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Bankruptcy Prediction Models and the Cost of Debt

Sattar A. Mansi, William F. Maxwell, and Andrew Zhang

June 8, 2010

Abstract

Financial institutions and academic researchers utilize bankruptcy prediction models toassess distress risk. However, predicting default can be problematic since (i) few firmsactually experience default in any one year, (ii) the lag between practical and actualdefault can vary significantly, (iii) firms can strategically default, (iv) firms can reworktheir obligations outside of bankruptcy, and (v) default frequency varies significantly

over economic life cycles. Thus, relying on bankruptcy data alone to calibrate andvalidate these models can be problematic. We take a simpler approach by relying on thefirms cost of debt as a market proxy for distress risk. We then assess the validity of fourwidely used bankruptcy models including two accounting-based models (Altmans,1968; Ohlsons, 1980), one reduced form model (Campbell, Hilscher, and Szilagyi, 2010)and one structural distance to default model (Merton, 1974). We find dramaticallydifferent assessment of risk based on the models used. The Campbell, Hilscher, andSzilagyi (2010) model has the most explanatory power on the cost of debt followed bythe Merton model. The accounting based approaches of Altman (1968)s Z-Score andOhlson (1980)s O-Score are highly ineffective. We caution researchers when using Z-and O-Scores and recommend the use of Campbell, Hilscher, and Szilagyi model to

di t i k W l d t t th bl f t t lli f i d t

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measure distress risk We also demonstrate the problems of not controlling for industry

1. Introduction

The goal of financial distress models is to utilize information about the firm to construct asingle variable allowing for the comparison of default risk across firms. The literature on

financial distress risk provides four main models that forecast default including two

accounting-based models (Altman, 1968; Ohlsons, 1980), one reduced form model (Campbell,

Hilscher, and Szilagyi, 2010) and one structural model (Merton, 1974). These models lead to

four proxy variables, namely, Altmans Z-Score, Ohlsons O-Score, CHS Score, and Mertons

Distance to Default (Merton-DD). These measures are widely used in the literature to proxy for

distress risk, especially in the areas of accounting and financial economics. According to Social

Sciences Citation Index, as of December 2009, Altman (1968), Ohlson (1980), Merton (1974), and

Campbell et al. (2010) have been cited 691, 295, 709, and 9 times respectively 1

Given that empirical results differs based on the default measure utilized, the relative

performance of these models in forecasting financial failures is of significant concern in the

literature.

Based solely on

citations, the z-score and o-score remain highly popular distress risk measure in the academic

literature, as they were 132 and 59 times in 2009 alone. Our results suggest that this is highly

problematic. We find evidence suggesting that the Altman and Ohlson model are very weakly

related to distress risk and in fact do no better than a naive distress measure, the leverage ratio.

2 While the results are mixed, extant studies have never researched these four distress

measures all together in a unified and comprehensive framework. Also ignored is the relative

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significantly reflect the changes in corporate capital structure and the riskiness of corporate

activity. According to Campbell et al. (2010), these changes can partially explain the changes in

financial failures through time. As a result, to locate a distress measure that has robust superior

forecasting power of bankruptcy is crucial to many empirical studies. Our results find a very

significant difference across these models with accounting based measure faring poorly.

In this paper, we attempt to reconcile the differences in extant studies by examining the

relation between financial distress measures and bond spreads, an assessment of the markets'

perception of risk, to determine the relative performance of these models. Given that bond

investors require stable cash flows and demand default risk premium in yield spreads, many

studies have related yield spreads to distress risk from various perspectives (see e.g., Almeida

and Philippon, 2007; Anginer and Yildizhan, 2010; Bharath and Shumway, 2008; Davydendo

and Strebulaev, 2007). We posit that distress risk is efficiently impounded in bond market

prices; therefore, yield spreads are a significant reflection of the probability of financial failure.

Hence, we are not modeling actual default risk as in prior research, but instead analyzing the

ability of default models to capture market based distress risk. Our results indicate that the

CHS Score is a superior forecasting model followed by Merton-DD, O-Score, and Z-Score. This

is true in both early and late periods, and across normal and shock economic periods. The

outperformance of CHS is more evident for firms with small size, low M/B ratio, and high

equity volatility.

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failures were extremely rare until the late 1960s, and in the 3 years (1967 to 1969), there were no

bankruptcies at all (Campbell et al., 2010).

These studies also suffer from problems in defining financial failure and constructing

distressed sample. Specifically, these studies conduct tests based on a sample of distressed

firms, where a firm enters into the sample upon occurrence of one or more of the following

events: default in payment of interest or principal, announcement of bankruptcy, or being

delisted from exchanges for financial problems. Some important distress signals like dividend

cut or omission have never been counted, however. These studies are usually different in their

definition of financial distress and hence the sample construction of distressed firms. As a

result, testing results are usually sample-specific and may be sensitive to sample size and

sample period used in their model estimations.

Even more importantly, firms often become financially distressed either much earlier orlater than the actual default or bankruptcy filing date, and that lag or lead time can be

significant. In practice, some financially distressed firms can manage its operating earnings,

working capital, and cash flows to meet debt covenants and interest payment to delay default

or bankruptcy. On the other hand, some firms will file for bankruptcy even when they are

economically solvent. Strategic default brings firms into default early to break unfavorable

contracts and obtain forced debt concessions. Additionally, a firm may have market assets

greater than total liability but does not have enough cash and liquid assets to meet its current

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of capital. In this study, we focus on the corporate bond spread since it is extracted based on

publicly traded debt and represents not only a sensitive measure of distress risk, but also a

timely and continuous one. Consequently, corporate bond spreads will provide a consistent

and comprehensive benchmark for the assessment of the relative performance of different

distress measures without the need of the sample construction of distressed firms.

