Have Financial Statements Become Less Informative - Evidence From the Ability of Financial Ratios to Predict Bankruptcy

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)


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)


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)


Intercept -7.0885 1575.6654


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Panel D: Out-of-Sample Prediction Test (Period 1, Subsample A)


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)


Intercept -6.001 801.4173


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Panel G: Hazard Model Estimation Results (Period 2, Subsample B)


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


Intercept -11.9351 989.5295


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Panel D: In-Sample Prediction Test for Period 1




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


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)


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


Panel A: Hazard Model Estimation Results (Period 1, Subsample A)


Intercept -13.2415 322.2811


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Panel D: Out-of-Sample Prediction Test (Period 1, Subsample A)




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


Panel G: Hazard Model Estimation Results (Period 2, Subsample B)


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


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


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


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.

Have Financial Statements Become Less Informative - Evidence From the Ability of Financial Ratios to Predict Bankruptcy

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