The impact of diverse measures of default risk on UK stock returns

Journal of Banking & Finance 37 (2013) 5118–5131

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The impact of diverse measures of default risk on UK stock returns Jie Chen, Paula Hill ⇑ University of Bristol, 8 Woodland Road, Bristol BS8 1TN, United Kingdom

a r t i c l e

i n f o

Article history: Received 13 January 2012 Accepted 28 June 2013 Available online 23 July 2013 JEL classification: G32

a b s t r a c t A number of recent papers examine the relationship between default risk and equity returns, and the results are mixed. These studies employ different measures of default risk and we find that correlations between eight diverse measures of default risk tend to be less than 50%. Nonetheless, we find that the relationship between stock returns and diverse measures of default risk tends to be consistent; default risk is a significant determinant of stock returns and this relationship is ‘‘hump backed’’, as predicted by Garlappi and Yan (2011). Ó 2013 Elsevier B.V. All rights reserved.

Keywords: Default risk Credit rating Probability of default Stock returns

1. Introduction Default risk assessments allow those who lend and those who insure debts to accurately assess the risks to which they are exposed and thus whether and on what terms they are prepared to enter into a debt-related contract. More recently a number of papers have highlighted the relationship between default risk and equity returns, thereby widening the utility of default risk assessments to include equity investors. However, the results of studies on the relationship between stock returns and default risk leave the true relationship open to some doubt. Vassalou and Xing (2004) report that returns are highest to high default risk stocks,1 whereas Dichev (1998), Avramov et al. (2009) and Garlappi and Yan (2011) report that high default risk firms deliver lower stock returns than low default risk firms. Vassalou and Xing (2004) also present evidence that default risk is systematic and thus priced in stock returns, whereas Avramov et al. (2009) argue that the relationship between stock returns and default risk is driven by firms with low credit quality during periods of financial crisis, and outside this

⇑ Corresponding author. Tel.: +44 117 331 0532; fax: +44 117 928 8577. E-mail address: [email protected] (P. Hill). See Table III, page 845, Vassalou and Xing (2004). The returns to portfolios sorted by default risk show that returns are lowest to the portfolio in the lowest default risk quintile (decile) and highest to the portfolio in the highest default risk quintile (decile). 1

0378-4266/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jbankfin.2013.06.013

subset of stocks and time periods there is no relationship between stock returns and default risk.2 A number of authors report non-linear relationships between default risk and stock returns but the reported shape of this relationship is again inconsistent across studies. Vassalou and Xing (2004) find that in the presence of a book to market (BM) variable (but not a size variable) the relationship between stock returns and default risk is positive and non-linear with a minimum turning point (outside the range of feasible default risk values), after which as default risk increases, returns increase.3 By contrast, Garlappi and Yan (2011) report a ‘‘hump-backed’’ relationship between stock returns and default risk: as default risk increases so do stock returns up to a maximum turning point, and thereafter returns decrease. The portfolio results of Dichev (1998) also support this ‘‘hump-backed’’ non-linear relationship, but Dichev fails to account for non-linearities in his regression analysis. Garlappi and Yan (2011) seek to explain the ‘‘hump-backed’’ relationship between default risk and stock returns by suggesting that provided that shareholders are able to recover some of their investment when firms are under financial distress, after distress reaches a certain point, firms are able to lower their gearing via debt rescheduling and thus returns decrease. 2 In related work, Chava and Purnanandam (2010) focus on the implications of using ex-post rather than ex-ante returns. Employing expected stock returns they conclude that there is a significant positive risk premium for high default risk stocks. The calculation of expected returns is not without its problems and in this paper we focus on the (larger) body of work which employs ex-post returns. 3 They find that firm size is not a significant determinant of stock returns in the presence of default risk. These results are from regressions based on individual equity returns. See Table IX, page 858, Vassalou and Xing (2004).

J. Chen, P. Hill / Journal of Banking & Finance 37 (2013) 5118–5131

The first aim of this paper is to examine the extent to which diverse measures of default risk give rise to inconsistent empirical results for the relationship between default risk and stock returns. In light of this we comment on the mixed results reported in prior studies. Fiordelisi and Marqués-Ibañez (2013) suggest that mixed results for the relationship between bankruptcy risk and systematic risk might be due to the variety of measures employed to capture bankruptcy risk. Measures of default risk employed in the above-cited studies vary from the credit ratings of Standard & Poor’s (S&P) (Avramov et al., 2009) to default probabilities derived from contingent claim models based on the theories of Black and Scholes (1973) and Merton (1974) (Vassalou and Xing, 2004; Garlappi and Yan, 2011) to accounting-based models of bankruptcy (Dichev, 1998). Most of the papers which test the relationship between default risk and stock returns employ only one measure of default risk. Our second contribution is a comparison of the default risk assessments of the leading credit-rating agencies (CRAs) with those which arise from leading academic models, to determine the extent of agreement between alternative assessments of default risk. Even where default risk measures appear similar, such as those based on the theories of Black and Scholes (1973) and Merton (1974), we show that different assumptions can lead to divergent assessments of default risk. Throughout this paper we employ the term ‘‘default risk’’ to refer to the probability of default (PD)/failure/bankruptcy and credit ratings (which may incorporate both the PD and the loss given default (LGD)). We look at firms listed on the London Stock Exchange where the relationship between stock returns and default risk has not yet been analysed. The London Stock Exchange is of interest to investors worldwide. The UK Office of National Statistics (2012) estimates that at the close of 2010, 41.2% of shares listed on the London Stock Exchange (representing investments worth £732.6 billion) were owned by investors from outside the UK, of which European investors held 28% and North American investors 56%. The default risk assessments of the leading CRAs have recently been called into question in the wake of the ongoing financial crisis where inaccurate assessments of the default risk of a number of collateralised debt instruments came to light in 2007. A potential lack of trust in the rating assessments of the CRAs is not new; Pinches and Singleton (1978) report that ‘‘In recent years bond rating agencies have been under increasing scrutiny because of their obvious failures to accurately predict and warn investors of impending firm-related financial difficulties’’ (page 29). Although the CRAs have clearly made significant errors, the question we consider is whether their corporate default risk assessments disagree with those based on academic models. A substantial academic literature exists on the modelling of default and/or bankruptcy and/or corporate failure, yet relatively few of these publicly available assessments of credit quality have been employed out of sample in academic studies to determine whether the default risk assessments of these models tend to agree with those of the CRAs.4 This would provide useful information about both credit ratings and alternative assessments of default risk readily available to investors. We compare the credit-rating assessments of the two leading CRAs, S&P and Moody’s, and the default risk assessments generated by the following academic models: ‘‘z-score’’ models

4 Löffler (2004) compares ratings-based assessments of default risk with marketbased assessments derived from the theories of Black and Scholes (1973) and Merton (1974). Agarwal and Taffler (2008) compare z-score-based assessments of default risk with market-based assessments. A number of academic authors and practitioners have employed the model of Altman (1968) out of sample (see, inter alia, Dichev (1998)).

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of Altman (1968) and Taffler (1977) – this latter is set out in the papers of Taffler (1984) and Agarwal and Taffler (2008); multi-period logit (discrete time hazard) models of Campbell et al. (2008), and Chava and Jarrow (2004); a Cox proportional hazards model with time-varying covariates from Bharath and Shumway (2008); contingent claims models derived from the theories of Black and Scholes (1973) and Merton (1974), from the papers of Hillegeist et al. (2004) and Bharath and Shumway (2008). We follow Hillegeist et al. (2004) by terming these BSM models. We begin our analysis by examining the relationship between various measures of default risk from both our selected academic models and the credit ratings of S&P and Moody’s. We find considerable variation in the mean PD across our academic models. However, we are more interested in relative rather than absolute measures of default risk. We find that correlations between the measures of default risk are significant at the 1% level and yet tend to be less than 50%. Given these relatively low correlations between default risk assessments, investors in UK-listed firms might be left in some doubt as to the true relative default risk of a firm. Of the academic models, the Altman z-score model has the highest correlation with Moody’s and S&P ratings, which given the accounting ratio-based nature of the Altman model suggests a relatively high reliance on ratios in the default risk assessments of the CRAs. Despite the fact that correlations between different measures of default risk tend to be less than 50%, our analysis of the relationship between default risk and stock returns tends to produce consistent results. We find that default risk is a significant determinant of stock returns for all measures of default risk employed, in addition to size and BM, and we tend to find that this impact is nonmonotonic; as default risk increases, so do returns up to a maximum turning point, after which returns decrease, which is the ‘‘hump-shaped’’ relationship predicted by Garlappi and Yan (2011).5 In general we find little evidence that differences in the conclusions of previous studies about the relationship between stock returns and default risk can be attributed to the different models of default risk employed, since there is reasonable consistency in the empirical results of the relationship between stock returns and default risk across diverse measures of default risk. We make further comment on one specific case: Vassalou and Xing (2004) employ a BSM model with the same assumptions as the model of Bharath and Shumway (2008) employed in this paper. Vassalou and Xing (2004) argue that their measure of default risk does not differ significantly from the Moody’s KMV measure employed by Garlappi and Yan (2011),6 and Garlappi and Yan argue that their results differ from those of Vassalou and Xing on account of portfolio-selection procedures, namely that much of Vassalou and Xing’s analysis is based on quintiles rather than the deciles employed in Garlappi and Yan. However, Vassalou and Xing also report returns sorted by default risk deciles (see Table III, page 845, Vassalou and Xing, 2004), and these suggest a monotonic increase in returns as default risk increases. This left open the possibility that a difference in the default risk measure might, at least in part, explain the different results. However, when we employ the same default risk measure as Vassalou and Xing (2004), our results confirm those of Garlappi and Yan (2011) and we find no evidence that the differ5 While the relationship between default risk and stock returns is found to be nonlinear for the academic measures of default risk, this is not the case for the CRAs’ measures of default risk, although in the case of Moody’s the coefficient on the squared default risk variable approaches significance at the 10% level, which would again suggest that as default risk increases (rating decreases), returns increase up to a maximum turning point after which returns decrease. 6 ‘‘the difference between our measure of default risk and that produced by KMV is not material for the purpose of our study’’ (page 837, Vassalou and Xing, 2004).

