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The second column shows the number of bankruptcies, and the third column the corresponding percentage of active ﬁrms that went bankrupt in each year. The fourth and ﬁfth columns repeat this information for our failure series.

It is immediately apparent that bankruptcies were extremely rare until the late 1960’s. In fact, in the three years 1967—1969 there were no bankruptcies at all in our dataset. The bankruptcy rate increased in the early 1970’s, and then rose dramatically during the 1980’s to a peak of 1.5% in 1986. It remained high through the economic slowdown of the early 1990’s, but fell in the late 1990’s to levels only slightly above those that prevailed in the 1970’s.

Some of these changes through time are probably the result of changes in the law governing corporate bankruptcy in the 1970’s, and related ﬁnancial innovations such as the development of below-investment-grade public debt (junk bonds) in the 1980’s and the advent of prepackaged bankruptcy ﬁlings in the early 1990’s (Tashjian, Lease, and McConnell 1996). Changes in corporate capital structure (Bernanke and Campbell 1988) and the riskiness of corporate activities (Campbell, Lettau, Malkiel, and Xu 2001) are also likely to have played a role, and one purpose of our investigation is to quantify the time-series eﬀects of these changes.

The broader failure indicator tracks the bankruptcy indicator closely until the early 1980’s, but towards the end of the sample it begins to diverge signiﬁcantly. The number of failures increases dramatically after 1998, reﬂecting the ﬁnancial distress of many young ﬁrms that were newly listed during the boom of the late 1990’s.

In order to construct explanatory variables at the individual ﬁrm level, we combine quarterly accounting data from COMPUSTAT with monthly and daily equity market data from CRSP. From COMPUSTAT we construct a standard measure of proﬁtability: net income relative to total assets. Previous authors have measured total assets at book value, but we ﬁnd better explanatory power when we measure the equity component of total assets at market value by adding the book value of liabilities to the market value of equities. We call this series NIMTA (Net Income to Market-valued Total Assets) and the traditional series NITA (Net Income to Total Assets). We also use COMPUSTAT to construct a measure of leverage: total liabilities relative to total assets. We again ﬁnd that a market-valued version of this series, deﬁned as total liabilities divided by the sum of market equity and book liabilities, performs better than the traditional book-valued series. We call the two series TLMTA and TLTA, respectively. To these standard measures of proﬁtability and leverage, we add a measure of liquidity, the ratio of a company’s cash and short-term assets to the market value of its assets (CASHMTA). We also calculate each ﬁrm’s market-to-book ratio (MB).

In constructing these series we adjust the book value of assets to eliminate outliers, following the procedure suggested by Cohen, Polk, and Vuolteenaho (2003). That is, we add 10% of the diﬀerence between market and book equity to the book value of total assets, thereby increasing book values that are extremely small, probably mismeasured, and create outliers when used as the denominators of ﬁnancial ratios.

We also winsorize all variables at the 5th and 95th percentiles of their cross-sectional distributions. That is, we replace any observation below the 5th percentile with the 5th percentile, and any observation above the 95th percentile with the 95th percentile.

We are careful to adjust each company’s ﬁscal year to the calendar year and lag the accounting data by two months. This adjustment ensures that the accounting data are available at the beginning of the month over which bankruptcy is measured. The Appendix to this paper describes the construction of these variables in greater detail.

We add several market-based variables to these two accounting variables. We calculate the monthly log excess return on each ﬁrm’s equity relative to the S&P 500 index (EXRET), the standard deviation of each ﬁrm’s daily stock return over the past three months (SIGMA), and the relative size of each ﬁrm measured as the log ratio of its market capitalization to that of the S&P 500 index (RSIZE). Finally, we calculate each ﬁrm’s log price per share, truncated above at $15 (PRICE). This captures a tendency for distressed ﬁrms to trade at low prices per share, without reverse-splitting to bring price per share back into a more normal range.

