Morningstar Advisor - December/January 2010 - 23

Ordinal Results Exhibit 1 plots the cumulative percentage of bankruptcies on the y-axis and the ratings percentiles on the x-axis for each of the three models (plus a non-predictive model and an ideal model). The companies in the first percentile are the safest from going bankrupt; the companies on the 100th percentile are most in danger. This graph is called a Lorenz curve (named after economist Max O. Lorenz), also known as a cumulative accuracy profile. It typically is used to show the inequality of a distribution. The y-axis represents the total number of bankruptcies from the first percentile to the respective percentile of the point on the line. At Point A Z on the line that depicts the non-predictive scoring system (the blue 45-degree line), 50% of the companies that went bankrupt originally received a credit rating that placed them in first 50 percentiles (companies that seemed safe from bankruptcy), and 50% of the companies that went bankrupt originally received a credit rating that placed them in last 50 percentiles (unsafe companies more prone to go bankrupt). This equal distribution is why this type of rating model would have no real predictive ability; a “safe” rated company is just as likely to go bankrupt as an “unsafe” company. What would an ideal credit-scoring model look like? The answer follows from our analysis of the non-predictive model. The ideal creditscoring model, depicted by the orange line in the graph, would maximize the inequality of bankruptcy distribution. In other words, an ideal model would rate all of the firms that eventually went bankrupt in its most at-risk category (at the far right end of the graph) and all the firms that did not go bankrupt in categories other than its most at-risk category. As shown in the graph, the Lorenz curves depicting both the Distance to Default and Z-Score models are examples of an unequal distribution. At Point B X, approximately 10% of the companies that eventually Exhibit 2 More Durable Distance to Default is superior over longer time horizons. The widening spread indicates that the decay of its predictive ability is less than that of the other models. Ordinal Score 9 Distance to Default Z-Score TLTA 1 Years went bankrupt had received a credit rating from both models that placed them in the first, or safest, 50 ratings percentiles within one year before bankruptcy; approximately 90% of the companies that eventually went bankrupt had received a credit rating that placed them in the last, or unsafest, 50 percentiles within one year of bankruptcy. The more a model’s line bows out toward the lower right, the better the model is at differentiating between companies not likely to go bankrupt and companies likely to go bankrupt—and the more predictive power the model possesses. Our indicator for measuring inequality is the accuracy ratio. It is the ratio of the area between the non-predictive line (the blue 45-degree line) and the scoring system’s curve, and the non-predictive line and the ideal scoring system’s curve (the orange line). (See “Accuracy Ratio Explained” on Page 25.) The accuracy ratios of the credit-scoring models shown in Exhibit 1 are: Accuracy Ratio Ideal Distance to Default TLTA Z-Score Non-Predictive 1.00 0.70 0.60 0.60 0.00 In our study, Distance to Default has superior ordinal performance to the Z-Score and the simple TLTA model. In addition, Distance to Default approaches the ordinal rating accuracy of credit-rating agencies Moody’s and Standard & Poor’s, which have estimated accuracy ratios for large public companies of 0.68 to 0.85 and 0.60 to 0.83, respectively (Bemmann 2005). The cumulative accuracy profile displayed in Exhibit 1 provides more detail to the accuracy ratio. We can see that the Z-Score holds its own against Distance to Default for companies in the safest 80 percentiles. As the risk of bankruptcy increases, however, the Z-Score’s ordinal ranking ability deteriorates, as demonstrated by its concavity between the 80th and 100th percentiles. MorningstarAdvisor.com 23

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Morningstar Advisor - December/January 2010

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