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8/13/2019 Have Financial Statements Become Less Informative - Evidence From the Ability of Financial Ratios to Predict Bankruptcy
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Abstract. Using a hazard model, we examine secular changes in the ability of financial
statement data to predict bankruptcy from 1962-2002. We identify three trends in
financial reporting that could influence predictive ability with respect to bankruptcy:FASB standards, the perceived increase in discretionary financial reporting behavior, and
the increase in unrecognized assets and obligations. A parsimonious three-variable
model provides significant explanatory power throughout the time period, with only aslight deterioration in predictive power from the first to the second time period. The
striking feature of the results is the robustness of the predictive models over a forty-yearperiod.
Keywords: Bankruptcy, accounting information, financial ratios.
JEL Classification: M41, G14, G33, C41
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A significant body of research in accounting examines the relation between financial
statement information and security returns. Recent research has focused on questions of
secular changes in the ability of the income statement to explain security returns (e.g.,
Collins, Maydew and Weiss, 1997; Francis and Schipper, 1999, among others).1 The
results are mixed and are subject to diverse interpretations. In a comprehensive review of
the literature, Dechow and Schrand (2004) conclude there has been a secular decline in
the informativeness of earnings for security prices. Brown, Lo and Lys (1999) on the
other hand find no such decline. Landsman and Maydew (2002) find that trading volume
and incremental variance at the time of earnings announcements have, if anything,
increased over time, not diminished.
A second body of research in accounting has sought to examine the ability of
financial statement information to predict bankruptcy. The use of financial ratios to
predict bankruptcy has a long history (Beaver, 1966). It is well established that financial
ratios do have predictive power up to at least five years prior to bankruptcy. In this
paper, we extend this literature and the literature on the secular change in the explanatory
power of financial statements by examining changes in the predictive ability of financial
ratios with respect to bankruptcy.
Several forces over the last forty years potentially affect the ability of financial
ratios to predict bankruptcy. Here we identify three major trends: (1) The establishment
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The intent of the FASB and the SEC is to set standards that make financial
statements more useful and relevant to investors and other user groups. To the extent that
standard-setting has been successful in its goals, we would expect the quality of financial
statement data to be enhanced, and the predictive ability with respect to bankruptcy to
increase. The second force, other things being equal, acts to impair the quality of
accounting. Many intangible assets and financial derivatives are not captured by extant
financial ratios and constitute potentially important omitted variables. The third force,
the increase in discretion, in principle, could operate to enhance or impair financial
statement data to the extent it is used to signal management’s private information or used
to obscure important aspects of a firm’s financial performance, although prior research
largely finds opportunistic behavior. It is difficult to predict which of these diverse
effects will dominate.
In order to provide evidence on this issue, we examine a sample of bankrupt and
non-bankrupt firms for the years 1962 through 2002. In addition to verifying the findings
of prior research regarding predictive power, we divide the sample into two major sub-
periods: 1962-1993 and 1994-2002.
The first sub-period experienced many major developments with respect to
accounting standards. Prior to 1973, the Accounting Principles Board set accounting
standards. In 1973, the FASB was formed and issued its first standard. Since then, the
FASB has issued 150 standards, most of which added to the required accounting methods
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retirement benefits (1990), No. 107 with respect to disclosure of the fair value of
financial instruments (1991), No. 115 with respect to accounting for investments in debt
and equity securities (1993) are major examples. Of course, the effects of the standards
are not reflected immediately in the financial statements, since many of the standards
contain a time span over which the standard may be adopted.
The relative importance of intangible assets has increased over time as a result of
technology-based assets generated through research and development expenditures. A
crude approximation of the relative importance of intangible assets is reflected in market-
to-book ratios. From 1992 through 1999, the average market-to-book ratio for our
sample firms was at a forty-year high, ranging between 2 to 2.5, although there has been
a marked decline since.
The financial derivatives market experienced an explosion in the 1990’s, although
it is unclear how this affected measures such as financial ratios, since the fair value of
off-balance sheet derivative items could be either positive or negative. Many of the
financial derivatives were used as a substitute for leverage. To that extent, traditional
calculations of leverage variables are understated. On the other hand, derivatives may
constitute a correlated omitted variable to the extent that firms that are highly levered
with on-balance sheet financing are more likely to use off-balance sheet financing as
well. In any event, financial derivatives constitute an omitted variable that potentially
increases measurement error in the financial ratios.
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2002 period, and even in 1997 was high by historical standards. Of course, an earnings
restatement made in a given year applies to prior years’ financial statements. Lu (2003)
examines a sample of firms from 1988-2000 and reports a substantially higher litigation
level in the 1994-2000 period than the 1988-1993 period. Certainly, recent high profile
cases, such as Enron and WorldCom, have led to the perception that manipulation of the
financial statements is on the rise. We are careful to state that the perception is that
discretion has increased, because it is difficult to determine whether there is in fact an
increase or merely that instances of discretion are being better documented over time. In
a similar vein, the number of academic articles devoted to discretion and earnings
management has substantially grown over time, although it is not clear whether this is
because the underlying phenomenon is more prevalent or whether there is an increase in
awareness in the academic literature of the role of discretion in financial reporting.
While it is difficult to select a single “watershed” year that clearly divides the
sample time series, our analysis examines two time periods, pre-1994 and post-1994. We
believe these represent different regimes with respect to the secular features discussed
above. However, as a robustness check, we also conduct a time series analysis that is not
dependent upon decomposing the overall time period into subperiods and results are
essentially unaltered.
The layout of the paper is as follows. Section 1 discusses prior research and its
implications for the modeling of bankruptcy. Section 2 describes our data and presents
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of models including financial statement and market-related variables, and section 6
concludes.
