Systematic Distress Risk:Evidence from State-Contingent Failure Prediction*

Preliminary and incomplete

Maria Ognevaa, Joseph D. Piotroskib, and Anastasia A. Zakolyukinac

April 9, 2014

Abstract

We develop a measure of firm-specific systematic distress risk using an empiricalmodel of state-contingent probability of failure, where states correspond to economicrecessions and expansions. We find a positive distress risk premium of 5-8% per annumassociated with this measure in the cross-section of stock returns. This result standsin stark contrast to the previously documented distress risk anomaly—a negative cor-relation between unconditional probability of failure and stock returns. A distress-riskmimicking portfolio that is long (short) in high (low) recessionary failure probabilitystocks can track aggregate incidence of failure and future macroeconomic conditions.

JEL classification: G11, G12, G32, G33.

Keywords : Distress risk, state-contingent failure, distress anomaly, failure prediction.

*We greatly appreciate the generosity of Sudheer Chava and Robert Jarrow who shared their bankruptcydata with us. We thank John Cochrane, Stefano Giglio, Bryan Kelly, Christian Leuz, Yuhani Linnainmaa,Toby Moskowitz, seminar participants at UC Irvine and brown bag participants at the University of Chicagofor helpful comments. We are grateful to Adam Johnson, Maria Kamenetsky, and Vincent Pham for providingexcellent research assistance. Maria Ogneva gratefully acknowledges financial support from the MarshallGeneral Research Fund. Anastasia Zakolyukina thanks Neubauer Family Foundation, Harry W. KirchheimerFaculty Research Fund, and the University of Chicago Booth School of Business for financial support.

aMarshall School of Business, University of Southern California, Los Angeles, CA 90089. Correspondingauthor: ogneva@marshall.usc.edu

bStanford Graduate School of Business, Stanford University, Stanford, CA 94305.cBooth School of Business, University of Chicago, IL 60637.

1. Introduction

We develop a measure of firm-specific systematic distress risk that is based on an empir-

ical model of state-contingent probability of failure. Using this measure, we find a positive

distress risk premium in the cross-section of stock returns. Our results help reconcile con-

flicting evidence on the existence of systematic distress risk. Namely, although correlation

with aggregate failure probability is in part responsible for the asset pricing ability of size

and book-to-market factors (e.g. Vassalou and Xing, 2004 and Kapadia, 2011), firms with

higher probability of failure earn abnormally low returns relative to their healthier counter-

parts (e.g. Dichev, 1998; Griffin and Lemmon, 2002; and Campbell, Hilscher, and Szilagyi,

2008). We suggest that the latter research finds no evidence on distress risk- return tradeoff

because it relies on measures that largely capture idiosyncratic distress risk.

Arguments in favor of the existence of systematic distress risk typically rely on clus-

tering of failures that largely coincides with adverse economic conditions. Such clustering

should lead to significant co-movement among distressed stocks, which creates exposure to

a non-diversifiable risk (Fama and French, 1993).1 When expecting firms with higher failure

probabilities to have higher exposure to systematic distress risk, prior research implicitly

assumes that such firms are more likely to fail during a bad state of the world when other

firms are also failing. However, this may not be true. For example, firms that are highly

distressed may be equally likely to fail in both good and bad states of the world. For such

firms, high probability of failure indicates largely an idiosyncratic risk. In contrast, relatively

healthier firms may survive in a good state but fail in a bad state when a sufficiently large

adverse shock is more likely. For such firms, a higher probability of failure means higher

exposure to systematic risk. Overall, probability of failure that does not take into account

the state of the world may capture systematic distress risk poorly.

We propose to measure systematic distress risk as a relative likelihood of failure in a bad

state compared to a good state of the world, where bad (good) states are approximated by

economic recessions (expansions). This measure is consistent with conventional asset pricing

models that describe systematic risk in terms of a correlation between asset payoffs and

states of the world. We further show that such measure, in the cross-section, is proportional

to the probability that the economy is in recession when a firm fails. Accordingly, we refer

1In addition, because clustering of failures is associated with bad states of the world, it should makedistress stocks more exposed to macroeconomic risk (Chan and Chen, 1991). Systematic distress risk mayrepresent a separate factor if aggregate incidence of failures is associated with a state variable that is notcaptured by the stock market portfolio, such as deteriorating investment opportunities in Merton (1973)ICAPM or decreases in aggregate human capital, as in Fama and French (1996).

1

to our empirical estimate as probability of recessionary failure.

Our main analysis consists of two parts. First, we develop a reduced form statistical

model that predicts recessionary failures. Second, we use the estimated recessionary failure

probabilities to predict stock returns. Our analyses rely on a comprehensive sample of busi-

ness failures that includes bankruptcies, performance-related delistings, and credit defaults

from January 1972 to December 2011. This period covers six economic recessions according

to the NBER business cycle classification. The final sample includes 3,202 failures, 1,090 of

which we classify as recessionary.

We rely on prior literature in macroeconomics and finance to identify a pool of funda-

mental variables that can distinguish among recessionary and expansionary failures. The

variables that we explore include firm size, age, profitability, liquidity, R&D and fixed asset

intensity, business seasonality and cyclicality, as well as earnings volatility.2 Later, we aug-

ment our list of predictors with variables from Campbell et al.’s (2008) unconditional failure

prediction model, all of which are constructed using stock market information.

Our reduced form model is estimated with logit regressions that use firm-specific infor-

mation available at the end of June of each year to predict recessionary failure over the next

twelve months. To narrow down our extensive list of predictors to a parsimonious set, we use

lasso variable selection technique (Tibshirani, 1996) that improves prediction accuracy by

choosing an optimal subset of predictors. Our parsimonious model includes six fundamental

variables: sales beta, firm size, short-term borrowings, sales seasonality, earnings volatility,

and fixed asset intensity. We label this model FV (fundamental variables). In addition,

we estimate recessionary failure probabilities using variables from Campbell et al. (2008)

unconditional failure prediction model, which we label CHS, and a combination of the two

models, which we label FV+CHS. The classification ability of the CHS model is similar to

the FV model, while FV+CHS improves over CHS and FV estimated separately.

Each month, we sort stocks into portfolios based on recessionary failure probabilities

estimated at the end of preceding June using only historical information. Our primary tests

use returns from July 2001 until June 2012, which eliminates any look-ahead bias in asset

pricing tests related to model selection—we use no failure data beyond June 2001 when

choosing model specification. To ensure that our results are robust to using longer time-

series of returns, we replicate return tests for July 1991 – June 2012 and find similar results.

We use only stocks within the highest quintile of unconditional probability of failure for

return prediction tests because recessionary failure risk is relevant only for distressed firms

2A detailed discussion of these variables in the context of prior literature can be found in Section 2.

2

and because our recessionary failure probabilities are estimated using failed firms.

We find that portfolios comprised of stocks with higher probabilities of recessionary fail-

ure, on average, earn significantly higher returns relative to their lower failure probability

counterparts. Returns on hedge portfolios that are long (short) in the top (bottom) quintile

or decile of the recessionary failure probability distribution are significantly positive, irrespec-

tive of return weighting procedure or failure prediction model specification. When portfolios

are based on the prediction model with the best classification performance, FV+CHS, re-

turns increase almost monotonically across recessionary failure probability portfolios, except

for the top 5% (10%) portfolios with equal- (value-) weighted returns. These results are

robust to controlling for exposure to market, size, book-to-market, and momentum factors.

They are also economically significant—the four-factor alpha of the median equal- (value-)

weighted hedge portfolio is 5%-7% (5%-8%) per annum. These results suggest not only that

stocks with higher recessionary failure probabilities are riskier than stocks with lower proba-

bilities of failure, but also that this risk is not fully spanned by the conventional multi-factor

models.

Our recessionary failure results paint a picture that is drastically different from the dis-

tress anomaly. To confirm that this difference is not purely a product of our research design

choices or our more recent sample period, we replicate portfolio formation procedures using

the unconditional probability of failure based on Campbell et al. (2008) model. The results

of these tests confirm the presence of the distress anomaly in our sample period among the

top 20% of the most distressed stocks. Namely, decile portfolios that are long (short) in

stocks with high unconditional probabilities of failure earn significantly negative returns.

Our additional tests aim to describe the source of risk underlying recessionary failure

risk premiums. First, we document that returns on recessionary failure hedge portfolios

are negatively related to innovations in aggregate failure rates. The relation is statistically

significant for equal-weighted hedge returns. The fact that our measure of failure risk is

associated with aggregate incidence of failure, while unconditional probability of distress

is not (Kapadia, 2011), helps reconcile our results with the distress anomaly. Second, we

investigate whether returns on recessionary failure hedge portfolios contain macroeconomic

information. Our state-contingent failure is defined with respect to economic recessions,

so prices on stocks with high recessionary failure probabilities should react negatively to

news suggesting an increasing chance of recession. We find that returns on both equal- and

value-weighted recessionary risk of failure hedge portfolios are able to track future real GDP

growth and unemployment. Further, their tracking ability is incremental to that of returns

on the market portfolio, as well as size, book-to-market, and momentum factors.

3

Our last set of tests directly compares statistical models of recessionary and uncondi-

tional failure for our full sample period. Several insights emerge. More profitable firms,

although less likely to fail in general, in case they fail, are more likely to do so in recessions.

In contrast, firms with short-term borrowings, although more likely to fail in general, are

less likely to fail in recessions. These results are consistent with healthier firms requiring a

larger adverse shock to be forced into distress and with short-term lenders developing a closer

relationship with borrowers, which preserves borrowers’ access to credit during recessions.

Sensitivity of firms’ sales to business cycles is only important for predicting recessionary

failures, while several significant predictors of unconditional failures cannot distinguish be-

tween recessionary and expansionary failures. Overall, even though some of the variables

are useful in predicting both unconditional and recessionary failures, the statistical models

are different to the extent that unconditional failure probabilities have no ability to identify

recessionary failures.

Our paper is related to the literature that seeks to explain the distress anomaly. The

proposed explanations range from the anomaly arising by chance in a limited sample period

(Chava and Purnanandam, 2010) to endogenous leverage choice (George and Hwang, 2010),

debt-renegotiation (Garlappi, Shu, and Yan, 2008; Garlappi and Yan, 2011), or investors’

gambling proclivities (Conrad, Kapadia, and Xing, 2012).3 Although we do not explain why

stocks with high unconditional risk of failure underperform in the future, we highlight the

importance of distinguishing between the unconditional and state-contingent probability of

failure, as only the latter leads to systematic distress risk.

2. The Setting

2.1. Related Literature

Following Chan and Chen (1991) and Fama and French (1993), who originally proposed

that exposure to systematic distress risk explains size and book-to-market anomalies, a

large literature in asset pricing seeks to uncover a link between financial distress and non-

diversifiable risk. The main argument behind such link is as follows. The incidence of failures

is correlated across firms and peaks during adverse economic conditions, which leads to a

significant co-movement in returns of distressed stocks and makes them more susceptible

to macroeconomic risk. Further, risk associated with distress may not be captured by a

standard Capital Asset Pricing Model (CAPM) if aggregate incidence of failures is associated

3We discuss this literature in more detail in Section 2.

4

with state variables other than the stock market portfolio, such as deteriorating investment

opportunities in Merton (1973) ICAPM or decreases in aggregate human capital, as proposed

by Fama and French (1996).4

Empirical evidence related to a distress risk premium is mixed. While there has been

some success in linking size and book-to-market effects to distress risk (e.g. Vassalou and

Xing, 2004; Griffin and Lemmon, 2002; and Kapadia, 2011), there is little evidence that firm-

specific risk of failure is associated with higher expected returns. On the contrary, several

studies, including Dichev (1998), Griffin and Lemmon (2002), and Campbell et al. (2008),

find that stocks with higher risk of failure on average earn lower future returns.5

Multiple subsequent studies seek to explain the negative association between the prob-

ability of failure and stock returns. Chava and Purnanandam (2010) suggest that anomaly

exists in realized returns due to noise coming from information shocks that have historically

been more negative for distressed stocks. They find that an alternative measure of expected

returns—implied cost of equity—is positively related to the probability of default. George

and Hwang (2010) explain the anomaly by endogenous leverage choice—although firms with

greater costs of financial distress have higher systematic risk, these costs force them to scale

back on leverage, which decreases their estimated risk of failure. Garlappi et al. (2008)

and Garlappi and Yan (2011) suggest that firms that are close to default have increased

probabilities of debt re-negotiation and asset re-distribution, which de-levers their betas and

brings their systematic risk down. Finally, Conrad et al. (2012) attribute distress anomaly to

lottery-like characteristics of some distressed stocks that have a high probability of extreme

positive future returns.6

Several studies attempt to capture systematic distress risk directly. Vassalou and Xing

(2004) and Guo and Jiang (2010) use aggregate changes in default probabilities as a state

variable capturing systematic distress risk. Kapadia (2011) constructs a tracking portfolio for

4Bond pricing literature identifies systematic risk as an important driver of bond prices—default spreadsare too high to be explained solely by expected costs of default (e.g. Collin-Dufresne, Goldstein, and Martin,2001; Elton, Gruber, Agrawal, and Mann, 2001; and Longstaff, Mithal, and Neis, 2005). However, systematicrisk in bonds is largely related to bond-market liquidity and is not significantly associated with changes inaggregate default rates (Giesecke, Longstaff, Schaefer, and Strebulaev, 2011). Together, these findings pointto a segmentation of the bond market and complicate extrapolation of bond-market results to equity markets.

5Vassalou and Xing (2004) use Merton (1973) default probability to show that more distressed firms earnhigher returns on average; however, subsequent studies document that this is a small-stock effect (Georgeand Hwang, 2010; Garlappi et al., 2008). When the smallest stocks are excluded from the sample, or whenreturns are value-, instead of equal-, weighted, the association between Merton’s default probability andsubsequent returns becomes negative.

6Chen and Manso (2010) suggest that a three-factor model motivated by the q-theory of investment canbe used to explain the distress anomaly. Specifically, distressed firms have lower ROA and lower loadings onthe ROA factor.

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aggregate incidence of defaults. These studies find that returns on size and book-to-market

portfolios are related to exposure to aggregate distress risk. However, they stop short of

generating a firm-specific measure of exposure to systematic distress risk, which is a purpose

of our study.

2.2. A Measure of State-Contingent Risk of Failure

In this paper, we suggest that firm-specific probability of failure largely captures idiosyn-

cratic, not systematic, risk.7 The existence of systematic distress risk relies on clustering of

failures, especially during adverse economic conditions, i.e. bad states of the world. Much of

prior research implicitly assumes that a higher probability of default thus leads to a higher

probability of incurring distress costs during a bad state of the world, which increases sys-

tematic risk exposure. However, a firm with a high probability of distress is likely to fail

both during economic recessions and expansions. In contrast, a relatively less distressed firm

may fail only when a large adverse shock forces it into distress, which is more likely to occur

during an economic recession. As a result, relatively healthier firms may have a greater

exposure to systematic distress risk factor. A higher unconditional probability of distress

may thus be a poor measure of a systematic risk of failure.

Consider valuing a firm at time t that has value of Vt+1 at t + 1. Under no-arbitrage

conditions, there exists a stochastic discount factor, Λt+1, such that the firm’s price at time

t is equal to:

Pt = Et [Λt+1Vt+1] =1

Rf

Et [Vt+1] + covt [Λt+1, Vt+1] , (1)

where Rf = 1Et[Λt+1]

is a risk-free rate. Equation (1) implies that lower prices or, equivalently,

higher expected returns correspond to a more negative covariance between the pricing kernel,

Λt+1, and the future value, Vt+1. Using the definition of a conditional expectation, the

covariance term is equivalent to covt[Λt+1,Et

[Vt+1

∣∣Λt+1

]].

In the consumption-based asset pricing model, the pricing kernel is high in recessionary

periods when marginal utility of consumption is high. Accordingly, if we assume that the

pricing kernel corresponds to a recession indicator, RECt+1, and the low future value corre-

sponds to the indicator of a poor performance or failure, Ft+1, the corresponding covariance

expression becomes −covt[RECt+1,Pt

[Ft+1

∣∣RECt+1

]], where Pt(.) denotes a probability

7Kapadia (2011) also suggests that a high probability of default is unrelated to systematic distress risk.He finds that returns on stocks with a high probability of failure measured using Campbell et al. (2008) arenot sensitive to news about aggregate incidence of defaults.