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ence in results between these two studies is driven by a difference in default risk measurement. For all measures of default risk, the relationship between default risk and stock returns holds after controlling for very high default risk firms, which contrasts with the findings of Avramov et al. (2009) that the relationship between stock returns and default risk is driven by firms with low credit quality. A separate analysis of firm-years with the highest default risk leads us to qualify our support for the model of Garlappi and Yan (2011). The mean equity returns across this very high default risk sub-sample are very sensitive to the measure of default risk employed. Even default risk models which appear to be similar, such as the two BSM models we employ, give markedly different conclusions about the relationship between returns and default risk across the subset of firm-years with the highest default risk. However, this analysis is limited by the size of the sub-sample of very high default risk firm-years and these findings are primarily useful to alert investors to the potential variability in defaultrisk assessments under different models at the level of the individual firm. The remainder of our paper proceeds as follows. Section 2 outlines the various methodologies employed in leading academic papers for calculating default risk. In Section 3 we evaluate the differences which might emerge between the default risk measures of academic models and the default risk assessments incorporated in credit ratings on theoretical grounds. In Section 4 we summarise our data. In Section 5 we analyse the relationship between different measures of default risk. Section 6 presents our analysis of the relationship between default risk and stock returns. Section 7 concludes.

2. Academic models of default risk Academic studies focus almost exclusively on quantitative analyses of the probability of corporate failure or default. Default-risk models in the academic literature are commonly characterised as either reduced form or structural (see, inter alia, Bharath and Shumway, 2008). Duffie and Singleton (2003) also characterise default risk models by methodological approach (duration vs. qualitative response vs. discriminant analysis). The qualitative response models and discriminant models discussed in Duffie and Singleton (2003) are assumed to be single-period models and are referred to by Shumway (2001) as ‘‘static’’ models of default risk (the alternative being a multi-period model), giving an alternative characterisation of ‘‘static’’ (single-period qualitative response and discriminant models) and ‘‘non static’’ (duration models). Finally, default-risk models have been characterised by the extent to which they incorporate market-based data (see Hillegeist et al., 2004). As set out in the Introduction, we apply four categories to our academic models: (i) z-score models; (ii) discrete time hazard models; (iii) Cox proportional hazards (ph) models; (iv) contingent claim models based on the theories of Black and Scholes (1973) and Merton (1974) (BSM). In Table 1 we provide an overview of the model categorisations employed in different studies and of the relationship between these categorisations. Readers are referred to the cited literature for a detailed discussion of the model types. Details of the models we employ are given in Table 2, where we undertake a ‘‘within category’’ comparison. We follow the methods set out in each of the papers from which our models are taken,

Table 1 Summary of academic models employing reconciliation of categorisations of default models. z-score

Discrete hazard

Cox ph

BSM

Description

Accounting data

Market data

Market data

Market data

Market vs. accounting data  BSM-type models are assumed to be more heavily reliant on market data than hazard models, which incorporate a wider range of accounting data. Bharath and Shumway (2008) employ a ‘‘hybrid’’ model which incorporates a BSM-type model output as one input into the Cox ph model  Market-based models are heavily reliant on an efficient market; in the BSM model as the market value of equity decreases, the PD increases  Accounting-based models suffer from problems related to historical data, accounting policy conventions and managerial discretion

na

Reduced form

Reduced form

Structural

Structural vs. reduced form  Structural models are theoretically derived from the theories of Black and Scholes (1973) and Merton (1974). Default occurs when the market value of a firm’s assets falls below a certain threshold (e.g. the face value of its liabilities) at a point in time  Reduced form models assume that default time is inaccessible and governed by an intensity process dependent on the current state variables, with the choice of variables being empirically derived. Intensity models are often referred to as duration or hazard models  Jarrow and Procter (2004) argue that structural models assume that the modeller has the same information set as the firm’s managers – that is, complete knowledge of firm asset values and liabilities – whereas reduced form models assume that the modeller has the same information set as the market

Static

Non-static

Non-static

na

Static vs. non-static  Non-static multi-period models observe each firm at risk of bankruptcy in each period  Static models are single-period models in which data for the sample firms are observed only once, despite the samples spanning several years. The probability of bankruptcy for any one firm from such a model is time invariant  Bias and inconsistency in the estimation of the model parameters via a static logit model arise from a misspecified maximum likelihood function which fails to consider the firms at risk of bankruptcy in each period (Shumway (2001))  Multi-period models would also be preferred over static models on the grounds of efficiency since they utilise data available for each firm at each point in time rather than excluding all but 1 year of data

Discrete time hazard

Altman (1968) Z = 1.2WC/TA + 1.4RE/TA + 3.3EBIT/TA + 0.6MV/TL + 0.999S/TA Inputs: WC/TA is working capital to total assets; RE/TA is retained earnings to total assets; EBIT/TA is earnings before interest and tax to total assets; MV/TL is market value of equity to total liabilities; and S/TA is sales to total assets

z-score

log[pi/(1  pi)] = 8.2221 + 0.2138NITA + 2.2177TLTA  1.658EXPERT  0.2237RSIZE + 0.9524SIGMA  0.8231IND2  0.1790IND3  0.1602NITA ⁄ IND2 + 0.9717TLTA ⁄ IND2  2.7675NITA ⁄ IND3  0.4049TLTA ⁄ IND3 Common inputs: SIGMA is the standard deviation of each firm’s daily stock return; RSIZE is the natural log of a firm’s market capitalisation divided by that of an index Campbell et al. inputs: NIMTA is the ratio of net income to the market value of total assets (NIMTAAVG is geometric average); TLMTA is total liabilities to the market value of total assets; LNEXRET is the monthly log excess return on each firm’s equity relative to an index (LNEXRETAVG is the lagged geometric average); CASHMTA is a firm’s cash and short-term assets to the market value of its assets; MB is the market to book value; PRICE is the log of price per share winzorised above $15 Chava and Jarrow inputs: NITA is net income to the book value of total assets; TLTA is (the book value of) total liabilities to total assets; EXRET is the monthly return on the firm minus the index return; IND1 is miscellaneous industries; IND2 is manufacturing and minerals; IND3 is transportation, communications and utilities

Chava and Jarrow (2004), ‘‘public firm model with industry effects’’ (Table 3, page 556)

log[p1/(1  pi)] = 9.16Constant  20.26NIMTAAVG + 1.42TLMTA  7.13LNEXRETAVG + 1.41SIGMA  0.045RSIZE1  2.13CASHMTA + 0.075MB  0.058PRICE

Campbell et al. (2008), 1-year horizon, Table IV (model labelled 12), page 2913

Inputs: PBT/CL is profit before tax to current liabilities; CA/TL is current assets to total liabilities; CL/TA is current liabilities to total assets; and NOCRED is the no-credit interval computed as (quick assets  current liabilities)/((sales  PBT  depreciation)/365)

Taffler (1977) Z = 3.20 + 12.18PBT/CL + 2.50CA/TL  10.68CL/TA + 0.029NOCRED

Models

Group

Table 2 Summary of academic models employing within-category comparison.

(continued on next page)

NIMTA vs. NITA; LNEXRET vs. EXRET and TLMTA vs. TLTA; the Campbell et al. model employs market values and geometric averages in place of book values in the C&J model No equivalent of CASHMTA appears in the C&J model The C&J model reflects their argument that different industries face different levels of competition and may have different accounting conventions. Thus the probability of bankruptcy may differ for firms in different industries with otherwise identical balance sheets

Dependent variables Campbell et al. (2008) – ‘‘failure’’ which incorporates financially driven delistings, ‘‘default’’ rating, bankruptcy Chava and Jarrow (2004) (C&J) – ‘‘bankruptcy’’ (filings under either Chapter 7 or Chapter 11 of the bankruptcy code) The Campbell et al. model estimates failure probability over a 1-month period and the coefficients are not directly comparable with the C&J model in which estimates of bankruptcy are over a 1-year horizon Explanatory variables SIGMA is calculated employing the last 3 months of daily returns (Campbell) and 60 days (C&J) RSIZE is relative to the value-weighted S&P 500 index, measured with a 1-year lag (Campbell) and the NYSE/AMEX market value (C&J)

Dependent variables Altman (1968) – Bankruptcy, defined as filing for a ‘‘bankruptcy petition under Chapter X of the National Bankruptcy Act’’ (page 593) Taffler (1977) – Not provided in available references but employed in Agarwal and Taffler (2008) to forecast firm failures where failure is defined as entry into administration, receivership or creditors’ voluntary liquidation procedures (page 1543) Explanatory variables The selected ratios for the model of Altman (1968) reflect a firm’s working capital position, profitability, gearing and efficiency (with which assets are used to generate sales). Unlike the model of Altman (1968), the model of Taffler (1977) includes no measure of profitability (profit or sales generated by assets) nor gearing (equity to longterm debt), and in place of these measures there is a greater focus on working capital (current assets and liabilities)

Comparison

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ld pffiffi rA T

A 2

r2

T

A

 1

where N(.) is the cumulative density function of the standard normal distribution (under the Merton (1974) model the natural log of future asset values at any time has a normal distribution) Inputs: V is the (market) value of assets; X is the book value of liabilities; l is the continuously compounded expected return on assets; d is the continuous dividend rate (not applicable in Bharath and A Shumway model); and r is the standard deviation of future asset values. VA and rA are derived from the value and standard deviation of equity (VE and rE) A

The BSM default probability (with dividends) is given by Pr :def ¼ N @



Hillegeist et al. (2004), Bharath and Shumway (2008)

BSM lnðV A =XÞþ

Bharath and Shumway (2008). Model 7, Table 3, page 1355 In the absence of knowledge about the baseline hazard rate we employ the above model to compute an estimated risk score: RiskScorei(t) = 1.526Prnaive  0.255 ln (VE)  0.269 ln (X)  0.518/rE  0.834(EXRET)  0.044NITA Inputs: Prnaive is PD via a simplified BSM model (see Bharath and Shumway (2008)); ln(VE) and ln(X) are the natural logs of market value of equity and book value of debt, respectively; 1/rE is the inverse of the volatility of returns on equity, measured with daily data over the previous year; EXRET is the stock’s return over the previous year minus the market return over the same period; and NITA is the ratio of net income to (the book value of) total assets