Using a large sample of bond data from the Lehman Brothers Fixed Income database

covering the period from 1980 through 2006, we find that the four measures of financial distress

are significantly related to bond spreads with CHS Score obtaining the highest t-statistic and

adjusted R-squared followed by Merton-DD, O-Score and Z--Scores, before and after controlling

for years to maturity and industry effect. Since it is well known that corporate spread is too

high to be explained only by expected default, we use offering amount, bond age, and coupon

rate to control for liquidity and tax effect, and find the relative outperformance of CHS remains

intact. Extant studies suggest that the underperformance of accounting-based Z- and O-Scores

might be due to the staleness of parameters and failure to accounting for R&D effects in their

predictive variables. We use updated coefficients from Hillegeist et al. (2004) to construct

updated Z- and O-Scores. We also follow Franzen, Rodgers, and Simin (2007) and re-construct

these two scores by accounting for R&D effects. However, these two scores continue to have

poor performance.

The remainder of the paper is organized as follows. Section 2 describes data, distress

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nonconvertible bonds that are used in the Lehman Brothers Bond Indexes. The database is

commonly used in the finance literature (e.g., Mansi, Maxwell, and Wald, 2009; Bharath and

Shumway, 2008; Klock, Mansi, and Maxwell, 2005).

For a firm-year observation to be included in the analysis, firms must have a debt issue that

is present in the LBFI dataset and financial information must also be available in the Compustat

and CRSP databases to compute all four distress measures (described in detail below). For

firms with multiple issues, we only include the bond with the greatest term to maturity since it

is more representative of the cost of debt.3

We follow the convention in the literature to exclude

regulated utilities with SIC codes 4949 to 4999 and financial firms with SIC codes 6000 to 6999,

since some financial ratios used to construct distress measures are not applicable and have

different meanings in these industries. Similar to Bharath and Shumway (2008) and Campbell

and Taksler (2003) we also exclude all AAA rated bonds because the data for these bonds may

not be reliable. We further eliminate all corporate floating rate debt, bonds with an odd

frequency of coupon payments, inflation-indexed bonds, and bonds with less than one year to

maturity due to their illiquidity. Merging the databases and applying these requirements yields

a data set of 120,608 monthly observations on 1,752 firms covering the period from 1980

through 2006.

2.2 Measuring Bankruptcy Prediction Models

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to allow accounting information from annual filing to be available to bond investors when

constructing these two measures. The primary specification for the z-score model is

Z-Score=-1.2*wcta-1.4*reta-3.3*ebitta-0.60*mvliab-sata (1)

where wctais working capital, or current assets (annual item 4) minus current liability (annual

item 5) scaled by total assets (annual item 6), retais retained earnings (annual item 36) scaled by

total assets (annual item 6), ebittais earnings before interest and tax (annual item 170 plus item

15) divided by total assets (annual item 6), mvliab is market value of equity (annual item 199

times item 25) divided by total liability (annual item 181), and sata is sales (annual item 12)

divided by total assets (annual item 6). For comparison with other models, we reverse the signs

of original coefficients so the Z-Score is increasing in the probability of bankruptcy.

And the primary specification for the O score model is

O-Score = -1.32 - 0.407*asset + 6.03*tlta - 1.43*wcta + 0.0757*clca

- 2.37*nita- 1.83*ffotl + 0.285*intwo - 1.72*oeneg - 0.521*chin (2)

where asset is the log of total assets (annual item 6), tlta is total liabilities (annual item 181)

divided by total assets (annual item 6), wcta is working capital to total assets (as defined in

equation (1) above), clca is current liability (annual item 5) divided by current assets (annual

item 4) nita is net income (annual item 172) divided by total assets (annual item 6) ffotl is fund

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by multiplying the adjusted net income by (1 - tax rate), where the tax rate is defined as the

appropriate annual statutory tax rate: 46% in the period 1980-1986, 40% in the year 1987, 34% in

1988-1992, and 35% in 1993-2006. The variable adjust total assets is total assets plus R&D capital

defined as RD+0.8*RDt-1+0.6*RDt-2+0.4*RDt-3+0.2*RDt-4. If net income (annual item 172) is

positive, we adjust total liability as total liability (annual item 181) plus deferred tax liability

defined as R&D capital times the tax rate. After adjusting net income, total assets, and total

liability, we re-construct all constituent variables in Z- and O-Scores respectively and apply the

original coefficients to these variables to construct a new set of Z- and O-Scores, labeled

hereafter as adjusted Z-Score and Adjusted O-Score.

Several studies have argued that the original coefficients in each model have substantially

changed from their original values (e.g., Begley, Ming, and Watts, 1996; Hillegeist et al. 2004).

Therefore, we use the coefficients based on the re-estimation by Hillegeist et al. and construct an

updated Z-Score and O-Score measures. That is

Updated Z-Score=-4.34-0.08 wcta+0.04*reta-0.1*ebitta-0.22mvliab+0.06sata (3)

Updated O-Score = -5.91 + 0.04*asset+ 0.08*tlta+ 0.01*wcta-0.01*clca

+ 1.20*nita + 0.18*ffotl+ 0.01*intwo+ 1.59*oeneg- 1.10*chin (4)

where all constituent variables are defined in the same manner as in the original model without

adjustment for the R&D effect.