1. Modeling the Probability of Bankruptcy
Models of bankruptcy focus on three areas: profitability, cash flow generation, and
leverage. Beaver (1966) uses a univariate analysis, while multivariate analyses have
included multiple regression (Beaver, 1965), discriminant analysis (Altman, 1968),
logistic regression (Ohlson, 1980), and hazard analysis (Shumway, 2001; Chava and
Jarrow 2005; Hillegeist et al., 2004; and Suh, 2003). The results have been robust with
respect to the predictive power of financial statement data. The precise combination of
ratios used seems to be of minor importance with respect to overall predictive power,
because the explanatory variables are correlated. Shumway, among others, reports
improved predictive power via the use of hazard analysis.
Hazard models have been applied to a variety of accounting issues. Beatty, et al.
(2002) use a hazard model to predict the duration of consecutive earnings increases for
public and private banks. Roundtree (2003) predicts the duration of the time between the
announcement of SAB 101 and the first disclosure by firms of its impact. Lin et al.
(2003) use hazard models to predict the duration of the time between an equity offering
and the first downgrade by analysts. The statistical method also enjoys widespread use in
the biological and social sciences.
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t . However, the ex post event is either zero or one in any finite period of time. Many
hazard models are applied in a context where the passage of time naturally affects the
hazard rate. A typical example would be the study of living organisms with a finite life.
The basic hazard rate is a function of time since birth and is coupled with the notion that
the cumulative probability of death prior and up to time t is an increasing function of
time, starting at zero and approaching one over a finite time period.
Various estimation methods allow the hazard rate to come from a family of
distributions that are a function of time (Allison, 1999). In addition to an estimation of
the basic hazard rate, hazard models permit the examination of a variety of covariates to
affect the hazard rate (e.g., the effect of DDT exposure on mosquitoes). In many
applications, the covariates are constant over time. However, a subclass of models
permits the covariates to vary over time. This class of hazard models is of interest here
because the financial condition of the firm as manifest in the financial ratios varies over
time. The time-varying covariates can be somewhat tedious to incorporate into many of
the traditional hazard models.
However, it has been shown that the familiar logistic model can be used to
estimate the effect of time-varying covariates on the hazard rate. In our context, the
“dependent variable” is either one if the firm is bankrupt in year t or zero if it is not. In a
sample of non-bankrupt and bankrupt firms, the non-bankrupt firms are coded zero every
year they are in the sample, while the bankrupt firms are coded zero in every sample year
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final year before bankruptcy. Shumway argues that the inclusion of these additional
observations can increase the efficiency and reduce the bias of the estimated coefficients.
Specifically, in contrast to a static model with only a single firm-year observation for a
non-failed firm, the multiperiod logit approach considers the hazard of bankruptcy in
multiple years for firms that do not go bankrupt.
We examine whether the predictive ability of financial ratios for bankruptcy has
declined from the first to the second sample period. A general form of the hazard model
used here is:
).()()(ln t X t t h j j Β+=α (1)
In this model, h j(t) represents the hazard, or instantaneous risk of bankruptcy, at time t for
company j, conditional on survival to t ; α (t) is the baseline hazard; B is a vector of
coefficients; and X j(t) is a matrix of observations on financial ratios, which vary with
time. Here the hazard ratio is defined as the likelihood odds ratio in favor of bankruptcy
and the baseline hazard rate is assumed to be a constant. The model is estimated as a
discrete time logit model using maximum likelihood methods, and provides consistent
estimates of the coefficients B.
The primary question we address is whether the ability of financial ratios to predict
bankruptcy has changed over time. We test this by comparing the accuracy with which
the estimated probability of bankruptcy conditional on financial ratios can be used to
classify firms that declare bankruptcy in the first and second sample periods
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2. Data and Descriptive Statistics
The sample consists of NYSE and AMEX-listed Compustat firms. Bankrupt firms were
identified through a variety of sources including the 2003 Compustat Annual Industrials
file, the 2003 CRSP Monthly Stock file, the website Bankruptcy.com, the Capital
Changes Reporter, and a list of firms generously supplied by Shumway. The bankrupt
year is defined as the calendar year that a firm files for bankruptcy.
Following Shumway (2001), all NYSE- and AMEX-listed firms that did not file
for bankruptcy and are not in financial or utility industries are included in the sample as
non-bankrupt firms. The independent variables are lagged to ensure that the data are
observable prior to the declaration of bankruptcy. Since all sample firms file annual
financial statements with the SEC (i.e., 10-Ks), it is assumed that financial statements are
available by the end of the third month after the firm’s fiscal year-end. Of course,
quarterly statements have also been filed several months prior to this time. However, for
a firm that declares bankruptcy within three months of its fiscal year-end, it is assumed
that the most recent year’s financial statements are not available and the prior fiscal year
is defined as the year before bankruptcy. Because of the availability of quarterly
financial statements, this rule is a “conservative” one that will tend to understate the
predictive power of financial statement data. The process resulted in the identification of
585 bankrupt firms, of which 544 were used in the analysis. Table 1 describes the
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bankrupt firms. As reported in Table 1, similar exclusions resulted in a sample of 4,237
non-bankrupt firms with 74,823 observations.
The sample sizes of the bankrupt and non-bankrupt firms for each sample year
from 1962-2002 are reported in Table 2. Note that the frequency of bankrupt firms
reflects the number of bankruptcies (that is, the number of bankrupt firms), while the
frequency of non-bankrupt firms reflects the number of firm-years provided by the non-
bankrupt firms. In particular, a bankrupt firm appears in the number count only once (the
year bankruptcy is declared). Hence, the ratio of bankrupt to non-bankrupt firms in a
given year is an approximation of the overall relative frequency of bankruptcy. Overall,
the ratio is less than one percent (544/82,953). Table 2 also indicates how the bankrupt
firms are distributed across the years. Poorer economic conditions are reflected in the
clustering of observations in 1990-92 and 1999-2002.