Cox proportional hazards (ph)

0

Models

Group

Table 2 (continued)

The risk score contains both market and accounting-based variables. It is compared with the BSM models and the discrete time hazard models Dependent variable Firm defaults (from default databases of Edward Altman and Moody’s (see page 1351)) Explanatory variables The model contains the output of a BSM-type model as an explanatory variable in addition to further market- and accounting-based variables. Market-based variables are VE and rE (common to BSM and discrete time hazard models) and EXRET (common to the discrete time hazard). Accounting-based variables are X (common to BSM model) and NITA (common to discrete time hazard model) Dependent variables The estimation of the BSM-based contingent claims models is invariant to assumptions made about what the outputs represent. The outputs are assumed to represent the PD (Bharath and Shumway, 2008 (B&S)) - or the probability of bankruptcy (Hillegeist et al., 2004 – hereafter below (H) (2004)) Explanatory variables d: In H (2004) the formula relating the value of a firm’s assets to its equity allows for the fact that dividends accrue to equity holders (vs. no adj. in B&S) l: set to a minimum of the risk-free rate in H (2004) vs. no minimum in B&S rA: In H (2004) the market value and standard deviation of assets (VA and rA) are calculated from the simultaneous solution of equations which relate these to the market value of volatility of equity (VE and rE). For the model of B&S the market value of each firm’s assets is inferred every day for the previous year. The log return on assets each day is calculated from the daily values of each firm’s assets and then the returns series is employed to generate new estimates of rA and l. X: Equals short-term debt plus half of long-term debt in B&S vs. the book value of total liabilities in H (2004)

Differences

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J. Chen, P. Hill / Journal of Banking & Finance 37 (2013) 5118–5131

which are not repeated here, and similarly the inputs to each model follow those of the original papers (including winzorisation of variables). However, in place of all stock-market indices we employ the FTSE All Share index. Further variations in the input variables are discussed below. The version of Altman’s (1968) z-score model which we employ is that reported in Hillegeist et al. (2004) and Shumway (2001) in which all of the coefficients other than S/TA are multiplied by 100. A prominent UK-based model is set out on page 1544 of Agarwal and Taffler (2008). The model details are given in Taffler (1984) under the heading ‘‘Taffler, 1977’’ and we refer to this model as ‘‘Taffler, 1977’’. Where profit before tax is negative, this value is set to zero for the calculation of the PBT/CL variable (following Purda, 2007; Blume et al., 1998). Our selected discrete time hazard models are the model for a 1-year horizon as per Table IV (model labelled 12) of Campbell et al. (2008; page 2913),7 and the ‘‘public firm model with industry effects’’ (Table 3, page 556) from Chava and Jarrow (2004). We modify the average of NIMTA in the model of Campbell et al. (2008) to allow for the fact that our accounting data are annual rather than quarterly.8 Further, unlike the NYSE there is no minimum share price threshold on the London Stock Exchange and we therefore set the value of the variable PRICE to (the log of) 15 for all of our companies. We select Model 7 (Table 3, page 1355) of Bharath and Shumway (2008) as our proportional hazards model. Cox (1972) proposed employing a partial likelihood function to estimate the proportional hazards model such that the regression coefficients (bs) can be estimated without knowledge of the baseline hazard function. However, the baseline hazard function is required to produce the hazard rate for any one particular firm at a point in time, and in its absence we employ the proportional hazards model to compute an estimated risk score, as shown in Table 2. The risk score is only meaningful as a measure of the relative PD. Across our sample the risk score ranges from 5.47 to 3.08 with an average of 1.68. We outline the estimation of values for two sample firm-years at either end of the spectrum. Firm A (B) has the following input values and risk score: Prnaive = 1.18  1032 (0.85), ln(E) = 22.53 (13.63), ln(F) = 21.26 (14.72), 1/rE = 6.39 (1.17), rit1  rmt1 = 0.03 (0.24), NITA = 0.11 (0.13), Risk Score = 3.36 (1.37). Firm-years which have a higher expected risk of default have higher (positive) values while those with a lower expected risk of default have lower (negative) values. We employ two methods based on the theories of BSM to calculate the PD/bankruptcy, being the methods of, inter alia, Hillegeist et al. (2004) and Bharath and Shumway (2008).9 In the BSM-based models the continuously compounded risk-free rate is given by the UK Treasury bill rate rather than the US Treasury bill rate.

7 The result from the above model is the probability of failure in 12 months, conditional on survival for the first 11 months, which of course is different from the cumulative probability of bankruptcy during the entire 12 months. Campbell et al. (2008) also produce a model which gives the probability of bankruptcy in the next month, and we also calculate, but do not report, the probability of bankruptcy employing this model. Results are qualitatively similar and are available from us on request. 8 Thus we calculate NIMTAAVG with geometrically declining weights using 3 years of annual data as follows:

NIMTAAVGt1;t3 ¼

1 0:5 0:25 NIMTAt1 þ NIMTAt2 þ NIMTAt3 : 1:75 1:75 1:75

9 The key inputs into the market-based BSM models are the face value of debt and the market value and volatility of equity. The value and volatility of assets are derived from these last two via the following models (with dividend adjustment):

V E ¼ V A edT Nðd1 Þ  XerT Nðd2 Þ þ ð1  edT ÞV A , wher e d1 ¼ pffiffiffi dT 1 Þ rA . d2 ¼ d1  rA T rE ¼ V A e VNðd E

lnðV A =XÞþ½rdþðr2A =2Þ pffiffi rA T

T

and

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Differences in financial reporting practices may mean that models of default risk derived from US accounting data are not readily applicable to UK companies (the BSM models, which have a theoretical derivation, can be readily applied to UK companies by using UK data). Across the rated UK-listed companies in our sample, default and failure are rare events. As such, we address the issue of the extent to which the models of default risk derived employing US accounting data can be applied to assess the default risk of UK-listed firms by looking at the relationship between accounting variables and default risk in an alternative context. A number of academic papers build rating models for US companies based on accounting and market data (see, inter alia, Blume et al., 1998; Purda, 2007). Employing the model of Purda (2007) we find that the accounting variables of UK companies tend to be related to rating scores in the same manner as US companies, as reported in Purda (2007), and we therefore find no evidence of material differences between UK and US accounting numbers. These results are available from us on request. 3. Default risk assessments of the leading CRAs S&P and Moody’s are the two leading CRAs. In this paper we focus on the default risk of a corporation and thus on the ratings assigned to corporate issuers of debt (ratings by both CRAs are assigned to both debt issues and to issuers). In the case of Moody’s the issuer rating is set equal to the (estimated) senior unsecured debt rating. We argue that credit ratings might give a different assessment of default risk to leading academic models due to several factors: (i) The ratings assignments of S&P are designed to reflect the probability that a borrower will default on a loan (the PD), and the individual bond ratings of Moody’s are designed to reflect both the PD and the LGD, this latter being based upon the seniority of the debt and any securitisation.10 As set out in Section 2, the approach to modelling default risk in academic papers has tended to rely on an assessment of the probability of bankruptcy or failure (often as a proxy for the PD). However, more recently, academic studies have modelled the PD (e.g. Bharath and Shumway, 2008). (ii) Ratings-based measures of default cluster firms into a limited number of rating bands. (iii) CRAs focus on both quantitative and qualitative measures of default risk (see, inter alia, Blume et al., 1998), whereas academic models focus on quantitative measures of default risk. (iv) Credit ratings are designed to be ‘‘through the cycle’’ rather than point in time – that is, to reflect permanent (longerterm) changes in the creditworthiness of a company rather than shorter-term changes (see Löffler, 2004). Further, CRAs need to ensure that their ratings are timely and yet do not destabilise markets. Hill and Faff (2010) argue that ‘‘the rating agencies tread a fine line between downgrading debt either ‘too early’ or ‘too late’, both of which have been argued to contribute to a worsening of debt crises’’ (page 1310). Academics are not constrained by the fact that their rating assessments might destabilise markets, and academic models of the PD (often proxied by the probability of bankruptcy or failure) are point-in-time estimates based on the latest data available. However, in the case of accounting numbers, these data may be updated only once a year.

10 Güttler and Wahrenburg (2007) argue that this will create a divergence between the ratings of the two CRAs, particularly for ratings which are sub-investment grade (below BBB/Baa) where ‘‘LGD considerations become much more relevant’’ (page 756).

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Table 3 Sample details for 716 UK firm-years with complete data for academic models (i) rated by both S&P and Moody’s, (ii) rated by S&P only and (iii) rated by Moody’s only. Year

Rated by S&P and Moody’s

Rated by S&P only

Rated by Moody’s only

Total

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

9 11 22 35 39 44 51 54 51 46 41 39 38

1 2 7 9 7 11 9 9 12 14 17 15 15

5 7 8 8 8 9 8 9 11 10 9 8 8

15 20 37 52 54 64 68 72 74 70 67 62 61

Totals

480

128

108

716

608 firm-years are rated by S&P and 588 firm-years by Moody’s. Throughout the paper the ratings are read at the accounting year end. There was a temporary withdrawal of the rating of two firms rated by Moody’s at a year end point when we examine the rating and two firm-years had a default rating from S&P. These firmyears are excluded from our analysis and do not appear in the table below.

