James Li

# New Calculation: The Probability of Financial Distress

## A new method for computing bankruptcy risk

We are pleased to announce a new method of computing the bankruptcy risk of companies, the “Probability of Financial Distress.”

Background

John Campbell, Jens Hilscher and Jan Szilagyi developed a logit probability model based on eight explanatory variables:

1. Net income to market total assets (NIMTAAVG).
2. Total liabilities to market total assets (TLMTA).
3. Cash to market total assets (CASHMTA).
4. Excess return compared to the S&P 500 (EXRETAVG).
5. Standard deviation of daily returns over the past three months (SIGMA).
6. Relative size (RSIZE).
7. Market-to-book equity ratio (MB).
8. The log of the stock price, capped at log(15) (PRICE).

The logit formula to compute the probability of financial distress (PFD) is given below:

LPFD = -20.12 * NIMTAAVG + 1.60 * TLMTA – 7.88 * EXRETAVG + 1.55 * SIGMA – 0.005 * RSIZE – 2.27 * CASHMTA + 0.070 * MB – 0.09 * PRICE – 8.87

To compute the PFD, we take the ratio of exp (LPFD) to 1 plus exp (LPFD), where “exp” stands for the exponential function. This PFD measures the probability that a company will go bankrupt within the next 12 months given its current financial position.

Example calculation

Consider Apple Inc. (NASDAQ:AAPL), which currently has a PFD of approximately 0.02%.

Although most of the X variables have straightforward calculations, three of them require deeper calculations: NIMTAAVG, EXRETAVG and SIGMA.

For NIMTAAVG, we consider the net income over the market total assets over the past four quarters. Table 1 shows the NIMTA ratios of Apple for the past four quarters.

 Quarter Latest 2nd latest 3rd latest 4th latest Net income 10714 8717 11029 17891 Market cap 796766.5 744551.72 749020.3 608960.7 Total liabilities 241272 212748 200450 198751 NIMTA 0.010321 0.0091058 0.011616 0.02215 Weight 0.5333 0.2666 0.1333 0.0666 Adjusted NIMTA 0.005504 0.0024276 0.001548 0.001475

Table 1: NIMTA Ratios for Apple, Past Four Quarters

We then take the sum of the adjusted NIMTA’s (last row of Table 1) to obtain 0.01095, the NIMTAAVG for Apple.

Note the “Weight” row in Table 1. According to the research paper, the NIMTAAVG is a “geometrically weighted average level of profitability where the weight is halved each quarter.” We compute the EXRETAVG in a similar way, i.e., we place more weight on the more recent returns. Table 2 illustrates the EXRETAVG calculation for Apple.

 Month EXRET Factor EXRETADJ 0 -0.03552 0.220053 -0.007816 1 0.102908 0.174656 0.017974 2 -0.10422 0.138625 -0.014447 3 0.055511 0.110026 0.006108 4 0.067974 0.087328 0.005936 5 -0.07853 0.069312 -0.005443 6 0.043868 0.055013 0.002413 7 -0.00742 0.043664 -0.000324 8 0.047817 0.034656 0.001657 9 0.043014 0.027507 0.001183 10 0.094222 0.021832 0.002057 11 -0.02874 0.017328 -0.000498

Table 2: Excess Returns (EXRET) for Apple, Past 12 Months

The “Month” column in Table 2 refers to Month m,  i.e., Month 0 refers to the current month and Month 1 refers to the previous month. The “Factor” column is constructed so the weight is halved each quarter. This means the weight for Month m is 2 ^ (-1/3) times the weight for Month m-1.

For sigma, we consider the annualized standard deviation of a company’s returns over the past 92 days (or 63 trading days). Figure 1 shows the exact formula for sigma according to the research paper.

Figure 1

The other calculations should be straightforward: the TLMTA is simply total liabilities over market total assets while CASHMTA is simply cash and equivalents over market total assets. For relative size, we take the log of market equity over the market value of the Standard & Poor’s 500 index. For the market-to-book value, we take the market equity over the adjusted book value of equity, which is the maximum value of one and the following sum: book equity plus one-tenth of the difference between market equity and book equity. Finally, we take the log of 15 or the company’s share price, whichever is lower.