6

measure. Therefore, expected returns should be higher for firms that have a high probability

to fail during recessions and, at the same time, have a low probability to fail during expan-

sions. Taking into consideration these two implications of the covariance term, we propose

to measure firms’ exposure to systematic distress risk as a ratio of probabilities of failure in

recessions and expansions:

P Ft,SY S =

Pt(Ft+1|RECt+1)

Pt(Ft+1|EXPt+1), (2)

where P Ft,SY S is systematic risk of failure, Pt(Ft+1|RECt+1) is probability to fail in a recession,

and Pt(Ft+1|EXPt+1) is probability to fail in an expansion. We use the NBER’s classification

of recessions and expansions.

Low incidence of failures in the overall population makes it difficult to estimate Pt(Ft+1|RECt+1)

and Pt(Ft+1|EXPt+1) reliably, because characteristics associated with distress dominate char-

acteristics associated with recessionary distress. Accordingly, we use the Bayes rule to convert

systematic risk of failure from (2) into a measure that can be estimated using a sample of

only failed firms:8

P Ft,SY S =

Pt(RECt+1|Ft+1)

1− Pt(RECt+1|Ft+1)

Pt(EXPt+1)

Pt(RECt+1)(3)

The systematic risk measure in (3) is strictly increasing in the probability that economy is

in a recession when a firm fails, Pt(RECt+1|Ft+1). We refer to this probability as a probability

of recessionary failure. We use a statistical model to estimate firm-specific recessionary failure

probabilities, as described in detail in Section 4.

2.3. Predictors of Recessionary Failures

While to our knowledge our study is the first to estimate firm-specific probabilities of

recessionary failure, a large body of research in macroeconomics and finance seeks to explain

why risk of failure is countercyclical. We rely on this research in selecting firm characteristics

that distinguish recessionary from expansionary failures.9

8Omitting time subscripts for simplicity: P(F |REC)P(F |EXP ) = P(F,REC)

P(REC) /P(F,EXP )P(EXP ) =

P(REC|F )P(F )P(REC) /P(EXP |F )P(F )

P (EXP ) = P (REC|F )(1−P(REC|F ))

P(EXP )P(REC)

9Although some results discussed in this section pertain to variation in failure rates along monetary orcredit cycles, we assume that they are pertinent for the business cycles as well. All six NBER-classifiedrecessions in our sample (1972 – 2011) were preceded by periods of Federal Reserve’s monetary tighteningand, except for the 2001 recession, were accompanied by an episode of non-price credit rationing, i.e. creditcrunch (Bordo and Haubrich, 2010).

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Liquidity, Seasonality, Variability, and Profitability

The decreased ability of firms to raise capital during economic recessions is partly re-

sponsible for the countercyclical nature of failures. For example, Bernanke (1981) notes that

bankruptcies in recessions largely occur due to “technical insolvency—the inability to meet

current cash obligations” (p. 155). Thus, lack of liquidity or binding financing constraints

may be distinguishing features of recessionary failures, as opposed to poor operating per-

formance that is a predictor of failure in general (e.g. Altman, 1968; Ohlson, 1980; and

Campbell et al., 2008). We include both the stock- and flow-type liquidity indicators in our

list of recessionary failure predictors. We also consider business seasonality as well as profits

and sales volatility because seasonal businesses or businesses with more volatile revenues are

more likely to rely on continuous access to external financing which can be limited during

recessions. Finally, we expect firms failing in recessions to be relatively more profitable com-

pared to firms failing in expansions because recessionary failures are more likely to be related

to technical defaults. We include both profitability and its components—sales turnover and

profit margin—as predictors of recessionary failures.

Size and Age

Not all firms are equally financially constrained during recessions. In the presence of

financial frictions, capital providers engage in “flight to quality” and ration capital for “poor

quality” firms. Size has traditionally been used to measure borrowers’ quality in macroeco-

nomic literature. Gertler and Gilchrist (1994) find significantly higher declines in small firms’

sales and inventories following tightening credit conditions. Sharpe (1994) finds that small

leveraged firms lay off workers quicker in recessions.10 Covas and Haan (2007) provide direct

evidence that smaller firms face more difficulties when raising capital in recessions. They

find that both equity and debt issuance is procyclical for a majority of firms, but it is either

countercyclical or insensitive to the business cycle for the largest firms.11 Fort, Haltiwanger,

Jarmin, and Miranda (2012) suggest that it is not just size, but a combination of small

size and young age that makes firms more financially constrained during recessions. Finally,

Hadlock and Pierce (2010) find that size and age are the most important determinants of

10Moscarini and Postel-Vinay (2012) suggest that Sharpe’s results are sensitive to identifying bad statesof the world and to inclusion of more recent data; they find that in periods of high unemployment large firmsdestroy more jobs.

11Additional evidence in favor of the “flight to quality” argument comes from Erel, Julio, Kim, andWeisbach (2012). They find that capital raising is pro-cyclical for noninvestment-grade borrowers, and coun-tercyclical for investment-grade borrowers. In a related study, Korajczyk and Levy (2003) find that targetleverage is countercyclical for financially unconstrained sample, but pro-cyclical for relatively constrainedfirms.

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financial distress in general. Accordingly, we include both size and age as recessionary failure

predictors.

Leverage

Leveraged firms suffer more during economic recessions—they experience sharper sales

drops (Campello, 2003) and more drastic employee layoffs (Sharpe, 1994)12. Highly leveraged

firms also tend to have a higher incidence of failure during adverse macroeconomic conditions

(Opler and Titman, 1994; Denis and Denis, 1995). In addition to including leverage, we

distinguish between the long- and short-term debt.

R&D and Fixed Asset Intensity

Borrowing during recessions is also affected by drop in collateral value (Bernanke and

Gertler, 1989). We expect tangible assets to both be more “collateralizeable” and to lose

less value in adverse economic conditions. Consistent with that, Braun and Larrain (2005)

find that industries relying on external financing are less susceptible to economic downturns

when they have higher levels of tangible capital (property, plant, and equipment). In a

similar vein, Opler and Titman (1994) find that leveraged firms that engage in R&D are

more susceptible to industry downturns. We include both R&D intensity and fixed capital

intensity in our model.

Business Cyclicality

The need to access capital markets during recessions is exacerbated by the cyclical nature

of some businesses that operate in industries with demand that is highly sensitive to the

business cycle. We use accounting betas—covariations between firm-specific and aggregate

earnings—to measure business cyclicality (e.g. Beaver, Kettler, and Scholes, 1970). We also

consider cyclicality of earnings components—sales and profit margins.

Variables from Campbell, Hilscher and Szhilagyi (2008)

When selecting recessionary failure predictors, we purposefully avoid using information

contained in stock prices, which allows identifying inherent (fundamental) characteristics of

firms that are prone to recessionary failures. However, we do this at the expense of ignoring

more timely information contained in stock prices. We investigate whether the stock prices

have an incremental ability to distinguish between recessionary and expansionary failures

12The relation between leverage and recessionary performance is in fact more nuanced and depends onindustry competitiveness and industry-wide leverage (Chevalier and Scharfstein, 1996; Campello, 2003). Inour pursuit of a simple measure of systematic distress, we omit interactions from our logit model.

9

by augmenting our list predictors with Campbell et al. (2008) variables, all of which utilize

stock market information.

3. Data

3.1. Sample

We define business failures as bankruptcies, performance-related delistings, or credit de-

faults. The bankruptcy data is taken from Chava and Jarrow (2004), Chava, Stefanescu,

and Turnbull (2011), Bankruptcy.com13, UCLA-LoPucki Bankruptcy Research Database,

and SDC Database. We include both Chapter 7 and Chapter 11 bankruptcies reported in

the Wall Street Journal, SEC filings, the Capital Changes Reporter, and the U.S. Bankruptcy

Courts for publicly traded companies for the NYSE, AMEX, and NASDAQ. As in Campbell,

Hilscher, and Szilagyi (2011), performance-related delistings come from CRSP and credit de-

faults come from Standard and Poor’s.14

Our sample includes all observations with non-missing total assets from COMPUSTAT

from January 1972 to December 2011 and excludes firms in finance (SIC 6000-6999) and

utilities (SIC 4900-4999) industries. Figure 1 plots failure rate and the percentage of assets

under distress in our sample period. The latter represents percentage of failed firms’ assets

relative to assets of all active firms, which better conveys economic magnitude of distress

costs. Recessionary periods are shaded in grey. The two rates track each other well except

for 2001—a year of Enron bankruptcy. The incidence of failure increases drastically in

1979, which is consistent with Fama and French (2004) who find a significant increase in

performance delistings of small firms, largely new lists, after 1979. Peaks in the failure rate

weighted by total assets are especially pronounced in recessions of November 1973 - March

1975, July 1990 - March 1991, March 2001 - November 2001, and December 2007 - June

2009. However, there are two periods of significant increases in the rates of failures 1986 -

1989 and 2004 - 2005 that do not fall into a recessionary period.

Table 1 shows the distribution of failures by year for the full sample of firms and our final

sample that is constrained by the availability of failure predictors. Failure rates are lower

in the final sample than in the full sample. Total number of failures in our final sample is

3,202, which corresponds to a 2.9% average failure rate.

13We thank Joseph Gerakos and Frank Zhou for their help with Bankruptcy.com data.14According to Shumway (1997), performance-related delisting codes are 500 and 520-584. Credit defaults

include issuers with the D (default) and SD (selective default on some obligations) ratings.

10

Our logit model of recessionary failures and subsequent asset pricing tests use a failure

indicator that is set to one at the end of June of year t if a firm fails within the next twelve

months. We classify a failure as recessionary if at least one of the calendar quarters within

these twelve months ends in a recession, where recessions are defined by the National Bureau

of Economic Research (NBER). Our sample period spans six recessions and includes 1,090

recessionary failures, which represents 34% of all failures. The recessionary failure rate of

3.08% is higher than expansionary failure rate of 2.80%. The difference in percentages of

assets under distress is even more pronounced at 1.58% and 0.67% for recessionary and

expansionary failures, respectively.

3.2. Variable definitions

As discussed in Section 2.2, we consider a broad set of accounting variables for the

model of recessionary failure. All variables are constructed using information that is publicly

available as of June of each year. In particular, we require that at least three months has

passed between the end of the fiscal year and the end of June. Appendix A describes variables

construction in greater detail.

We measure size as a logarithm of total assets expressed in 2011 dollars (LOGAT2011 ).

Firm’s age is a number of years passed since the first non-zero sales record in COMPUSTAT

(AGE ). Return on equity is decomposed into profit margin and asset turnover. Profit margin

is the ratio of income before extraordinary items to sales (PM ); asset turnover is the ratio

of sales to lagged net assets (ATRN ). Our debt-related variables include the ratio of total

liabilities to total assets (LTAT ) and the ratio of short-term borrowings to sales (STS ). We

also include a measure of liquidity stock—quick ratio—and a measure of liquidity flow—cash

flow ratio. Quick ratio is the ratio of cash and short-term investments and receivables to

total current liabilities (QR). Cash flow ratio is the ratio of cash from operations to total

current liabilities (CFOL). The dividend payout ratio is measured as dividends over net

income (DP). Finally, we measure fixed asset intensity as the ratio of net property, plant,

and equipment to total assets (FAI ) and R&D intensity as the ratio of R&D expenditures

to sales (IRD).

To measure firms’ sensitivity to aggregate economic conditions, we estimate three ac-

counting betas for return on equity (βROE) and its components—profit margin beta (βPM)

and sales beta (βATRN). These betas represent slopes from regressions of firm-specific sea-

sonal changes in profitability on the corresponding economy-wide seasonal changes in prof-

itability. Firm-specific regressions are estimated using five-year rolling windows with at least

11

ten non-missing quarterly observations. Seasonal changes are measured relative to the same

quarter a year ago. Economy-wide measures represent weighted averages of firm-specific

return on equity or asset turnover (profit margins) with net assets (sales) used as weights.15

To measure earnings volatility, we compute standard deviations of return on equity

(σROE) and its components, profit margin (σPM) and assets turnover (σATRN), using a

three-year rolling window with at least six non-missing quarterly observations. Finally, we

estimate Mian and Smith’s (1992) measure of seasonality in sales. For each rolling three-year

window, we compute a fraction of sales attributable to one of the four calendar quarters.

Sales seasonality equals the difference between the highest and the lowest fractions.

As previously discussed, we augment our list of fundamental variables with unconditional

failure predictors from Campbell et al. (2008). These predictors include three accounting-

based variables—moving average of profitability over prior three years (NIMTAAVG), cash

holdings divided by market-valued total assets (CASHMTA), and total liabilities divided by

market-valued total assets (TLMTA)—and five market-based variables.16 The latter include

moving average of log excess stock return relative to S&P 500 index over prior twelve months

(EXRETAVG), market-to-book ratio (MB), standard deviation of stock returns over the

previous three months (SIGMA), logarithm of the stock price in 2011 dollars (PRICE2011 ),

and a relative measure of size—a log ratio of a firm’s market capitalization to that of the

S&P 500 index (RSIZE ).17 As in Campbell et al. (2008), we replace missing observations

with their cross-sectional means. All variables are winsorized at the 1st and 99th percentiles.

3.3. Summary statistics

Table 2 presents summary statistics for our final sample split into failures and non-failures

(Panel A), as well as failures split into recessionary and expansionary (Panel B). In Panel

A, most variables significantly differ between failed and non-failed firms. Firms that fail

are smaller (average total assets for failures is five times smaller than for non-failures, i.e.

$62 and $316 million, respectively), younger (average age of failures and non-failures is 12

and 17 years, respectively), have lower profit margins (average profit margin for failures and

non-failures is -0.80 and -0.16, respectively) and higher sales turnover (average turnover for

15If a firm’s fiscal quarter does not coincide with the calendar quarter, we assign observation to the closestfollowing calendar quarter.

16To estimate market-valued assets, we adjust the book value of assets as described in Campbell et al.(2008). Specifically, we adjust the book value of equity by the 10% of the difference between market andbook equity to eliminate outliers. Further, we replace negative book values of equity with small positivevalues of $1. We eliminate outliers by winsorizing our market-to-book ratios at the 5th and 95th percentile.

17Before converting price to 2011 dollars we set prices above $15 to $15 as in Campbell et al. (2008).

12

failures and non-failures is is 4.5 and 3.5, respectively). Differences in βROE and βPM suggest

that failing firms have return on equity and profit margin ratios that are two times more

sensitive to economy-wide changes compared to survivors. However, the sensitivity of sales

to economy wide changes (βATRN) is lower for failing firms relative to survivors. In addition,

failing firms have more volatile operations with standard deviations in ROE, PM, and ATRN

about three times higher compared to survivors. Failing firms also have higher leverage,

lower liquidity, lower dividend payout, lower fixed asset intensity, and higher research and

development intensity. Finally, failing firms on average have lower returns (average return

of -5.7% compared to -0.9% for non-failing firms), higher return volatility, and lower share

prices.

The differences between recessionary and expansionary failures reported in Panel B of

Table 2 are less drastic. Recessionary and expansionary failures differ in terms of size and

sensitivity of sales to economy-wide changes. On average, recessionary failures are 60%

larger than expansionary failures—mean total assets for recessionary (expansionary) failures

is $85 million ($53 million). Recessionary failures occur among slightly older firms (the mean

difference in age between recessionary and expansionary failures is 1.2 years) and firms with

lower short-term borrowings. The mean sales beta for firms that fail in recessions is 0.90;

in contrast, the mean sales beta for firms that fail in expansions is -1.56. The difference

in the median sales betas is also statistically significant, but less pronounced—the median

sales beta for recessionary (expansionary) failures is 0.40 (−0.06). At the same time, there

are no statistically significant differences between recessionary and expansionary failures in

terms of return on equity and profit margins, as well as earnings betas. Finally, prior twelve

month stock returns are more negative for recessionary than failures, with means of −6.7%

and to −5.2%, respectively.

