In addition to the Altman Z-score, GuruFocus computes an alternative 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:
- Net income to market total assets (NIMTAAVG).
- Total liabilities to market total assets (TLMTA).
- Cash to market total assets (CASHMTA).
- Excess return compared to the S&P 500 (EXRETAVG).
- Standard deviation of daily returns over the past three months (SIGMA).
- Relative size (RSIZE).
- Market-to-book equity ratio (MB).
- 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. (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
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. (BAC) as financial institutions do not have typical current assets or current liabilities like inventories or accounts payable.
See also
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