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a simply way to take account of the fact that long-term debt may not mature until after the

horizon of the distance to default calculation. If book debt (BD) is missing, we use BD=median

(BD/TL)*TL, where the median is calculated for the entire dataset and TL is the total liabilities

(quarterly item 54). This captures the fact that empirically, BD tends to be much smaller than

TL. If BD=0, we use BD= median (BD/TL)*TL, where now we calculate the median only for

small but nonzero values of BD (0 < BD

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where nimtaavg and exretavg are the moving average of lagged four quarterly nimta and 12

monthly exret, respectively, with geometrically declining weights on lags. The variable nimtais

computed as net income (quarterly item 69) divided by the sum of market equity (the product

of number of shares outstanding and month end stock prices, both from CRSP) and total

liability (quarterly item 54). The moving average nimtaavgsuggests that a long history of loss is

a better predictor of bankruptcy than one large quarterly loss in a single month. Exret is the

monthly log excess return on each firms equity relative to the S&P 500 index. The moving

average exretavgsuggests that a sustained decline in stock market value is a better predictor of

bankruptcy than a sudden drop in stock price in a single month. When lagged exertor nimtais

missing, we replace it with the cross-sectional mean in order to avoid losing observations.

Tlmtais the ratio of total liabilities (quarterly item 54) divided by the sum of market equity and

total liabilities. Stdev is the annualized three-month rolling sample standard deviation. To

eliminate cases in which few observations are available, we code stdevas missing if there are

fewer than five nonzero observations over the three months used in the rolling window

computation. When computing CHS Score, we replace missing stdev observations with the

cross-sectional mean of stdev. Rsizeis the relative size of each firm measured as the log ratio of

its market equity to that of the S&P 500 index. Cashmta, a proxy for liquidity position of the firm,

is the ratio of cash and short term investments (quarterly item 36) divided by the sum of marketequity and total liabilities. Mtb is the ratio of market-to-book equity, where book equity is the

sum of stockholders equity (quarterly item 60) and deferred tax credit (quarterly item 52)

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2.3Measuring the Cost of Debt FinancingWe use the month-end bid price from the LBFI database to compute the cost of debt for each

corporate bond. The cost of debt, or yield spread, is the difference between the yield to maturity

on a corporate bond and the yield to maturity on its maturity equivalent Treasury security. The

yield to maturity on a corporate bond is the discount rate that equates the present value of its

future cash flows to its current price. The yield to maturity on a Treasury security is the yield

on the constant maturity series obtained from the Federal Reserve Bank in its H15 release based

on a par bond. In the cases where no corresponding Treasury yield is available for a given

maturity, the yield spread is calculated using linear interpolation. For some of our analysis, we

rely on raw yield spread. But due to the skewness of the yield data, we use the log of bond

yield spread instead of raw yield spread in our regressions. When utilizing the log of the yield

spread, we find a slightly higher r-squared in the regression results but our results are invariant

when using raw yield spread.

2.4 Descriptive Statistics

Panel A of Table 1 reports summary statistics for sample firms from 1980 to 2006. The mean,

median, and standard deviation of the main variable in our analysis, yield spread, is 283, 189,

and 288 basis points (bps), with upper and lower quartile values of 341 and 119, respectively.

As discussed before, because the yield spread is highly skewed, we use the log transformed

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in the sample have average annualized daily volatility of stock return of 37%. In terms of debt

variables, the mean and median bond rating variable equates to S&P ratings of BB and BB-,

respectively, with standard deviation ranging from B- to BBB+, which indicates a large portion

of the sample has slightly below average quality debt. The mean and median traded debt has

maturity of 15 and 13 years and, on average, has been outstanding for about 3.1 years with

coupon rate of 9.368%.

Panel B of Table 1 describes the industry distribution of the sample (in absolute number and

in percentage) using the standard Security Industry Classification (SIC) codes. Industries

include agriculture, forestry, fishing, mining, construction, manufacturing (food through

petroleum and plastics through electronics), transportation and communications excluding

utilities, wholesale and retail trade, real estate, services, and public administration. Based on

the sample, a large portion is concentrated in manufacturing (about 47%), transportation and

communication (22%), wholesale and retail trade (11%), services (10%), and mining and

construction (9%).

[Insert Panel B of Table 1 about here]

Panel C of Table 1 provides the Pearson correlation between the variable used in theanalysis and the four distress measures. We find that yield spread to be positively correlated

with market leverage and each of the four measures of financial distress, with the highest

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liquidity. Years to maturity is negatively correlated to yield spreads, indicating that bonds with

longer years to maturity have higher liquidity and lower yield spreads. Except for Z-Score,

years to maturity are negatively correlated with distress measures, with correlation coefficients

between -0.24 to -0.27.

[Insert Panel C of Table 1 about here]

3. Empirical Analysis

3.1 Distress Measures and Bond Ratings

Some studies rely on bond ratings to assess financial distress (see e.g., Avramov, Chordia,

Jostova, and Philipov, 2008; Dhaliwal and Reynolds, 1994), and as first attempt at examining theveracity of the distress measures, we examine how the distress measures are related to bond

rating.4 While bond ratings can clearly be erroneous measures of default risk, they are known

to be related to future default probability. A possible criticism of the rating analysis is that

while the results do not reflect any problems with the distress risk measures, poor performance

of some distress measures based on the rating analysis is simply due to problems with the bond

ratings. For this reason, we move to an analysis of credit spreads in the next section. However,

bond ratings serve as one measures of risk and provide a starting point for our analysis.

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only focus on the originally constructed Z- and O-score, but our results are generally similar

when using the adjusted and updated measures.

