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A More Powerful Bankruptcy Prediction Model

Distance to Default does a better job than traditional methods of gauging a company's financial health.

Warren Miller, James P. Harrington, and Magdalena Mroczek, 01/12/2010

In light of ongoing economic turmoil and continuing uncertainty in credit markets, it's more important than ever for investors to accurately identify companies in distress and their potential for default. Morningstar's Financial Health Grade, a data point available across Morningstar's equity research products, is a way for investors to quickly do just that.

The grade is based upon Morningstar's Distance to Default methodology, a slightly modified structural model similar to those created by Black, Scholes, and Merton.Distance to Default takes advantage of both market information and accounting financial information to estimate companies' probability of (or "distance" to) default. Every day, Morningstar calculates Distance to Default values for the universe of U.S. stocks and then ranks these values and awards Financial Health Grades to each company: The most-healthy 10% of the universe earn A's, the next 20% get B's, the next 40% earn C's, the next 20% get D's, and the bottom 10% get F's.

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Recently, Morningstar's valuation research team re-examined Distance to Default and another bankruptcy prediction model-the Z-Score-to assess their predictive power. Under the extreme conditions of the financial crisis, are these models proving their mettle?

The Models
The Z-Score, developed by Edward Altman, a professor of finance at New York University, is perhaps the most familiar model for predicting financial distress (Bemmann 2005). Altman identified five common accounting ratios that significantly predict default. The five pillars are combined in an equation that result in a company's Z-Score (Altman 2002).

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Each factor is intuitively appealing to investors because it captures a different credit-relevant aspect of a company's operations. Liquidity, cumulative profitability, asset productivity, market-based financial leverage, and capital turnover are addressed by the five ratios. The Z-Score presumes that each ratio is linearly related to a company's probability of bankruptcy.

Morningstar's Distance to Default model is less intuitive than the Z-Score because it does not specifically address the cash accounting values that practitioners and professionals typically examine in a default or bankruptcy. The Distance to Default model considers a company's equity as a call option on the firm's assets with a strike price equal to the book value of its liabilities and a market price equal to the market value of the firm's assets. Distance to Default describes the probability that this hypothetical call option will end up worthless-in effect, the potential that it will default if the value of the firm's assets drops below the book value of the firm's liabilities.

Based on the current market value of a company's assets, the historical volatility of those assets, and the current book value of a company's liabilities, we can calculate Distance to Default. (For the complete methodology, see Warren Miller's paper, "Comparing Models of Corporate Bankruptcy Prediction: Distance to Default vs. Z-Score." It is available for free download from the White Paper Bank on MorningstarAdvisor.com.)  In our study, we also included a simple, single-variable model based on the ratio of total liabilities to total assets (TLTA) to act as a benchmark for comparing the bankruptcy prediction models; even individual accounting ratios and measures of capital structure may predict bankruptcy potential to some degree. In this case, we would expect the probability of bankruptcy to increase as the TLTA ratio increases.

Our comparison of the Z-Score and Distance to Default models is not a contest. Rather, it sheds light on the strengths and weaknesses of each and gives investors an understanding of what's available to them in order to evaluate the creditworthiness of public and private companies. We are also cognizant of the fact that the Z-Score was intended to gauge the financial health of manufacturing compa­nies (Altman 2002). Nonetheless, we included non-manufacturing companies in our study because, in practice, the Z-Score is commonly used to evaluate the financial health of all companies.

Collecting and Refining the Data
Using data from Bloomberg, we first compiled a master bankruptcy list of 502 companies that declared chapter 7 or 11 bankruptcy between March 1998 and June 2009.

Next, we extracted the necessary data from Distance to Default values provided by the Center for Research in Security Prices at the University of Chicago's Booth School of Business. We then calculated Z-Score and TLTA values with data from Morningstar's Equity XML Output Interface. We transformed each of the three ratings into a percentile score using breakpoints based on all the data over a 10-year history. The higher the percentile, the more prone to default a company was rated.