2.1 Descriptive Statistics
First, we begin with some descriptive statistics. Table 3 reports the mean (median)
values for each of the explanatory variables. The three explanatory variables are ROA,
ETL, and LTA. ROA is return on total assets, which is earnings before interest divided by
beginning of year total assets. ETL is EBITDA to total liabilities, which is net income
before interest, taxes, depreciation, depletion and amortization divided by beginning total
liabilities (both short term and long term). In prior studies (e.g., Beaver, 1966), ETL is
called the “cash flow” to total liabilities ratio. LTA is a measure of leverage, which is
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of the explanatory power of the financial statement variables used in the three models.
This result is not surprising since the financial ratios are highly correlated. Because
model comparison is not the purpose of this study, we have chosen the parsimonious
route of examining the predictive performance over time of the parsimonious three
variable model.
The three variables capture three key elements of the financial strength of a firm.
ROA is a measure of the profitability of the assets. Profitability is expected to be a
critical element, since prior research has shown that capital markets are concerned about
the ability of the firm to repay its debts and profitability is a key indicator of ability to
pay. The second element is the ability of cash flow from operations pre-interest and pre-
taxes to service the principal and interest payments. EBITDA has been widely used as an
available proxy for pre-interest, pre-tax cash flow from operations. Total liabilities are a
proxy for the amount of principal and interest to be paid. Beaver (1966) found this ratio
to be the best single ratio for bankruptcy prediction purposes. The third element, LTA, is
a measure of the debt to be repaid relative to the total assets of the firm available as a
source for repaying the debt.
Table 3 provides a description of the mean (median) value of the individual ratios
for the bankrupt and non-bankrupt firms in each of the 4 years prior to bankruptcy. Here,
the year before bankruptcy represents the financial statements reported in the year prior
to the year of bankruptcy.2 Since the non-bankrupt firms have no year of bankruptcy,
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year of bankruptcy approaches. These results are similar in spirit to those reported by
Beaver (1966) and subsequent research. This manner of presentation of the data, of
course, exploits the ex post knowledge of which firms failed and does not show the
degree of overlap of the two distributions. However, they can provide some preliminary
visual indication of the behavior of the ratios.
Following Shumway, we mitigate the effects of outliers on the estimates of the
hazard model parameters by “winsorizing” all observations at the 1 percent and 99
percent level respectively. As a result, the minimum and maximum values of each of the
three years before bankruptcy and for the non-bankrupt firm distribution are identical, as
reported in Table 3.
In order to simplify the presentation of the non-bankrupt firms, a single pooled
distribution of non-bankrupt firms is reported. However, in unreported results, we
conducted a similar analysis where we matched each bankrupt firm with a non-bankrupt
mate from the same industry and for the same calendar years. The resulting distribution
of non-bankrupt firms (i.e. pooled relative to year before bankruptcy) was constant across
event time and hence is well approximated by a single pooled sample here. This is not
surprising, since the ex ante probability of bankruptcy for the entire sample of ex post
non-bankrupt firms is likely to be low.
The mean ROA for the non-bankrupt firms is .05, while the mean for the bankrupt
firms is -.03, -.04, -.10, and -.18, declining over the four years prior to bankruptcy. For
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bankruptcy. When compared with the means of the non-bankrupt firms, the poor
profitability, poor cash flow, and higher leverage positions are evident as early as four
years prior to bankruptcy. Moreover, the mean ratios of the bankrupt firms deteriorate as
the year of bankruptcy approaches.
Figures 1 through 4 show similar information in a different format. Each figure
reports the cumulative distribution function (cdf) for the bankrupt and non-bankrupt firms
for each of the four years prior to bankruptcy for each of the three financial ratios. Figure
4 shows the cdf for the combined ratio model. An advantage of the cdf’s is that they
report the entire distribution. As the figures indicate, the cdf for the bankrupt firms is
distinct from that of the non-bankrupt firms for at least four years prior to bankruptcy and
as the year of bankruptcy approaches, the cdf of the bankrupt firms moves farther away
from that of the non-bankrupt firms.
3. Secular Change in the Predictive Ability of Financial Ratios
Table 4 reports the estimated coefficients (Panel A) and predictive results for logistic
estimation for the entire period (1962-2002). All three ratios are significant and have the
predicted sign. The probability of bankruptcy within the next year is an increasing
function of leverage and a decreasing function of profitability and cash flow. With
respect to predictive results, the predicted scores of the entire sample are ranked and
divided into deciles. The data are divided into deciles based on the combined distribution
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group (bankrupt and non-bankrupt) would be 10 percent. In order to facilitate
comparison across tables, the same firm-year observations are used throughout, which
requires availability of all of the accounting and market value based variables. This
reduces the sample to 457 bankrupt firm-years and 63,398 nonbankrupt firm-years.
Unreported results indicate that the inferences are essentially the same if the maximum
number of observations is used for each respective model.
In Panel B, the first three columns report the bankruptcy index for bankrupt firms
in the year prior to bankruptcy by decile. Each decile is computed from the sample of
both bankrupt and nonbankrupt firm-years, and is ranked in descending order, so decile 0
has the highest predicted probability of bankruptcy (or alternatively, the lowest
probability of survival). In decile 0, 68.71 percent of the bankrupt firms appear. The
number of bankrupt firms declines in each subsequent decile and bankrupt firms are
virtually nonexistent in the three highest deciles. In the two (three) lowest deciles, 82.71
(89.72) percent of the bankrupt firms appear, as compared with an expected 20 (30)
percent under the null hypothesis of no predictive power.
The remaining firm-years are separated for descriptive purposes into two groups,
the number of firm-years of bankrupt firms (years prior to the year before bankruptcy)
and the firm-years of nonbankrupt firms. Columns 4 and 5 of Panel B indicates that
years prior to the year of bankruptcy tend to be higher in the lower deciles than would be
expected by chance. The number of firms in each decile declines monotonically. This is
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but the same general behavior is exhibited in the subsequent analyses as well. By
contrast, the last two columns in Panel B show that the non-bankrupt firms have fewer
firms in the lowest two deciles and the percentage monotonically increases for the higher
deciles.
