the Altman Z-Score was found to be 72% accurate in predicting bankruptcy two years prior to the event. In subsequent tests over 31 years up until 1999, the model was found to be 80-90% accurate in predicting bankruptcy one year prior to the event.

In 2009, Morgan Stanley strategy analyst, Graham Secker, used the Z-score to rank a basket of European companies. He found that the companies with weaker balance sheets underperformed the market more than two thirds of the time. Morgan Stanley also found that a company with an Altman Z-score of less than 1 tended to underperform the wider market by more than 4%.

Calculation / Definition

For public companies, the z-score is calculated as follows: 1.2*T1 + 1.4*T2 + 3.3*T3 + 0.6*T4 + 1.0*T5.

  • T1 = Working Capital / Total Assets. This measures liquid assets as firm in trouble will usually experience shrinking liquidity.
  • T2 = Retained Earnings / Total Assets. This indicates the cumulative profitability of the firm, as shrinking profitability is a warning sign.
  • T3 = Earnings Before Interest and Taxes / Total Assets. This ratio shows how productive a company in generating earnings, relative to its size.
  • T4 = Market Value of Equity / Book Value of Total Liabilities. This offers a quick test of how far the company's assets can decline before the firm becomes technically insolvent (i.e. its liabilities exceed its assets).
  • T5 = Sales/ Total Assets. Asset turnover is a measure of how effectively the firm uses its assets to generate sales.

Geek Stuff

The usefulness of the original Z score measure was limited by two of the ratios.The first ratio is T4, the Market Value of Equity divided by Total Liabilities. Obviously, if a firm is not publicly traded, its equity has no market value. To deal with this, there is a revised Z score for private companies:

  • Z1 = .717*T1 + .847*T2 + 3.107*T3 + .42*T4A + .998*T5 (in this case, T4 = Book Value of Equity / Total Liabilities).
The other ratio is Asset Turnover. This ratio varies significantly by industry but, because of the original sample, the Z Score expects a value that is common to manufacturing. To deal with this, there is a more general revised Z-score for non-manufacturing businesses:

  • Z2 = 6.56*T1 + 3.26*T2 + 6.72*T3 + 1.05*T4A
NB: Both these revised measures have slightly different Zones of Interpretation.

Watch Out for

The Z Score is not intended to predict when a firm will actually file for legal bankruptcy. It is instead a measure of how closely a firm resembles other firms that have filed for bankruptcy, i.e. it tries to assess the likelihood of economic bankruptcy. The model has also drawn several statistical objections over the years. The model uses unadjusted accounting data; it uses data from relatively small firms; and it uses data that is around 60 years old. Nevertheless, despite these flaws, the original Z Score model is stil the most widely used measure of corporate financial distress.

From the Source

Altman’s original paper is reasonably heavy going and you might in any case be better off reading his follow-up paper published in 2000, entitled: Predicting the Financial Distress of Companies: Revisiting the Z-Score.

Other Resources on Altman Z-Score

About the author:

Dave Brickell
GuruFocus - Stock Picks and Market Insight of Gurus

Rating: 3.6/5 (7 votes)

Comments

yswolinsky
Yswolinsky - 3 years ago
Nice article, a lot of insightful information.
batbeer2
Batbeer2 premium member - 3 years ago
Thanks for the article.

I'm no fan of the Altman-Z score.

Ingersoll-Rand http://www.gurufocus.com/forum/read.php?2,51334,51456#msg-51456

Bristow http://www.gurufocus.com/news/52678/the-bull-case-for-bristow

Conn's http://www.gurufocus.com/news/84523/the-bull-case-for-conns

Level 3 http://www.gurufocus.com/news/107811/level-3-sanborn-maps-and-burlington-northern-santa-fe

Aircastle http://www.gurufocus.com/forum/read.php?2,30674,page=1

The formula is very often wrong because:

1) Stated book value is not equal to economic (or market) value of the assets and

2) Take a good look at "T4"...... Altman is telling you to avoid cheap stocks. That's not value investing.

