Bubble Valuations and Their Impact on the Z-Score Model
The wisdom of hindsight now permits most economic experts to safely conclude that the wild equity market valuations of the late-90s were indeed symptomatic of a market bubble. While the truly stratospheric valuations were reserved for only a few rarefied sectors, such as tech stocks and the evanescent dot-coms, investors' munificence was spread liberally throughout the broader market—resulting in historically high valuations relative to any measurement of operating performance. The S&P 500 Index doubled between January 1997 and its peak valuation of over 1,500 in March 2000. We are all too familiar with what has happened since then. This fairly compact boom-and-bust cycle led us to wonder how well Altman's Z-Score model held up as a predictor of financial distress during this tumultuous period, given that one of its five ratios incorporates market-based information (equity values) in its calculation. Our initial expectation prior to testing the model was that these excessive equity valuations would have unduly influenced the standard Z-Score model, resulting in abnormally large Z-Scores for myriad companies during the bubble period and consequently a deterioration in the model's ability to correctly identify candidates for future bankruptcy (i.e., increasing Type I errors). Surprisingly, this premise proved to be largely unfounded.
In order to test the Z-Score model, we selected all publicly owned manufacturing companies (SIC codes 2000-3999) with annual run-rate sales in excess of $100 million from Compustat's database of active companies. More than 1,200 companies were identified. Z-Scores were computed for each of these companies for the four years from 1998 through 2001 using Altman's original 1968 model (herein referred to as the standard model or the public firm model) and a subsequent model he developed for privately held firms. The latter model replaced the market value of shareholders' equity with book value in the computation of the X4 variable. The four remaining variables were left intact, but their coefficients changed in the re-estimation of the model. Furthermore, cut-off scores changed in the private company model, resulting in a wider zone of ignorance (1.23-2.90) than in the public firm model (1.81-2.99). For purposes of this exercise, the private firm model served as a quasi-control group since it differs conceptually from the standard Z-Score model only with respect to our one variable of interest, X4.
Not unexpectedly, the average Z-Score of the standard model increased significantly to approximately 7.0 by year-end 1999 (Chart 1a), which in terms of timing was close to the ultimate stock market peak made in 1Q00. Extreme values had a fairly significant impact on average Z-Scores, particularly in 1999, as evidenced by median and trimmed mean Z-Scores that were smaller and considerably more stable throughout the four-year period. As expected, the private firm model (Chart 1b) produced far smaller and more stable Z-Scores—both owing to the omission of lofty and volatile market-based data.
Underscoring the relative importance of the X4 variable in the standard Z-Score model, Chart 2a indicates that X4 accounted for between 35-39 percent of a typical company's Z-Score throughout the four-year period compared to about half that proportion using the private firm model (Chart 2b). This approximate relationship also held true for median values, which are unaffected by extreme observations.
With respect to the classification of Z-Scores (into either the bankrupt, non-bankrupt or zone of ignorance groups), the standard model was far more conclusive than the private firm model, which consistently assigned well over one-half of all companies into the zone of ignorance category, compared to about one-quarter for the standard model (Charts 3a and 3b). Of course, whether or not these classifications were ultimately accurate will be the true test of the models! As for a classification agreement between the two models, they concurred about two-thirds of the time in each year of the four-year period.
The wisdom of hindsight now permits most economic experts to safely conclude that the wild equity market valuations of the late-90s were indeed symptomatic of a market bubble.
Of the more than 1,200 firms in our population, 58 filed for bankruptcy protection between the first quarter of 2001 and the second quarter of 2002. (An additional eight companies filed during this period, but had been transferred by Compustat to its inactive database, and were excluded from our population.) Testing the Z-Score model entailed tabulating Type I errors (categorizing any of these 58 failed companies into a non-bankrupt group either one or two periods prior to the bankruptcy filing) and Type II errors (classifying a non-bankrupt company into the bankrupt group either one or two years prior to FY01). Our results are broken out as follows:
With respect to Type I accuracy, the public company model's performance was consistent with most historical test results (typically 80-90 percent accuracy one year prior to bankruptcy) despite the influence of overvalued equity prices, and clearly outperformed the application of the private company model to these publicly owned firms. Overall, the public firm model correctly categorized 48 of the 58 failed firms one year prior to bankruptcy and 42 of 58 two years prior to bankruptcy. The Type I accuracy rate of 72.4 percent two years prior to failure is especially impressive considering we were at a market top right around that time. However, the prevalence of Type II errors is somewhat troubling, with about one in five non-failing companies categorized as bankrupt by the model. For enterprises making credit decisions strictly based on the standard Z-Score model, the increasing presence of Type II errors above its historically tested norms would translate into a growing rejection rate of good credit risks.
Though its overall categorization accuracy is somewhat less impressive compared to many tests of decades past, the standard Z-Score model still gets a passing grade from us and remains sufficiently prescient more than 30 years after its development. Our initial suspicion that bubble-period equity valuations would diminish the model's ability to correctly categorize future failed firms did not materialize from the data. Yes, equity market prices have a tendency to overshoot both on the up side and down side, but they also adjust very quickly to new information and shifting expectations. Indeed, the inclusion of this market-based data in the standard model helps make it robust and gives it a forward-looking dimension rather than forces it to wait for the impact of anticipated events to become embedded in the financial statements.
The continuing relevance and popularity of the Z-Score model in the field of financial distress after three decades is all the more remarkable when one considers the vastly increased complexity of business and accounting since 1968. One word of caution: Z-Score is not a "one size fits all" model. The standard public firm model is applicable only to manufacturing entities and other capital-intensive firms. Altman and others have also developed variants of the original model for service-type entities and other non-manufacturing firms, as well as other industry-specific revisions.