The combined percentage of nonbankrupt firm-years in the lowest decile is 9.6
per cent. The estimated likelihood odds ratio for the lowest decile is 7.16 times
(68.71/9.6 per cent), which implies that a firm whose financial ratio index is in the lowest
decile is 7.16 times more likely to fail within the next year than the population.
Obviously, if we were to use a finer partition than deciles, the likelihood odds ratios
would be even higher for the lowest partitions.
Table 5 reports the estimation and prediction results for each of our two sub-
periods: 1962-1993 and 1994-2002. Panels A and C report the estimation results for each
of the two sub-periods. In both cases, all three variables are significant and the signs are
as predicted. The coefficient on the leverage variable appears to be similar across the
sub-periods, while there are decreases in both the ROA and the ETL coefficient.
Table 5, Panels B and D report the prediction results for each sub-period. For the
first sub-period, the cumulative percentage of bankrupt firms in the lowest two (three)
deciles are 84.85 (92.05) percent, respectively, while for the second sub-period, the
percentages are 80.31 (86.01), which represents a slight deterioration from sub-period 1
to sub-period 2. In other words, there is a reduction of about 5 per cent. These in-sample
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to use the coefficients from period 1 to predict bankruptcy in period 2. Panel E reports
the results of one out-of-sample test, where the coefficients from sub-period 1 were used
to predict bankruptcy in sub-period 2. The percentage of bankrupt firms in the lowest
two (three) deciles is 80.31 and 86.53, respectively, which is identical to the percentages
observed using sub-period 2 coefficients. The sub-period 1 weighting scheme is as
effective in correctly classifying the bankrupt firms as those derived from fitting the sub-
period 2 coefficients to the sub-period 2 data. This finding reflects the similarity of the
coefficients and the degree of collinearity among explanatory variables. It suggests that
the index of bankruptcy based on financial ratios is robust over time.
Of course, some deterioration in predictive power could have occurred to the
extent that the in-sample estimates “over-fit” the data or the relative weighting changes
over time. We also conducted another out-of-sample test that does not require the
coefficients to be constant over time. We call this test a contemporaneous out-of-sample
test. To conduct such a test, within each sub-period the firms are randomly divided into
two sub-samples (sub-samples 1A, 1B, 2A and 2B, respectively).
Panels A, C, E, and G of Table 6 report the estimated coefficients for each of the
four groups, as well as the out-of-sample results. Again the coefficients for each of the
variables are always significant, the coefficients are always of the predicted sign, and the
magnitudes of the coefficients are remarkably similar across sub-samples for a given time
period.
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the three lowest deciles are 91.53 and 93.84 for time period 1 and 84.62 and 87.64
percent for sub-period 2. There is a slight deterioration in the combined predictive power
from sub-period 1 to sub-period 2, from an average of 92 percent to 86 percent. Using a
χ2 test for the difference between two samples, the value is 5.68, which is not significant
at the conventional 5 per cent significance level.3
Although not reported in Table 6, the in-sample prediction percentages for the
four groups are about the same as the out-of-sample prediction percentages. Hence, the
out-of-sample deterioration between periods 1 and 2 is not due to a change in the
coefficients over time nor due to differences in the coefficients across random sub-
samples within a given sub-period.
These tests do not support a dramatic change in the predictive power of financial
ratios with respect to bankruptcy. The time-series in-sample test shows a decline from 91
per cent accuracy to 86 per cent accuracy with respect to the bottom three deciles.
Similarly, the contemporaneous out-of-sample tests show a decline from 92 per cent to 86
per cent when conducted out-of-sample.
4. Secular Change in the Predictive Ability of Market-Based Variables
Prior research has also examined the ability of variables based on market values to
predict bankruptcy (Hillegeist et al., 2004, Chava and Jarrow, 2005, Shumway, 2001).
The inclusion of market-based variables is appealing for several reasons. First, prior
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observed series of security prices, the resulting model can potentially provide superior
estimates of the probability of bankruptcy. The difference in the predictive power of
models based on financial statement variables and more comprehensive models can be
used to assess the importance of information that is not contained in financial statements.
As discussed shortly, this feature is of particular interest to our study.
Second, the market-based variables can be measured with a finer partition of time.
While financial statements are available at best on a quarterly basis and prior research
largely uses annual data (including our study), market-based variables can exploit the
availability of prices daily. Third, the market value based variables can provide direct
measures of volatility, as we discuss shortly.
Of course, it is a nontrivial exercise to extract the probability of bankruptcy from
an observed series of market prices. The market price of a security reflects the expected
present value of future cash flows. Embedded in the market price is an assessment of the
probability of bankruptcy, but it is not a direct measure of that probability. As the
probability of bankruptcy increases, the nonlinear nature of the payoff function for
common stock becomes increasingly more important because of risky debt and limited
liability. Another deterrent to extracting information about bankruptcy risk from equity
prices is that they may not fully reflect publicly available information and in this sense
are not informationally efficient.
The market-based variables typically used in prior research are: logarithm of
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by the market capitalization of the market index of NYSE, AMEX, and NASDAQ firms.
Security return and standard deviation are defined over a twelve-month period ending
with the third month after the end of the fiscal year. This rule provides assurance that the
fourth quarter financial statement data have been filed. Obviously, this rule also permits
market-based variables to reflect any other information announced after the fiscal year
end, including information about the first fiscal quarter performance.4
The logarithm of market capitalization is a measure of firm size. The notion is
that the market value of common equity represents the equity cushion available to debt-
holders before their principal and interest become jeopardized. This variable reflects the
amount by which the value of assets can decline before they are insufficient to cover the
present value of the debt payments.
As discussed earlier, the option-like feature of common stock and risky debt may
impair the informativeness of this variable. Moreover, the market capitalization variable
is not “scaled” in that it is not compared with the magnitude of debt outstanding. Of
course, market capitalization may also proxy for the volatility of returns to the extent that
the firm’s asset returns are less than perfectly correlated with each other. This
diversification effect would imply ceteris paribus that large firms have a smaller
probability of bankruptcy. In any event, prior research indicates that the probability of
bankruptcy is a decreasing function of market capitalization.