4. Empirical Results

4.1. A Logit Model of Recessionary Failure

4.1.1. Model Selection

We model recessionary failure probability using a logit model:

Pt(Yit+1 = 1|failt+1) =1

1 + e−α−βxi,t, (4)

where Yit+1 is an indicator that equals one (zero) for a recessionary (expansionary) failure

13

in the next twelve months, i.e., starting in July of year t and ending in June of year t + 1,

and xit is a vector of explanatory variables as of end of June of year t.

The model is selected using a sample of failures reported up to June 2001. By not

including subsequent failures in model selection and estimation, we set aside the July 2001-

June 2012 period for purely out-of-sample asset pricing tests.

We consider eighteen fundamental variables that can potentially differentiate between re-

cessionary and expansionary failures. Estimating a model that includes all eighteen variables

is problematic for two reasons (Friedman, Hastie, and Tibshirani, 2009). First, using a large

number of predictors may over-fit the data in sample and, as a result, decrease the accuracy

of out-of-sample predictions. Second, a large number of explanatory variables complicates

coefficients’ interpretation. Using a smaller subset of explanatory variables that captures

the strongest effects may facilitate identification of robust links. To narrow down our list

of predictors to a parsimonious set, we use lasso (“least absolute shrinkage and selection

operator”) variable selection technique. Lasso allows estimating a sparse solution for a re-

gression problem by setting some of the regression coefficients to zero (Tibshirani, 1996).

Lasso solves for regression coefficients by minimizing a sum of the usual regression objective

function and a penalty equal to the sum of coefficients’ absolute values. Lasso is similar

to a ridge regression that also shrinks coefficients subject to a penalty, but, unlike a ridge

regression, it shrinks coefficients down to zero by using a different penalty form. Details on

lasso estimation are provided in Appendix B.

Lasso estimation results suggest a parsimonious model may include two subsets of fun-

damental variables. The first subset includes six variables: sales beta (βATRN), logarithm of

total assets (LOGAT2011 ), standard deviation of the return on equity (σROE), sales season-

ality (SSNSALE ), ratio of short-term borrowings to sales (STS ), and fixed asset intensity

(FAI ). We refer to this subset as a six-variable model, FV6. The second subset includes

eleven variables in addition to those included in the six-variable model: asset turnover ratio

(ATRN ), dividend payout ratio (DP), R&D intensity (IRD), profit margin beta (βPM), and

return on equity beta (βROE). We refer to this subset as an eleven-variable model, FV11.

For completeness, we also consider a comprehensive set that includes all eighteen variables,

which we refer to as eighteen-variable model, FV18.

We estimate recessionary failure prediction models using these three sets of variables.

In addition, we combine each of these sets with variables from Campbell et al.’s (2008)

unconditional failure prediction model in models FV6+CHS, FV11+CHS, and FV18+CHS.

Finally, we estimate a model that uses only variables from Campbell et al. (2008), which we

refer to as CHS.

14

4.1.2. Model Performance

Having chosen a parsimonious set of recessionary failure predictors, we turn to selecting

a model that has the best ability to classify failures into recessionary and expansionary.

Instead of selecting a model that has the best in-sample fit, we estimate model’s out-of-

sample predictive performance. To evaluate models’ out-of-sample prediction error, we could

randomly split the sample into two parts, and use one part to estimate the model and the

other—to obtain out-of-sample prediction error. However, a single split may not exhibit

enough variation to both fit the model and consistently estimate the out-of-sample prediction

error. Instead, we perform a ten-fold cross-validation (Efron and Tibshirani, 1993; Witten

and Frank, 2005; Friedman et al. (2009)) by splitting data randomly into ten equal samples

(folds), estimating the model using nine folds, and evaluating model’s performance using the

tenth fold. We repeat this procedure ten times keeping the proportion of recessionary and

expansionary failures in each random data split the same as in the original sample.

We first evaluate models’ performance using measures that depend on a cutoff for the

probability of recessionary failure. All failures with estimated recessionary failure probability

above (below) the cutoff are classified as recessionary (expansionary). We estimate model’s

accuracy (the overall rate of correctly classified failures), true positive rate (the rate of cor-

rectly classified recessionary failures), false positive rate (the rate of expansionary failures

incorrectly classified as recessionary), and precision (the rate of correctly classified recession-

ary failures among all failures classified as recessionary). An increase in the cutoff for the

recessionary failure probability reduces a chance of misclassifying expansionary failures as

recessionary, but, at the same time, reduces a chance of correctly classifying recessionary

failures.

Table 3 Panel A reports models’ performance with cutoffs set at the 80th, 90th, and

95th percentiles of the in-sample estimate of the recessionary failure probability. Across

all cutoffs, FV6 has the highest precision and accuracy relative to FV11, FV18, and CHS.

For the models that combine fundamental variables and variables from CHS, performance

ranking is less clear. While the FV6+CHS model has the highest precision and accuracy at

the 80th percentile cutoff, the FV11+CHS model has the highest precision and accuracy at

the 90th and 95th percentile cutoffs.

To avoid limitations related to an arbitrary choice of a cutoff, we estimate a general

measure of classification performance based on the Receiver Operating Characteristics (ROC)

curve that combines the true positive rate and the false positive rate in one graph. The area

under ROC curve (AUC) represents a summary measure of the classification performance.

15

AUC corresponds to the probability that a randomly chosen recessionary failure will be

ranked as more likely to be recessionary than a randomly chosen expansionary failure. The

higher is AUC, the better is the classification performance of a model. A perfect classifier

would have AUC equal to 100%.

Panel B of Table 3 reports AUC measures computed for all models. Diagonal elements

correspond to AUC measures for each model, t-statistics below compare AUC of the model

to AUC of a random classifier (AUC=50%). The off-diagonal elements correspond to a

difference in the AUC measures between the model in the column and the model in the row,

with t-statistics for the differences reported below. Statistical significance is estimated based

on corrected resampled t-test (e.g., Nadeau and Bengio, 2003; Witten and Frank, 2005).18

The AUC results confirm conclusions from the lasso analysis. Once the model includes

six fundamental variables selected by lasso, adding remaining twelve variables provides no

significant improvement in the classification performance. The out-of-sample AUC of FV6 is

8.64% better than a random guess. The CHS model’s AUC is 7.81% better than a random

guess but not statistically different from FV6, despite using stock price information. Adding

CHS variables to FV6 improves classification performance to a 15.09% advantage over a

random guess. Based on these findings, we use the six fundamental variables model and the

combination of FV6 and CHS models, hitherto referred to FV and FV+CHS, respectively,

in our return prediction tests.

4.2. State-Contingent Failure Probability, Risk, and Stock Returns

4.2.1. Cross-Sectional Return Prediction

In this section, we investigate whether our distress risk measure is associated with ex-

posure to systematic risk, in which case we expect stocks with a greater probability of

recessionary failure to have abnormally high returns.

Each month we sort stocks into portfolios based on the estimated probability of recession-

18For cross-validation, the standard t-test is inappropriate because the training samples overlap in a singlecross-validation run. The corrected resampled t-test is

t =d√(

1k + n2

n1

)σ̂2d

,

where d is the paired difference in a performance measure (in our case, the AUC), k is the total number ofcross-validation runs (in our case, k = 100), n1 is the number of instances used for training, and n2 is thenumber of instances used for testing (in our case, n2/n1 = 1/9).

16

ary failure estimated as of the most recent June. Portfolios are formed using only information

that is available prior to portfolio formation date. For each firm i and year t, the recessionary

failure probability is estimated as x′itβ[1972,t], where β[1972,t] is a vector of coefficients from the

logit regression (4) estimated using all failures reported between 1972 and the end of June

of year t and xi,t is a vector of firm i’s characteristics as of June of year t. To ensure that

accounting information used in estimating failure probabilities is publicly available at the

portfolio formation date, we require that at least three months have passed between the end

of the fiscal year and the end of June of year t.

We use three different models to estimate recessionary failure probabilities based on (1)

six fundamental variables from our parsimonious state-contingent failure prediction model

(FV), (2) Campbell et al. (2008) variables (CHS), and (3) a combined model (FV+CHS).

To compare our results to distress risk anomaly in Campbell et al. (2008), we also estimate

unconditional probabilities of failure using a dynamic logit model that predicts failure among

all firms with variables from Campbell et al. (2008).

Recessionary failure probabilities are relevant only for firms with high unconditional

probabilities of failure and we use only failed firms in the model estimation. For these reasons,

we restrict return prediction tests to stocks within the highest quintile of unconditional

probability of failure based on Campbell et al. (2008) model.

We sort stocks into unequal portfolios with finer partitions at the tails: 0-5%, 5-10%,

10-20%, 20-40%, 40-60%, 60-80%, 80-90%, 90-95%, and 95-100%. In addition, we construct

two hedge portfolios that are long (short) in the top (bottom) half, quintile, or decile portfo-

lios, respectively. We do not construct hedge portfolios using extreme five percent portfolios

because they contain a low number of stocks (on average 26). For a similar reason, we do not

tabulate decile hedge returns, although we discuss them when they are qualitatively differ-

ent from the tabulated statistics. We estimate both the value-weighted and equal-weighted

returns on each portfolio. If a firm delists from CRSP, then portfolio return for that month

is compounded from the partial monthly return and delisting return reported by CRSP. We

substitute missing delisting returns with average delisting returns from Shumway (1997) and

Shumway and Warther (1999).

Post-Model-Selection Test Period: 2001 - 2012

We first report portfolio returns from July 2001 – June 2012. Using this period eliminates

look-ahead bias related to model selection because our model is chosen based on failures

reported up to June of 2001. To ensure that our results are not specific to this period, we

17

also replicate the cross-sectional return prediction tests using 1991-2012 period and discuss

them in the next subsection.

Panel A (B) of Table 4 contains equal- (value-) weighted returns on portfolios sorted by

either unconditional probability of failure or one of the recessionary failure probabilities, as

well as hedge portfolios. For each portfolio, we report average return in excess of a risk-free

rate, as well as alphas from time-series regressions of excess returns on the market (CAPM

alpha), three Fama-French factors (3-factor alpha), and Fama-French factors plus momentum

(4-factor alpha). Factor returns are from Professor Kenneth French’s data library on WRDS.

Due to space constraints, we report t-statistics only for hedge portfolios. All returns are

reported in monthly percentage points.

The top portions of both panels in Table 4 contain results for portfolios sorted on the

unconditional probability of failure. Excess returns on portfolios with higher probability of

failure do not differ significantly from their counterparts with lower probability of failure.

Further, consistent with the distress anomaly, both the equal- and value-weighted excess re-

turns are significantly negative for decile hedge portfolios (untabulated). These “anomalous”

results are robust to controlling for risk exposure.

The lower portions of both panels in Table 4 contain portfolios sorted on the three reces-

sionary failure probabilities. Irrespective of the weighting procedure or model specification,

we find that portfolios with higher recessionary failure probabilities tend to have higher re-

turns relative to those with lower recessionary failure probabilities. All equal-weighted hedge

portfolio returns are positive and statistically significant. The value-weighted hedge portfolio

returns are in general of similar magnitudes, but the median hedge portfolio returns are only

significant for the FV+CHS model before controlling for the Fama-French factors. The lack

of statistical significance in value-weighted returns is likely due to a low statistical power of

the tests that are based on 132 monthly returns. The magnitude of hedge portfolio returns

is most easily interpretable for the median hedge portfolios that correspond to deciles of the

overall stock population (recall that the sample is first split into five portfolios based on un-

conditional failure probability and the top quintile is then split into halves). The four-factor

alphas for the median hedge portfolio range from 0.42% to 0.59% for the equal-weighted and

from 0.40% to 0.64% for the value-weighted portfolios, which corresponds to 5% - 7.1% and

4.8% - 7.7% on the annualized basis, respectively.

Figure 2 plots portfolio returns for the FV+CHS model that has the highest ability to

predict recessionary failures. When equally weighted, returns increase monotonically with

recessionary failure probability until the 95th percentile, and then drop for the highest 5%

portfolio. When value weighted, returns are not as monotonic in general and the drop is

18

apparent at the 90th percentile. Non-monotonic returns in extreme portfolios may be a joint

product of a relatively low precision of recessionary failure estimates based on our limited

sample of failures and a low number of stocks in the extreme portfolios. When aggregated

into top and bottom decile portfolios, returns on the top decile remain significantly higher

than returns on the bottom decile.

We also explore the risk profile of portfolios sorted on recessionary failure probabilities.

Table 5 reports loadings on the market, SMB, HML, and momentum factors for each port-

folio. Irrespective of the model specification, both quintile and decile hedge portfolios have

a significantly positive exposure to the HML factor. This finding is consistent with prior

research on HML being associated with non-diversifiable distress risk. Figure 3 plots factor

betas for equal- and value-weighted portfolios for the FV+CHS model that has the highest

ability to classify failures into recessionary and expansionary. While exposure to the HML

factor increases almost monotonically across portfolios, there is no discernible pattern in

loadings on other factors.

Table 6 reports additional statistics for the portfolios from Table 4, including the average

number of stocks, predicted probabilities of failure and recessionary failure, as well as Sharpe

ratios for the hedge portfolios. The Sharpe ratios for the statistically significant hedge

returns, reported earlier in Table 4, range from 0.15 to 0.19. For the same period, Sharpe

ratios for the market, SMB, and HML equal 0.06, 0.08, and 0.03, respectively.

We find no evidence of a strong correlation between sorting based on unconditional and

recessionary failure probabilities. When stocks are sorted based on recessionary failure prob-

ability, the unconditional probability of failure slightly decreases (for FV portfolios), slightly

increases (for FV+CHS portfolios) or remains virtually constant (for FV+CHS portfolios).

In all recessionary-failure based sorts, the spreads in average unconditional probability of

failure between the extreme portfolios remain substantially lower relative to the spread be-

tween extreme unconditional failure portfolios. Overall, our findings are not mechanically

related to the distress anomaly.

Full Test Period: 1991 - 2012

Next, we report return results for the period of 1991–2012. Starting portfolio formation in

1991 ensures a sufficient number of observations to estimate recessionary failure probability

for the first rolling window. The 1972–1991 period includes four recessions and 21% of

all failures (672 out of a total of 3,202 failures). All portfolio formation procedures are as

previously described.

Table 7 contains portfolio returns and factor loadings for the combined FV+CHS model.

19

Results based on FV and CHS models (untabulated) are qualitatively similar. The quintile

and the median hedge portfolios are significantly positive both for excess returns and after

controlling for exposure to the four factors. Hedge returns are still strongly associated with

the HML factor, but now a significantly negative exposure to the SMB factor is also present.

Such negative exposure is likely due to RSIZE entering negatively into FV+CHS model (see

Appendix B). The magnitudes of the hedge portfolio returns remain economically significant:

the four-factor alphas for median hedge portfolios are 4.1% (9.1%) on the annualized basis

for equal- (value-) weighted returns.

Overall, we find that firms with a higher probability of recessionary failure on average

earn higher returns. These returns cannot be fully explained by exposure to conventional

risk factors, including market, size, book-to-market, and momentum. Accordingly, the doc-

umented abnormal returns likely result from exposure to a systematic distress risk that is

not fully spanned by these factors.

4.2.2. Systematic Distress Risk, Aggregate Failures, and Macroeconomy

Having established that recessionary failure probability predicts returns in the cross-

section, we turn our attention to the source of risk underlying return predictability. First,

we examine whether returns on recessionary failure hedge portfolios can predict aggregate

failures. Kapadia (2011) finds that unconditional probability of failure is unrelated to ag-

gregate failure incidence. Confirming such link for recessionary failure probabilities could

explain the difference between our results and distress anomaly. Second, we investigate how

hedge returns on recessionary failure risk portfolios are related to macroeconomic indicators.

We define state-contingent failures using economic recessions. Accordingly returns on stocks

with high recessionary failure should be positively (negatively) correlated with innovations in

procyclical (countercyclical) macroeconomic variables. We choose three business cycle indi-

cators, two of which—real GDP growth and unemployment—are related to the real economy,

as well as inflation. Real GDP growth is procyclical, while unemployment and inflation are

largely believed to be countercyclical macroeconomic indicators (Stock and Watson, 1999).