2.1 Summary statistics Table 2 summarizes the properties of our ten main explanatory variables. The ﬁrst panel in Table 2 describes the distributions of the variables in almost 1.7 million ﬁrmmonths with complete data availability, the second panel describes a much smaller sample of almost 800 bankruptcy months, and the third panel describes just over 1600 failure months.4 In interpreting these distributions, it is important to keep in mind that we weight every ﬁrm-month equally. This has two important consequences. First, the distributions are dominated by the behavior of relatively small companies; value-weighted distributions look quite diﬀerent. Second, the distributions reﬂect the inﬂuence of both cross-sectional and time-series variation. The cross-sectional averages of several variables, in particular NIMTA, TLMTA, and SIGMA, have experienced signiﬁcant trends since 1963: SIGMA and TLMTA have trended up, while NIMTA has trended down. The downward trend in NIMTA is not just a consequence of the buoyant stock market of the 1990’s, because book-based net income, NITA, displays a similar trend. The inﬂuence of these trends is magniﬁed by the growth in the number of companies and the availability of quarterly accounting data over time, which means that recent years have greater inﬂuence on the distribution than earlier years. In particular, there is a scarcity of quarterly Compustat data before the early 1970’s so years before 1973 have very little inﬂuence on our empirical results.

These facts help to explain several features of Table 2. The mean level of NIMTA, for example, is almost exactly zero (in fact, very slightly negative). This is lower than the median level of NIMTA, which is positive at 0.6% per quarter or 2.4% at an annual rate, because the distribution of proﬁtability is negatively skewed. The gap between mean and median is even larger for NITA. All these measures of proﬁtability are strikingly low, reﬂecting the prevalence of small, unproﬁtable listed companies in recent years. Value-weighted mean proﬁtability is considerably higher. In addition, For a ﬁrm-month to be included in Table 2, we must observe leverage, proﬁtability, excess return, and market capitalization. We do not require a valid measure of volatility, and replace SIGMA with its cross-sectional mean when this variable is missing.

the distributions of NIMTA and NITA have large spikes just above zero, a phenomenon noted by Hayn (1995), suggesting that ﬁrms may be managing their earnings to avoid reporting losses.5 The average value of EXRET is -0.011 or -1.1% per month. This extremely low number reﬂects both the underperformance of small stocks during the later part of our sample period (the value-weighted mean is almost exactly zero), and the fact that we are reporting a geometric average excess return rather than an arithmetic average.

The diﬀerence is substantial because individual stock returns are extremely volatile.

The average value of the annualized ﬁrm-level volatility SIGMA is 56%, again reecting the strong inﬂuence of small ﬁrms and recent years in which idiosyncratic volatility has been high (Campbell, Lettau, Malkiel, and Xu 2001).

A comparison of the top and the second panel of Table 2 reveals that bankrupt ﬁrms have intuitive diﬀerences from the rest of the sample. In months immediately preceding a bankruptcy ﬁling, ﬁrms typically make losses (the mean loss is 4.0% quarterly or 16% of market value of assets at an annual rate, and the median loss is 4.7% quarterly or almost 19% at an annual rate); the value of their debts is extremely high relative to their assets (average leverage is almost 80%, and median leverage exceeds 87%); they have experienced extremely negative returns over the past month (the mean is -11.5% over a month, while the median is -17% over a month); and their volatility is extraordinarily high (the mean annualized volatility is 106% and the median is 126%). Bankrupt ﬁrms also tend to be relatively small (about 7 times smaller than other ﬁrms on average, and 10 times smaller at the median), and they have only about half as much cash and short-term investments, in relation to the market value of assets, as non-bankrupt ﬁrms.

The market-book ratio of bankrupt ﬁrms has a similar mean but a much higher standard deviation than the market-book ratio of other ﬁrms. It appears that some ﬁrms go bankrupt after realized losses have driven down their book values relative to market values, while others go bankrupt after bad news about future prospects has driven down their market values relative to book values. Thus bankruptcy is associated with a wide spread in the market-book ratio.