One measure of the usefulness of a distress variable is its stability across time and industry

since researchers often compare the risk of firms at different points in time and across different

industries. Hence, we examine how stable the relation is between the distress measures and

bond ratings. We examine whether the distress measures and bond rating correctly align over

shorter-time frames, whether they are stable over time, and across industries.

We begin by examining the stability of the distress measures over time with the idea that a

stable distress measure allows for comparison of firms across time. As such, we compute the

distress measures for the sample over three-year horizons and report the median levels within

bond ratings. The results are presented in Table 2. Market leverage does not correctly align

with bond ratings in two of the nine periods in the BBB thru B categories. The Z-score is highly

problematic as the distress measure does not correctly align in six of the nine time periods (the

relative rankings across the BBB, BB and B categories). All the other measures, correctly align

with rankings in sub-time periods. As it relates to the stability of ranking over time, we find

significant variation of rankings for market leverage, Z-score, O-score and Merton-DD. That is,

the median value of BB in one time period might in fact be rated a BBB or B in another time

period. We do find some variation over time for the CHS Score, but it is clearly the most stable.

bl b h

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suggests that it is difficult to have useful comparisons across time and industry. This is

especially true for the Z-Score and less so for the CHS Score.

[Insert Table 3 about here]

3.2 Decile Sorts

Noting the limitation of assuming that bond ratings are an accurate proxy for default risk,

we move to examine the relation between distress measures and credit spreads. Credit spreads

are assumed to reflect the markets perception of default risk plus a liquidity component. We

begin with the assumption that for a distress measures to be an informative tool, it should

differentiate the relative riskiness of firms. We begin our analysis by sorting firms into distress

deciles based on the different distress measures. If the distress measure is properly capturing

risk, we should see credit spreads increasing across deciles.

Panel A of Table 4 provides analysis by examining the mean and median credit spread

within distress measure deciles for a fixed time period (as of June 2006). The results suggest

that, in general, all models correctly distinguish the firms in the most extreme deciles. Both the

Merton DD and CHS distress models correctly align firms within deciles to credit spreads,

spreads are increasing with the deciles. In contrast, the Z- and O-score models do not correctly

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leverage does a better job in every decile when compared to the Z- and that the O-Score seems

to do slightly better than market leverage. Using the updated or R&D adjusted Z- and O-Score

don't really change these conclusions. Both the Merton DD and CHS do better on average than

market leverage. Across all the measures, the extremes are more easily differentiated than the

middle deciles.

[Insert Panel B of Table 4 about here]

As an overall conclusion to the decile analysis, we find very little difference between the

market leverage and the O-Score in performance. If anything the Z-score seems to perform

worse than market leverage. The Merton DD and the CHS model seem to clearly outperform

the other measures. On aggregate, the R&D adjusted Z- and O-score don't perform very

differently than the unadjusted models, and the updated Z and O-score models seem to do aparticularly poor job of assessing risk. While this is only one analysis, in the remainder of the

paper we find similar results for the R&D adjusted and updated Z and O-score models. The

R&D adjusted models in aggregate produce similar results to the original models, and the

updated models perform worse than the original models. Hence for brevity, for the remainder

of the paper, we focus solely on the original Z- and O-score models.

3 3 Distress Measures & Credit Spreads a Regression Analysis

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outperforms the market leverage model by 18%, but the Merton DD and CHS model have

notably higher explanatory power. Next, we add year fixed effects to capture macro level risk

changes in Panel B. While the explanatory power improves, the ranking of the different distress

scores remains the same with the Z-Score having the lowest and the CHS score the highest. 5

3.4 Relative Performance across Industries

A researcher may be concerned that distress measures could have significant variation

across industries. First, distress measures use financial information in their construction, but

firms in different industries have different accounting rules. Firms may be more or less

sensitive to the risk factors included in distress measures, implying that the probability of

bankruptcy can differ for firms in different industries with otherwise identical financial

statements. Second, industries respond differently to macro economic shocks. Differentindustries also face different levels of competition. Despite the strong economic intuition

suggesting that industry effects should be an important component in bankruptcy prediction,

not much attention has been paid to industry effects in extant literature, mostly likely due to the

limited number of bankruptcies in each industry. The only exception is Chava and Jarrow

(2004), which group sample firms into four industry categories and find that predictive

variables have different power to forecast bankruptcy for different groupings.

For a distress measure to be accurate, we would hope to see a high and similar R-Squared

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power for the Merton DD and CHS Score as compared to the other 3 measures. This is

universal across all industry types. We also find much less variation in the explanatory power

across industries for these two measures. Overall, CHS Score is still the best measure of

financial distress in all 6 industries.

3.5 Relative Performance over Time

There is a broad variation in corporate failures over time, including the long-lasting increase

in the 1980s and cyclical spikes in the early 1990s and early 2000s. A good bankruptcy

forecasting models must quantify the time-series effects of the change in economic structure on

financial distress. For this reason, in Table 7 Panel B, we conduct our regression analysis in

three different time periods and in normal and shock economic periods, where shock period

includes the year 1987, 1989, 1994, 1997, 2000, and 2001, and normal period includes the

remaining years. It shows that CHS Score outperforms other measures in each time period and

in both normal and shock period. The CHS Score outperformance is more evident during years

of economic shocks. The CHS Score can explain 54% of cross-sectional variation of yield spread

in shock periods. This number is much greater than the corresponding numbers for Merton-DD

(45%), O-Score (36%), Z-Score (27%), and market leverage (37%).