Our tests use quintile hedge returns based on the FV+CHS model for the 1991– 2012

period, which ensures a sufficiently long time-series of aggregate failures and macroeconomic

variables.19 Every month, we estimate future aggregate failure rates using failures that fall

into the next twelve months window. We estimate both average incidence of failures and

19Regressions predicting aggregate failure rates use returns from July 1991 – December 2010 because futuretwelve-month failure rates cannot be estimated beyond December 2010.

20

percentage of assets under distress:

Aggregate Failure Rate[t+1,t+12] =Number of failed stocks[t+1,t+12]

Number of all stockst

% Assets Under Distress[t+1,t+12] =Total assets of failed stocks[t+1,t+12]

Total assets of all stockst

To control for persistence in failure rates and macroeconomic variables, all regressions

include their corresponding lagged values. We also control for returns on the four factors

following Liew and Vassalou (2000) and Kapadia (2011) who document that returns on the

market, size, and book-to-market factors predict real GDP growth and aggregate failures.

Regressions predicting failure rates are specified as:

Failure rate[t+1,t+12] = α + β1FAILt + β2MKTRFt + β3SMBt

+ β4HMLt + β5UMDt + β6Failure rate[t−11,t] + εt, (5)

where Failure rate[t+1,t+12] is a logarithm of either Aggregate Failure Rate[t+1,t+12] or

% ofAssets Under Distress[t+1,t+12]; FAILt is return on the quintile hedge portfolio based

on the FV+CHS model; MKTRFt, SMBt, HMLt, and UMDt are the market, size, book-

to-market, and momentum factors from the Kenneth French data library at WRDS; and

Failure rate[t−11,t] is a logarithm of Failure rate lagged by twelve months.

Regressions predicting macroeconomic variables are specified as:

Macroq+1 = α + β1FAILt(q) + β2MKTRFt(q) + β3SMBt(q)

+ β4HMLt(q) + β5UMDt(q) + β6Macroq + εt (6)

where Macroq+1 is a logarithm of either real GDP growth rate, CPI, or unemployment rate

from quarter q + 1, while FAILt(q), MKTRFt(q), SMBt(q), HMLt(q), and UMDt(q) are

monthly factor returns earned in quarter q. All macroeconomic variables are seasonally ad-

justed and obtained from the “Real Time Dataset for Macroeconomists” maintained by the

Federal Reserve Bank of Philadelphia. Real GDP growth and CPI are in annualized percent-

age points. Macroq is a logarithm of the corresponding macroeconomic variable for quarter

q. In all predictive regressions, we adjust standard errors for twelve-lag autocorrelation that

21

arises because we use overlapping estimation windows.

Panel A (B) of Table 8 reports regression results with recessionary failure risk factor

(FAIL) constructed using equal- (value-) weighted returns. Aggregate failure prediction

results vary depending on the weighting procedure used in constructing the factor. Only

equal-weighted failure factor is negatively associated with future aggregate failures at the

5% significance level. Among conventional risk factors, only returns on the market portfolio

are negatively associated with aggregate future failure rate.

The association between the failure factor returns and future macroeconomic indicators

is more robust. Both equal- and value-weighted failure factors are significantly positively

(negatively) associated with future real GDP growth (unemployment). A similar predictive

ability is observed for the market portfolio. Both for the failure factor and market portfolio,

returns are higher when news suggest a decreased probability of recession, i.e. higher real

GDP growth and lower unemployment. Neither returns on the failure factor nor market

returns predict future inflation.

Overall, the documented associations suggest that returns on a hedge portfolio con-

structed using recessionary failure probabilities are related to a state variable that captures

aggregate distress and macroeconomic conditions.

4.3. Distress versus State-Contingent Distress

The difference in returns on portfolios sorted by unconditional and state-contingent failure

probabilities suggests that these probabilities identify different firms as distressed. In this

section, we look for the source of the difference.

Table 9 reports coefficients for logit regressions that predict either recessionary failures

or unconditional failures using FV, CHS, or FV+CHS models for a period 1972 – 2011. In

Panel A, the outcome variable is recessionary failure and the sample includes only firms that

failed. In Panel B, the outcome variable is any failure and the sample includes all firm-years.

There are clear differences in several variables’ ability to distinguish between failures

and non-failures compared to ability to distinguish between recessionary and expansionary

failures. Firms that are more profitable and have larger total assets are less likely to fail.

However, if they fail, they have higher likelihood to fail in recessions when the adverse shock

is larger. Firms with higher short-term borrowings are more likely to fail. However, if

they fail, they are less likely to fail in recessions. The sign on the short-term borrowings

is somewhat surprising, given that refinancing is more difficult during recessions. However,

short-term borrowers may have a closer relationship with their lenders due to repeated

22

borrowing. Short-term borrowings may also increase the effectiveness of lenders’ monitoring

(Barclay and Smith, 1995).

Furthermore, economic importance of some variables differs depending on whether they

are used as failure predictors or to distinguish between recessionary and expansionary fail-

ures. Firms’ cash holdings, market-to-book ratio, and share price are economically significant

predictors of failures although they do not predict failures in recessions.20 In contrast, sales

beta is only important for predicting failures in recessions.

The results in Table 9 suggest that we should not expect that unconditional failure

probability and state-contingent failure probability identify the same firms as risky. Figure 4

presents non-parametric evidence of a low correspondence between sorts based on failure and

recessionary failure probabilities from the FV+CHS model. Specifically, we sort all failures

into twenty portfolios based on a fitted probability of either failure or recessionary failure.

We then compute the average frequency of recessionary failures within each portfolio. As

expected, when sorting is based on a fitted recessionary failure probability, the incidence of

recessionary failures increases across portfolios almost monotonically. However, when sorting

is based on a fitted unconditional failure probability, there is no clear pattern in the incidence

of recessionary failures across portfolios—unconditional failure probabilities have no ability

to distinguish between recessionary and expansionary failures.

To further corroborate nonparametric evidence, we estimate area under the ROC curve

(AUC) for unconditional and recessionary failure models. The fitted values from the CHS

(FV+CHS) unconditional failure prediction model produce AUC equal to 88.11% (88.65%)

when predicting unconditional failures. When the same fitted values are used to predict

recessionary failures, AUC drops to 51.09% (51.93%), which is only slightly higher than

AUC of a random classifier (50%). In contrast, in-sample AUC for the fitted values from

a recessionary failure model is 58.12% (64.58%) when CHS (FV+CHS) model is used to

predict recessionary failures.

Overall, even though some variables are useful in both predicting failures and distinguish-

ing between recessionary and expansionary failures, the statistical models are substantially

different. Prediction of recessionary failures using unconditional failure probability does

not perform better than a random guess, which underscores the importance of developing

a model tailored to predicting state-contingent failures when searching for the evidence of

systematic distress risk.

20Two variables in the FV model—sales seasonality and standard deviation of ROE—do not load signifi-cantly in the full sample. However, they are significantly associated with recessionary failure probability inthe sample 1972–2001 that we use for model selection. Details are available in Appendix B.

23

5. Conclusion

We provide evidence in support of the existence of systematic distress risk. Our proposed

measure of state-contingent failure risk is significantly positively associated with stock re-

turns in the cross-section. A factor-mimicking hedge portfolio based on our state-contingent

failure risk measure can track aggregate incidence of failures and macroeconomic conditions.

These results differ from the previously documented distress anomaly—a negative associ-

ation between unconditional probability of failure and stock returns. Although we do not

provide an explanation for the distress anomaly, our results underscore the importance of

distinguishing between the systematic and idiosyncratic risk implications of distress. To our

knowledge, our paper is the first to attempt measuring firm-specific state-contingent risk of

failure and to show that such measure is related to systematic distress risk.

24

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29

Appendix A. Variable Definitions

Compustat data mnemonics are included in parentheses.

Fundamental variableslogat2011 Logarithm of total assets (AT), in millions of 2011 dollars;age Number of years since the first non-zero sales has been recorded in Compustat;pm Profit margin equal to income before extraordinary items (IB) divided by sales (SALE);atrn Asset turnover equal to sales (SALE) divided by lagged stockholders’ equity (SEQ);betaroefs ROE beta is a slope from a regression of firm-specific quarterly seasonal changes in ROE

on economy-wide seasonal changes in ROE, estimated over prior five years; ROE is incomebefore extraordinary items (IB) divided by lagged stockholders’ equity (SEQ);

betapmfs Profit margin beta is a slope from a regression of firm-specific quarterly seasonal changesin profit margins on economy-wide seasonal changes in profit margins, estimated over priorfive years;

betaatrnfs Sales beta is a slope from a regression of firm-specific quarterly seasonal changes in assetturnover on economy-wide seasonal changes in asset turnover, estimated over prior five years.

ltat Total liabilities (LT) divided by total assets (AT);sts Short-term borrowings (NP) divided by sales (SALE);ssnsaleq Sales seasonality estimated for the preceding three-year window as a difference between the

highest and the lowest fractions of sales attributable to each of the four calendar quarters;sd12roeq Standard deviation in quarterly ROE over preceding three-years with at least six non-missing

quarterly observations;sd12pmq Standard deviation in quarterly profit margins over preceeding three years with at least six

non-missing quarterly observations;sd12atrnq Standard deviation in quarterly asset turnover ratio over preceeding three years with at least

six non-missing quarterly observations;qr Quick ratio equal to cash and short-term investments and receivables (CHE + RECT)

divided by total current liabilities (LCT);dp Dividend payout ratio equal to dividends (DVT) divided by net income (NI);cfol Cash flow ratio equal to cash from operations (CFO) divided by total current liabilities

(LCT);fai Fixed asset intensity equal to net property, plant, and equipment (PPENT) divided by total

assets (AT);ird R&D intensity equal to R&D expenditures (XRD) divided by sales (SALE);

30

Variables from Campbell et al. (2008)nimtaavg Moving average of profitability over prior three years, where profitability is equal to net

income (NIQ) divided by market-valued total assets. Market-valued total assets are esti-mated as total assets (AT) plus 10% of the difference between the market value of equity(CSHOQ*PRCCQ) and book value of equity. The latter is defined similar to Davis, Fama,and French (2000) as stock-holders’ equity (SEQ) plus deferred taxes (TXDB) and invest-ment tax credit (ITCB), plus postretirement benefit liabilities (PRBA), minus the book valueof preferred stock (PSTK). If stockholders’ equity is missing, we use book value of commonequity (CEQ) plus the par value of preferred stock (PSTK), or the difference between totalassets (AT) and total liabilities (LT);

tlmta Total liabilities (TLQ) divided by market-valued total assets defined as previously;exretavg Moving average of log excess stock return relative to S&P 500 index over prior twelve months,

with higher weights assigned to more recent returns as in Campbell et al. (2008);sigma Standard deviation of stock returns over the previous three months;rsize A logarithm of the ratio of stock’s market value of equity to the total market capitalization

of the S&P 500 index at the fiscal year end;cashmta Cash holdings divided by market-valued total assets defined as previously;mb Ratio of the market value of equity (CSHOQ*PRCCQ) to the adjusted book value of equity.

The latter is a sum of book value of equity plus 10% of the difference between the marketvalue of equity (CSHOQ*PRCCQ) and its book value of equity defined as previously;

price2011 Logarithm of the stock price (PRCCQ) in 2011 dollars.

31

Appendix B. Model Selection

B.1. Lasso regression

We use (Tibshirani, 1996) lasso (“least absolute shrinkage and selection operator”) vari-

able selection technique to choose a parsimonious set of fundamental variables for our reces-

sionary failure prediction model. Lasso allows estimating a sparse solution for a regression

problem by setting some of the regression coefficients to zero. It solves for regression coeffi-

cients by minimizing the sum of the usual regression objective function and a penalty equal

to the sum of coefficients’ absolute values. It is similar to a ridge regression that shrinks

coefficients based on a penalty function, but, unlike a ridge regression, it shrinks coefficients

down to zero and thus reduces a number of explanatory variables. For a linear regression,

lasso solves the following problem:

min(α,β)

[1

N

N∑i=1

(yi − α− x′iβ)2 + λ

p∑j=1

|βj|], (7)

where yi is a dependent variable, x′i is a vector of predictors, (α, β) is a 1× (p+ 1) vector of

regression coefficients, and λ is a lasso penalty parameter. In case of the logistic regression,

lasso is fit by maximizing the penalized log likelihood as described in Friedman, Hastie, and

Tibshirani (2010).

We select our model using failures reported up to June 2001. We start with eighteen

variables described in Appendix A and use glment package by Friedman et al. (2010) in R

(R Core Team, 2013) to estimate lasso for our logistic regression. The penalty parameter

λ is commonly chosen by the ten-fold cross-validation for a specific performance measure.

We use area under the ROC curve (AUC) as a performance measure because we are mostly

concerned with the out-of-sample classification performance of our model. Friedman et al.

(2010) suggest to use the “one-standard-error” rule to select the best model. Instead of

selecting a λ that corresponds to the best performing model with the highest AUC, the

“one-standard-error” rule selects λ that corresponds to the most parsimonious model that

has AUC within one standard deviation of the highest AUC. This rule acknowledges that

cross-validated curves for performance measures are generated with error and errs on a side

of parsimony.

The left panel of Figure B1 shows the mean cross-validated AUC and a one-standard-

deviation band around it for different values of the penalty parameter. The left vertical

line corresponds to the maximum AUC, while the right vertical line corresponds to the

32

largest value of λ, for which AUC is within one standard deviation of the the maximum

AUC. The top of the plot shows the number of variables included into the models. The

right panel of Figure B1 shows profiles of coefficients estimated for different values of the

penalty parameter. As the penalty parameter λ increases from left to right, the magnitude

of coefficients shrinks as an increasing number of coefficients is set to zero.

−7 −6 −5 −4

0.50

0.52

0.54

0.56

0.58

log(Lambda)

AU

C

●●

●

●

●

●

●

●●

●

●

●●

●●●●

●●

●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●

18 18 18 18 17 17 15 14 11 11 11 11 6 5 4 1

−7 −6 −5 −4

−0.

2−

0.1

0.0

0.1

0.2

Log Lambda

Coe

ffici

ents

18 17 11 6

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

logat2011

atrn

betaroefsbetapmfs

betaatrnfs

sts

ssnsaleq

sd12roeq

dp

faiird

Profiles of lasso coefficients for predicting recessionary failures

Fig. B1. Lasso for the recessionary failure prediction model. The left panel shows mean AUC obtained

using ten-fold cross-validation, as well as a one-standard-deviation band. The left vertical line corresponds

to the maximum AUC, while the right vertical line to the largest value of λ, for which error is within one

standard error of the maximum AUC. The right panel shows profiles of the estimated coefficients as penalty

parameter λ changes. The top of each plot is annotated with the number of variables included into each

model.

The “one-standard-error” rule suggests that the optimal model should include five vari-

ables. However, the right panel of Figure B1 suggests two distinct sets of variables. The

first set includes six fundamental variables (FV6): sales beta βATRN , logarithm of total

assets (LOGAT2011), standard deviation of the return on equity (σROE), sales seasonal-

ity (SSNSALE), ratio of short-term borrowings to sales (STS), and fixed asset intensity

(FAI). The second subset includes eleven variables (FV11): all variables from FV6 plus asset

turnover ratio (ATRN), dividend payout ratio (DP), R&D intensity (IRD), profit margin

beta (βPM), and return on equity beta (βROE).

33

B.2. In-sample logit regressions

Although our model-selection is entirely based on the out-of-sample model performance,

we also describe the models’ in-sample performance by estimating logit regressions using

failures reported up to June 2001. Table B1 reports logit estimation results for the two

models selected using lasso—FV6 and FV11—as well as a model based on a full set of

explanatory variables—FV18.

