In the post titled How do you identify weak companies (stocks to short-sell)?, I stated that a corporation's fiscal stability can be ascertained through examining the relationship between its capital structure and its (micro and macro) environmental risks. If a corporation is 'fiscally stable', its risk in capital structure varies inversely with its (micro and macro) environmental risks.
In this post, I'm going to discuss how to use Multiple Discriminant Analysis (MDA modeling) to assess a firm's insolvency risk. The MDA indicator I'll discuss is a statistical harmonization of five weighted financial ratios--derived from a firm's balance sheet and income statement--called Altman's z-score.
So what is Altman's z-score?
It is a multivariate formula developed by Edward Altman to 'measure' a corporation's financial 'soundness'. Altman's z-score is a highly effective diagnostic tool, that helps to forecast a corporation's probability of entering bankruptcy within a two year period. This model has an accuracy rate ranging between 72%-80%, and studies show that it is universally applicable!
The five weighted inputs for Altman's model include:
Where:
Z is the z-score
x1 is the Return on Assets ratio
x2 is the Sales to Assets ratio
x3 is the Equity to Debt ratio
x4 is the Retained Earnings to Total Assets
x5 is the Working Capital to Total Assets
From the equation you can see that the Return on Assets Ratio receives the highest weighting and that the equity to debt ratio receives the lowest weighting.
Interpretation of the z-score:
I then take all the z-scores that are less than 2.7, categorize them into very narrow ranges and plot the normal distribution of the scores.
You'll have something that looks like this:
The normal distribution will ALWAYS be positively skewed. I suspect that this is because bankruptcy (for listed companies) is a rare occurrence. I then focus my attention on everything that lies to the left of the mean--the green zone on the graphical illustration. That's where the 'gold' is!
So what is Altman's z-score?
It is a multivariate formula developed by Edward Altman to 'measure' a corporation's financial 'soundness'. Altman's z-score is a highly effective diagnostic tool, that helps to forecast a corporation's probability of entering bankruptcy within a two year period. This model has an accuracy rate ranging between 72%-80%, and studies show that it is universally applicable!
The five weighted inputs for Altman's model include:
- Return on Assets ratio (ROA): which is equal to earnings before interest and taxation divided by total assets (EBIT/Total Assets). This ratio gauges how efficiently a corporation generates revenues from its assets.
- Sales to Assets ratio: which is equal to sales divided by total assets (Sales/Total Assets). This ratio measures the efficiency of a corporation's sales and marketing function.
- Equity to Debt ratio: which is equal to market value of equity divided by book of value debt. (Market Value of Equity/Book Value of Debt). This ratio measures a firm's level of leverage and is a general indicator of its capital structure. Note: The book value of debt gives an inflated picture of a firm's true leverage. For an accurate picture of a firm's leverage, use the market value of long term debt i.e the discounted present value of debt interest and principal payments.
- Retained Earnings to Total Assets: which is equal to retained earnings divided by total assets (Retained Earnings/Total assets). This ratio shows the degree to which assets have been paid for by company profits.
- Working Capital to Total Assets: which is equal to working capital divided by total assets (Working Capital/Total Assets). This ratio tests for financial distress.
Z= 3.3x1 + 0.999x2 + 0.6x3 + 1.4x4 +1.2x5
Where:
Z is the z-score
x1 is the Return on Assets ratio
x2 is the Sales to Assets ratio
x3 is the Equity to Debt ratio
x4 is the Retained Earnings to Total Assets
x5 is the Working Capital to Total Assets
From the equation you can see that the Return on Assets Ratio receives the highest weighting and that the equity to debt ratio receives the lowest weighting.
Interpretation of the z-score:
- If a firm has a z-score that is greater than 3, it is safe
- If a firm has a z-score that lies between 2.7 and 2.99, it is financially weak
- If a firm has a z-score that lies between 1.8 and 2.7, it has strong changes of entering into bankruptcy within a year
- if a firm has a z-score that is less than 1.8, it is in the danger zone
I then take all the z-scores that are less than 2.7, categorize them into very narrow ranges and plot the normal distribution of the scores.
You'll have something that looks like this:
The normal distribution will ALWAYS be positively skewed. I suspect that this is because bankruptcy (for listed companies) is a rare occurrence. I then focus my attention on everything that lies to the left of the mean--the green zone on the graphical illustration. That's where the 'gold' is!