Table 4 Summary statistics for input values of default risk models. Variable

Mean

Max

Min

Original mean

Agarwal and Taffler (2008) – z-score model PBT/CL (GBP m) 0.286 0.287 CA/TL 0.496 0.295 CL/TA 0.325 0.157 NOCRED 138.915 162.104

2.963 4.394 1.471 432.952

0.000 0.027 0.012 2815.413

na na na na

Altman (1968) – z-score model WC/TA 0.002 RE/TA 0.105 EBIT/TA 0.320 MV/TL 0.988 S/TA 0.867

0.849 2.063 1.366 10.768 7.327

1.586 4.882 0.520 0.006 0.000

0.177 0.136 0.083 1.439 1.700

Campbell et al. (2008) – Discrete NIMTA 0.029 NIMTAAVG 0.029 TLMTA 0.446 LNEXRET 0.004 LNEXRETAVG 0.002 RSIZE (1) 6.434 SIGMA3month 0.359 CASHMTA 0.049 MB 3.152 PRICE 2.708

SD

0.174 0.636 0.240 0.918 0.528

hazard/multi-period logit model 0.021 0.109 0.160 0.017 0.108 0.109 0.126 0.987 0.003 0.078 0.145 0.168 0.038 0.134 0.316 1.011 5.535 13.607 0.207 1.077 0.066 0.028 0.383 0.000 2.158 8.200 0.196 2.708 2.708 2.708

0.000 na 0.445 0.011 na 10.456 0.562 0.084 2.041 2.019

Chava and Jarrow (2004) – Discrete hazard/multi-period logit model NITA 0.044 0.105 0.277 1.144 na TLTA 0.691 0.230 2.060 0.015 na EXRET 0.066 0.351 2.265 0.807 na RSIZE 5.958 1.405 4.420 14.425 na SIGMA60day 0.363 0.226 1.782 0.000 na Bharath and Shumway below) rit1  rmt1 (%) NITA Pr.naïve (%)

(2008) – Cox proportional hazards model (VE, rE, X as 8.08 0.04 6.26

35.76 0.11 18.25

274.12 0.28 99.99

101.79 1.14 0.00

8.69 1.08 8.95

BSM models – Hillegeist et al. (2004), Bharath and Shumway (2008) VE (GBP/USD m) 11102.06 20520.30 209764.10 0.83 808.80 rE (%) 34.52 17.81 177.59 1.83 82.07 VA (H) – derived (GBP 17903.99 29105.59 219831.27 3.36 na m) 1072.33 VA (BS) – derived (GBP/ 15780.50 25667.00 170498.24 3.67 USD m)

Table 4 (continued) Variable

Mean

SD

Max

Min

Original mean

X (H) (GBP m) X (BS) (GBP/USD m) rA (H) – derived (%) rA (BS) – derived (%) r (%) d (%) l (H) – derived (%) l (BS) – derived (%)

7081.89 4577.21 18.52 23.49 4.28 1.99 14.86 1.53

10864.53 6825.80 9.49 10.36 1.55 1.80 18.37 18.43

93248.37 53789.63 108.88 87.84 7.50 30.69 100 127.25

2.60 2.47 0.24 1.00 0.39 0.00 0.39 83.04

na 229.92 na 56.00 6.46 na na 3.25

We supply details of the mean input variables for the models we employ. Our sample mean values are in all cases based on 716 firm-years for UK non-financial listed firms. Where available we also supply the input values for the original models. No input values are available for the BSM models of Hillegeist et al. (2004), the z-score model of Agarwal and Taffler (2008) and the multi-period logit model of Chava and Jarrow (2004). ‘‘GBP/USD m’’ reflects the fact that our mean is in millions of GBP whereas the mean in the original model is in millions of USD. The suffix (H) means that the value is based on the method of Hillegeist et al. (2004) and the suffix (BS) means that the value is based on the method of Bharath and Shumway (2008). Variable definitions are given in Table 2. na = not available.

(v) Moody’s and S&P have access to much richer data on corporate default. For example, Vassalou and Xing (2004) indicate that Moody’s KMV has access to a database containing over 100,000 firm-years of data with 2000 incidences of default. Under the contingent claims method outlined in Section 2, to calculate a default probability it is necessary to make an assumption about the distribution of default probabilities. The CRAs are able to empirically determine the distribution of defaults given their rich data on corporate default histories. Academics rely on an assumption that defaults are normally distributed when estimating default probabilities via the BSM models. 4. Data Our sample is UK non-financial firms listed on either the Main or the AIM markets of the London Stock Exchange for which both accounting data and ratings data are available. Our sample is restricted by the number of UK firm-years rated by either S&P or Moody’s and we have a final sample of 716 firm-years for the period 1997–2009. Table 3 gives details of our sample by year. The number of firm-years increases from 1997 (15 firm-years) to 2005 (74 firm-years) before declining again (61 firm-years) in 2009. Table 4 gives statistics for the input variables of our models across both our sample of 716 firm-years and samples employed in the original studies. For each firm we calculate the input values at the accounting year end.11 From Table 4 it is evident that our sample firm-years are on average larger with less volatile equity than the firm-years in the studies from which the models of default risk are derived. This is not surprising since most models of corporate default or failure include non-listed firms where default/failure are more common. It is worth noting the different mean input values for the two models based on the theories of BSM. Under the Bharath and Shumway BSM model the value of debt is short-term debt plus half of long-term debt (average £4577 m), whereas under the Hillegeist et al. BSM model it is the value of total liabilities (average £7082 m). Thus for this input value, ceteris paribus, the average 11 23 firms go onto delist within our sample period. We calculate our default measures up to the last accounting date before delisting for 12 firms. For 11 firms, data are only available up to the year before this and we thus calculate our default measures up to the date of the last available accounting data. One firm delists owing to financial restructuring, two firms delist due to buy-out and 20 delist due to merger and acquisition.

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J. Chen, P. Hill / Journal of Banking & Finance 37 (2013) 5118–5131 Table 5 Average default risk assessments of academic models: original samples vs. sample employed in this paper.

z-score Agarwal & Taffler z-score Altman Multi-period logit Campbell et al. Multi-period logit (Variation) Campbell et al. Multi-period logit Chava & Jarrow Cox ph Bharath & Shumway BSM Hillegeist et al. BSM Bharath & Shumway

Mean

SD

Min

Max

Original mean

Risk

0.4643

0.4017

0.0000

1.0000

0.2633

Prob. of failure

0.1406

0.1243

0.0000

0.9313

0.1539 (calculated)

Prob. of bankruptcy

0.0004

0.0009

0.0001

0.0167

na

Prob. of failure

0.0005

0.0024

0.0000

0.0574

0.0007

Prob. of failure

0.0100

0.0314

0.0001

0.6254

na

Prob. of bankruptcy

1.6715

1.1401

3.0826

5.4689

0.4258 (calculated)

Risk score

0.0096

0.0501

0.0000

0.7889

Prob. of bankruptcy

0.0423

0.1444

0.0000

0.9993

0.0561 (solvent) 0.2476 (bankrupt) 0.1095

Prob. of default

The above table provides the output statistics from our default risk models and compares the average default risk value across our sample with that across the original sample. The risk value calculated is described in the far right-hand column using the wording of the original paper (other than in the case of the Cox ph model). An average default risk value is not provided in the original papers for the proportional hazards (ph) model of Bharath and Shumway (2008) and the multi-period logit models of Chava and Jarrow (2004) and Campbell et al. (2008). In the case of the model of Bharath and Shumway (2008) we are able to calculate a ‘‘risk score’’ for their ph model by employing the mean values of their input data. This risk score is similar to that calculated by Hill et al. (2010) and is only meaningful relative to other firms’ risk scores under this ph model. Campbell et al. (2008) do not provide data for the mean values of two variables in their model (NIMTAAVG and EXRETAVG) but they do provide data for NIMTA and EXRET. We therefore report a mean value employing NIMTA and EXRET in place of NIMTAAVG and EXRETAVG under ‘‘Logit (Variation) Campbell et al. (2008)’’. We recognise that these variables are only proxies for the true values of the variables in the model. Chava and Jarrow (2004) do not provide summary statistics for the subset of firm-years for non-financial US-listed firms for the period 1962–1999 on which the model we select is based and we do not therefore compute an output value.

probability that the value of liabilities exceeds the value of assets at a point in time (i.e. the average PD) should be higher for the Hilligeist et al. model. Conversely, the relative mean value of assets (£15,781 m for the Bharath and Shumway model vs. £17,904 m for the Hillegeist et al. model), the volatility of assets (23.49% for the Bharath and Shumway model vs. 18.52% for the Hillegeist et al. model) and the growth rate in assets (1.53% for the Bharath and Shumway model vs. 14.86% for the Hillegeist et al. model) each suggest that, ceteris paribus, the average PD will be higher under the model of Bharath and Shumway. There is considerable difference in the growth rate of assets under each model. Under the model of Bharath and Shumway (Hillegeist et al.) our sample produces maximum values of the growth rate in assets of 127.25% (100%) and minimum values of 83.04% (0.39%).12 Details of the calculations of the growth rate under each model are set out in Table 2 from which it is notable that the Hillegeist et al. model sets a minimum for the growth rate in assets equal to the risk-free rate, thereby removing the negative tail of the distribution of this variable. In Table 5 we examine the default-risk values arising from our academic models. The two models based on the theory of BSM give very different results for the average PD at 0.96% (Hillegeist et al. model) and 4.23% (Bharath and Shumway model). Different assumptions lead to markedly different probabilities of default, and these differences are set out in Table 2 and discussed above in relation to Table 4. We conclude that the major reason for the different average probabilities of default is the difference in the value of the growth rate of assets. If the Bharath and Shumway growth rates in assets are applied to the Hillegeist et al. BSM model in place of the Hillegeist et al. growth rates the average PD across our sample is 5.4% under the Hillegeist et al. BSM model. The average probability of failure/default varies considerably across our sample from 46.43% (z-score model of Agarwal and Taffler (2008)) to 0.04% (logit model of Campbell et al. (2008)). The

12

The values in the original article by Bharath and Shumway are a mean of 3.25% (see Table 4), a standard deviation of 57.17%, a maximum of 210.37% and a minimum of 253.58%.

average PD given by the z-score model compares with an average of 26.33% reported by Agarwal and Taffler (2008), neither of which are realistic averages across samples dominated by firms which are going concerns. The primary reason for such high values across our sample of firms is that a number of firms have very low values of quick assets relative to current liabilities. The z-score value is then dominated by the value of the ‘‘no credit interval’’ leading to probabilities of failure which approach 1. This is obviously very unrealistic for a listed firm. The z-score model is perhaps more useful for determining relative risk scores rather than realistic probabilities of default or failure, and the risk score derived from the Cox proportional hazard model of Bharath and Shumway is similar in this respect. Given the unrealistic outputs of the Agarwal and Taffler (2008) z-score model we prefer to employ only the z-score model of Altman (1968) for the remainder of this paper. The average PD for the Altman model is also high at 14.06% and again it is likely that this model is more useful for determining relative default risk scores. The average PD for the Campbell et al. (2008) model across our sample is 0.04%. We calculate the average probability of default using the mean values of variables set out in the original paper and arrive at a mean PD of 0.07%13 (this latter is based on a sample of both listed and non-listed non-financial US firms). The relatively low probabilities of default and low variation in the PD under this model are dictated by the impact of the constant term. The highest PD under this model is 1.67% to which the variable LNEXRETAVG, the annual geometric mean of the monthly log excess return relative to a market index, contributes the largest impact, followed by SIGMA, the annualised standard deviation of stock returns measured over the last 3 months. We employ the Cox proportional hazard model of Bharath and Shumway (2008) to compute relative risk scores and as such these are meaningful only relative to this measure of default risk for other firms. Firms which have a higher expected risk of default

13 Campbell et al. (2008) do not provide data for the mean values of two variables in their model (NIMTAAVG and EXRETAVG) but they do provide data for NIMTA and EXRET. The value of 0.07% is calculated employing NIMTA and EXRET in place of NIMTAAVG and EXRETAVG.