The second market-based variable is prior year security returns, LERET. The
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omits information on the amount of debt outstanding. However the prediction would be
that the probability of bankruptcy is decreasing in lagged security returns.
The third market-based variable is the standard deviation of security returns,
LSIGMA, computed as standard deviation of residual return from a linear regression of
the security’s monthly return regressed on the return on the market portfolio. The
regression is computed using monthly returns from the twelve-month period ending with
the third month after the end of the fiscal year. This time period provides reasonable
assurance that the fourth quarter financial statements are available. This volatility
measure potentially offers additional information regarding bankruptcy risk that is not
contained in traditional financial statement analysis. Conceptually, we would expect that
the probability of bankruptcy is not only a function of the current expected value of the
key variables but also a function of the variability of those key drivers. For example,
simple bankruptcy models that predict “stock-outs” of a liquid asset include a measure of
the variability of the cash flows as well as their expected values. Similarly, the
variability of future asset returns is a key variable in the option based Black-Scholes-
Merton default model.5 Traditional financial ratios do not provide estimates of
variability, perhaps because of the relative infrequency with which financial statement
data are reported. The notion is that the greater the volatility, ceteris paribus, the higher
the probability of bankruptcy. Again, as with the other market-based variables, there is
no explicit consideration of debt. For example, an all equity firm has volatility in its
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exclusive alternatives or asks how much predictive power is added to the market-based
model by also including accounting variables. Our perspective is that the market-based
variables differ from the accounting-based measure in at least one more important way.
The market-based measures are endogenous variables and a function, among other things,
of the financial statement variables themselves. In this sense, they are not a substitute for
the accounting-based information, but rather a proxy for the predictive power attainable
by capturing the total mix of information, including both financial statement and non-
financial statement information. From our perspective, a central question is how much is
added to predictive power by including nonfinancial statement information. We provide
evidence on this issue by examining the predictive power of a combined model of
accounting and market value variables vis-à-vis a model of accounting variables.
Earlier we discussed several forces that could operate to impair or improve the
predictive ability of financial statement data with respect to the prediction of bankruptcy.
Those same forces affect the relative importance of non-financial statement data. This
emphasizes the competing nature of financial and non-financial statement data to capture
the economically relevant characteristics of bankruptcy risk. In particular, to the extent
that FASB standards improve the quality of reported financial statement data, this
provides less opportunity for non-financial statement data to provide incremental
explanatory power. Also to the extent that increased discretion impairs the quality of
financial statement data, it provides an opportunity for non-financial statement data to to
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predictive power provided by non-financial statement data. We address both questions in
a model that combines both accounting and market-based variables.
5. Secular Change in the Combined Predictive Ability of Financial Ratios and
Market-Based Variables
Table 8 reports the estimated coefficients and prediction results for a combined model of
both financial statement and market-based variables. The market-based variables remain
significant even in the presence of the financial statement variables. However, ROA and
ETL are no longer significant. This is consistent with the notion that the market-based
variables contain the financial statement variables as a subset. Note however, consistent
with our earlier arguments, leverage remains significant, since the market-based variables
do not distinguish between volatility induced by business risk and that induced by
financial risk.
The cumulative percentage of bankrupt firms in the bottom two (three) deciles for
the total period and the two sub-periods are 90.59 (95.19), 92.05 (96.21), and 90.16
(94.30) percent, respectively. Using period 1 coefficients to predict period 2 bankruptcy
probability, the percentage of bankrupt firms in the bottom two (three) deciles are 88.08
(94.30) percent. Based on the in-sample tests, the accuracy with respect to the bottom
three deciles shows little decline (96 to 94 per cent). In the time-series out-of-sample
test, the accuracy for period 2 is 94.30 per cent, which is the same as that obtained for
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essentially the same, 98.31 and 93.83 per cent for period 1 with 94.23 and 94.38 per cent
for period 2. This reflects a decline over time from 96 to 94 per cent that is smaller than
that observed for the financial ratio model. The χ2 value for a test of a difference in the
two distributions is .87, which is not significant at the .05 significance level.
The estimation results for the accounting model reported in Tables 4 and 5 can be
compared with those of the combined model in Table 8). The findings indicate that the
addition of market-related variables in the combined model increases the cumulative
percentage of bankrupt firms in the bottom three deciles by 5, 4, and 8 percent for the
total period and the two sub-periods, respectively. For the use of period 1 coefficients to
predict bankruptcy in period 2, the increase is from 86.53 percent to 94.30 per cent, or
7.77 percent.
For the contemporaneous out-of-sample tests, the cumulative percentage in the
bottom three deciles for the combined model is 98.31 and 93.84 per cent for period 1
with 94.23 and 94.38 for period 2, in contrast to 91.53 and 93.84 for period 1 and 84.62
and 87.64 per cent for the accounting model. The incremental predictive power is 4 per
cent in period 1 and 8 per cent for period 2. As indicated earlier, the difference is viewed
as evidence of the incremental explanatory power of nonfinancial ratio data. Using a χ2
test for differences in the two distributions, the difference for period 1 is not significant
(a χ2 value of .108), while the difference in period 2 is significant (a χ
2 value of 7.47).
Not surprisingly, the market-based variables absorb a great deal of the predictive
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financial statement variables declines slightly. The overall predictive power of the
combined model remains essentially unchanged when accuracy is measured with respect
to the bottom three deciles. The evidence is consistent with the market-related variables
compensating for the slight reduction in predictive power of the financial ratios.