Table B1: In-sample logit estimation for recessionary failure

FV6 FV11 FV18

logat2011 0.08∗∗∗ (2.79) 0.08∗∗∗ (2.58) 0.08∗∗∗ (2.61)age 0.00 (−0.19)pm −0.02 (−0.53)atrn 0.01 (1.07) 0.01 (0.59)betaroefs 0.00 (−0.64) 0.00 (−0.61)betapmfs 0.00 (−0.87) 0.00 (−0.85)betaatrnfs 0.01∗∗∗ (3.98) 0.01∗∗∗ (3.99) 0.01∗∗∗ (3.97)ltat −0.08 (−0.31)sts −0.59∗∗ (−2.45) −0.57∗∗ (−2.31) −0.62∗∗ (−2.41)ssnsaleq −0.91 (−1.61) −0.74 (−1.24) −0.97 (−1.60)sd12roeq −0.38∗∗∗ (−2.78) −0.43∗∗∗ (−2.88) −0.55∗∗ (−2.44)sd12pmq 0.01 (0.62)sd12atrnq 0.04 (0.81)qr −0.02 (−0.65)dp −0.28 (−1.41) −0.27 (−1.35)cfol −0.04 (−0.58)fai −0.48∗∗ (−2.22) −0.45∗∗ (−2.05) −0.47∗∗ (−2.08)ird −0.08 (−0.72) −0.20 (−1.35)(Intercept) −0.80∗∗∗ (−5.21) −0.83∗∗∗ (−5.26) −0.75∗∗∗ (−3.51)

Obs. 1991 1991 1991Failures 587 587 587Area under theROC curve

59.36 60.12 60.19

Log-likelihoodvalue

-1181.49 -1178.53 -1177.10

Pseudo−R2 0.021 0.024 0.025

Five out of six regression coefficients in FV6 model are statistically significant. Coefficient

on sales seasonality is marginally significant with a p-value of 0.11. Among all failures, larger

firms are more likely to fail during recessions. Such firms are more robust and it requires

a large adverse shock to force them into insolvency, which is more likely to occur during

recessions. Firms with higher short-term debt and fixed asset intensity are less likely to fail

34

during recessions. Larger fixed asset intensity may be indicative of higher collateral value

of firm’s assets, which may facilitate access to external debt financing during recessions.

The sign on the short-term debt variable suggests that the difficulty of refinancing during

recessions is outweighed by a closer relationship that short-term borrowers may have with

the lender due to repeat borrowing in the past. Intuitively, firms with more pro-cyclical sales,

i.e. higher sales betas, are more likely to fail during recessions. The negative coefficients

on sales seasonality and standard deviation in earnings are more difficult to interpret. The

most likely explanation is that these variables capture fundamental uncertainty that is a

more important cause of expansionary failures, whereas recessionary failures are more likely

to be caused by technical issues, such as lack of liquidity.

35

Fig

ure

1:

Aggre

gate

frequ

en

cy

of

failu

re

Th

efi

gure

plo

tsag

greg

ate

freq

uen

cyof

fail

ure

esti

mate

dev

ery

month

usi

ng

the

nex

ttw

elve

month

s’fa

ilu

res.

%F

ail

(t+

1,

t+12)

isaggre

gate

fail

ure

rate

over

the

nex

ttw

elve

mon

ths.

%A

UD

(t+

1,

t+12)

isth

ep

rop

ort

ion

of

ass

ets

un

der

dis

tres

s,i.

e.ass

ets

of

fail

edfi

rms

rela

tive

to

asse

tsof

all

acti

vefi

rms.

Sh

aded

area

sco

rres

pon

dto

rece

ssio

ns

acc

ord

ing

toth

eN

BE

Rb

usi

nes

scy

cle

defi

nit

ion

s.

0%1.2%2.4%3.6%4.8%6%7.2%8.4%

Dec 72

Dec 73

Dec 74

Dec 75

Dec 76

Dec 77

Dec 78

Dec 79

Dec 80

Dec 81

Dec 82

Dec 83

Dec 84

Dec 85

Dec 86

Dec 87

Dec 88

Dec 89

Dec 90

Dec 91

Dec 92

Dec 93

Dec 94

Dec 95

Dec 96

Dec 97

Dec 98

Dec 99

Dec 00

Dec 01

Dec 02

Dec 03

Dec 04

Dec 05

Dec 06

Dec 07

Dec 08

Dec 09

Dec 10

Dec 11

% F

ail (

t+1,

t+12

)%

AU

D (

t+1,

t+12

)

36

Figure 2: Returns on portfolios sorted by recessionary failure probability

The figure plots average excess returns, CAPM alphas, Fama-French three-factor alphas, and Fama-

French plus momentum alphas for portfolios sorted on the FV+CHS recessionary failure probability from

July 2001 until June 2012. Portfolios are formed monthly based on predicted recessionary failure probabilities

from the most recent June. Panel A (Panel B) is based on equal- (value-) weighted portfolio returns. Returns

are in monthly percentage points.

Panel A: Equal-weighted returns

−1.

0−

0.5

0.0

0.5

1.0

1.5

2.0

%

0005 0510 1020 2040 4060 6080 8090 9095 9500

Mean excess returnCAPM alpha3−factor alpha4−factor alpha

Panel B: Value-weighted returns

−2.

0−

1.5

−1.

0−

0.5

0.0

0.5

1.0

1.5

%

0005 0510 1020 2040 4060 6080 8090 9095 9500

Mean excess returnCAPM alpha3−factor alpha4−factor alpha

37

Figure 3: Factor loadings on portfolios sorted by recessionary failure probability

The figure plots factor loadings from the time-series regressions of excess portfolio returns on the Fama-

French plus momentum factors. Portfolios are formed monthly from July 2001 until June 2012 based on the

FV+CHS recessionary failure probability from the most recent June. Panel A (Panel B) is based on equal-

(value-) weighted portfolio returns.

Panel A: Equal-weighted returns

−0.

50.

00.

51.

0

0005 0510 1020 2040 4060 6080 8090 9095 9500

RMHMLSMBUDM

Panel B: Value-weighted returns

−0.

50.

00.

51.

01.

5

0005 0510 1020 2040 4060 6080 8090 9095 9500

RMHMLSMBUDM

38

Figure 4: Does unconditional failure probability predict recessionary failures?

We estimate a proportion of recessionary failures among all failures (1972-2011) sorted into twenty

portfolios by failure probability. The sorting in Panel A (Panel B) is based on predicted probabilities of

unconditional (recessionary) failure.

Panel A: Portfolios sorted on unconditional failure probability

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

Failures in recession as a fraction of all failures by unconditional probability of failure

Failu

res

in r

eces

sion

Unconditional probability of failure

27%

29%

31%

33%

35%

37%

39%

41%

43%

45%

0.62% 1.92% 3.67% 5.42% 7.39% 10.22% 13.96% 19.26% 28.09% 44.62%

Panel B: Portfolios sorted on recessionary failure probability

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

● ●

Failures in recession as a fraction of all failures by probability of failure in recession

Failu

res

in r

eces

sion

Probability of failure in recession

19%

22%

25%

28%

31%

34%

37%

40%

43%

46%

49%

52%

19.10% 25.62% 28.41% 30.58% 32.50% 34.10% 35.95% 38.12% 40.96% 45.46%

39

Table 1Failures by year

The table reports yearly failure counts and failure rates before and after imposing variable availabilityrestrictions. %Fail is failures as a percentage of all active firms, %AUD is percentage of assets under distress,i.e. assets of failed firms relative to assets of all active firms.

Year Full sample Final sample

Active Fail % Fail %AUD Active Fail % Fail %AUD

1972 2,043 16 0.78 0.07 250 0 0.00 0.001973 2,986 36 1.21 0.30 1,458 1 0.07 0.021974 3,475 42 1.21 0.56 1,715 3 0.17 0.021975 3,831 27 0.70 0.44 2,019 5 0.25 0.031976 3,807 22 0.58 0.09 2,074 5 0.24 0.031977 3,780 46 1.22 0.35 2,086 17 0.81 0.081978 3,740 36 0.96 0.60 2,012 15 0.75 0.131979 3,708 40 1.08 0.06 1,965 14 0.71 0.041980 3,804 56 1.47 0.19 1,878 16 0.85 0.251981 3,864 72 1.86 0.30 1,790 17 0.95 0.361982 4,104 119 2.90 0.25 1,708 8 0.47 0.211983 4,156 92 2.21 0.18 1,689 10 0.59 0.181984 4,503 181 4.02 0.34 1,653 26 1.57 0.381985 4,606 220 4.78 0.66 2,290 63 2.75 0.911986 4,600 187 4.07 1.60 2,908 95 3.27 1.611987 4,754 194 4.08 0.82 2,951 67 2.27 0.231988 4,949 219 4.43 2.23 2,898 87 3.00 0.191989 4,835 224 4.63 1.30 2,980 106 3.56 0.531990 4,682 264 5.64 1.47 3,072 117 3.81 0.311991 4,638 284 6.12 0.88 3,112 148 4.76 0.481992 4,697 206 4.39 0.42 3,082 118 3.83 0.291993 4,863 148 3.04 0.19 3,106 87 2.80 0.311994 5,693 174 3.06 0.17 3,230 77 2.38 0.171995 6,011 154 2.56 0.16 3,438 75 2.18 0.221996 6,157 155 2.52 0.33 3,636 81 2.23 0.201997 6,677 226 3.38 0.20 3,832 112 2.92 0.221998 6,755 411 6.08 0.84 3,964 219 5.52 0.891999 6,345 235 3.70 0.70 3,947 144 3.65 0.962000 6,075 408 6.72 1.13 3,922 258 6.58 1.772001 5,910 353 5.97 3.33 3,724 192 5.16 3.112002 5,274 368 6.98 2.41 3,682 233 6.33 2.362003 4,843 155 3.20 0.67 3,651 120 3.29 1.072004 4,512 104 2.30 0.60 3,525 77 2.18 0.312005 4,414 130 2.95 1.48 3,405 88 2.58 0.622006 4,328 114 2.63 0.97 3,244 78 2.40 1.372007 4,279 146 3.41 4.74 3,106 99 3.19 4.822008 4,197 230 5.48 2.15 2,996 135 4.51 1.622009 3,964 122 3.08 3.25 2,971 77 2.59 1.642010 3,735 91 2.44 0.67 2,925 58 1.98 0.742011 3,650 87 2.38 0.84 2,792 54 1.93 0.60

Total 183,244 6,394 3.49 1.20 110,686 3,202 2.89 0.99NBER recessions 59,517 2,199 3.69 2.00 35,436 1,090 3.08 1.58

40

Table 2Univariate tests

The table reports univariate tests for 1972-2011 period. Panel A compares failures to non-failures. PanelB compares recessionary to expansionary failures. p-values for the differences are calculated based on t-testsfor the means and Mann-Whitney two-sample rank sum test for the medians. Variable definitions can befound in Appendix A.

Panel A: Failures compared to non-failures

Mean t-test Median WMW

Fail Not fail p-value Fail Not fail p-value

logat2011 4.13 5.76 0.00 3.85 5.65 0.00age 12.14 16.81 0.00 9.00 14.00 0.00pm −0.80 −0.16 0.00 −0.10 0.03 0.00atrn 4.51 3.51 0.00 2.62 2.51 0.02betaroefs 2.06 0.95 0.00 1.10 0.58 0.00betapmfs 3.98 1.97 0.01 0.79 0.41 0.00betaatrnfs −0.72 0.32 0.00 0.10 0.39 0.00ltat 0.64 0.47 0.00 0.66 0.48 0.00sts 0.09 0.03 0.00 0.00 0.00 0.00ssnsaleq 0.10 0.07 0.00 0.07 0.05 0.00sd12roeq 0.24 0.07 0.00 0.11 0.03 0.00sd12pmq 2.10 0.58 0.00 0.17 0.04 0.00sd12atrnq 0.74 0.29 0.00 0.22 0.11 0.00qr 1.28 1.84 0.00 0.77 1.21 0.00dp 0.02 0.16 0.00 0.00 0.00 0.00cfol −0.33 0.34 0.00 −0.05 0.35 0.00fai 0.28 0.31 0.00 0.21 0.26 0.00ird 0.18 0.10 0.00 0.00 0.00 0.00nimtaavg −0.05 0.00 0.00 −0.03 0.01 0.00tlmta 0.55 0.39 0.00 0.59 0.36 0.00exretavg −0.06 −0.01 0.00 −0.05 −0.01 0.00sigma 1.04 0.57 0.00 0.91 0.46 0.00rsize −12.65 −10.17 0.00 −12.82 −10.25 0.00cashmta 0.10 0.10 0.93 0.04 0.05 0.00mb 2.54 1.89 0.00 1.43 1.49 0.07price2011 1.01 2.59 0.00 1.03 2.85 0.00

Number of obs. 3,202 105,147 3,202 105,147

41

Table 2(continued)

Panel B: Recessionary failures compared to expansionary failures

Mean t-test Median WMW

Fail Fail p-value Fail Fail p-valuein recession in expansion in recession in expansion

logat2011 4.44 3.97 0.00 4.10 3.73 0.00age 12.94 11.72 0.00 10.00 9.00 0.00pm −0.80 −0.81 0.94 −0.08 −0.11 0.01atrn 4.58 4.47 0.60 2.81 2.49 0.00betaroefs 1.90 2.14 0.68 1.34 1.05 0.97betapmfs 2.54 4.72 0.19 0.77 0.80 0.22betaatrnfs 0.90 −1.56 0.00 0.40 −0.06 0.00ltat 0.64 0.64 0.96 0.66 0.65 0.66sts 0.07 0.10 0.00 0.00 0.00 0.15ssnsaleq 0.10 0.10 0.10 0.07 0.07 0.15sd12roeq 0.22 0.25 0.02 0.10 0.11 0.03sd12pmq 2.17 2.07 0.75 0.14 0.20 0.00sd12atrnq 0.73 0.75 0.76 0.22 0.22 0.53qr 1.22 1.32 0.16 0.76 0.77 0.98dp 0.01 0.02 0.83 0.00 0.00 0.04cfol −0.32 −0.33 0.82 −0.04 −0.06 0.20fai 0.27 0.29 0.07 0.21 0.21 0.28ird 0.18 0.18 0.98 0.00 0.00 0.73nimtaavg −0.05 −0.05 0.13 −0.03 −0.03 0.10tlmta 0.58 0.54 0.00 0.62 0.57 0.00exretavg −0.07 −0.05 0.00 −0.06 −0.04 0.00sigma 1.06 1.03 0.10 0.92 0.91 0.15rsize −12.69 −12.63 0.32 −12.90 −12.77 0.11cashmta 0.10 0.10 0.92 0.04 0.04 0.88mb 2.33 2.64 0.00 1.28 1.52 0.00price2011 1.00 1.02 0.74 1.07 1.02 0.93

Number of obs. 1,090 2,112 1,090 2,122

42

Table 3Model classification performance

The table compares out-of-sample classification performance of recessionary failure prediction modelsfor a sample of failures reported in 1972-2001. Panel A reports classification performance relative to reces-sionary failure probability cutoffs, where cutoffs are percentiles of in-sample recessionary failure probabilitydistribution. Failures with recessionary failure probabilities above (below) the cutoff are classified as pre-dicted recessionary (expansionary) failures. TPR is true positive rate equal to the ratio of correctly classifiedrecessionary failures over all recessionary failures. ACC is model accuracy equal to the ratio of correctlyclassified recessionary failures plus correctly classified expansionary failures over total number of failures.FPR is false positive rate equal to the ratio of expansionary failures incorrectly classified as recessionary overall expansionary failures. PREC is precision equal to the ratio of correctly classified recessionary failuresover all failures classified as recessionary.

Panel B reports area under the ROC curve (AUC) for recessionary failure prediction models evaluatedout-of-sample. Reported values are average AUCs from the ten-fold cross-validation repeated ten times.Diagonal elements correspond to AUC for each model, t-statistics below compare AUC of the model to arandom classifier (AUC=50%). The off-diagonal elements correspond to a difference in AUC between themodel in the column and the model in the row, with t-statistics for the differences reported below. Statisti-cal significance is estimated using corrected re-sampled t-test (e.g., Nadeau and Bengio (2003), Witten andFrank (2005)). *, **, and *** denotes significance at the 10%, 5%, and 1%, respectively.