Finally, ﬁrms that go bankrupt typically have low prices per share. The mean There is a debate in the accounting literature about the interpretation of this spike. Burgstahler and Dichev (1997) argue that it reﬂects earnings management, but Dechow, Richardson, and Tuna (2003) point out that discretionary accruals are not associated with the spike in the manner that would be expected if this interpretation is correct.

price per share is just over $1.50 for a bankrupt ﬁrm, while the median price per share is slightly below $1.

The third panel of Table 2 reports the summary statistics for our failure sample through December 2003. The patterns are similar to those in the second panel, but some eﬀects are stronger for failures than for bankruptcies (losses are more extreme, volatility is higher, price per share is lower, and market capitalization is considerably smaller), while other eﬀects are weaker (leverage is less extreme and cash holdings are higher).

** 3 A logit model of bankruptcy and failure**

The summary statistics in Table 2 show that bankrupt and failed ﬁrms have a number of unusual characteristics. However the number of bankruptcies and failures is tiny compared to the number of ﬁrm-months in our dataset, so it is not at all clear how useful these variables are in predicting bankruptcy. Also, these characteristics are correlated with one another and we would like to know how to weight them optimally. Following Shumway (2001) and Chava and Jarrow (2004), we now estimate the probabilities of bankruptcy and failure over the next period using a logit model.

where Yit is an indicator that equals one if the ﬁrm goes bankrupt or fails in month t, and xi,t−1 is a vector of explanatory variables known at the end of the previous month. A higher level of α + βxi,t−1 implies a higher probability of bankruptcy or failure.

Table 3 reports logit regression results for various alternative speciﬁcations. In the ﬁrst three columns we follow Shumway (2001) and Chava and Jarrow (2004), and estimate a model with ﬁve standard variables: NITA, TLTA, EXRET, SIGMA, and RSIZE. This model measures assets in the conventional way, using annual book values from COMPUSTAT. It excludes ﬁrm age, a variable which Shumway (2001) considered but found to be insigniﬁcant in predicting bankruptcy. Column 1 estimates the model for bankruptcy over the period 1963-1998, column 2 estimates it for failure over the same period, and column 3 looks at failure over the entire 1963-2003 period.

All ﬁve of the included variables in the Shumway (2001) bankruptcy model enter signiﬁcantly and with the expected sign. As we broaden the deﬁnition of ﬁnancial distress to failure, and as we include more recent data, the eﬀects of market capitalization and volatility become stronger, while the eﬀects of losses, leverage, and recent past returns become slightly weaker.

In columns 4, 5, and 6 we report results for an alternative model that modiﬁes the Shumway speciﬁcation in several ways. First, we replace the traditional accounting ratios NITA and TLTA that use the book value of assets, with our ratios NIMTA and TLMTA that use the market value of assets. These measures are more sensitive to new information about ﬁrm prospects since equity values are measured using monthly market data rather than quarterly accounting data.

Second, we add lagged information about proﬁtability and excess stock returns.

One might expect that a long history of losses or a sustained decline in stock market value would be a better predictor of bankruptcy than one large quarterly loss or a sudden stock price decline in a single month. Exploratory regressions with lagged values conﬁrm that lags of NIMTA and EXRET enter signiﬁcantly, while lags of the other variables do not. As a reasonable summary, we impose geometrically declining weights on these lags. We construct

Third, we add the ratio of cash and short-term investments to the market value of total assets, CASHMTA, in order to capture the liquidity position of the ﬁrm. A ﬁrm with a high CASHMTA ratio has liquid assets available to make interest payments, and thus may be able to postpone bankruptcy with the possibility of avoiding it altogether if circumstances improve.

Fourth, the market to book ratio, MB, captures the relative value placed on the ﬁrm’s equity by stockholders and by accountants. Our proﬁtability and leverage ratios use market value; if book value is also relevant, then MB may enter the regression as a correction factor, increasing the probability of bankruptcy when market value is unusually high relative to book value.6 Chacko, Hecht, and Hilscher (2004) discuss the measurement of credit risk when the market-tobook ratio is inﬂuenced both by cash ﬂow expectations and discount rates.