6. Concluding Remarks
Our study of secular change in the predictive ability of financial ratios for
bankruptcy documents two striking findings: (1) The robustness of the predictive models
is strong over time, showing only slight changes. (2) The slight decline in the predictive
ability of the financial ratios is offset by improvement in the incremental predictive
ability of market-related variables. When the financial ratios and market-related
variables are combined, the decline in predictive ability appears to be very small. The
finding is consistent with non-financial-statement information compensating for a slight
loss in predictive power of the financial ratios. In terms of the three financial reporting
trends discussed at the outset, this finding is also consistent with deterioration in the
predictive ability of financial ratios for bankruptcy due to increased discretion or the
increase in intangible assets not being offset by improvements due to additional FASB
standards.
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Acknowledgments
The authors thank Tyler Shumway for providing us with his sample of bankrupt firms,
and thank Jim Ohlson (the editor), an anonymous referee, and the 2005 Stanford
Accounting Summer Camp participants for many helpful comments. The authors
gratefully acknowledge the financial support of the Stanford Graduate School of
Business.
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Notes
1. While the main title is in the spirit of Francis and Schipper (1999), the study is
directed explicitly toward the predictive ability of financial ratios. No claim is made
about the changing predictive power of other information in financial statements,
such as footnotes.
2. Because failure can occur at any time during the year, the year prior to bankruptcy
represents a varying number of days between the end of the fiscal year of the
financial statements and the declaration of bankruptcy.
3. In conducting this test, each distribution is divided into two groups, the lowest three
deciles and the upper seven deciles. This results in a two-by-two panel. The degrees
of freedom for the χ2 test are 2. To mitigate the potential arbitrary nature of dividing
the time period into two subperiods, we conducted an alternative test that requires no
partitioning. The percentage of bankrupt firms whose predicted value in the year
before bankruptcy falls in the bottom three deciles is computed for each calendar
year. The yearly percentage was then regressed on time. The results are consistent
with those reported here. In particular, there is a decline over time in the predictive
power of the accounting model but it is not significant at the conventional .05
significance level. We are indebted to George Foster for suggesting this test.
4. Following Shumway, cumulative residual return is the sum of monthly residual
returns computed as the difference between the actual monthly return minus the
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5. The Black-Scholes-Merton default model, as well as other option based default
models is set forth in Duffie and Singleton (2003), which contains an excellent review
of the empirical default literature.
6. In other words, a firm could have high operating risk but without leverage would not
face bankruptcy risk.
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31
Table 1
Characteristics of Sample, Bankrupt and Non-Bankrupt Firms (1962 – 2002)and Reasons for the Attrition Rate in the Sample
Number of FirmsBankrupt Non-Bankrupt Total
NYSE- and AMEX-listed Compustat firms 585 6,385 6,971
Less: Firms in financial or utility industries 41 2,148 2,189
Final Sample (Number of firms) 544 4,237 4,781
Final Sample (Number of firm-years) 8,130 74,823 82,953
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Table 2
Distribution by Calendar Year of Bankrupt and Non-Bankrupt Firms (1962 – 2002)
Bankrupt Firms Non-Bankrupt Firms
Year Frequency Percent Frequency Percent
1962 0 0.00 1241 1.66
1963 1 0.18 1342 1.79
1964 3 0.55 1422 1.90
1965 2 0.37 1500 2.00
1966 1 0.18 1588 2.12
1967 0 0.18 1670 2.23
1968 0 0.18 1784 2.38
1969 1 0.18 1850 2.47
1970 7 1.29 1868 2.50
1971 8 1.47 1918 2.56
1972 8 1.47 1959 2.62
1973 13 2.39 1975 2.64
1974 16 2.94 2013 2.69
1975 13 2.39 1989 2.66
1976 19 3.49 1953 2.611977 8 1.47 1889 2.52
1978 12 2.21 1820 2.43
1979 12 2.21 1760 2.35
1980 9 1.65 1735 2.32
1981 13 2.39 1683 2.25
1982 6 1.10 1687 2.25
1983 13 2.39 1707 2.28
1984 14 2.57 1666 2.231985 16 2.94 1703 2.28
1986 19 3.49 1729 2.31
1987 11 2.02 1752 2.34
1988 14 2.57 1719 2.30
1989 6 1.10 1721 2.30
1990 20 3.68 1754 2.34
1991 33 6.07 1816 2.43
1992 20 3.68 1904 2.54
1993 14 2.57 1997 2.67
1994 10 1.84 2067 2.76
1995 14 2.57 2204 2.95
1996 14 2.57 2264 3.03
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Table 3
Descriptive Statistics for Bankrupt and Non-Bankrupt Firms
by Year Before Failure
Panel A: Year Before Bankruptcy
Variable N Mean Median Std Dev Minimum Maximum
ROAb 524 -0.18 -0.12 0.28 -2.36 0.49
LTA 528 0.98 0.85 0.49 0.07 3.27
ETL 526 -0.05 0.01 0.43 -5.32 2.43
Panel B: Two Years Before BankruptcyVariable N Mean Median Std Dev Minimum Maximum
ROA 529 -0.10 -0.04 0.29 -2.36 0.49
LTA 532 0.82 0.76 0.39 0.07 3.27
ETL 530 -0.01 0.07 0.50 -5.43 1.97
Panel C: Three Years Before Bankruptcy
Variable N Mean Median Std Dev Minimum MaximumROA 507 -0.04 0.01 0.24 -2.36 0.49
LTA 519 0.74 0.70 0.35 0.03 3.27
ETL 515 0.05 0.10 0.51 -5.43 2.26
Panel D: Four Years Before Bankruptcy
Variable N Mean Median Std Dev Minimum Maximum
ROA 482 -0.03 0.01 0.25 -2.36 0.49LTA 500 0.71 0.67 0.33 0.03 3.27
ETL 497 0.09 0.13 0.57 -5.43 2.43
Panel E: Descriptive Statistics for the Full Sample
Variable N Mean Median Maximum
ROA 73106 0.05 0.06 0.49
LTA 75676 0.52 0.51 3.27
ETL 75384 0.35 0.28 2.43
Correlationa
ROA LTA ETL
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This table presents descriptive statistics on the three financial ratios that are explanatory
variables in the hazard model of bankruptcy. Panels A-D present the ratios for the firstthrough fourth years prior to the bankruptcy year, which is determined as the latest fiscal
year that has ended at least three months before the bankruptcy filing. Panel E presents
descriptive statistics and correlations for the full sample.