Panel A: Model performance relative to a cutoff

FV6 FV11 FV18 CHS FV6+CHS FV11+CHS FV18+CHS

Cutoff at the 80th percentile

TPR 26.34 25.56 25.73 24.41 34.14 33.92 33.94FPR 17.76 18.45 18.73 18.32 14.79 14.81 14.87PREC 38.63 36.99 36.69 35.95 49.15 48.98 48.88ACC 65.76 65.04 64.89 64.80 70.16 70.07 70.04

Cutoff at the 90th percentile

TPR 14.41 14.23 14.35 12.74 20.37 20.18 20.21FPR 8.61 8.60 8.97 9.23 6.07 5.88 6.31PREC 42.05 41.51 40.72 37.05 58.82 59.18 57.57ACC 68.70 68.65 68.42 67.77 72.24 72.33 72.03

Cutoff at the 95th percentile

TPR 8.56 8.48 8.37 6.19 11.03 11.45 11.51FPR 4.24 4.34 4.54 4.84 2.91 2.85 2.74PREC 46.68 46.13 44.85 36.57 61.63 62.87 63.93ACC 70.06 69.96 69.79 68.94 71.73 71.89 71.98

43

Table 3(continued)

Panel B: Area under the ROC curve

FV6 FV11 FV18 CHS FV6+CHS FV11+CHS FV18+CHS

FV6 58.64 −0.07 −1.25 −0.83 6.46 6.23 5.73(6.18)∗∗∗ (−0.13) (−2.00)∗∗ (−0.47) (4.44)∗∗∗ (4.23)∗∗∗ (3.90)∗∗∗

FV11 58.56 −1.18 −0.76 6.53 6.30 5.80(6.34)∗∗∗ (−2.98)∗∗∗ (−0.45) (4.65)∗∗∗ (4.62)∗∗∗ (4.25)∗∗∗

FV18 57.39 0.42 7.70 7.48 6.98(5.46)∗∗∗ (0.25) (5.38)∗∗∗ (5.35)∗∗∗ (5.25)∗∗∗

CHS 57.81 7.28 7.06 6.56(6.36)∗∗∗ (5.41)∗∗∗ (5.16)∗∗∗ (4.88)∗∗∗

FV6+CHS 65.09 −0.23 −0.72(10.82)∗∗∗ (−0.88) (−1.60)

FV11+CHS 64.87 −0.50(10.77)∗∗∗ (−1.39)

FV18+CHS 64.37(10.59)∗∗∗

44

Table

4P

ort

foli

ore

turn

s:P

ost

-model-

sele

ctio

np

eri

od

2001-2

012

Eac

hm

onth

bet

wee

nJu

ly20

01an

dJu

ne

2012,

we

sort

stock

sw

ith

inth

eto

pqu

inti

leof

un

con

dit

ion

al

fail

ure

pro

bab

ilit

yin

top

ort

foli

os

bas

edon

per

centi

les

ofre

cess

ion

ary

fail

ure

pro

bab

ilit

yd

istr

ibu

tion

,es

tim

ate

das

of

the

most

rece

nt

Ju

ne.

Port

foli

onam

esco

rres

pon

dto

low

eran

du

pp

erb

oun

ds,

e.g.

1020

conta

ins

stock

sb

etw

een

the

10th

an

d20th

per

centi

les.

LS

5050

an

dL

S8020

are

hed

ge

port

foli

os

that

are

lon

g(s

hor

t)in

the

top

(bot

tom

)h

alf

and

qu

inti

leof

rece

ssio

nary

fail

ure

pro

bab

ilit

y,re

spec

tivel

y.P

an

elA

(Pan

elB

)co

nta

ins

aver

age

equ

al-

(valu

e-)

wei

ghte

dp

ortf

olio

retu

rns

inex

cess

ofa

risk

-fre

era

tean

din

terc

epts

from

the

tim

e-se

ries

regre

ssio

ns

of

exce

ssre

turn

son

the

mark

etex

cess

retu

rn(C

AP

Mal

ph

a),

thre

eF

ama-

Fre

nch

fact

ors

(3-f

act

or

alp

ha),

an

dF

am

a-F

ren

chfa

ctors

plu

sm

om

entu

m(4

-fact

or

alp

ha).

t-st

ati

stic

sfo

rh

edge

retu

rns

are

inp

aren

thes

es.

Ret

urn

sar

ein

month

lyp

erce

nta

ge

poin

ts.

*,

**,

an

d***

den

ote

ssi

gn

ifica

nce

at

the

10%

,5%

,an

d1%

,re

spec

tive

ly.

Pan

el

A:

Equ

al-

weig

hte

dre

turn

s

Por

tfol

ios

0005

0510

1020

2040

4060

6080

8090

9095

9500

LS

5050

LS

8020

Sort

sb

ase

don

un

con

dit

ion

al

fail

ure

pro

bab

ilit

y

Mea

nex

cess

retu

rn1.

161.

82∗∗

1.23

1.03

1.72∗∗

1.38∗

1.00

1.16

−0.

03

-0.0

4(-

0.1

7)

-0.6

2(-

1.3

9)

CA

PM

alp

ha

0.78∗

1.49∗∗∗

0.85

0.65

1.36∗∗∗

1.02∗∗

0.64

0.74

−0.

41

-0.0

4(-

0.1

6)

-0.6

3(-

1.4

1)

3-fa

ctor

alp

ha

0.5

01.

18∗∗

0.47

0.33

1.04∗∗

0.75

0.36

0.38

−0.

72

0.0

2(0

.06)

-0.5

9(-

1.3

1)

4-fa

ctor

alp

ha

0.5

41.

24∗∗

0.58

0.39

1.09∗∗

0.80

0.41

0.49

−0.

69

0.0

1(0

.03)

-0.6

1(-

1.3

5)

Sor

tsb

ase

don

rece

ssio

nary

fail

ure

pro

bab

ilit

yfr

om

the

FV

mod

el

Mea

nex

cess

retu

rn0.

14−

0.18

1.02

1.10

1.59∗∗

1.59∗∗

1.64∗

1.18

1.51

0.5

8(2

.13)∗∗

0.9

9(2

.23)∗∗

CA

PM

alp

ha

−0.

24−

0.51

0.68

0.78

1.23∗∗

1.21∗∗

1.21∗∗

0.70

0.98

0.5

0(2

.04)∗∗

0.8

7(2

.14)∗∗

3-fa

ctor

alp

ha

−0.

39−

0.79

0.40

0.49

0.93∗∗

0.87∗

0.81∗

0.40

0.54

0.4

2(1

.70)∗

0.7

4(1

.84)∗

4-fa

ctor

alp

ha

−0.

33−

0.77

0.47

0.55

1.00∗∗

0.93∗∗

0.89∗

0.4

50.

64

0.4

2(1

.70)∗

0.7

6(1

.90)∗

Sor

tsb

ase

don

rece

ssio

nary

fail

ure

pro

bab

ilit

yfr

om

the

CH

Sm

od

el

Mea

nex

cess

retu

rn−

0.44

0.53

0.57

1.03

1.75∗∗

1.45∗∗

1.70∗∗

1.94∗∗

1.60∗

0.6

6(2

.18)∗∗

1.4

3(2

.85)∗∗∗

CA

PM

alp

ha

−0.

860.

100.

16

0.65

1.40∗∗∗

1.11∗∗

1.33∗∗

1.56∗∗

1.23∗

0.6

9(2

.29)∗∗

1.4

7(2

.96)∗∗∗

3-fa

ctor

alp

ha

−1.

11∗

−0.

21−

0.04

0.37

1.08∗∗∗

0.82∗

0.97∗

1.12∗

0.71

0.6

3(2

.56)∗∗

1.2

9(3

.24)∗∗∗

4-fa

ctor

alp

ha

−1.

03∗

−0.

090.

07

0.43

1.12∗∗∗

0.85∗∗

1.00∗

1.18∗∗

0.8

00.5

9(2

.48)∗∗

1.2

4(3

.18)∗∗∗

Sor

tsb

ase

don

rece

ssio

nary

fail

ure

pro

bab

ilit

yfr

om

the

FV

+C

HS

mod

el

Mea

nex

cess

retu

rn−

0.46

0.19

0.28

1.44∗

1.51∗∗

1.57∗∗

1.92∗∗

2.18∗∗

0.72

0.5

9(2

.18)∗∗

1.5

9(3

.50)∗∗∗

CA

PM

alp

ha

−0.

90−

0.19

−0.

10

1.07∗∗

1.14∗∗

1.23∗∗∗

1.52∗∗∗

1.78∗∗

0.30

0.5

9(2

.19)∗∗

1.5

8(3

.45)∗∗∗

3-fa

ctor

alp

ha

−1.

07−

0.44

−0.

37

0.79∗

0.82∗

0.87∗∗

1.16∗∗

1.47∗∗−

0.06

0.5

3(2

.26)∗∗

1.4

7(3

.82)∗∗∗

4-fa

ctor

alp

ha

−0.

96−

0.33

−0.

29

0.84∗

0.89∗∗

0.92∗∗

1.22∗∗∗

1.51∗∗

0.0

20.5

0(2

.18)∗∗

1.4

4(3

.75)∗∗∗

45

Table

4(c

onti

nued)

Pan

el

B:

Valu

e-w

eig

hte

dre

turn

s

Por

tfol

ios

0005

0510

1020

2040

4060

6080

8090

9095

9500

LS

5050

LS

8020

Sort

sb

ase

don

un

con

dit

ion

al

fail

ure

pro

bab

ilit

y

Mea

nex

cess

retu

rn1.

39∗

2.09∗∗

0.26

0.35

1.54∗

0.45

0.53

0.07

0.27

0.1

7(0

.39)

-0.5

6(-

0.9

3)

CA

PM

alp

ha

0.97∗

1.67∗∗

−0.

20

−0.

13

1.11∗

−0.

01

0.10

−0.

30

−0.

08

0.2

3(0

.54)

-0.4

9(-

0.8

3)

3-fa

ctor

alp

ha

0.7

31.

23∗

−0.

66

−0.

51

0.84

−0.

24

−0.

35

−0.

55

−0.

60

0.3

2(0

.76)

-0.5

5(-

0.9

2)

4-fa

ctor

alp

ha

0.7

11.

33∗

−0.

61

−0.

41

0.90

−0.

23

−0.

36

−0.

51

−0.

64

0.2

7(0

.65)

-0.6

1(-

1.0

4)

Sor

tsb

ase

don

rece

ssio

nary

fail

ure

pro

bab

ilit

yfr

om

the

FV

mod

el

Mea

nex

cess

retu

rn−

1.07

−0.

34−

0.50

1.12

0.56

0.80

1.57∗

0.43

1.47

0.6

5(1

.38)

1.8

6(2

.89)∗∗∗

CA

PM

alp

ha

−1.

45∗∗

−0.

70−

0.89

0.74

0.20

0.40

1.11∗∗−

0.08

0.89

0.5

4(1

.23)

1.7

3(2

.82)∗∗∗

3-fa

ctor

alp

ha

−1.

74∗∗

−0.

99−

1.19∗∗

0.46

−0.

14

−0.

04

0.69

−0.

60

0.60

0.4

7(1

.06)

1.6

4(2

.66)∗∗∗

4-fa

ctor

alp

ha

−1.

72∗∗

−1.

00−

1.15∗∗

0.49

−0.

13

−0.

03

0.69

−0.

52

0.78

0.5

1(1

.15)

1.7

1(2

.81)∗∗∗

Sor

tsb

ase

don

rece

ssio

nary

fail

ure

pro

bab

ilit

yfr

om

the

CH

Sm

od

el

Mea

nex

cess

retu

rn−

0.84

0.14

0.59

1.17

0.85

1.14

0.49

2.00∗∗

1.40

0.4

5(1

.07)

1.1

8(1

.96)∗∗

CA

PM

alp

ha

−1.

33−

0.29

0.10

0.70

0.44

0.74∗

0.11

1.62∗∗

1.01∗

0.5

2(1

.26)

1.2

6(2

.14)∗∗

3-fa

ctor

alp

ha

−1.

69∗∗

−0.

50−

0.34

0.43

−0.

01

0.39

−0.

24

1.18∗

0.57

0.4

6(1

.19)

1.1

9(2

.22)∗∗

4-fa

ctor

alp

ha

−1.

67∗∗

−0.

47−

0.21

0.47

0.03

0.39

−0.

24

1.18∗

0.61

0.4

0(1

.07)

1.1

0(2

.13)∗∗

Sor

tsb

ase

don

rece

ssio

nary

fail

ure

pro

bab

ilit

yfr

om

the

FV

+C

HS

mod

el

Mea

nex

cess

retu

rn−

1.47

0.04

−0.

18

1.12

1.20

1.05

1.44

0.96

0.91

0.7

9(1

.71)∗

1.7

6(2

.99)∗∗∗

CA

PM

alp

ha

−1.

95∗∗∗−

0.38

−0.

63

0.68

0.73

0.62

1.00

0.56

0.46

0.7

9(1

.70)∗

1.7

7(2

.98)∗∗∗

3-fa

ctor

alp

ha

−2.

16∗∗∗−

0.70

−0.

87∗

0.37

0.33

0.19

0.57

0.18

0.12

0.6

7(1

.59)

1.6

3(3

.20)∗∗∗

4-fa

ctor

alp

ha

−2.

13∗∗∗−

0.62

−0.

82

0.43

0.34

0.26

0.65

0.26

0.13

0.6

4(1

.52)

1.6

4(3

.21)∗∗∗

46

Table

5Four-

fact

or

regre

ssio

nco

effi

cients

:P

ost

-model-

sele

ctio

np

eri

od

2001-2

012

Eac

hm

onth

bet

wee

nJuly

2001

and

Ju

ne

2012

we

sort

stock

sw

ith

inth

eto

pqu

inti

leof

un

con

dit

ion

alfa

ilu

rep

rob

ab

ilit

yin

top

ort

foli

os

base

don

per

centi

les

ofre

cess

ion

ary

fail

ure

pro

bab

ilit

ydis

trib

uti

on

,es

tim

ate

das

of

the

most

rece

nt

Ju

ne.

Port

foli

on

am

esco

rres

pon

dto

low

eran

du

pp

erb

oun

ds,

e.g.

1020

conta

ins

stock

sb

etw

een

the

10th

an

d20th

per

centi

les.

LS

5050

an

dL

S8020

are

hed

ge

port

foli

os

that

are

lon

g(s

hort

)in

the

top

(bot

tom

)h

alf

and

qu

inti

leof

rece

ssio

nary

fail

ure

,re

spec

tive

ly.

Pan

elA

(Pan

elB

)co

nta

ins

tim

e-se

ries

regre

ssio

nco

effici

ents

for

equ

al-

(val

ue-

)w

eigh

ted

por

tfol

ioex

cess

retu

rns

onth

eF

am

a-F

ren

chfa

ctors

plu

sm

om

entu

m.t-

stati

stic

sfo

rth

elo

ad

ings

on

hed

ge

port

foli

os

are

inp

aren

thes

es.

*,**

,an

d**

*d

enot

essi

gnifi

can

ceat

the

10%

,5%

,an

d1%

,re

spec

tive

ly.

Pan

el

A:

Equ

al-

weig

hte

dp

ort

foli

os

Por

tfol

ios

0005

0510

1020

2040

4060

6080

8090

9095

9500

LS

5050

LS

8020

Sort

sb

ase

don

un

con

dit

ion

al

fail

ure

pro

bab

ilit

y

RM

1.1

1∗∗∗

0.9

1∗∗∗

0.9

1∗∗∗

1.0

8∗∗∗

1.0

4∗∗∗

1.0

7∗∗∗

1.0

3∗∗∗

1.0

8∗∗∗

1.1

1∗∗∗

0.0

5(0

.66)

0.1

1(0

.92)

HM

L0.1

90.

35∗

0.2

8∗

0.2

7∗

0.2

00.

14

0.14

0.56∗

−0.1

1-0

.11

(-1.0

6)

-0.1

0(-

0.5

5)

SM

B0.8

1∗∗∗

0.8

0∗∗∗

1.0

9∗∗∗

0.8

8∗∗∗

0.9

3∗∗∗

0.8

0∗∗∗

0.8

5∗∗∗

0.8

7∗∗

1.0

9∗∗∗

-0.1

2(-

1.0

8)

-0.0

6(-

0.3

3)

UD

M−

0.1

5∗

−0.2

5∗∗

−0.4

3∗∗∗−

0.2

5∗∗∗−

0.2

2∗∗

−0.2

0∗∗

−0.2

2∗

−0.4

4∗∗

−0.1

30.0

3(0

.57)

0.0

8(0

.82)

Sor

tsb

ase

don

rece

ssio

nary

fail

ure

pro

babil

ity

from

the

FV

mod

el

RM

1.1

5∗∗∗

0.9

5∗∗∗

0.9

3∗∗∗

0.8

6∗∗∗

0.9

9∗∗∗

1.0

6∗∗∗

1.1

3∗∗∗

1.5

3∗∗∗

1.4

9∗∗∗

0.2

5(3

.88)∗∗∗

0.3

3(3

.21)∗∗∗

HM

L−

0.3

20.