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Table 6 Ratings distribution across our sample. S&P

Moody’s

Rating number (fine)

Rating no. (broad)

Frequency S&P

Frequency Moody’s

AAA AA+ AA AA A+ A A BBB+ BBB BBB BB+ BB BB B+ B B CCC+ CCC CCC CC C

Aaa Aa1 Aa2 Aa3 A1 A2 A3 Baa1 Baa2 Baa3 Ba1 Ba2 Ba3 B1 B2 B3 Caa1 Caa2 Caa3 Ca C

21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

8 7 7 7 6 6 6 5 5 5 4 4 4 3 3 3 2 2 2 1 1

0 18 9 15 62 51 67 91 127 53 20 31 26 19 8 11 0 0 0 0 0

1 15 8 26 60 73 89 86 75 60 15 22 19 12 10 9 7 1 0 0 0

Total

608

588

This table summarises the credit-rating measures applied by S&P and Moody’s and describes the rating distribution across our sample of firm-years. Our data are 716 firm-years for UK-listed companies (608 firm-years available for S&P ratings and 588 available for Moody’s ratings). AAA/Aaa/21/8 is the highest credit-rating category.

have higher (positive) values while those with a lower expected risk of default have lower (negative) values. Thus, as with other measures of default risk derived from the academic models, as the value of the risk score increases, so does default risk. Illustrative calculations were given in Section 2. The distribution of credit ratings across our sample of listed firmyears is shown in Table 6. S&P ratings are available for 608 firmyears, of which 493 ratings (i.e. 81%) are at investment grade (BBB) or above and 19% of ratings are sub-investment grade. Moody’s ratings are available for 588 firm-years, of which 493 ratings (i.e. 84%) are at investment grade (Baa) or above and 16% of ratings are sub-investment grade. The mean, median and mode values for S&P ratings, calculated by converting the finer rating categories (i.e. those which employ ‘‘+’’ and ‘‘’’ qualifiers) to a numerical score and reconverting to the nearest S&P category, are BBB + (13.6), BBB + (14) and BBB (13), respectively (we employ the numerical scores set out in Table 1, page 1329 of Hill et al. (2010) for this purpose). The mean, median and mode values for Moody’s calculated in the same way are Baa1 (13.9), Baa1 (14) and A3 (15). Avramov et al. (2009) find that higher default risk stocks (i.e. those with low ratings) provide lower stock returns but that this result is driven by the lowest decile of rated stocks with an average rating of B–. We therefore provide further discussion of the negative tail of the rating values across our sample. Of 608 firm-years rated by S&P, no firm-years were rated below B and thus an average rating of B is achieved employing the bottom 11 firm-years with a B rating or 1.81% of the sample. Of 588 firm-years rated by Moody’s, 8 were at a level below B and an average rating of B is achieved by employing the bottom 27 firm-years of data (average rating value = 6.04 on the finer scale) – that is, 4.59% of the sample. 5. A correlation analysis of rating assessments In this section we examine the relationship between default risk assessments via a correlation analysis. We also present the output

from our academic models across different rating categories. We continue to employ eight measures of default risk as follows: (i) z-score model of Altman (1968); (ii) discrete time hazard model of Campbell et al. (2008); (iii) discrete time hazard model of Chava and Jarrow (2004); (iv) risk score arising from the Cox proportional hazards model of Bharath and Shumway (2008); (v) BSM-based model of Hillegeist et al. (2004); (vi) BSM-based model of Bharath and Shumway (2008); (vii) S&P rating; and (viii) Moody’s rating. The correlation analysis is presented in Table 7. The academic models (i) to (vi) above have a negative correlation with ratings since their output is the probability of default/ bankruptcy and the higher this measure the lower the credit rating. Table 7 shows that all correlations have the expected sign and all are significant at the 1% level. However, the correlations between the different measures of default risk tend to be less than (greater than) 0.5 (0.5). The highest correlation is between the rating scores of Moody’s and S&P (0.962) followed by the logit model of Chava and Jarrow and the logit model of Campbell et al. (0.594), the logit model of Campbell et al. and both of the BSM-based models (0.587 and 0.586), and the logit model of Chava and Jarrow and the BSM-based model of Hillegeist et al. (0.574). The two models based on the theories of BSM have a correlation of 0.502 and this surprisingly low correlation in large part arises from the assumptions made about the growth rates in assets as discussed in Section 4. If the Bharath and Shumway growth rates in assets are applied to the Hillegeist et al. model, the correlation between the two BSM-based measures of default risk is in excess of 90%. Of the academic models, the Altman z-score model has the highest correlation with the ratings (50% with Moody’s ratings and 39% with S&P ratings). Given that the Altman model is dominated by accounting ratios, this suggests a relatively high reliance on accounting ratios in the default risk assessments of the CRAs.14 Finally, as discussed at the end of Section 2, some of the leading academic models we select are derived either partly or fully from US accounting data (see Table 2). The fact that these models were all devised employing US accounting data may reduce the correlations between the models when they are applied to UK data. However, neither the BSM-based models nor the credit ratings are derived from US accounting data and it is in fact these measures of default risk which have the lowest bilateral correlations. Overall the correlations between default risk assessments do not approach 1 and as such investors in UK-listed firms might be left in some doubt as to the true default risk of a firm. It remains to be seen how the different measures of default risk are related to stock returns, which is the subject of Section 6. We continue our analysis by presenting the output from our academic models across different rating categories (Table 8). Across most rating categories there is a monotonic increase in the probability of default/bankruptcy as measured by our selected academic models. It is worth noting that the logit model of Campbell et al. shows little variation until issuer ratings reach the BB (Ba) level. The mean PD from the academic models for each rating level can be compared with those implied by the ratings by employing data from prior studies. Thus Lando and Skodeberg (2002) employ S&P ratings data for (primarily) US firms for the period 1981–1997 to calculate 1-year default rates for the BBB category of 0.18% (under a discrete time assumption in which only the year start and

14 In untabulated results we examine the relationship between changes in the default risk measures arising from our academic models and changes in credit ratings. The z-score model is the best indicator of both concurrent and future changes in ratings. However, all of the academic models are good predictors of multiple notch downgrades by both Moody’s and S&P. That is, firms downgraded by more than one notch in year j are associated with a significant increase in default risk as measured by all academic models during year j  1. These results are available from us on request.

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J. Chen, P. Hill / Journal of Banking & Finance 37 (2013) 5118–5131 Table 7 Correlation matrix. z-score Altman (1968) z-score Altman (1968)

1.000

Logit Campbell et al. (2008)

0.309 <0.0001 0.421 <0.0001 0.376 <0.0001 0.287 <0.0001 0.384 <0.0001 0.389 <0.0001 0.498 <0.0001

Logit C&J (2004) Cox ph B&S (2008) BSM Hillegeist et al. (2004) BSM B&S (2008) S&P rating Moody’s rating

Logit Campbell et al. (2008)

Logit C&J (2004)

Cox ph B&S (2008)

BSM Hillegeist et al. (2004)

BSM B&S (2008)

S&P rating

Moody’s rating

1.000 0.594 <0.0001 0.396 <0.0001 0.587 <0.0001 0.586 <0.0001 0.239 <0.0001 0.247 <0.0001

1.000 0.302 <0.0001 0.574 <0.0001 0.448 <0.0001 0.249 <0.0001 0.254 <0.0001

1.000 0.450 <0.0001 0.506 <0.0001 0.300 <0.0001 0.356 <0.0001

1.000 0.502 <0.0001 0.237 <0.0001 0.240 <0.0001

1.000 0.240 <0.0001 0.310 <0.0001

1.000 0.962 <0.0001

1.000

This table presents the correlation matrix of all default risk measures including six default risk measures derived from academic models and two rating scores. The six default risk measures derived from academic models in the order in which they appear in Table 7 below are (i) z-score model of Altman (1968), (ii) discrete time hazard/multi-period logit model of Campbell et al. (2008), (iii) discrete time hazard/multi-period logit model with industry effects of Chava and Jarrow (2004), (iv) Cox proportional hazard model of Bharath and Shumway (2008), (v) the BSM-based model of Hillegeist et al. (2004) and (vi) the BSM-based model of Bharath and Shumway (2008). The rating measures of default risk are the ratings of S&P and Moody’s. 716 firm-years are available for the six academic models, 608 firm-years are rated by S&P and 588 firm-years by Moody’s.

year end rating values are considered) and 0.08% (under a continuous time assumption which allows for all intermediate transitions from the BBB state to default). These figures can be compared with the figures of default probability for a firm rated BBB by S&P across the academic models we employ as follows: 0.03% (Campbell et al. model), 0.60% (Hillegeist et al. BSM model), 0.95% (Chava and Jarrow logit model), 3.37% (Bharath and Shumway BSM model) and 13.57% (Altman z-score model). Employing Moody’s data for senior unsecured debt ratings (equivalent to the issuer rating) for the period 1970–1997, Nickell et al. (2000) calculate default rates for a 1-year period for the Baa rating category of 0.1%, which is in line with other studies that they report. This figure can be compared with the default probabilities for a firm rated Baa by Moody’s across the academic models that we employ as follows: 0.03% (Campbell et al. model), 0.46% (Hillegeist et al. BSM model), 0.86% (Chava and Jarrow logit model), 2.08% (Bharath and Shumway BSM model) and 13.70% (Altman zscore model). It is clear that relative to default rates based on the history of default for different rating categories our models tend to overestimate the PD. This does not preclude models which tend to overestimate default risk from being excellent measures of relative default risk and therefore useful determinants of relative stock returns. In conclusion, the default risk assessments of academic models diverge in their outputs, as is evident from the fact that correlations tend to be less than 50%. The outputs from the two BSM-related models have a surprisingly low correlation of 50%, largely due to the removal of the negative tail of the asset growth rate distribution under the Hillegeist et al. model. The CRA assessments of default risk have a very high correlation with each other (of 96%) but a low correlation with the output from the academic models. The z-score model has the highest correlation with both CRA measures of default risk. The impact of the various assessments of default risk on stock returns is the subject of the following section of this paper.