a The lower diagonal refers to Pearson product moment correlations, while the upper
diagonal refers to Spearman rank correlations.b ROA = Net income divided by total assets
LTA = Total liabilities divided by total assets
ETL = EBITDA divided by total liabilities
EBITDA = Earnings before interest, taxes, depreciation, and amortization
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Table 4
Hazard Model Estimation and Prediction for the Full Sample Period (1962 – 2002)
Panel A: Hazard Model Estimation Results
Coefficients Chi-square p value
Intercept -6.4446 5307.5313
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Table 5
Hazard Model Estimation and Prediction
for 1962 – 1993 (Period 1) and 1994 – 2002 (Period 2)
Panel A: Hazard Model Estimation Results (Period 1)
Coefficients Chi-square p value
Intercept -6.8542 3156.088
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Panel D: In-Sample Prediction Test (Period 2)
Bankrupt Firms Non-bankrupt Firms
Rank N
Cumulative
Percentage N
Cumulative
Percentage
0 117 60.62 1419 8.43
1 38 80.31 1580 17.82
2 11 86.01 1683 27.83
3 8 90.16 1705 37.96
4 8 94.30 1688 47.99
5 6 97.41 1719 58.216 1 97.93 1747 68.59
7 2 98.96 1751 79.00
8 2 100 1764 89.48
9 0 100 1770 100
Total 193 16,826
Panel E: Out-of-Sample Prediction Test
(Period 1 Coefficients used to Predict Period 2)
Bankrupt Firms Non-bankrupt Firms
Rank N
Cumulative
Percentage N
Cumulative
Percentage
0 118 61.14 1422 8.45
1 37 80.31 1577 17.82
2 12 86.53 1676 27.78
3 7 90.16 1710 37.95
4 9 94.82 1688 47.98
5 5 97.41 1720 5820
6 1 97.93 1746 68.58
7 2 98.96 1754 79.00
8 2 100 1763 89.48
9 0 100 1770 100
Total 193 16,826
Table 5 presents the estimation results for our two sub-periods, 1962-1993 and 1994-2002. Panel A presents the hazard model estimation results for the first period and Panel
C presents the estimation results for the second period. Panels B and D show the in-
sample predictive ability of the models for periods 1 and 2, respectively. Panel E showsthe out of sample predictive accuracy obtained using period 1 coefficients to predict
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Table 6
Hazard Model Estimation and Prediction:
Two Time Periods and Two Samples Within Each Time Period
Panel A: Hazard Model Estimation Results (Period 1, Subsample A)
Coefficients Chi-square p value
Intercept -7.0885 1575.6654
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Panel D: Out-of-Sample Prediction Test (Period 1, Subsample A)
Bankrupt Firms Non-bankrupt Firms
Rank NCumulativePercentage N
CumulativePercentage
0 108 73.97 1900 7.96
1 15 84.25 2219 17.26
2 14 93.84 2370 27.19
3 3 95.89 2421 37.33
4 4 98.63 2435 47.54
5 0 98.63 2473 57.906 1 99.32 2518 68.45
7 0 99.32 2498 78.92
8 0 99.32 2498 89.38
9 1 100 2534 100
Total 146 23,866
Panel E: Hazard Model Estimation Results (Period 2, Subsample A)
Coefficients Chi-square p value
Intercept -6.001 801.4173
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Panel G: Hazard Model Estimation Results (Period 2, Subsample B)
Coefficients Chi-square p value
Intercept -5.5743 1031.6915
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Table 7
Market-Based Hazard Model:
Estimation and Prediction for Two Time Periods
Panel A: Market-based Hazard Model Estimation Results
Coefficients Chi-square p value
Intercept -11.9351 989.5295
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Panel D: In-Sample Prediction Test for Period 1
Bankrupt Firms Non-bankrupt Firms
Rank NCumulativePercentage N
CumulativePercentage
0 197 74.62 3771 8.10
1 39 89.39 4284 17.30
2 8 92.42 4451 26.85
3 10 96.21 4608 36.75
4 6 98.48 4748 46.94
5 1 98.86 4846 57.35
6 2 99.62 4878 67.82
7 1 100 4947 78.44
8 0 100 4997 89.17
9 0 100 5042 100
Total 264 46,572
Panel E: Estimation Results for Period 2, 1994-2002
Coefficients Chi-square p value
Intercept -10.3263 336.2529
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Panel G: Out-of-Sample Prediction (Time Period 1 Coefficients
Used to Predict in Period 2)
Bankrupt Firms Non-bankrupt Firms
Rank N
Cumulative
Percentage N
Cumulative
Percentage
0 138 71.50 1452 8.63
1 23 83.42 1600 18.14
2 17 92.23 1665 28.03
3 6 95.34 1696 38.11
4 1 95.85 1689 48.15
5 3 97.41 1732 58.45
6 2 98.45 1730 68.73
7 2 99.48 1740 79.07
8 0 99.48 1758 89.52
9 1 100 1764 100
Total 193 16,826
LERET = Cumulative residual return defined as the difference between thecumulative monthly return for the firm less the cumulative
monthly return on a market index of NYSE, AMEX, and
NASDAQ firms.
LSIGMA = The standard deviation of the residual return from a regression oftwelve monthly returns of the firm on monthly returns of the
market index.
LRSIZE = Logarithm of the ratio of the market capitalization of the firm
divided by the market capitalization of the market index.