3.6 Relative Performance over Size, Market-to-Book, and volatility quartiles

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each specification. Overall, the effect of distress risk on yield spread is in general more

prominent in small firms. The Adjusted R-squared is around 25%-37% and decreases in size for

Merton-DD and CHS Score and is around 22% for market leverage, O-Score, and Z-Score. In

terms of relative performance, CHS outperforms other measures in smallest size quartiles but

does not outperform other measures in larger size quartiles. Similarly, we sort sample firms

into quartiles by market-to-book ratio and equity volatility. While CHS Score outperforms

other three measures in each M/B quartile, it only outperforms other measures among firms

with largest volatility. We conclude that CHS outperforms other measures among firms with

highest distress risk.

3.7 Liquidity and Tax Effects

The literature suggests that liquidity and tax factors explain a significant part of yield

spreads. Because the LBFI does not provide data on bid-ask spreads, we proxy for cross-

sectional difference in corporate bond liquidity using time to maturity, log of bond age, and log

of offering amount. We use time to maturity to control for liquidity risk in our main analysis.

We also proxy for tax effect on the cross-sectional variation in bond spreads using bond coupon.

We conduct two additional tests to examine the robustness of our results to liquidity and tax

effects. First, we include log of offering amount (log of bond age) and coupon as regressors in

the multivariate regression. We obtain similar results, which are not tabulated. Second, we sort

firms into quartiles by bond age offering amount and coupon rate respectively and conduct

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al. (CHS) measure. We utilize credit spreads to measure distress risk and compare the default

models and our naive measure, market leverage, to see which one is the most accurate measure

of distress risk. We define the best based on the distress measures ability to explain credit

spreads in aggregate, over time, across industries, and relative to market priced risk factors

(size, market-to-book, and volatility).

We find that CHS Score has the greatest explanatory power over cross-sectional variation of

cost of debt followed closely by Merton-DD. The two accounting-based measures, the Z-Score

and O-Score, while having a significant impact on yield spread and thus containing distress

information, perform poorly comparing to other two measures. The Z-Score, in fact, most often

performs worse than what we consider the naive model, market leverage. We also find that

adjusting predictive variables to control for R&D effect and using updated coefficients do not

improve the relative performance of these two accounting measures.

Our findings are consistent when relying on bond rating or credit spreads to assess risk. We

find similar results when relying on either a regression or decile approach, which should

mitigate a concern that we are not capturing some non-linearity in the regression analysis. The

results suggest that relying on either the Z- or O-score for distress risk is highly problematic,

and that there are easily calculated alternatives with notably greater power in capturing distress

risk.

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Table 1Summary Statistics

Panel A: Descriptive Statistics

Mean MedianStandardDeviation

25thPercentile

75thPercentile

Yield Spread (bps) 282.628 188.799 288.307 118.838 341.064Log (Spread) 5.276 5.181 0.751 4.729 5.788

Distress MeasuresMarket Leverage 0.399 0.377 0.208 0.232 0.546

Z Score -2.481 -2.292 1.447 -3.244 -1.439O Score -1.062 -1.176 1.432 -2.044 -0.231R&D Adj. Z Score -2.471 -2.285 1.432 -3.214 -1.445R&D Adj. O Score -1.098 -1.208 1.424 -2.084 -0.266Updated Z Score -4.564 -4.487 0.26 -4.634 -4.406Updated O Score -5.447 -5.469 0.556 -5.705 -5.199KMV DD -6.057 -5.798 3.333 -8.241 -3.562

Control VariablesMktCap ($B) 5.019 1.728 10.561 0.56 4.746Market-to-Book 1.865 1.49 1.303 1.021 2.22Volatility 0.369 0.318 0.188 0.246 0.428Maturity 15.795 13.072 8.51 9.17 23.949Rating BB BB- BBB+/B- B- BBB

Panel B: Industry Classifications

SICCode Industry Classification

No. ofObservations

Percentage(%)

Cumulative(%)

0 Agriculture 394 0.33 0.33

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Panel C: Selected Pearson Correlation

YieldSpread MarketLeverage Z-Score O-Score Merton-DD CHSScore

Market Leverage 0.565 1.000Z Score 0.363 0.677 1.000O Score 0.582 0.669 0.587 1.000KMV DD 0.656 0.602 0.422 0.571 1.000CHS Score 0.680 0.588 0.420 0.638 0.725 1.000R&D Adj Z Score 0.359 0.674 0.999 0.582 0.418 0.416

R&D Adj O Score 0.587 0.679 0.583 0.991 0.571 0.634

Up. Z Score 0.347 0.696 0.646 0.543 0.449 0.391Up. O Score 0.052 0.089 0.097 0.287 0.045 0.168MktCap -0.384 -0.298 -0.228 -0.363 -0.340 -0.280

Market-to-Book 0.037 -0.135 -0.148 0.247 -0.062 0.074Volatility 0.583 0.308 0.149 0.406 0.594 0.728Maturity -0.234 -0.099 0.062 -0.247 -0.270 -0.236Rating 0.776 0.552 0.354 0.621 0.686 0.611

