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JRF
8,1 Mapping corporate drift towards
default
Part 2: a hybrid credit-scoring model
46
Arindam Bandyopadhyay
National Institute of Bank Management (NIBM), Pune, India

Abstract
Purpose – The purpose of this paper is to develop a hybrid logistic model by using the inputs
obtained from BSM equity-based option model described in the companion paper, “Mapping corporate
drift towards default – Part 1: a market-based approach” that can more accurately predict corporate
default.
Design/methodology/approach – In a set of logistic regressions, the ability of the market value of
assets, asset volatility and firm’s leverage structure measures to predict future default is investigated.
Next, a check is made as to whether accounting variables and other firm specific characteristics can
provide additional significant information in assessing the real world credit quality of a firm in a
multifactor model
Findings – From analysis of 150 publicly-traded Indian corporates over the year 1998 to 2005 it was
found that in a volatile equity market like India, one needs to enhance the BSM model with other
accounting information from financial statements and develop hybrid models. The results in this
paper indicate that a mix of asset volatility, market value of asset and firm’s leverage structure along
with other financial and non financial factors can give us a more accurate prediction of corporate
default than the ratio-based reduced form model.
Originality/value – The hybrid model developed in this paper allows us to integrate information
from the structural model as well as profitability of firms, liquidity risk, other firm specific
supplementary information and macroeconomic factors to predict real world corporate distress
potential through a multivariate analysis.
Keywords Credit, Risk analysis, Modelling, Emerging markets, India
Paper type Research paper

Introduction
There is a vast literature in credit risk models. The first generation of credit risk
models are mainly of two types: Merton’s structural model using the principles of
option pricing (Black and Scholes, 1973) and Altman (1968) type only ratio-based (or
intensity-based) statistical model. While in many cases, multivariate accounting-based
credit-scoring models have been shown to perform quite well over many different time
periods and across many different countries (Altman and Narayanan, 1997), they have
also been criticized because they are based primarily on book value accounting data.
Many researchers have questioned the traditional ratio-based statistical models which
are based on only discrete accounting data and do not allow non-linear effects among

This is a companion paper of “Mapping corporate drift towards default – Part 1: a market-based
The Journal of Risk Finance
Vol. 8 No. 1, 2007 approach” published in this journal issue. The author would like to thank the Editor, Michael
pp. 46-55 R. Powers, and an anonymous referee of this journal for their useful comments and guidance.
q Emerald Group Publishing Limited
1526-5943
Assistance from Nagendra Pande and Kuntal Biswas is also acknowledged. All remaining
DOI 10.1108/15265940710721073 errors, if any, are of course mine.
different credit risk factors. In such a case, these models would not be able to capture Drift towards
the effect of adverse business cycle effects on the creditworthiness of corporate clients. default. Part 2
The neural network approach may be criticized for its ad hoc theoretical foundation
and its use of data mining to identify hidden correlations among the explanatory
variables. In a comparison test, Altman et al. (1994) concluded that the neural network
approach did not materially improve upon the linear discriminant structure in
predicting bank failure. 47
The pioneering work of Black and Scholes (1973) in their seminal paper on options
pricing theory and further extensions of their work by Merton (1974) (hereafter referred
to as BSM) have tackled these issues by incorporating factors such as the market value
of assets and the business risk of firms. They introduced a contingent claims approach
to valuing corporate debt using option pricing theory. Default is assumed to occur
when the market value of firm’s assets has fallen to a sufficiently low level relative to
the issuer’s total liabilities. Essentially, the issuer’s shareholders receive an option to
default on its debt. The issuer will likely to exercise this option when its assets no
longer have enough value to cover its debt obligations.
Although the structural model has some restrictive theoretical assumptions (e.g.
underlying asset value of the firm follows a geometric Brownian motion and that each
firm has issued just one zero-coupon bond), it is practically very useful in predicting
corporate bond defaults because it is primarily based on the time series equity price
data which is readily available. The ability to diagnose the inputs and outputs of the
structural model in terms of understandable economic variables facilitates better
communication among loan originators, credit analysts and credit portfolio managers
(Arora et al., 2005). While the market value of firm’s asset proxy for market’s
assessment of an entrepreneur’s risk, the asset volatility captures the business risk
portion of its value and the leverage captures the solvency status of the firm.
Conversely, a scoring model based on only balance sheet ratios may not be able to
distinguish between company asset volatility and leverage (Kealhofer, 2003). In this
regard, the Merton approach can be adapted to include relevant financial and non
financial variables within a causal framework (Kealhofer, 2003).
The risk neutral distance to default metric that measures the changes in the market
value of firm’s assets in number of standard deviations (obtained from BSM option
theoretic approach), however, does not take into account credit risk factors such as
liquidity, profitability, efficiency etc. Hillegeist et al. (2004) have documented that
theoretical probabilities estimated from structural models do not capture all available
information about the credit risk of a firm. Shumway (2001) and Chava and Jarrow
(2001a, b) have found that accounting data improves the explanatory variable of
equity-based default models. Moody’s KMV (2003) has developed a hybrid RiskCalcw
model for more than 8,000 US and Canadian public firms. They have also found that
RiskCalc’s ability to predict default is significantly improved over simpler models
based on Merton theory only. Recently, Benos and Papanastasopoulos (2005) in
investing North American and Canadian rated industrial and commercial public firms,
have observed that by enriching the risk neutral distance to default metric with
accounting ratios into a hybrid ordered probit model can improve both in sample fit of
credit ratings and out of sample predictability of defaults.
In light of the above, a few crucial empirical questions need to be investigated
empirically. First, how well the Merton metrics obtained in the companion paper,
JRF “Mapping corporate drift towards default – Part 1: a market-based approach” can
8,1 work in volatile market condition like India. Next, whether accounting variables and
other firm specific characteristics can provide additional significant information in
assessing the real world credit quality of a firm in a multifactor model. If this is
happens to be true, then how Merton model can be further extended to include these
additional information to better predict corporate expectations. In this paper, we look
48 for answering all these questions.
In a set of logistic regressions, we investigate the ability of the market value of
assets, asset volatility and firm’s leverage structure measures to predict default. The
appeal of the maximum likelihood methods is that it allows for statistical inference on
likelihood of actual default incidents since it yields unbiased estimates of parameters.
In this regard, we examine whether incorporation of crucial outputs of Merton model
(like asset value, distance to default) along with some financial and non-financial
information about the firm can produce a better hybrid kind default predictor
statistical model. The hybrid model allows us to integrate information from the
structural model as well as profitability of firms, liquidity risk, other firm specific
supplementary information and macroeconomic factors to predict real world corporate
distress potential through a multivariate analysis. Our empirical results reveal that
integrating information from the structural model significantly improves the
prediction of probability of default in accounting-based model. This multivariate
logistic hybrid model also outperforms the structural model.

