The predicted probability of financial distress for each firm in Model Ⅳ is calculated with the fitted logistic model using the samples from 1998 to 2001. The frequencies of the resulting probabilities are tabulated in Table 7 in which probabilities are categorized into five intervals of equal size.
We find 93.19% of healthy firms to have an estimated probability of financial distress below 0.1999, and 36.84% of distressed firms to have an estimated probability over 0.8000. The cumulative distributions for the two groups of firms can be seen from Figure 2 in which strong discriminating power is visualized.
Table 7: The frequency distribution of the estimated probability of financial distress Probability
Interval
No. and % of healthy firms
No. and % of distressed
firms
Difference in %
Cumulative
% of healthy firms
Cumulative % of distressed
firms 0-0.1999 424(93.19)* 11(19.30) 73.89% 93.19% 19.30%
0.2000-0.3999 16(3.52) 5(8.77) -5.26% 96.70% 28.07%
0.4000-0.5999 12(2.64) 11(19.30) -16.66% 99.34% 47.37%
0.6000-0.7999 1(0.22) 9(15.79) -15.57% 99.56% 63.16%
0.8000-0.9999 2(0.44) 21(36.84) -36.40% 100.00 100.00%
Total 455(100.00) 57(100.00) 0.00
* Numbers in parentheses are percentages
0%
20%
40%
60%
80%
100%
120%
0-19.99 20-39.99 40-59.99 60-79.99 80-99.99 Estimated probability of financial distress (%)
Cumulative percentages
healthy firms distress firms
Figure2: The cumulative percentage of firms in all intervals of estimated probability of financial distress in the integrated prediction model.
The choice of cutoff point represents a trade-off between type I and type II error.
If we maximize the sum of percentages of correct classification for the two groups of firms, the optimal cutoff point falls around 0.2000. In this case, the percentage of correct classification will be 93.19% for healthy firms and 80.70% for distressed firms.
Thus we propose a cutoff point of 0.2000 whereas firms with estimated probability greater or equal to 0.2000 are classified as potential distressed firms, as shown in Table 8.
Table 8: In-sample classification accuracy under a cutoff point of 0.2000 Predicted outcome
Healthy Distressed
Healthy 424 (93.19%) 31 (6.81%)
Actual
outcome Distressed 11 (19.30%) 46 (80.70%)
We then try out-sample prediction under the proposed cutoff scheme. Using
samples between 1998 and 2000 to fit the integrated model and plugging in data of 2001, we find 90% of distressed firms are accurately classified as such and 85.40% of healthy firms are predicted as healthy with our model. In other words, nine out of ten financially distressed firms in year 2001 are accurately predicted to be so using an integrated model built upon samples between 1998 and 2000.
V. Conclusions
We integrated accounting, corporate governance, and macroeconomic variables to build up a binary logistic regression model for the prediction of financially distressed firms. Debt ratio and ROA are found to be the most explanatory accounting variables while the percentage of directors controlled by the largest shareholder (which measures negative entrenchment effect), management participation, and the percentage of shares pledged for loans by large shareholders are shown to have positive contribution to the probability of financial distress. For macroeconomic sensitivities, firms with higher sensitivities to the annualized growth rates of manufacturing production index and money supply (M2) are more vulnerable to financial distress.
On the issue of sampling technique, we find that oversampling of distressed firms is subject to the problem of choice-based sample bias pointed out by Zmijewski (1984). The classification accuracy is overstated consequently. To tackle the problem, we try to include as many healthy firms as possible in our sample instead of following the traditional 1: 1 or 1: 2 matching principle. The results show that the classification accuracy is mostly significantly improved in our integrated prediction model when the sample is closest to the actual population.
For the trade-off between type I and type II errors in the predicted probability classification, we maximize the sum of classification accuracy for both groups of
firms (the healthy and the distressed). It is found that an estimated probability of financial distress of 0.2000 represents the optimal cutoff point for predicting financial distress. Under such a cutoff scheme, our integrated model produces an in-sample classification accuracy of 80.7% for distressed firms and 93.2% for healthy firms. For out-sample prediction, 90% of the distressed firms and 85.4% healthy firms in 2001 are correctly identified using an integrated model built upon samples from 1998 to 2000.
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