070.

320.

18

0.03

0.19

0.58∗∗∗

0.3

90.

73∗∗∗

0.2

3(2

.36)∗∗

0.4

6(2

.92)∗∗∗

SM

B0.7

3∗∗

0.8

9∗∗∗

0.7

4∗∗∗

0.8

4∗∗∗

0.9

6∗∗∗

0.9

9∗∗∗

0.9

7∗∗∗

0.7

2∗∗∗

1.0

0∗∗∗

0.1

4(1

.38)

0.1

4(0

.86)

UD

M−

0.2

4−

0.0

9−

0.2

7∗∗

−0.2

3∗∗

−0.2

5∗∗∗−

0.2

2∗∗

−0.3

3∗∗∗−

0.1

7−

0.4

0∗∗∗

-0.0

1(-

0.1

5)

-0.0

9(-

1.0

6)

Sor

tsb

ase

don

rece

ssio

nary

fail

ure

pro

bab

ilit

yfr

om

the

CH

Sm

od

el

RM

1.1

5∗∗∗

1.0

6∗∗∗

1.1

1∗∗∗

1.0

6∗∗∗

1.0

1∗∗∗

1.0

2∗∗∗

1.1

0∗∗∗

1.0

0∗∗∗

0.8

7∗∗∗

-0.0

3(-

0.5

2)

-0.0

9(-

0.8

8)

HM

L−

0.9

4∗∗∗−

0.4

7∗

−0.4

9∗∗

−0.1

00.

43∗∗∗

0.5

8∗∗∗

0.6

7∗∗∗

0.5

9∗∗

1.0

9∗∗∗

0.7

9(8

.48)∗∗∗

1.3

6(8

.96)∗∗∗

SM

B1.4

6∗∗∗

1.3

8∗∗∗

1.0

1∗∗∗

1.0

0∗∗∗

0.7

8∗∗∗

0.5

8∗∗∗

0.7

5∗∗∗

1.0

8∗∗∗

1.0

2∗∗∗

-0.3

0(-

3.1

0)∗∗∗

-0.3

1(-

1.9

5)∗

UD

M−

0.3

4∗∗∗−

0.5

0∗∗∗−

0.4

6∗∗∗−

0.2

3∗∗

−0.1

9∗∗

−0.1

4−

0.1

4−

0.2

6∗∗

−0.3

7∗∗∗

0.1

4(2

.83)∗∗∗

0.2

2(2

.69)∗∗∗

Sor

tsb

ased

on

rece

ssio

nary

fail

ure

pro

bab

ilit

yfr

om

the

FV

+C

HS

mod

el

RM

1.2

2∗∗∗

0.9

7∗∗∗

1.0

3∗∗∗

1.0

3∗∗∗

0.9

9∗∗∗

0.9

5∗∗∗

1.1

7∗∗∗

1.2

4∗∗∗

1.1

4∗∗∗

0.0

3(0

.51)

0.1

2(1

.17)

HM

L−

0.5

4∗∗

−0.2

5−

0.4

7∗∗

0.0

00.

34∗∗

0.5

0∗∗∗

0.6

5∗∗∗

0.4

8∗

0.8

8∗∗∗

0.6

4(7

.16)∗∗∗

1.1

1(7

.36)∗∗∗

SM

B0.9

4∗∗∗

1.0

3∗∗∗

1.2

1∗∗∗

0.9

5∗∗∗

0.8

5∗∗∗

0.8

7∗∗∗

0.7

4∗∗∗

0.7

1∗∗

0.6

5∗∗

-0.2

0(-

2.1

1)∗∗

-0.3

8(-

2.4

3)∗∗

UD

M−

0.4

4∗∗∗−

0.4

3∗∗∗−

0.2

9∗∗∗−

0.2

0∗∗

−0.2

5∗∗∗−

0.1

8∗∗

−0.2

1∗∗

−0.1

7−

0.3

4∗∗

0.1

1(2

.41)∗∗

0.1

3(1

.66)∗

47

Table

5(c

onti

nued)

Pan

el

B:

Valu

e-w

eig

hte

dp

ort

foli

os

Por

tfol

ios

0005

0510

1020

2040

4060

6080

8090

9095

9500

LS

5050

LS

8020

Sort

sb

ase

don

un

con

dit

ion

al

fail

ure

pro

bab

ilit

y

RM

1.4

5∗∗∗

1.0

5∗∗∗

1.2

9∗∗∗

1.3

1∗∗∗

1.2

8∗∗∗

1.5

2∗∗∗

1.3

0∗∗∗

1.1

0∗∗∗

1.0

7∗∗∗

-0.0

7(-

0.6

8)

-0.1

5(-

1.0

2)

HM

L−

0.1

30.

350.

50∗∗

0.2

70.

03

−0.0

5−

0.0

80.

12

0.15

-0.4

5(-

2.8

1)∗∗∗

-0.3

5(-

1.5

1)

SM

B0.8

6∗∗∗

1.2

3∗∗∗

1.1

9∗∗∗

1.1

0∗∗∗

0.8

8∗∗∗

0.7

9∗∗∗

1.5

2∗∗∗

0.7

7∗∗

1.5

6∗∗∗

-0.0

2(-

0.1

3)

0.3

8(1

.57)

UD

M0.0

8−

0.4

0∗∗∗−

0.2

1∗∗

−0.4

2∗∗∗−

0.2

4∗

−0.0

40.

01

−0.1

80.

17

0.2

1(2

.48)∗∗

0.2

5(2

.07)∗∗

Sor

tsb

ase

don

rece

ssio

nary

fail

ure

pro

babil

ity

from

the

FV

mod

el

RM

1.1

7∗∗∗

1.1

2∗∗∗

1.1

1∗∗∗

1.1

4∗∗∗

1.0

4∗∗∗

1.1

7∗∗∗

1.4

5∗∗∗

1.3

9∗∗∗

1.5

1∗∗∗

0.2

8(2

.40)∗∗

0.3

1(1

.98)∗∗

HM

L−

0.2

1−

0.0

70.

16−

0.1

30.

05

0.22

0.44∗∗

0.7

9∗∗∗

0.2

40.3

5(2

.04)∗∗

0.4

8(2

.02)∗∗

SM

B1.0

9∗∗∗

1.0

1∗∗∗

0.9

2∗∗∗

1.0

1∗∗∗

1.1

1∗∗∗

1.2

9∗∗∗

1.0

8∗∗∗

1.2

1∗∗∗

0.8

8∗∗∗

0.0

2(0

.09)

0.0

1(0

.03)

UD

M−

0.1

10.

01−

0.1

9∗

−0.1

0−

0.0

6−

0.0

30.

00

−0.2

9∗∗

−0.7

5∗∗∗

-0.1

4(-

1.5

4)

-0.2

7(-

2.1

5)∗∗

Sor

tsb

ase

don

rece

ssio

nary

fail

ure

pro

bab

ilit

yfr

om

the

CH

Sm

od

el

RM

1.4

6∗∗∗

1.3

5∗∗∗

1.2

2∗∗∗

1.5

0∗∗∗

1.1

6∗∗∗

1.2

7∗∗∗

1.2

3∗∗∗

1.1

6∗∗∗

1.1

0∗∗∗

-0.1

0(-

1.0

6)

-0.1

0(-

0.7

7)

HM

L−

0.5

7∗

−0.7

5∗∗∗

0.1

30.

03

0.60∗∗∗

0.6

3∗∗∗

0.6

9∗∗∗

0.7

6∗∗∗

0.6

1∗∗∗

0.6

9(4

.71)∗∗∗

1.1

2(5

.56)∗∗∗

SM

B1.5

6∗∗∗

1.1

5∗∗∗

1.4

0∗∗∗

0.8

7∗∗∗

1.0

9∗∗∗

0.7

4∗∗∗

0.6

9∗∗∗

0.9

5∗∗∗

1.0

6∗∗∗

-0.2

8(-

1.8

2)∗

-0.5

1(-

2.4

0)∗∗

UD

M−

0.1

0−

0.1

2−

0.5

4∗∗∗−

0.1

6−

0.1

6∗

0.0

10.

01

0.02

−0.1

70.2

4(3

.13)∗∗∗

0.3

4(3

.17)∗∗∗

Sor

tsb

ased

on

rece

ssio

nary

fail

ure

pro

bab

ilit

yfr

om

the

FV

+C

HS

mod

el

RM

1.5

3∗∗∗

1.1

2∗∗∗

1.3

6∗∗∗

1.2

7∗∗∗

1.4

7∗∗∗

1.1

6∗∗∗

1.2

1∗∗∗

1.0

9∗∗∗

1.4

7∗∗∗

0.0

5(0

.42)

-0.0

7(-

0.5

1)

HM

L−

0.5

7∗∗∗−

0.5

4∗

−0.4

7∗∗

−0.1

20.

35

0.49∗∗∗

0.9

0∗∗∗

0.7

7∗∗

0.6

8∗∗∗

0.9

5(5

.80)∗∗∗

1.4

0(6

.99)∗∗∗

SM

B1.0

6∗∗∗

1.4

4∗∗∗

1.1

1∗∗∗

1.1

1∗∗∗

1.0

8∗∗∗

1.1

2∗∗∗

0.8

3∗∗∗

0.7

8∗∗

0.6

7∗∗

-0.2

2(-

1.2

7)

-0.4

4(-

2.0

7)∗∗

UD

M−

0.1

3−

0.3

2∗∗

−0.2

1∗

−0.2

6∗∗

−0.0

3−

0.2

9∗∗∗−

0.3

1∗∗∗−

0.3

2∗

−0.0

20.1

3(1

.50)

-0.0

6(-

0.5

6)

48

Table

6P

ort

foli

osu

mm

ary

stati

stic

s:P

ost

-model-

sele

ctio

np

eri

od

2001-2

012

Eac

hm

onth

bet

wee

nJu

ly20

01an

dJu

ne

2012,

we

sort

stock

sw

ith

inth

eto

pqu

inti

leof

un

con

dit

ion

al

fail

ure

pro

bab

ilit

yin

top

ort

foli

os

bas

edon

per

centi

les

ofre

cess

ion

ary

fail

ure

pro

bab

ilit

yd

istr

ibu

tion

,es

tim

ate

das

of

the

most

rece

nt

Ju

ne.

Port

foli

on

am

esco

rres

pon

dto

low

eran

du

pp

erb

oun

ds,

e.g.

1020

conta

ins

stock

sb

etw

een

the

10th

an

d20th

per

centi

les.

Th

ela

sttw

oco

lum

nts

conta

inth

eS

harp

era

tios

for

the

LS

5050

and

LS

8020

hed

gep

ortf

olio

sth

atar

elo

ng

(sh

ort

)in

the

top

(bott

om

)h

alf

an

dqu

inti

leof

rece

ssio

nary

fail

ure

pro

bab

ilit

y,re

spec

tivel

y.P

anel

A(P

anel

B)

conta

ins

aver

age

equ

al-

(valu

e-)

wei

ghte

dp

rob

ab

ilit

ies

of

un

con

dit

ion

al

an

dre

cess

ion

ary

fail

ure

.

Pan

el

A:

Equ

al-

weig

hte

dp

ort

foli

os

Por

tfol

ios

0005

0510

1020

2040

4060

6080

8090

9095

9500

LS

5050

LS

8020

Sh

arp

era

tio

Sh

arp

era

tio

Sort

sb

ase

don

un

con

dit

ion

al

fail

ure

pro

bab

ilit

y

Mea

nnu

mb

erof

stock

sin

por

tfol

ios

27

25

52

105

105

105

52

26

27

-0.0

1-0

.12

Un

con

dit

ion

alp

rob

.0.

04

0.04

0.04

0.05

0.07

0.11

0.18

0.26

0.44

Rec

essi

onar

yfa

ilu

rep

rob

.F

V0.3

50.

35

0.35

0.34

0.34

0.33

0.33

0.32

0.31

Rec

essi

onar

yfa

ilu

rep

rob

.C

HS

0.2

90.

29

0.29

0.29

0.30

0.30

0.30

0.30

0.30

Rec

essi

onar

yfa

ilu

rep

rob

.F

V+

CH

S0.

35

0.35

0.36

0.35

0.36

0.36

0.36

0.36

0.37

Sor

tsb

ase

don

rece

ssio

nary

fail

ure

pro

babil

ity

from

the

FV

mod

el

Mea

nnu

mb

erof

stock

sin

por

tfol

ios

27

25

52

105

105

105

52

26

27

0.1

90.1

9U

nco

nd

itio

nal

pro

b.

0.16

0.14

0.12

0.12

0.10

0.09

0.09

0.09

0.09

Rec

essi

onar

yfa

ilu

rep

rob

.F

V0.2

20.

26

0.29

0.31

0.34

0.36

0.39

0.41

0.45

Sor

tsb

ase

don

rece

ssio

nary

fail

ure

pro

bab

ilit

yfr

om

the

CH

Sm

od

el

Mea

nnu

mb

erof

stock

sin

por

tfol

ios

27

25

52

105

105

105

52

26

27

0.1

90.2

5U

nco

nd

itio

nal

pro

b.

0.12

0.10

0.11

0.11

0.11

0.10

0.11

0.12

0.13

Rec

essi

onar

yfa

ilu

rep

rob

.C

HS

0.1

80.

21

0.23

0.26

0.30

0.33

0.36

0.38

0.42

Sor

tsb

ase

don

rece

ssio

nary

fail

ure

pro

bab

ilit

yfr

om

the

FV

+C

HS

mod

el

Mea

nnu

mb

erof

stock

sin

por

tfol

ios

27

25

52

105

105

105

52

26

27

0.1

90.3

0U

nco

nd

itio

nal

pro

b.

0.11

0.11

0.11

0.10

0.10

0.10

0.11

0.12

0.17

Rec

essi

onar

yfa

ilu

rep

rob

.F

V+

CH

S0.

18

0.23

0.27

0.31

0.36

0.40

0.45

0.48

0.55

49

Table

6(c

onti

nued)

Pan

el

B:

Valu

e-w

eig

hte

dp

ort

foli

os

Por

tfol

ios

0005

0510

1020

2040

4060

6080

8090

9095

9500

LS

5050

LS

8020

Sh

arp

era

tio

Sh

arp

era

tio

Sort

sb

ase

don

un

con

dit

ion

al

fail

ure

pro

bab

ilit

y

Mea

nnu

mb

erof

stock

sin

por

tfol

ios

27

25

52

105

105

105

52

26

27

0.0

3-0

.08

Un

con

dit

ion

alp

rob

.0.

04

0.04

0.04

0.05

0.07

0.11

0.17

0.25

0.43

Rec

essi

onar

yfa

ilu

rep

rob

.F

V0.3

80.

38

0.38

0.38

0.38

0.36

0.35

0.33

0.32

Rec

essi

onar

yfa

ilu

rep

rob

.C

HS

0.2

80.

28

0.28

0.28

0.28

0.28

0.27

0.28

0.28

Rec

essi

onar

yfa

ilu

rep

rob

.F

V+

CH

S0.

35

0.35

0.36

0.36

0.36

0.36

0.36

0.36

0.37

Sor

tsb

ase

don

rece

ssio

nary

fail

ure

pro

babil

ity

from

the

FV

mod

el

Mea

nnu

mb

erof

stock

sin

por

tfol

ios

27

25

52

105

105

105

52

26

27

0.1

20.2

5U

nco

nd

itio

nal

pro

b.

0.12

0.12

0.10

0.11

0.09

0.08

0.07

0.08

0.07

Rec

essi

onar

yfa

ilu

rep

rob

.F

V0.2

20.

26

0.29

0.31

0.34

0.36

0.39

0.41

0.47

Sor

tsb

ase

don

rece

ssio

nary

fail

ure

pro

bab

ilit

yfr

om

the

CH

Sm

od

el

Mea

nnu

mb

erof

stock

sin

por

tfol

ios

27

25

52

105

105

105

52

26

27

0.0

90.1

7U

nco

nd

itio

nal

pro

b.