Note: Our sample firms include all non-financial issuers in LBFI (198001-200612) with necessary CRSP and Compustat

information to compute distress measures and controlling variables. For firms with multiple issues only the one withgreatest maturity is selected so that each firm will only have one bond in the analysis. We remove AAA bonds andbonds with less than one-year to maturity. Z-Score is Altman (1968) and O-Score is Ohlson (1980) bankruptcymeasures. R&D Adj. Z-Score and Adj. O-Score are constructed by following Franzen et al. (2007) to adjust the R&Deffects for constituent variables. Up. Z-Score and Up. O-Score are constructed by using updated coefficients byHillegeist et al. (2004). DD is distance to default based on Merton (1974) structural model. CHS Score is thebankruptcy score based on the reduced form model by Campbell et al. (2010). The signs of the coefficients have beenchanged to original, adjusted, and updated Z Scores and Merton-DD so they are increasing in the probability ofbankruptcy. As a result, a greater value of all measures signifies higher probability of bankruptcy. Firm size ismarket equity cap. Market-to-book is the ratio of market equity to book equity. Volatility is the annualized 3-monthrolling standard deviation of daily stock returns constructed on by following Campbell et al. (2010). Rating is S&Pbond rating. Maturity is the number of years until bond maturity. All variables are winsorized at 1 and 99percentiles, and the time series average of their cross-sectional distributions is reported in Panel A. Panel B reportsthe number of firm-month observations for each of the 8 industries. Panel C reports Pearson correlations between

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Table 2Bond Ratings and Distress Measures

AA A BBB BB B

Market LeverageAll Periods 0.20 0.26 0.36 0.44 0.541980-1982 0.26 0.39 0.65 0.50 0.561983-1985 0.31 0.35 0.50 0.53 0.581986-1988 0.25 0.29 0.43 0.47 0.561989-1991 0.24 0.28 0.49 0.48 0.701992-1994 0.17 0.28 0.41 0.52 0.591995-1997

0.13

0.22

0.31

0.44

0.53

1998-2000 0.10 0.18 0.29 0.42 0.522001-2003 0.10 0.19 0.33 0.45 0.582004-2006 0.09 0.15 0.28 0.35 0.46

Z-ScoreAll Periods -3.24 -2.92 -2.17 -2.09 -1.751980-1982 -3.19 -2.91 -2.06 -2.57 -2.281983-1985 -2.78 -2.77 -2.16 -1.74 -1.91

1986-1988 -2.93 -2.86 -2.13 -1.90 -2.011989-1991 -2.82 -2.79 -1.79 -2.01 -1.711992-1994 -3.35 -2.62 -1.78 -1.82 -1.541995-1997 -3.72 -2.83 -2.29 -2.06 -1.701998-2000 -4.42 -3.15 -2.31 -2.19 -1.632001-2003 -4.79 -3.19 -2.16 -2.20 -1.422004-2006 -5.06 -3.11 -2.48 -2.14 -1.87

O-Score

All Periods -2.37 -1.83 -1.19 -0.72 0.101980-1982 -2.66 -2.10 -1.30 -0.55 0.061983-1985 -2.42 -1.91 -1.42 -0.82 0.081986 1988 2 11 1 72 1 35 0 66 0 18

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All Periods -8.25 -8.11 -7.89 -7.66 -7.271980-1982 -8.21 -8.13 -7.91 -7.61 -7.331983-1985 -8.28 -8.15 -7.96 -7.68 -7.411986-1988 -8.24 -8.11 -7.89 -7.64 -7.29

1989-1991 -8.25 -8.14 -7.84 -7.66 -7.031992-1994 -8.30 -8.08 -7.87 -7.51 -7.251995-1997 -8.31 -8.12 -7.91 -7.66 -7.251998-2000 -8.03 -7.85 -7.62 -7.26 -6.922001-2003 -8.24 -8.10 -7.86 -7.63 -7.142004-2006 -8.44 -8.33 -8.14 -7.98 -7.67

Note: This table reports the median distress measures during the entire sample period and nine sub-periods by majorrating categories.

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Table 3Credit Ratings, Industry and Distress Measures

A BBB BB B

Market Leverage

Mining & Construction 0.18 0.30 0.38 0.52Light Manufactured 0.22 0.33 0.44 0.56Heavy Manufactured 0.24 0.30 0.41 0.56Communications & Electric 0.43 0.50 0.57 0.55Wholesale & Retail Trade 0.25 0.32 0.44 0.57Business Service 0.19 0.28 0.49 0.52

Z-Score

Mining & Construction -4.15 -4.16 -2.64 -1.99Light Manufactured -4.04 -2.80 -2.45 -1.93Heavy Manufactured -3.26 -2.96 -2.67 -2.33Communications & Electric -1.65 -1.37 -1.23 -0.55Wholesale & Retail Trade -5.49 -4.74 -3.18 -3.61Business Service -2.89 -3.39 -1.30 -1.48

O-Score

Mining & Construction -3.87 -3.44 -2.70 -1.71Light Manufactured -2.63 -1.76 -1.67 -0.22Heavy Manufactured -2.47 -2.10 -1.87 -0.83Communications & Electric -2.44 -1.09 -0.85 0.11Wholesale & Retail Trade -3.05 -2.25 -1.68 -0.86Business Service -0.94 -2.40 -0.06 -0.41

Merton DD

Mining & Construction -9.45 -6.90 -5.55 -5.73Light Manufactured -14.38 -9.70 -7.47 -5.26Heavy Manufactured -12.23 -8.86 -6.87 -5.91

Communications & Electric -12.09 -10.95 -9.09 -4.66Wholesale & Retail Trade -14.58 -11.14 -5.48 -4.12Business Service -16.85 -13.80 -6.62 -6.94

CHS Score

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Table 4Decile Analysis

DecileMarket

LeverageZ-ScoreOriginal

Z-Score

R&DAdjusted

Z-ScoreUpdated

O-ScoreOriginal

O-Score

R&DAdjusted

O-ScoreUpdated DD CHS

Panel A Average yield Spread Across Deciles

1 126 130 130 131 134 126 308 100 1422 138 174 176 175 168 163 291 132 1443 174 201 200 171 203 194 233 161 1534 178 190 187 215 175 183 225 167 1665 237 236 237 181 219 217 190 206 1966 246 245 245 233 228 260 161 228 2067 245 291 277 249 234 225 160 275 233