Finally, we matched our master bankruptcy list with the three percentile datasets. When compiling data for the models, we expunged each company-date pairing that did not include all relevant data points from that model's dataset. Therefore, the company data we used overlapped within the three models, but they did not include identical company-date records.

The Results
The best way to compare the performance of credit-scoring models with non-identical sample sets is to measure their ability to differentiate between companies that are most likely to go bankrupt within a year from those that are least likely (Bemmann 2005). We tested each model's ability to rank companies from least to most likely to declare bankruptcy as well as the rankings' durability and stability. We also performed two tests of each model's cardinal ability to predict bankruptcy.

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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 credit-scoring 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 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.PAGEBREAK

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). The accuracy ratios of the credit-scoring models shown in Exhibit 1 are:

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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.

Durability Results
The ordinal-ranking ability of any bankruptcy prediction model would presumably decay as the time horizon for bankruptcy lengthens. Exhibit 2 shows the ordinal predictive capability of all three models over one- to 10-year bankruptcy time horizons.

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Distance to Default's predictive ability is superior to the other two models over all bankruptcy time horizons. The widening spread between Distance to Default and the other two models also demonstrates that the decay of its predictive ability is less than that of the other two, meaning Distance to Default produces a more durable signal.

Stability Results
Rating stability can determine the potential applications of a credit-scoring system. In most models, ordinal and cardinal accuracy are at odds with rating stability; that is, accuracy must be sacrificed for stability, and vice versa. Drift distance is a measure of how each model's ratings vary from period to period, from 0 (maximum stability) to 9 (minimal stability).

Exhibit 3 shows Distance to Default is the least-stable rating system, followed by the Z-Score and then the TLTA. This is expected, because market-based model inputs are typically more volatile than accounting-based inputs. Distance to Default relies more on the former, and TLTA and Z-Score rely primarily on the latter.

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Cardinal Results
Our secondary performance tests gauged each model's cardinal ability to predict bankruptcy. The table examines the default rates of the companies to which the models assigned the lowest risk.

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Of the three models, Distance to Default proved to be most predictive of bankruptcy in absolute terms. On average, the most recent Distance to Default percentile before a bankruptcy event was 91. The high average means that there was a lower occurrence of the Distance to Default model classifying future bankrupt companies as safe compared with the Z-Score and TLTA. In addition, Distance to Default had the lowest occurrence of bankruptcies in its best-rated quintile of companies. The Z-Score placed second in both measures, followed by TLTA.PAGEBREAK

Summarizing the Study
Distance to Default, which is the basis of Morningstar's Financial Health Grades for companies, outperformed the Z-Score and our univariate TLTA model in both ordinal and cardinal bankruptcy prediction. Curiously, the Z-Score's predictive ability is nearly equal to the other two models when ranking relatively safe companies but performs worse in situations when the bankruptcy probability is high. Compared with the other two models, Distance to Default also had a higher average rating just before bankruptcy and a lower bankruptcy rate for companies it had categorized as safe.

If a bankruptcy signal is not durable and decays too rapidly to act on, then a predictive model will prove useless in practice. We found that all three models produced actionable scores. Distance to Default, however, generated more durable ratings, as its ordinal ability decayed at a slower rate than either of the other two models. It also displayed more volatile ratings than both the Z-Score and the TLTA model. This is intuitive, because Distance to Default relies more on market-based inputs than accounting-based inputs.

One final note: When valuing a business as a going concern, a firm is assumed to continue operations into the indefinite future. Does this mean that investors need to remove distressed companies from public-company risk premiums when applying the latter to the valuation of healthy, going-concern private entities? It does not. Although the firm is presumed to be a going concern, predictive ability is never 100%.

Applying risk premium data based on a portfolio of primarily healthy companies with a small slice of potentially distressed companies acknowledges the less-than-100% chance that a subject firm will be perfectly healthy for the indefinite future.
 
Warren Miller is a senior quantitative equity analyst with Morningstar. James P. Harrington is director of business valuation research in Morningstar's Financial Communications business. Magdalena Mroczek is a business valuation analyst with Morningstar.

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