0.10

0.09

0.09

0.08

0.08

0.08

0.08

0.08

0.09

Rec

essi

onar

yfa

ilu

rep

rob

.C

HS

0.1

80.

21

0.23

0.26

0.30

0.33

0.36

0.38

0.42

Sor

tsb

ase

don

rece

ssio

nary

fail

ure

pro

bab

ilit

yfr

om

the

FV

+C

HS

mod

el

Mea

nnu

mb

erof

stock

sin

por

tfol

ios

27

25

52

105

105

105

52

26

27

0.1

50.2

6U

nco

nd

itio

nal

pro

b.

0.09

0.08

0.09

0.08

0.09

0.08

0.08

0.09

0.10

Rec

essi

onar

yfa

ilu

rep

rob

.F

V+

CH

S0.

18

0.23

0.27

0.31

0.36

0.40

0.45

0.48

0.55

50

Table

7R

etu

rns

on

rece

ssio

nary

fail

ure

pro

babil

ity

stock

port

foli

os:

1991-2

012

Eac

hm

onth

bet

wee

nJuly

1991

and

Ju

ne

2012

we

sort

stock

sw

ith

inth

eto

pqu

inti

leof

un

con

dit

ion

al

fail

ure

pro

bab

ilit

yin

top

ort

foli

os

bas

edon

per

centi

les

ofre

cess

ion

ary

fail

ure

pro

bab

ilit

yd

istr

ibu

tion

,es

tim

ate

das

of

the

most

rece

nt

Ju

ne

usi

ng

FV

+C

HS

mod

el.

Port

foli

on

ames

corr

esp

ond

tolo

wer

-an

du

pp

er-b

oun

dp

erce

nti

les,

e.g.

1020

conta

ins

stock

sb

etw

een

the

10th

an

d20th

per

centi

les.

LS

5050

an

dL

S8020

are

hed

gep

ortf

olio

sth

atar

elo

ng

(sh

ort)

inth

eto

p(b

ott

om

)h

alf

an

dqu

inti

leof

rece

ssio

nary

fail

ure

,re

spec

tive

ly.

Pan

elA

(Pan

elB

)co

nta

ins

aver

age

equ

al-

(val

ue-

)w

eigh

ted

por

tfol

iore

turn

sin

exce

ssof

ari

sk-f

ree

rate

,as

wel

las

inte

rcep

tsfr

om

tim

e-se

ries

regre

ssio

ns

of

exce

ssre

turn

son

the

mar

ket

exce

ssre

turn

(CA

PM

alp

ha)

,th

ree

Fam

a-F

ren

chfa

ctors

(3-f

act

or

alp

ha),

an

dF

am

a-F

ren

chfa

ctors

plu

sm

om

entu

m(4

-fact

or

alp

ha)

.L

ower

par

tsof

each

pan

elco

nta

infa

ctor

load

ings

from

the

fou

r-fa

ctor

tim

e-se

ries

regre

ssio

ns.

t-st

ati

stic

sfo

rh

edge

retu

rns

are

inp

aren

thes

es.

All

retu

rns

are

rep

orte

din

mon

thly

per

centa

ge

poin

ts.

*,

**,

an

d***

den

ote

ssi

gn

ifica

nce

at

the

10%

,5%

,an

d1%

,re

spec

tive

ly.

Pan

el

A:

Equ

al-

weig

hte

dp

ort

foli

ore

turn

s

Por

tfol

ios

0005

0510

1020

2040

4060

6080

8090

9095

9500

LS

5050

LS

8020

Port

foli

ore

turn

s

Mea

nex

cess

retu

rn0.

670.

480.

97

1.77∗∗∗

1.76∗∗∗

1.69∗∗∗

2.28∗∗∗

1.72∗∗∗

1.83∗∗

0.4

8(2

.13)∗∗

1.2

4(3

.37)∗∗∗

CA

PM

alp

ha

−0.1

4−

0.2

30.

26

1.13∗∗

1.14∗∗∗

1.12∗∗∗

1.63∗∗∗

1.11∗∗

1.16∗

0.5

6(2

.51)∗∗

1.3

3(3

.61)∗∗∗

3-fa

ctor

alp

ha

−0.3

6−

0.3

30.

15

0.95∗∗

0.8

5∗∗

0.79∗∗

1.27∗∗∗

0.77

0.70

0.4

0(2

.16)∗∗

1.0

9(3

.40)∗∗∗

4-fa

ctor

alp

ha

0.0

90.

030.

48

1.17∗∗∗

1.0

7∗∗∗

1.0

1∗∗∗

1.55∗∗∗

1.07∗∗

1.01∗

0.3

4(1

.83)∗

1.0

2(3

.13)∗∗∗

Fact

or

load

ings

RM

0.9

2∗∗∗

0.8

0∗∗∗

0.8

9∗∗∗

0.85∗∗∗

0.87∗∗∗

0.84∗∗∗

0.96∗∗∗

0.90∗∗∗

0.94∗∗∗

0.0

1(0

.32)

0.0

7(0

.87)

HM

L−

0.2

4−

0.4

2∗∗−

0.2

6∗∗−

0.0

60.

27∗∗

0.38∗∗∗

0.45∗∗∗

0.42∗∗∗

0.56∗∗∗

0.5

2(8

.56)∗∗∗

0.7

7(7

.33)∗∗∗

SM

B2.0

5∗∗∗

1.7

2∗∗∗

1.3

6∗∗∗

1.3

5∗∗∗

1.2

3∗∗∗

1.1

4∗∗∗

1.13∗∗∗

1.07∗∗∗

1.55∗∗∗

-0.2

8(-

4.8

7)∗∗∗

-0.4

0(-

4.0

1)∗∗∗

UD

M−

0.5

2∗∗∗−

0.4

1∗∗∗−

0.3

8∗∗∗−

0.2

6∗∗∗−

0.2

6∗∗∗−

0.2

6∗∗∗−

0.33∗∗∗−

0.35∗∗∗−

0.36∗∗∗

0.0

7(1

.82)∗

0.0

8(1

.29)

51

Table

7(c

onti

nued)

Pan

el

B:

Valu

e-w

eig

hte

dp

ort

foli

ore

turn

s

Por

tfol

ios

0005

0510

1020

2040

4060

6080

8090

9095

9500

LS

5050

LS

8020

Port

foli

ore

turn

s

Mea

nex

cess

retu

rn−

0.68

−0.

230.

43

0.90

1.04

1.35∗∗

1.38∗∗

0.82

1.49∗∗

0.9

1(2

.56)∗∗

1.3

0(2

.71)∗∗∗

CA

PM

alp

ha

−1.

63∗∗

−1.

10−

0.44

0.09

0.23

0.60

0.68

0.20

0.73

1.0

3(2

.91)∗∗∗

1.4

8(3

.12)∗∗∗

3-fa

ctor

alp

ha

−1.

66∗∗∗−

1.12∗

−0.

45

−0.

05

−0.

11

0.27

0.23

−0.

25

0.33

0.7

2(2

.54)∗∗

1.0

4(2

.86)∗∗∗

4-fa

ctor

alp

ha

−1.

57∗∗∗−

1.07∗

−0.

34

0.02

−0.

09

0.52

0.38

0.11

0.41

0.7

6(2

.62)∗∗∗

1.1

6(3

.15)∗∗∗

Fact

or

load

ings

RM

1.3

1∗∗∗

1.04∗∗∗

1.20∗∗∗

1.13∗∗∗

1.25∗∗∗

1.12∗∗∗

1.15∗∗∗

0.96∗∗∗

1.25∗∗∗

-0.0

1(-

0.0

8)

-0.0

6(-

0.6

7)

HM

L−

0.49∗∗∗−

0.69∗∗∗−

0.45∗∗∗−

0.21

0.33∗∗∗

0.34∗∗∗

0.73∗∗∗

0.68∗∗∗

0.59∗∗∗

0.8

6(9

.27)∗∗∗

1.2

2(1

0.3

2)∗∗∗

SM

B1.6

7∗∗∗

2.25∗∗∗

1.40∗∗∗

1.65∗∗∗

1.5

5∗∗∗

1.2

7∗∗∗

1.1

2∗∗∗

1.0

1∗∗∗

1.1

8∗∗∗

-0.3

6(-

4.0

5)∗∗∗

-0.5

0(-

4.4

6)∗∗∗

UD

M−

0.1

0−

0.0

6−

0.1

3−

0.0

9−

0.0

2−

0.2

9∗∗∗−

0.1

8∗∗

−0.4

2∗∗∗−

0.1

0-0

.04

(-0.7

1)

-0.1

4(-

1.8

9)∗

52

Table 8Does systematic distress risk factor predict aggregate failure rates and

macroeconomic conditions?

We regress future aggregate failure rates and macroeconomic variables on monthly returns on the hedgeportfolio FAIL that is long (short) in the top (bottom) quintile of recessionary failure probability; the sortingis performed based on the FV+CHS model within the top quintile of unconditional failure probability. Re-gressions also include returns on the market (MKTRF), size (SMB), book-to-market (HML), and momentum(UMD) factors. Regressions predicting aggregate failure rates (macroeconomic indicators) use returns fromJuly 1991 to December 2010 (July 1991 to June 2012). % Fail (t+1, t+12) is aggregate failure rate over thenext twelve months. % AUD (t+1, t+12) is the proportion of assets under distress, i.e. assets of failed firmsrelative to assets of all active firms. GDP is real GDP growth over the next quarter. CPI is CPI inflationrate over the next quarter. UNEMP is unemployment rate over the next quarter. All variables exceptreturns are log-transformed. t-statistics are based on robust standard errors with Newey-West correction forautocorrelation with 12 lags. *, **, and *** denotes significance at the 10%, 5%, and 1%, respectively.

Panel A: Equal-weighted systematic distress factor

% Fail %AUD GDP CPI UNEMP(t+1, t+12) (t+1, t+12)

MKTRF −1.44∗∗∗ −5.38∗∗∗ 0.07∗∗ 0.07 −0.30∗∗

(−2.71) (−2.85) (2.26) (1.38) (−2.08)SMB −1.37 −0.51 0.02 −0.03 −0.01

(−1.56) (−0.25) (0.56) (−0.63) (−0.13)HML 1.27 2.83 −0.03 0.02 0.09

(1.26) (0.92) (−1.22) (0.46) (0.80)UMD 0.59 −0.12 −0.04∗∗ 0.04 −0.04

(1.39) (−0.08) (−2.04) (1.18) (−0.49)FAIL −1.43∗∗ −4.63∗∗ 0.04∗ −0.02 −0.14∗∗

(−2.51) (−2.54) (1.88) (−1.26) (−2.45)% Fail (t-11, t) 0.41∗∗∗

(3.76)% AUD (t-11, t) 0.39∗∗∗

(2.81)Lag(GDP) 0.42∗∗∗

(2.99)Lag(CPI) 0.15∗∗

(2.05)Lag(UNEMP) 0.99∗∗∗

(42.84)Intercept −2.02∗∗∗ −3.24∗∗∗ 0.01∗∗∗ 0.02∗∗∗ −0.01

(−5.42) (−4.06) (2.99) (9.37) (−0.16)

N 234 234 252 252 252adj. R-sq 0.280 0.257 0.240 0.028 0.966

53

Table 8(continued)

Panel B: Value-weighted systematic distress factor

% Fail %AUD GDP CPI UNEMP(t+1, t+12) (t+1, t+12)

MKTRF −1.55∗∗∗ −5.81∗∗∗ 0.08∗∗ 0.07 −0.32∗∗

(−2.74) (−2.68) (2.26) (1.35) (−2.05)SMB −0.91 0.75 0.03 −0.03 0.01

(−1.14) (0.37) (0.77) (−0.55) (0.14)HML 0.30 0.49 −0.05 0.01 0.07

(0.26) (0.16) (−1.60) (0.09) (0.56)UMD 0.45 −0.65 −0.03 0.04 −0.07

(0.95) (−0.36) (−1.57) (1.10) (−0.68)FAIL −0.13 −1.05 0.04∗∗ 0.00 −0.07∗

(−0.29) (−0.79) (1.98) (−0.09) (−1.80)% Fail (t-11, t) 0.42∗∗∗

(3.93)% AUD (t-11, t) 0.40∗∗∗

(2.70)Lag(GDP) 0.43∗∗∗

(3.17)Lag(CPI) 0.15∗

(1.90)Lag(UNEMP) 0.99∗∗∗

(43.25)Intercept −1.97∗∗∗ −3.22∗∗∗ 0.01∗∗∗ 0.02∗∗∗ −0.02

(−5.22) (−3.81) (2.89) (9.31) (−0.26)

N 234 234 252 252 252adj. R-sq 0.251 0.212 0.244 0.026 0.966

54

Table 9In-sample logits predicting failure and recessionary failure

We estimate logit models that predict either recessionary failures or unconditional failures using FV,CHS, or FV+CHS models for a period of 1972 to 2011. In Panel A, the outcome variable is recessionaryfailure and the sample includes only failures. In Panel B, the outcome variable is any failure and the sampleincludes all firm-years. All variables are defined in Appendix A. AUC is area under the ROC curve. In PanelB, “AUC: predicting recessionary failure” measures the ability of fitted values from the unconditional failureprediction model to predict recessionary failures. t-statistics based on robust standard errors clustered byfirm and year are in parentheses. *, **, and *** denotes significance at the 10%, 5%, and 1%, respectively.

Panel A: Recessionary failure Panel B: Unconditional failure

CHS FV FV+CHS CHS FV FV+CHS

nimtaavg 1.99∗∗∗ 1.56∗∗ −5.02∗∗∗ −4.85∗∗∗

(3.05) (2.35) (−9.94) (−10.18)tlmta 0.37∗∗ −0.69∗∗∗ 1.48∗∗∗ 1.01∗∗∗

(2.43) (−3.14) (9.97) (4.44)exretavg −2.95∗∗∗ −2.74∗∗∗ −2.22∗∗∗ −1.95∗∗∗

(−4.95) (−4.46) (−3.97) (−3.62)sigma 0.12 0.07 0.12 0.09

(1.36) (0.80) (1.03) (0.77)rsize −0.02 −0.31∗∗∗ −0.40∗∗∗ −0.54∗∗∗

(−0.71) (−6.11) (−8.77) (−8.31)cashmta 0.17 −0.44 −1.04∗∗∗ −1.40∗∗∗

(0.63) (−1.49) (−4.03) (−4.84)mb −0.03∗ 0.00 0.18∗∗∗ 0.16∗∗∗

(−1.85) (0.22) (14.83) (10.83)price2011 0.06 −0.05 −0.32∗∗∗ −0.34∗∗∗

(1.17) (−0.95) (−5.74) (−6.21)logat2011 0.13∗∗∗ 0.36∗∗∗ −0.41∗∗∗ 0.18∗∗∗

(6.40) (8.52) (−13.26) (3.12)betaatrnfs 0.01∗∗∗ 0.02∗∗∗ −0.01∗∗ 0.00

(4.84) (5.28) (−2.06) (−1.16)sd12roeq −0.09 −0.11 0.84∗∗∗ 0.25∗∗∗

(−0.97) (−1.02) (13.79) (3.68)ssnsaleq −0.18 −0.23 1.62∗∗∗ 2.14∗∗∗

(−0.44) (−0.55) (7.34) (11.19)sts −0.39∗∗ −0.37∗ 1.02∗∗∗ 0.34∗∗∗

(−2.08) (−1.87) (10.88) (3.56)fai −0.51∗∗∗ −0.61∗∗∗ 0.34∗∗ −0.30∗

(−3.03) (−3.43) (2.57) (−1.91)Intercept −1.37∗∗∗ −0.98∗∗∗ −5.51∗∗∗ −8.66∗∗∗ −1.85∗∗∗ −10.96∗∗∗

(−2.77) (−8.71) (−7.39) (−15.27) (−16.01) (−12.19)

AUC: predicting failures 88.11 75.85 88.65AUC: predicting reces-sionary failures

58.12 59.20 64.58 51.09 42.40 51.93

Log-likelihood −2024.24 −2012.11 −1958.62 −10 845.56−12 973.34 −10 727.64Pseudo−R2 0.014 0.020 0.046 0.248 0.101 0.257

55