LERET and LSIGMA are computed for a twelve month period ending with the thirdmonth after the fiscal year end by the firm. LRSIZE is computed as of the end of thethird month after the fiscal yearend. Table 7 presents the estimation results for the
market-based prediction model for the full sample period in Panel A, and the in-
sample prediction tests in Panel B. Panel C (E) separately shows the estimationresults for the 1962 1993 period ((1994 2002) and Panels D (F) show the in sample
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Table 8
Combined Hazard Model: Estimation and Prediction
Panel A: Combined Hazard Model Estimation Results (Total Period)Coefficients Chi-square p value
Intercept -12.3382 972.953
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Panel D: In-Sample Prediction Test (Period 1)
Bankrupt Firms
Rank N
Cumulative
Percentage
0 214 81.06
1 29 92.05
2 11 96.21
3 5 98.11
4 2 98.86
5 2 99.62
6 1 100
7 0 100
8 0 100
9 0 100
Total 264
Panel E: Combined Hazard Model Estimation Results (Period 2)
Coefficients Chi-square p valueIntercept -10.9064 352.7099
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Panel G: Out-of-Sample Prediction (Time Period 1
Coefficient Used to Predict Period 2)
Bankrupt Firms
Rank N
Cumulative
Percentage
0 149 77.2
1 21 88.08
2 12 94.30
3 3 95.85
4 2 96.89
5 2 97.93
6 2 98.96
7 0 98.96
8 1 99.48
9 1 100
Total 193
Table 8 presents the estimation results for the combined market and accountingprediction model for the full sample in Panel A, and the in-sample prediction testsin Panel B. Panel C (E) separately shows the estimation results for the 1962-1993period (1994-2002) and Panels D (F) show the corresponding in-sample
prediction results. Panel G shows the out-of-sample prediction results using
period 1 coefficients from Panel C to predict bankruptcy in period 2, 1994-2002.
T bl 9
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Table 9
Combined Hazard Model Estimation and Prediction
Two Time Periods and Two Samples Within Each Time Period
Panel A: Hazard Model Estimation Results (Period 1, Subsample A)
Coefficients Chi-square p value
Intercept -13.2415 322.2811
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Panel D: Out-of-Sample Prediction Test (Period 1, Subsample A)
Bankrupt Firms Non-bankrupt Firms
Rank NCumulativePercentage N
CumulativePercentage
0 115 78.77 1878 7.87
1 16 89.73 2208 17.12
2 6 93.84 2328 26.88
3 4 96.58 2377 36.83
4 2 97.95 2409 46.93
5 2 99.32 2472 57.296 1 100 2516 67.83
7 0 100 2540 78.47
8 0 100 2571 89.24
9 0 100 2567 100
Total 146 23,866
Panel E: Hazard Model Estimation Results (Period 2, Subsample A)
Coefficients Chi-square p valueIntercept -10.5381 157.0328
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Table 9 (Cont.)
Combined Hazard Model Estimation and Prediction
Two Time Periods and Two Samples Within Each Time Period
Panel G: Hazard Model Estimation Results (Period 2, Subsample B)
Coefficients Chi-square p value
Intercept -11.2076 194.5839
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50
0
0.2
0.4
0.6
0.8
1
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3
ROA
C u m u l a t i v e F r e q u e n c y o f R O A
Bankrupt (0) Bankrupt (-1) Bankrupt (-2) Bankrupt (-3) Non-Bankrupt
Figure 1. Cumulative distribution function of ROA for the entire sample period (1962-2002). The distribution of ROA at the year of
bankruptcy, marked as the black square, is the distribution of ROA from the latest fiscal year that ended at least 3 months before the
bankruptcy filing. The dark gray triangle, medium gray diamond, and light gray circle represent the distributions of ROA in one, two,
and three years before bankruptcy, respectively. The distribution of ROA of non-bankrupt firms is presented as a solid line.
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51
0
0.2
0.4
0.6
0.8
1
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
ETL
C u m u l a t i v e F r e q
u e n c y o f E T L
Bankrupt (0) Bankrupt (-1) Bankrupt (-2) Bankrupt (-3) Non-Bankrupt
Figure 2. Cumulative distribution function of ETL (EBITDA divided by total liabilities) for the entire sample period (1962-2002).The distribution of ETL at the year of bankruptcy, marked as the black square, is the distribution of ETL from the latest fiscal year that
has ended at least 3 months before the bankruptcy filing. The dark gray triangle, medium gray diamond, and light gray circle
represent the distributions of ETL in one, two, and three years before bankruptcy, respectively. The distribution of ETL of non-
bankrupt firms is presented as a solid line.
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52
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1 1.2
LTA
C u m u l a t i v e F r e q u e n
c y o f L T A
Bankrupt (0) Bankrupt (-1) Bankrupt (-2) Bankrupt (-3) Non-Bankrupt
Figure 3. Cumulative distribution function of LTA (total liabilities divided by total assets) for the entire sample period (1962-2002).The distribution of LTA at the year of bankruptcy, marked as black square, is the distribution of LTA from the latest fiscal year that has
ended at least 3 months before the bankruptcy filing. The dark gray triangle, medium gray diamond, and light gray circle represent the
distributions of LTA in one, two, and three years before bankruptcy, respectively. The distribution of LTA of non-bankrupt firms ispresented as a solid line.
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53
0
0.2
0.4
0.6
0.8
1
0 0.05 0.1 0.15 0.2 0.25 0.3
Hazard Rate
C u m u l a t i v e F r e q u e n c y
o f H a z a r d R a t e
Bankrupt (0) Bankrupt (-1) Bankrupt (-2) Bankrupt (-3) Non-Bankrupt
Figure 4. Cumulative distribution function of the hazard rate for the entire sample period (1962-2002). The hazard rates arecalculated from the estimates of the coefficients in Table 4. The distribution of the hazard rate at the year of bankruptcy, marked as
the black square, is the distribution of the hazard rate based on the latest fiscal year that ended at least 3 months before the bankruptcy
filing. The dark gray triangle, medium gray diamond, and light gray circle represent the distributions of the hazard rate in one, two,
and three years before bankruptcy, respectively. The distribution of the hazard rate of non-bankrupt firms is presented as a solid line.