6. The relationship between stock returns and default risk The purpose of this section is to determine the extent to which our different measures of default risk are related to equity returns

across the UK market. We employ a regression analysis to analyse the relationship between default risk and stock returns for our sample of firms. Vassalou and Xing (2004) examine individual stock returns via an equation in which stock returns are a function of default risk (DR), size (Size) and BM. They allow for non-linearities and interaction terms. We also allow stock returns to depend on beta (Beta) and we estimate the following regression equation for each of our eight default risk measures, 2

Ri;tþ1 ¼ a þ DRit þ DR2it þ Sizeit þ Sizeit þ BM it þ BM 2it þ Betait þ

Beta2it

þ ½Size x DR þ ½BM x DR þ ½Beta x DR

ð1Þ

where Ri,t+1 is the compound return for firm-year i in year t + 1, DRit is the default risk of firm i at point t, Sizeit is the size of firm i at time t, BMit is the BM of firm i at time t and Betait is the beta for firm i at time t, calculated employing 3 years of data prior to t. Preliminary analysis suggests that firm-fixed effects are present15 and as such we undertake a fixed effects regression analysis which allows for the possibility that time-invariant characteristics of each firm which are not specified in Eq. (1) above (e.g. managerial expertise) are determinants of stock returns. The fixed effects model only allows us to assess the determinants of within-firm variation in returns. However, 89% of the variation in stock returns is within firms rather than between firms.16 Of course, asset-pricing theory suggests that only systematic risk factors are priced and a pooled cross-section would therefore be appropriate. However, there are precedents for employing fixed-effects methods to examine the determinants of stocks returns (see, e.g., Wadhwani and Wall (1990)). Correlation between variables and their polynomial and interactive terms may create problems of multicollinearity when esti15 Specifically we undertake an F-test of the explanatory power of the firm-level fixed effects models (using the eight different measures of default risk) vs. pooled OLS models and we conclude in all cases that the firm-level fixed effects model is more suited to the data – that is, there are firm differences which are not fully captured by the regressors as set out in Eq. (1). We also employ Hausman tests to determine whether a random effects model is more appropriate than fixed effects for each model. In each case we reject the hypothesis that the random firm effect is uncorrelated with the regressors displayed in Eq. (1) above and thus we reject the random effects model in favour of the fixed effects model. 16 This figure is not driven by the volatile markets for 2007 et seq. during which period within firm volatility accounts for 83% of the variation in stock returns.

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Table 8 Default risk assessments via academic models for broad rating categories. N

z-score Altman (1968)

Logit Campbell et al. (2008)

Logit C&J (2004)

Cox ph B&S (2008)

BSM Hillegeist et al. (2004)

BSM B&S (2008)

Panel A: AAA AA A BBB BB Sub-BB

S&P – 42 180 271 77 38

– 0.0459 0.0972 0.1357 0.2227 0.1983

– 0.0002 0.0002 0.0003 0.0007 0.0012

– 0.0030 0.0041 0.0095 0.0169 0.0230

– 1.9364 1.8677 1.7000 1.1600 0.4178

– 0.0000 0.0019 0.0060 0.0273 0.0443

– 0.0004 0.0206 0.0337 0.0995 0.1509

Panel B: Aaa Aa A Baa Ba Sub-Ba

Moody’s 1 0.0233 49 0.0473 222 0.1101 221 0.1370 56 0.2701 39 0.2853

0.0004 0.0002 0.0002 0.0003 0.0009 0.0010

0.0068 0.0031 0.0040 0.0086 0.0297 0.0297

1.4543 2.1758 1.8699 1.7409 0.9260 0.4285

0.0002 0.0000 0.0015 0.0046 0.0450 0.0463

0.0166 0.0003 0.0187 0.0208 0.1134 0.1943

This table presents the average default risk value across each rating category for the six default risk measures derived from academic models; (i) z-score model of Altman (1968) (ii) discrete time hazard/multi-period logit model of Campbell et al. (2008), (iii) discrete time hazard/multi-period logit model with industry effects of Chava and Jarrow (2004), (iv) risk score from Cox proportional hazard model of Bharath and Shumway (2008) (v) the BSM-based model of Hillegeist et al. (2004), (vi) the BSM-based model of Bharath and Shumway (2008).

mating Eq. (1). These correlations are particularly acute for the ratings-based measures of default risk where the correlation between the ratings and their squares approaches 99% for both S&P and Moody’s. We therefore apply grand mean centring to the variables prior to the application of fixed effects for those regressions involving credit ratings.17 As predicted, the reduction in correlation between the credit ratings and their squares is considerable (to 0.198 for S&P and 0.425 for Moody’s). The results reported in Tables 9 and 10 reflect grand mean centring for the regressions involving credit ratings alone. However, all regressions are repeated with the grand mean centring of variables. The coefficients on the polynomial and interactive terms and their standard errors are entirely unaffected by this grand mean centring, as is the predictive power of the models (R2 value). Any difference between mean-centred and non-mean-centred results are highlighted in our discussion and the full results are available from us on request. To enter the analysis, firms must have 365 consecutive days of returns data following the date on which our independent variables are measured. Some 23 firms go on to delist within our sample period and for 12 firms we do not have 365 days of returns data following the final accounting year for which we measure our independent variables. The use of a fixed effects model further reduces our sample by two, since two firms have only one firm-year observation. Our final sample for the returns analysis is therefore 716  12  2 = 702 firm-years for the default risk measures based on the academic papers, 598 firm-years for S&P ratings, and 573 firm-years for Moody’s ratings after removal of one firm with a Moody’s rating for only one firm-year. Vassalou and Xing (2004) state that the ‘‘variables size and BM are rendered orthogonal to [their measure of default risk]’’ (page 858, ‘‘Default Risk in Equity Returns’’, Vassalou and Xing, 2004, Journal of Finance). We examine the correlation between our

17 By applying a fixed effects model we effectively group mean centre each variable after calculation of the polynomial and interactive terms. Multicollinearity is often addressed by mean centring prior to the calculation of polynomial and interactive terms, thereby reducing correlations (see, inter alia, Dalal and Zickar, 2012). We find that grand mean centring tends to reduce the correlation between all variables and their polynomials but in most cases the difference is not large. We are indebted to a referee for highlighting this issue and suggesting that we employ grand mean centring to remedy the problem.

various measures of default risk and both size and BM for our sample of 702 firm-years. The results are interesting. The correlations between BM and our eight measures of default risk lie between 0.19 (S&P rating) and 0.16 (risk score from Cox ph model). Since the PD is negatively related to ratings these correlations are as expected – the smallest absolute value of the correlation coefficient between BM values and default risk is 0.03 (BSM model of Bharath and Shumway). The correlations between size and our six measures of default risk based on academic models are negative (as expected since PD would be expected to be greater for smaller firms) and have a minimum of 0.23 (z-score). The correlations between size and the ratings-based assessments of default risk are positive (again, as expected, larger companies have higher ratings) at 0.51 for S&P and 0.45 for Moody’s. There is thus a much greater correlation between firm size and the ratings-based measures of default risk. Could this possibly be indicative of the conflict of interest given that rated firms pay the fees of the CRAs? Larger firms might be expected to yield a greater influence on ratings if the rating of larger firms is more lucrative. A front-page article in the (UK-based) Guardian newspaper of August 22nd 201118 highlighted damning evidence given by a former senior Moody’s executive of a conflict of interest at the heart of the rating process given that companies pay for their own rating assessments. This evidence was provided as part of the US Securities and Exchange Commission ongoing investigation into the rating process. We present results for our fixed effects regressions in Table 9. Our first set of results (Panel A) show that beta fails to be a significant determinant of stock returns across our sample in the presence of other variables and we therefore re-estimate Eq. (1) above without the variables containing beta (Panel B). The results in Panel B can be directly compared with those reported in Table IX of Vassalou and Xing (2004) and this is the focus of our discussion. Unlike Vassalou and Xing we find that size is a significant determinant of returns in the presence of default risk measures. Since the size-related variables are not significant in their paper, Vassalou and Xing argue that the size effect is in fact a default effect. Our results for the BM variable are similar to those reported in Vassalou and Xing (2004) – that is, BM is a significant linear determinant of stock returns because as it increases so do stock returns. There is evidence of non-linearities in the relationship between BM and returns in 4 out of 8 models, and given that the sign on BM squared is negative, as BM increases so do returns up to a maximum turning point, after which they decrease.19 From Panel B it is evident that default risk is a significant determinant of stock returns in addition to size and BM; the measures of default risk from our models are all significant at the 10% level or above. This impact tends to be non-linear for the academic models20 and given that the sign on default risk squared is negative (the one exception is discussed below), as default risk increases so do returns up to a maximum turning point, after which returns decrease, which is as predicted by Garlappi and Yan (2011). Vassalou and Xing (2004) report that in the absence of the (superfluous) variables relating to firm size the relationship between default risk and

18 ‘‘Ratings agencies suffer ’conflict of interest’, says former Moody’s boss’’, The Guardian, Monday 22nd August 2011. 19 While the results in Table 9 report a significant value of BM in all but three regressions, the mean-centred results confirm a significant relationship in all but one regression, that where default risk is given by the S&P rating. 20 The default risk measure (DR) from the Chava and Jarrow logit model fails to be significant in the mean-centred results for the regression models without beta. Grand mean centring in fact increases the correlation between DR and DR2 in this model. Grand mean centring improves the significance of the DR measure in the Altman zscore model to 1%, which is accounted for by the relatively large impact on the correlation between DR and DR2 in this model.