Screening for companies based on PFD

You can screen for companies based on their PFD through our All-in-one Guru Screener. The PFD filter is located in the first column, under the Fundamental tab as illustrated in Figure 2.

Figure 2

You can screen for PFD in increments of 5% using the drop-down menus for “Probability of Financial Distress” shown in Figure 2 above. For example, the highlighted filter in Figure 3 screens for companies with, at most, a 15% probability of financial distress.

Figure 3

We also have the PFD filter in our Customized section if you wish to screen for companies with at most a 7% probability of financial distress. If you click on the Customized tab and then the blue “Create New Filter” button, you should see an Edit Filter Formula pop-up window like the one shown in Figure 4.

Figure 4

If you enter ‘Probability of Financial Distress (%)’ < 7 in the formula box, you will screen for companies that have no more than a 7% chance of going bankrupt within the next year.

How is the PFD different from the Altman Z-score?

Like the Altman Z-score, the PFD measures a company’s bankruptcy risk in the upcoming year. However, the main drawback of the Z-score is it does not apply to banks and insurance companies. According to Investopedia, the concept of “working capital” does not apply to banks like Bank of America Corp. (NYSE:BAC) as financial institutions do not have typical current assets or current liabilities like inventories or accounts payable.

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James Li
I am an editorial assistant and researcher at GuruFocus. I have a Master's in Finance from SMU, and I enjoy writing reports on financial trends and investor portfolios. Follow me on Twitter at @JamesLiGuru!

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 Currently 4.33/512345 Rating: 4.3/5 (6 votes) Voters:

TaigaPilot - 10 months ago

Is this new probability of financial distress calculation available yet in the financial strength section when I type the ticker symbol of a stock into the search bar? If it could be added there, near the Altman Z Score, it would be great.

James Li - 10 months ago

Hi TaigaPilot,

We plan to add the PFD calculation to the financial strength section of a company's summary page. I will let people know when this is added.

Thanks!

Algaar999 - 10 months ago

How difficult would it be to include PFD in the prior year financials screen (and related xls download), so we can see how useful this metric has been as a predictor historically?

Okkerse - 10 months ago    Report SPAM

Dear James,

As inventor of the OK-Score (since 2000 real life with a GINI of 98,6%) I can only wish you lot of success.

Krobijake at dmn - 9 months ago    Report SPAM

hi i have a question. is there a good email address for you? i am krjacobs at dallasnews dot com

SciDeep - 9 months ago

Like the Altman Z-score, its' six components (WrkngCap/TA, RtndErngsTA, EBIT/TA, MktValEqty/TotLiab, Sales/TA) can be useful. However, the pre-factors (1.2, 1.4, 3.3, 0.6 and 1.0 respectively) are curve fitting done long ago in a different age (1960s). The Z-score boundaries <1.8 and >3.0 are again based on curve fitting. Having said that, the trend in the individual components can be useful for valuations.

The same might be said for the eight components in your analytics. It would be valuable to Premium subscribers to have access to the eight components in the Interactive Chart section. The six components of the Z-score are easily 'programmed user functions' in the Interactive Chart. Your eight cannot be easily programmed with the data access available.

If there are papers with data support the predictions you are planning to publish on the GuruFocus site, please provide them. Otherwise while the prediction looks analytically impressive, it might turn into a deceptive indicator. Interesting science => an parametric fitted equation, but poor risk execution on a stock by stock basis.

1richrich1 - 9 months ago

I am looking forward to adding it to my portfolio of preferred stocks where I review the issueing company. The z score doesn''t' work, at least for reits as it doesn't use FFO for cash flow. Probably didn't even have REITS when they invented the z score.

Billwzw - 9 months ago    Report SPAM

"In a 2008 paper called "In Search of Distress Risk", John Campbell, Jens Hilscher, and Jan Szilagyi comprehensively explore the determinants of corporate failure."

"The paper was updated on Januany, 2010 with new weights."

The study covers the 1963-2008 time period. Data come from Compustat and CRSP.

"This gives us about 800 bankruptcies, 1,600 failures"

Students of this area of study should aleady know that the classic Altman Z (1968) & his upgraded Altman Zeta (1977) have been superseded by better methods for some time - see Chava and Jarrow (2004)

I agree with SciDeep : there is probably good value in trend charting the individual components of this new PFD