8 229 259 277 234 257 255 167 285 2609 306 273 270 327 303 307 229 307 34810 429 378 378 464 457 450 418 519 531

Panel B Double Sorting Percentage Analysis1 50.9% 45.6% 45.2% 51.7% 50.7% 51.4% 11.0% 52.9% 45.5%2 57.1% 48.6% 48.9% 49.1% 53.5% 54.1% 24.4% 59.9% 56.7%3 43.5% 38.7% 38.9% 42.6% 44.6% 45.0% 28.5% 51.2% 46.2%4 42.0% 37.0% 37.1% 37.9% 44.8% 44.3% 36.2% 44.0% 42.2%5 40.6% 34.6% 34.8% 38.5% 40.1% 42.5% 37.5% 44.4% 40.5%

6 38.8% 33.9% 34.5% 40.0% 42.4% 42.3% 30.6% 44.1% 41.7%7 39.7% 33.9% 34.0% 37.3% 43.2% 42.5% 23.6% 50.0% 42.9%8 43.7% 35.7% 35.6% 43.8% 47.4% 48.3% 27.6% 60.3% 53.5%9 53.8% 37.4% 37.1% 57.9% 66.5% 66.6% 44.9% 72.3% 68.8%10 62.0% 50.8% 50.3% 55.4% 70.9% 69.8% 39.0% 73.0% 80.4%

Note: This table reports results based on single and double sorting. In Panel A, we sort firms into 10 deciles by each distress measure in June 2006 and compute theaverage yield spread for each decile. In Panel B, we sort firms into deciles based on each distress measure and also on credit spreads in June of each year. We thencompute the time-series average of the percentage of firms in the distress measure decile that are also in the same or the adjacent deciles based on credit spreadsorting.

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Table 5Credit Spreads and Distress Measures: Regression Analysis

MarketLeverage

AltmanZ-Score

OhlsonO-Score

MertonDD

CHSScore

Panel ADistress Measure 2.042 0.189 0.308 0.154 0.731

(t-stat) (38.15) (29.60) (33.23) (23.29) (38.83)

Adj. R-Squared 0.323 0.135 0.342 0.435 0.467Number of Firms 383 383 383 383 383

% Improvement n.a. -58% 6% 35% 45%

Panel BDistress Measure 1.957 0.196 0.294 0.15 0.711

(t-stat) (37.67) (29.82) (27.37) (23.36) (37.34)

Maturity -0.015 -0.022 -0.008 -0.005 -0.006(t-stat) (-11.10) (-12.88) (-3.28) (-2.23) (-3.14)

Adj. R-Squared 0.362 0.213 0.367 0.452 0.485Number of Firms 383 383 383 383 383% Improvement n.a. -41% 1% 25% 34%

Panel CDistress Measure 1.971 0.235 0.294 0.144 0.694

(t-stat) (39.81) (29.53) (31.09) (21.55) (34.02)

Maturity -0.011 -0.017 -0.004 -0.005 -0.004(t-stat) (-6.37) (-8.29) (-1.71) (-2.19) (-2.45)

Industry D.V. Included Included Included Included Included

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Table 6Regression with Fixed Firm and Year effects

MarketLeverage

Altman ZScore

Ohlson OScore Merton DD CHS Score

Panel A Firm and Industry Fixed effect

Distress Measures 1.709 0.249 0.286 0.131 0.683

t-stat (29.12) (22.6) (36.36) (40.25) (52.36)

Maturity -0.019 -0.022 -0.011 -0.011 -0.009

t-stat (-13.26) (-15.28) (-7.68) (-9.58) (-6.9)

Adjusted R-Squared 0.312 0.282 0.369 0.446 0.49

Number of Firms 10,306 10,306 10,306 10,306 10,306

% Improvement n.a. -10% 18% 43% 57%

Panel B Firm, Year, and Industry Fixed

Coef 1.811 0.246 0.288 0.134 0.679

t-stat (31.33) (23.8) (37.94) (38.2) (52.25)

Maturity -0.014 -0.02 -0.008 -0.008 -0.007

t-stat (-10.06) (-13.53) (-5.82) (-6.01) (-5.57)

Adjusted R-Squared 0.445 0.395 0.483 0.524 0.575

Number of Firms 10,306 10,306 10,306 10,306 10,306

% Improvement n.a. -11% 9% 18% 29%

Note: This table reports results for regressions with fixed effects using sample firms in June of each year. Panel Areports regression of log yield spread with fixed firm and industry effects. Panel B reports regression of log yield

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Table 7Regressions by Industry, Subperiods, Market Cap, Market-to-Book Ratio, and Volatility

Panel A. By Industry

Mining andConstruction

LightManufactured

HeavyManufactured

Communicationand Electronics

Whole and RetailTrade

BusinessService

Market Leverage 1.952 2.564 2.034 1.446 2.002 1.357t-stat 15.86 42.81 33.40 14.53 20.96 -7.62Adj. R-Squared 0.362 0.461 0.381 0.233 0.401 0.237

Z Score 0.267 0.236 0.267 0.256 0.195 0.187t-stat 5.28 24.23 22.28 11.85 16.16 -6.95Adj. R-Squared 0.267 0.233 0.237 0.197 0.253 0.197% Improvement -26% -49% -38% -15% -37% -17%

O Score 0.219 0.329 0.312 0.273 0.297 0.191

t-stat 9.06 23.29 34.66 25.27 16.71 -18.8Adj. R-Squared 0.318 0.383 0.381 0.31 0.384 0.187% Improvement -12% -17% 0% 33% -4% -21%