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J. Chen, P. Hill / Journal of Banking & Finance 37 (2013) 5118–5131 Table 9 Fixed effect regressions on stock returns. DR2

Size

Size2

BM

BM2

Beta

Beta2

SizeDR

Panel A: models with beta Altman z-score 1.331* 1.996** Campbell et al. 661.355*** 30082.6*** C&J 3.999*** 11.427*** 0.070*** Cox ph B&S 0.378*** BSM Hilligeist et al. 12.370*** 0.885 BSM B&S 1.136*** 0.822* S&P rating 0.043*** 0.001 Moody’s rating 0.031** 0.004

0.020*** 0.021*** 0.025*** 0.024*** 0.021*** 0.029*** 0.032*** 0.030***

0.000** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000***

0.041 0.443*** 0.357*** 0.068 0.392*** 0.317** 0.178 0.235**

0.014 0.028 0.044 0.059 0.045 0.054* 0.120*** 0.216***

0.111 0.135 0.113 0.089 0.096 0.090 0.064 0.057

0.032 0.052 0.035 0.053 0.031 0.002 0.031 0.055

0.046*** 4.292 0.197 0.001 0.011 0.161*** 0.003** 0.002**

1.649** 230.453*** 4.186 0.174*** 3.405*** 0.637* 0.078** 0.115***

Panel B: models without beta 2.054** Altman z-score 1.524** Campbell et al. 591.109*** 29830.7*** C&J 4.732** 4.572 0.067*** Cox ph B&S 0.350*** BSM Hilligeist et al. 7.796*** 8.000*** BSM B&S 0.960** 0.858* S&P rating 0.043*** 0.002 Moody’s rating 0.029** 0.004

0.019*** 0.021*** 0.023*** 0.024*** 0.021*** 0.028*** 0.031*** 0.028***

0.000** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000***

0.020 0.437*** 0.334*** 0.048 0.384*** 0.327*** 0.190 0.236**

0.020 0.042 0.047 0.042 0.047* 0.048* 0.124*** 0.222***

0.046*** 3.683 0.793** 0.001 0.018 0.165*** 0.003** 0.002**

1.582** 192.234*** 2.277 0.170*** 2.286** 0.636* 0.075** 0.111***

DR

BMDR

BetaDR

R2

N

0.112 26.980 1.954** 0.014 3.258*** 0.171 0.005 0.007

0.214 0.282 0.198 0.281 0.327 0.206 0.215 0.261

702 702 702 702 702 702 598 573

0.210 0.278 0.187 0.277 0.301 0.201 0.212 0.256

702 702 702 702 702 702 598 573

We estimate the following regression equation for each of our eight default risk measures: 2

Ri;tþ1 ¼ a þ DRit þ DR2it þ Sizeit þ Sizeit þ BMit þ BM2it þ Betait þ Beta2it þ ½Size x DR þ ½BM x DR þ ½Beta x DR where Ri,t+1 is the compound return for firm-year i in year t + 1, DRit is the default risk of firm i at point t, Sizeit is the size of firm i at time t, BMit is the BM of firm i at time t and Betait is the beta for firm i at time t employing 3 years of data prior to t. Our first set of results (Panel A) show that Beta fails to be a significant determinant of stock returns across our sample in the presence of other variables and we therefore reestimate the above equation without the variables containing Beta (Panel B). Preliminary analysis suggests that firm fixed effects are present and as such we employ a fixed effects model. The derivation of our sample for the returns analysis is set out in the main text and is 702 firmyears for the default risk measures based on the academic papers, 598 firm-years for S&P ratings, and 573 firm-years for Moody’s ratings. In the regressions involving credit ratings the variables are grand mean centred prior to the calculation of squares and interactive terms to reduce multicollinearity. *** ** *

Indicates significance at the 1% level. Indicates significance at the 5% level. Indicates significance at the 10% level.

Table 10 Fixed effect regressions on stock returns with dummy variables for firm-years with very high default risk. Size

Size2

BM

BM2

SizeDR

BMDR

Dummy 2%

Panel A: dummy for 2% of firms with highest 1.769* Altman z-score 1.484** Campbell et al. 434.321*** 22908.0*** C&J 0.533 0.577 Cox ph B&S 0.329*** 0.061*** BSM Hilligeist 6.316*** 6.692*** BSM B&S 0.774* 0.199 S&P rating 0.046*** 0.000 * Moody’s rating 0.023 0.007**

default risk 0.019*** 0.021*** 0.024*** 0.024*** 0.021*** 0.028*** 0.030*** 0.029***

0.000** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000***

0.013 0.400*** 0.303** 0.064 0.374*** 0.322*** 0.209* 0.243**

0.020 0.031 0.042 0.041 0.047* 0.047 0.149*** 0.244***

0.047*** 4.583 0.593 0.001 0.031 0.185*** 0.002** 0.003**

1.544** 189.586*** 2.454 0.178*** 2.431** 0.541 0.092*** 0.120***

0.119 0.664*** 0.501** 0.207 0.371* 0.379

Panel B: dummy for 5% of firms with highest Altman z-score 1.517** 2.628*** Campbell et al. 530.7*** 26650.8*** C&J 2.381 0.922 Cox ph B&S 0.371*** 0.071*** *** BSM Hilligeist 7.579 7.743*** BSM B&S 1.238** 0.940**

default risk 0.018*** 0.021*** 0.024*** 0.024*** 0.021*** 0.028***

0.000** 0.000*** 0.000*** 0.000*** 0.000*** 0.000***

0.028 0.432*** 0.352*** 0.047 0.383*** 0.329***

0.026 0.042 0.050* 0.043 0.046* 0.049*

0.052*** 3.347 0.679* 0.001 0.017 0.172***

1.484** 180.543*** 3.822 0.170*** 2.260** 0.631*

DR

DR2

Dummy 5%

Rating dummy

0.552** 0.311* 0.327** 0.114 0.231* 0.072 0.027 0.152

R2

N

0.210 0.290 0.193 0.279 0.304 0.203 0.220 0.260

702 702 702 702 702 702 598 573

0.218 0.279 0.192 0.277 0.301 0.202

702 702 702 702 702 702

The regression analysis of Table 9, Panel B (i.e. without beta) is repeated but dummy variables are now added to allow for the possibility that the impact of default risk on stock returns can be accounted for by firm-years with very high default risk, as per Avramov et al. (2009). Avramov et al. (2009) find that the relationship between stock returns and default risk is driven by the lowest decile of rated stocks with an average rating of B. For S&P-rated firms an average rating of B is achieved, employing the lowest rated 11 firm-years of data or approx. 2% of the sample. For Moody’s rated firms an average rating of B is achieved by employing the lowest rated 27 firm-years of data or approximately 5% of the sample. The ‘‘rating dummy’’ variables reflect the lowest rated 11 (27) firm-years for S&P (Moody’s). For the other models we create dummies for both the 2% and 5% of firm-years with the highest default risk under each default risk model. Again, the credit-rating measures of default risk are grand mean centred prior to calculation of squares and interactive terms to reduce multicollinearity. *** Indicates significance at the 1% level. ** Indicates significance at the 5% level. * Indicates significance at the 10% level.

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Table 11 Relative returns to firm-years with highest levels of default risk. 2% of firms with highest risk (HR)

z-score Altman (1968) Logit Campbell et al. (2008) Logit Chava and Jarrow (2004) Cox ph (risk score) Bharath and Shumway (2008) BSM Hillegeist et al. (2004) BSM Bharath and Shumway (2008) S&P rating Moody’s rating

5% of firms with highest risk

Mean HR (n = 14)

Mean rest (n = 688)

Sig.

Mean HR (n = 35)

Mean rest (n = 667)

0.092 0.465 0.230 0.386 0.937 0.255 0.007 (n = 11)

0.124 0.113 0.118 0.114 0.103 0.127 0.125 (n = 587)



0.133 0.360 0.148 0.399 0.587 0.067

0.119 0.107 0.118 0.105 0.095 0.130

0.167 (n = 27)

0.133 (n = 546)



  

Sig. 

  

Avramov et al. (2009) find that higher default risk stocks provide lower stock returns but that this result is driven by the lowest decile of rated stocks with an average rating of B. For S&P-rated firms an average rating of B is achieved employing the lowest rated 11 firm-years of data or approximately 2% of the sample. For Moody’s-rated firms an average rating of B is achieved by employing the lowest rated 27 firm-years of data or approximately 5% of the sample. Following on from our regression analysis of Table 9, in Table 10 we compare the returns to the bottom 2% (left-hand panel) and 5% (right-hand panel) of firm-years by default risk measure with returns to the rest of the sample across each of our academic models. Where credit ratings are employed as the measure of default risk we isolate the lowest-rated firms, which give an average rating of a B (i.e. 11 firm-years for S&P ratings and 27 firm-years for Moody’s ratings).