Just my two cents.
Alex Garcia
Alex Garcia premium member - 3 years ago
This isn't about value investing. It is about using the formula to determine if there is a possibility the company will go bankrupt
batbeer2
Batbeer2 premium member - 3 years ago
Hi Alex,

Yes, there's a difference; but I've seen soooo many false positives that I don't believe the statistics.
Alex Garcia
Alex Garcia premium member - 3 years ago
Batbeer,

Yeah that's fine. Would you mine going into further detail? I just wanted to point out (and I aplogize if it came out in a rude manner) what the formulas AIM is. I believe DaveinHackensack has a site on the formula, but the score easi available throughout the web for free including Gurufocus.
batbeer2
Batbeer2 premium member - 3 years ago
No reason to apologize.

I listed a number of stocks that I believe had poor Z-scores at the time I looked at them. None of them are now bankrupt.

If the formula is worth it's salt, it should be a simple exercise to compile an annual list of say.... a dozen stocks of which at least half would be bankrupt at yearend. I haven't seen such lists on the Internet, have you ?

Instead, when applied...

Morgan Stanley also found that a company with an Altman Z-score of less than 1 tended to underperform the wider market by more than 4%.

WOW.... underperforming by 4%..... that's not nearly the same as bankruptcy is it ?
DaveinHackensack
DaveinHackensack - 3 years ago
I believe DaveinHackensack has a site on the formula


The site you are thinking of is Short Screen.

In its initial test, the Altman Z-Score was found to be 72% accurate in predicting bankruptcy two years prior to the event. In subsequent tests over 31 years up until 1999, the model was found to be 80-90% accurate in predicting bankruptcy one year prior to the event.


I recognize those two sentences from the Wikipedia article, because I wrote them (I wrote them on Short Screen's About page, initially)

If the formula is worth it's salt, it should be a simple exercise to compile an annual list of say.... a dozen stocks of which at least half would be bankrupt at yearend. I haven't seen such lists on the Internet, have you ?


In the Altman paper from 2000 that Dave Brickell links to above (the same one, coincidentally, that's linked to on the About page of Short Screen), Altman lists a type II error (false positives) of 20% for the formula. My guess is that the type II errors have increased significantly in the last two years, as unprecedented liquidity has kept some companies afloat that might have gone bust without it.

Also, (and this is pretty intuitive) low Z-Score stocks with lower share prices and lower market caps seem to be more likely to go bankrupt (e.g., TRMA last year).

batbeer2
Batbeer2 premium member - 3 years ago
Hi Dave, thanks for chiming in.



Altman lists type II errors of 20%.....

To me this means it should be easy to compile a list of about a dozen stocks of which at least half should be bankrupt by yearend no ?

My guess is that the type II errors have increased significantly in the last two years,

So, Altman's Z-score fails during a credit crunch. AFAIK you're the only one out there putting this theory to the test.... and to date you haven't been able to replicate the results ?!
DaveinHackensack
DaveinHackensack - 3 years ago


To me this means it should be easy to compile a list of about a dozen stocks of which at least half should be bankrupt by yearend no ?

I'm guessing a finance academic would use a larger sample size, but according to the results of the 2000 paper, that's essentially correct.

So, Altman's Z-score fails during a credit crunch.

On the contrary, I would think that during a credit crunch the false positive rate would drop, because companies would be more likely to go bankrupt. What we've had over the last two years is the opposite of a credit crunch; it's been a surfeit of liquidity.



AFAIK you're the only one out there putting this theory to the test.


I'm far from the only one using the Altman models as part of his investment process. There's a testimonial on the home page of Short Screen by a market neutral investor who has outperformed the market for over a decade, and who uses the Altman models as part of his investing process. Also, Goldman Sachs ran long-short baskets for several years using the Altman models. I'm not sure if they're still running them, but, if memory serves, that strategy outperformed the market over about a five year period, but underperformed in '09, coming off the March '09 bottom.

and to date you haven't been able to replicate the results ?!

I haven't tried to replicate the results -- I'm not an academic. I've tried to make money, and the Altman models have given me opportunities to do so. But I'm still learning, and I've made some mistakes. For example, I was short TRMA 8 months before it went bankrupt, as part of a market neutral trade going long OII. I let myself get stopped out for a small gain, instead of letting that trade ride. Also, I noticed A&P on the screener, but waited too late to short it.

I am taking the rest of the weekend off of the Internet, but I'll stop by on Monday if you'd like to continue this conversation. In the meantime, here's an article I wrote about Japanese stocks you might find interesting.
batbeer2
Batbeer2 premium member - 3 years ago
Have a nice weekend !

Thanks for the link.

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