Merton DD 0.185 0.141 0.143 0.139 0.164 0.176t-stat 17.33 19.62 20.3 12.77 22.58 -10.03Adj. R2 0.449 0.441 0.409 0.399 0.489 0.435% Improvement 24% -4% 7% 71% 22% 84%

CHS Score 0.629 0.827 0.704 0.68 0.736 0.589t-stat 15.12 35.03 30.65 22.94 22.35 -10.06Adj. R-Squared 0.438 0.478 0.448 0.445 0.516 0.438

% Improvement 21% 4% 18% 91% 29% 85%

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Panel B Different Time Periods and Normal/Shock Macroeconomic Periods

1980-1989 1990-1999 1990-1999 Normal Shock

Mkt. Leverage 1.899 2.031 1.990 2.018 1.770t-stat (23.22) (27.68) (20.39) (38.3) (24.3)Adj. R-Squared 0.366 0.448 0.420 0.421 0.366

Z-Score 0.225 0.248 0.231 0.241 0.210

t-stat (20.56) (17.81) (15.56) (30.12) (13.98)Adj. R-Squared 0.248 0.331 0.299 0.297 0.270

% Improvement -32% -26% -29% -29% -26%O-Score 0.319 0.289 0.267 0.301 0.264

t-stat (17.16) (23.19) (30.67) (29.08) (19.46)Adj. R-Squared 0.440 0.429 0.340 0.423 0.355% Improvement 20% -4% -19% 0% -3%

Merton-DD 0.135 0.133 0.171 0.141 0.157

t-stat (16.89) (22.56) (10.08) (22.36) (8.18)Adj. R-Squared 0.391 0.495 0.561 0.479 0.453

% Improvement 7% 11% 34% 14% 24%

CHS Score 0.645 0.726 0.720 0.708 0.637

t-stat (18.04) (25.87) (21.86) (32.65) (17.49)Adj. R-Squared 0.422 0.557 0.584 0.508 0.539% Improvement 15% 24% 39% 21% 47%

Number of Firms 285 413 468 371 420

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Panel C. By Quartiles of Firm Size, Market-to-Book, and Volatility

Market Cap Market-to-Book VolatilityBottomQuartile

MiddleQuartiles

UpperQuartile

BottomQuartile

MiddleQuartiles

UpperQuartile

BottomQuartile

MiddleQuartiles

UpperQuartile

Mkt. Leverage 1.101 1.326 0.879 1.691 1.703 2.318 1.608 1.662 1.583

t-stat (9.66) (22.32) (11.31) (15.35) (23.17) (28.92) (23.66) (32.75) (19.43)Adj. R-Squared 0.225 0.253 0.258 0.388 0.325 0.496 0.296 0.336 0.316

Z-Score 0.177 0.160 0.085 0.190 0.165 0.274 0.164 0.174 0.226t-stat (7.81) (22.43) (6.78) (9.31) (18.7) (19.43) (14.94) (28.03) (13.27)Adj. R-Squared 0.191 0.204 0.231 0.283 0.203 0.416 0.211 0.209 0.239% Improvement -15% -19% -11% -27% -38% -16% -29% -38% -25%

O-Score 0.167 0.192 0.128 0.291 0.263 0.305 0.189 0.245 0.238t-stat (13.24) (27.12) (9.09) (21.6) (24.49) (28.1) (19.84) (22.33) (18.47)Adj. R-Squared 0.227 0.247 0.237 0.409 0.357 0.517 0.241 0.315 0.320% Improvement 1% -2% -8% 5% 10% 4% -19% -6% 1%

Merton-DD 0.166 0.099 0.049 0.169 0.113 0.159 0.070 0.118 0.247t-stat (11.75) (17.24) (10.01) (12.72) (19.65) (26.15) (13.61) (19.25) (18.71)Adj. R-Squared 0.366 0.321 0.275 0.488 0.361 0.546 0.265 0.330 0.471% Improvement 62% 27% 6% 26% 11% 10% -11% -2% 49%

CHS Score 0.443 0.557 0.383 0.666 0.661 0.686 0.606 0.653 0.558t-stat (17.23) (31.41) (16.56) (27.31) (30.9) (28.4) (19.86) (33.29) (22.9)Adj. R-Squared 0.446 0.318 0.257 0.571 0.370 0.550 0.252 0.298 0.467% Improvement 98% 26% 0% 47% 14% 11% -15% -11% 48%Number of Firms 95 191 96 95 191 96 96 191 96Note:In Panel A, we separate sample firms into 6 industries and conduct regression analysis within each industry. In Panel B, we separate sample firms into three

time periods (1980-1990, 1991-2000, 2001-2006) and into normal and shock macroeconomic periods, where shocks years include 1987 (stock market crash), 1989(real estate bubble), 1994 (high interest rates), 1997 (Asian financial crisis), 2000 (Internet bubble), and 2001 (9/11 incident), and normal years include all remainingyears, and conduct regression in each period. In Panel C, we first sort firms into four quartiles every month from 198001-200612 by market equity cap, market-to-book ratio, and equity volatility respectively and then conduct regression within each quartile of Q1 and Q4 and two quartiles of Q2 and Q3 together. In allPanels we control for maturity. In Panels B and C we also control for industry effect. We run cross sectional regression on distress measures and report the time-series average of coefficients and associated t-statistics (in the below parentheses) adjusted by Newey-West (1987) with lag 12. Also reported are the averageadjusted R-squared and the number of firms in the cross-sectional regression. Coefficients and t-statistics for intercept, maturity, and industry dummies are