stock returns is positive and non-linear. However, in the model of Vassalou and Xing (2004) the sign on default risk squared (DR2) is positive rather than negative (suggesting that after a minimum turning point, returns increase). When we employ the risk score derived from the proportional hazards model of Bharath and Shumway (2008), we find that the sign on DR2 is positive. However, Vassalou and Xing (2004) do not employ this risk score but rather a default risk measure, which is similar to the BSM Bharath and Shumway model. We now summarise the regression results thus far in light of the findings of previous studies. Both Garlappi and Yan (2011) and Vassalou and Xing (2004) employ a contingent claims model based on the theories of BSM, but while Garlappi and Yan employ an ‘‘expected default frequency’’ obtained directly from Moody’s KMV, Vassalou and Xing (2004) employ a contingent claims model with the same assumptions as the model of Bharath and Shumway (2008) which we employ in this paper. Given that our results from the BSM model of Bharath and Shumway (2008) support the findings of Garlappi and Yan (2011), we find no evidence that the difference in result between the Garlappi and Yan and Vassalou and Xing studies is caused by a difference in the default risk measure employed. We discussed this result in some detail in the Introduction where we pointed out that Vassalou and Xing (2004) in fact argued that there was no material difference between their measure of default risk and the Moody’s KMV measure. However, we were not convinced by Garlappi and Yan’s (2011) explanation of the difference in results between the two studies and it remained a possibility that a difference in the default risk measure might (in part) contribute to the different results. While the non-linear relationship between default risk and stock returns is confirmed for the academic measures of default risk, this is not the case for the CRAs’ measures of default risk.21 Neither of the squared terms for the ratings-based measures is significant, although the Moody’s coefficient just fails to be significant at the 10% level, which again would suggest that as default risk increases (rating decreases), returns increase up to a maximum turning point after which returns decrease – that is, the hump-shaped relationship predicted by Garlappi and Yan (2011). Avramov et al. (2009) employ S&P ratings and report that returns are significantly negatively related to the rating – that is, higher rated stocks have higher returns. They do not test for non-linearities but they do examine the stock returns across different rating categories and during periods around downgrades, and 21 Without grand mean centring the S&P measure of default risk fails to be a significant determinant of stock returns. As stated on page 20, all results with and without mean centring are available from us on request.

they conclude that their result is driven by low-rated firms in times of financial distress. Given the findings of Avramov et al. (2009), to allow us to assess the impact of very low credit quality firms, which Avramov et al. suggest drive the results between default risk and stock returns, we create two dummy variables based on our earlier analysis of Moody’s and S&P rating values. Avramov et al. suggest that it is the group of firms with an average rating of B which drive their results which correspond to either 2% or 5% of our sample depending on whether S&P or Moody’s ratings are employed (see the earlier analysis in Section 4). We create two dummy variables which relate to the 2% and 5% highest default risk firm-years and we test the impact of these dummy variables separately by re-running Eq. (1) above (without beta). Where credit ratings are employed as the measure of default risk we can isolate the lowest-rated firms which give an average rating of a B which corresponds to 11 firm-years for S&P ratings and 27 firm-years for Moody’s ratings. The dummy variables which represent the highest default risk firms are specific to the model of default risk employed. The results are reported in Table 10. Under all of our models, other than the logit model of Chava and Jarrow (2004), our default risk variables continue to be significant, and we therefore find that stock returns and default risk are related outside the subset of the firm-years with the highest default risk (as in Vassalou and Xing (2004)) and our results are not driven by the subset of firms with the lowest credit rating. The coefficients on the dummy variables which capture these high default risk firm-years suggest that the conclusion about the returns to these firm-years is very sensitive to the measure of default risk employed, with some models showing more negative returns for the high default risk subset and some more positive. We confirm this observation in Table 11 where we compare the returns to the bottom 2% and 5% of firm-years by default risk measure with returns to the rest of the sample. Table 11 confirms the conclusion that returns to the very lowest credit quality firm-years are highly dependent on the measure of default risk employed. Even models which appear to be similar, such as the two models based on the theories of BSM, give markedly different conclusions about the relationship between returns and default risk across the subset of firm-years with the highest default risk. The study of Avramov et al. (2009) employs S&P credit ratings as the measure of default risk and in Table 11 we report that the 2% of our sample with the lowest S&P ratings produces a mean 1-year return of 0.7% vs. 12.5% for the rest of the sample, which supports the findings of Avramov et al. (2009). However, we do not agree with their assertion that the relationship between stock returns and default risk for US firms is driven by firms with low credit quality during periods of financial crisis, given that we

J. Chen, P. Hill / Journal of Banking & Finance 37 (2013) 5118–5131

find a relationship between default risk and stock returns outside the subset of low credit quality firms. The theory of Garlappi and Yan (2011) is predicated on the highest default risk firms offering lower returns and the analysis in Table 11 suggests that we qualify our support for their theory; the model employing the BSM-based measure of default risk from Bharath and Shumway (2008) would appear to support the findings of Garlappi and Yan but other models of default risk do not.22 However, our sample of very high default risk firm-years is very small, and, as stated in the Introduction, these findings are primarily useful to alert investors to the potential variability in default risk measurements at the level of the individual firm. 7. Concluding remarks We find that correlations between six diverse measures of default risk based on leading academic articles are significant at the 1% level and yet tend to be less than 50%. The correlation between the outputs from the academic models of default risk vary from a high of 0.594 (logit models of Campbell et al. (2008) and Chava and Jarrow (2004)) to a low of 0.287 (z-score model of Altman (1968) and BSM-based model of Hillegeist et al. (2004)). The ratings-based measures of default risk are highly correlated with each other (0.962) but have a maximum correlation of 0.498 with the academic models. The z-score model of Altman has the highest correlation with the ratings-based measures of default risk, suggesting a high reliance on accounting ratios in the ratings-based assessments of default risk. The outputs from our default risk models allow for some variation in the ranking of firm-years by default risk. However, across our full sample the relationship between stock returns and our divergent measures of default risk is reasonably consistent. We find that default risk is a significant determinant of stock returns and that this relationship is non-monotonic – as default risk increases, so do returns up to a maximum turning point, after which returns decrease, which is as predicted by Garlappi and Yan (2011). We find that this relationship exists after controlling for very high default risk firm-years, which contrasts with the findings of Avramov et al. (2009), who argue that the relationship between stock returns and default risk for US firms is driven by firms with low credit quality during periods of financial crisis. Our analysis suggests that the relationship between stock returns and default risk across the US market should be revisited, employing a wider variety of default risk measures across the same sample of firms. Acknowledgements We would like to thank staff in the Department of Accounting and Finance, Bristol University, and in particular George Bulkley, for their helpful comments and suggestions. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version at http://dx.doi.org/10.1016/j.jbankfin.2013. 06.013.

22 The turning point for the Garlappi and Yan study is between deciles 8 and 9 with mean EDFs of 3.75% and 6.98%, respectively.

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References Agarwal, V., Taffler, R.J., 2008. Comparing the performance of market-based and accounting based bankruptcy prediction models. Journal of Banking and Finance 32, 1541–1551. Altman, E.I., 1968. Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. Journal of Finance 23, 589–609. Avramov, D., Chordia, T., Jostova, G., Philipov, A., 2009. Credit ratings and the crosssection of stock returns. Journal of Financial Markets 12, 469–499. Bharath, S.T., Shumway, T., 2008. Forecasting default with the Merton distance to default model. Review of Financial Studies 21, 1339–1369. Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654. Blume, M.E., Lim, F., MacKinlay, A.C., 1998. The declining credit quality of U.S. corporate debt: Myth or reality? Journal of Finance 53, 1389–1413. Campbell, J.Y., Hilscher, J., Szilagyi, J., 2008. In search of distress risk. Journal of Finance 63, 2899–2939. Chava, S., Jarrow, R.A., 2004. Bankruptcy prediction with industry effects. Review of Finance 8, 537–569. Chava, S., Purnanandam, A., 2010. Is default risk negatively related to stock returns? Review of Financial Studies 23, 2523–2559. Cox, D.R., 1972. Regression models and life-tables. Royal Statistics Society B 34, 187–220. Dalal, D.K., Zickar, M.J., 2012. Some common myths about centering predictor variables in moderated multiple regression and polynomial regression. Organizational Research Methods 15, 339–362. Dichev, L.D., 1998. Is the risk of bankruptcy a systematic risk? Journal of Finance 53, 1131–1147. Duffie, D., Singleton, K.J., 2003. Credit Risk: Pricing, Measurement and Management. Princeton Series in Finance, Princeton University Press, Princeton and Oxford. Fiordelisi, F., Marqués-Ibañez, D., 2013. Is bank default risk systematic? Journal of Banking and Finance 37, 2000–2010. Garlappi, L., Yan, H., 2011. Financial distress and the cross-section of equity returns. Journal of Finance 66, 789–822. Güttler, A., Wahrenburg, M., 2007. The adjustment of credit ratings in advance of defaults. Journal of Banking and Finance 31, 751–767. Hillegeist, S.A., Keating, E., Cram, D.P., Lunstedt, K.G., 2004. Assessing the probability of bankruptcy. Review of Accounting Studies 9, 5–34. Hill, P., Brooks, R., Faff, R., 2010. Variations in sovereign credit quality assessments across rating agencies. Journal of Banking and Finance 34, 1327–1343. Hill, P., Faff, R., 2010. The market impact of relative agency activity in the sovereign ratings market. Journal of Business, Finance and Accounting 37, 1309–1347. Jarrow, R.A., Procter, P., 2004. Structural versus reduced form models: A new information based perspective. Journal of Investment Management 2, 1–10. Lando, D., Skodeberg, T.M., 2002. Analyzing ratings transitions and rating drift with continuous observations. Journal of Banking and Finance 26, 423–444. Löffler, G., 2004. An anatomy of rating through-the-cycle. Journal of Banking and Finance 28, 659–720. Merton, R.C., 1974. On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance 29, 449–470. Nickell, P., Perraudin, W., Varotto, S., 2000. Stability of rating transitions. Journal of Banking and Finance 24, 203–227. Office of National Statistics, 2012. Ownership of UK Quoted Shares, 2010. 28 February 2012. Pinches, E.G., Singleton, J.C., 1978. The adjustment of stock prices to bond rating changes. Journal of Finance 33, 29–44. Purda, L.D., 2007. Stock market reaction to anticipated versus surprise rating changes. Journal of Financial Research 30, 301–320. Shumway, T., 2001. Forecasting bankruptcy more accurately: A simple hazard model. Journal of Business 74, 101–124. Taffler, R.J., 1977. Finding those companies in danger using discriminant analysis and financial ratio data: A comparative based study. Working Paper, City University Business School, London. Taffler, R.J., 1984. Empirical models for the monitoring of UK corporations. Journal of Banking and Finance 8, 199–227. Vassalou, M., Xing, Y.H., 2004. Default risk in equity returns. Journal of Finance 59, 831–868. Wadhwani, S., Wall, M., 1990. The effects of profit-sharing on employment, wages, stock returns and productivity: Evidence from UK micro-data. The Economic Journal 100, 1–17.