Indian practices in assessment of corporate default

Indian banks use credit-assessment models that are biased to analyzing the financial
ratios of their corporate customers. For banks and financial institutions, both the
balance sheet and income statement have a key role to play by providing valuable
information on a borrower’s viability. However, the approach of scrutinizing financial
statements is a backward looking approach. This is because; the focus of accounting is
on past performance and current positions. Operating margin, current ratio, cash flow
and fund flows are most commonly used to determine whether the loans have to be
extended. However, accounting policies (mostly projected figures) supplied by the
corporates in India have a lot of loopholes which leave a big room for manipulation. In
fact, most of the small and big corporates spend huge sums to chartered accountants to
make their balance sheet who know the margin of ratios banks look for. This led to a
plethora of faulty decisions and burgeoning non-performing accounts (NPAs). The
credit risk models need to go beyond the traditional balance sheet numbers to gauge
the business and management risks that may impact the creditworthiness of the banks’
customers. This is crucial because a bank’s performance depends on the health and
prosperity of its customers. Another plank of effective credit-risk management,
therefore, is to be able to deal with future NPAs quickly and efficiently and studying
their likely impact on bank’s risk adjusted performance.
With effect from March 2004, Reserve Bank of India (RBI), the central banker and
the financial system regulator in India, has suggested default status would be given to
a borrower if dues are not paid for 90 days. If any advance or credit facility granted by
bank to a borrower becomes non-performing, then the bank will have to treat all the
advances/credit facilities granted to that borrower as non-performing without having
any regard to the fact that there may still existing certain advances. The primary risk
faced by banks and FIs is credit risk which arises due to default when a firm fails to Drift towards
service its debt obligations. As a defense against future uncertain NPA growth, banks default. Part 2
are expected to develop effective internal credit risk models to closely monitor its
borrowers and track their performance on an on going basis. The strictly subjective
judgments of old are no longer an adequate basis for discriminating among firms’
default prospects. Internationally, the measurement of default probabilities has rapidly
evolved into a science. 49
Recently (February 2005), after the release of Reserve Bank of India draft guidelines
for the implementation of Basel II norms, the large Indian public sector banks have
started to develop (purchase) in house (vendor supplied) credit rating models for
assessing credit worthiness of corporate accounts[1]. The top rated private sector
banks like ICICI, HDFC banks have internal rating systems that generates transition
matrix and probability of default (PD) estimates for corporate accounts (Jayadev, 2006).
In all the other banks, the rating system comprises of only rating methodology and
assignment of rating. Bank corporate rating models are essentially focused on the
rating of borrowers to judge their ability to pay loan interest and installments. In India,
judgmental ratings are applied essentially to price loans, as the banks are yet to
explore the advanced uses of credit rating models for the estimation of loan loss
reserves, credit risk capital, profitability and loan pricing analysis for active portfolio
risk management. The availability of long-time series corporate database and stock
market information in India, thus making it possible to model the hybrid kind of
statistical credit risk model for banks.

Data, variables and empirical research design

The data used in this study consists of 150 Indian corporates listed in the National
Stock Exchange of India (NSE-India) from 1998 to 2005. These companies also issue
long term bonds which are rated by Credit Rating Information Services of India Ltd.
(CRISIL)[2]. The information on defaulted bonds is obtained from the CRISIL’s monthly
rating scan. According to CRISIL, default is defined as a credit event where the
underlying firm has any missed payments on a rated instrument. The stock price
information and market index (S&PCNX500) are obtained from the National Stock
Exchange (NSE) web site[3]. The individual investors in India have access to this stock
market data base site. All financial and company specific data are retrieved from the
Centre for Monitoring the Indian Economy’s (CMIE) Prowess database. Since it is
important for our analysis to control for industry effects, we grouped our sample firms
into 18 industry categories depending on their major economic activities. The industry
classifications have been made in concordance with the two digit codes of National
Industrial Classification (NIC) which is also followed by RBI. In order to capture the
time varying effects on corporate default analysis, we have incorporated a macro
variable: growth rate of gross national product at factor cost valued in current price
(GNPGRRCP). This macro information is collected from the Annual Survey of Indian
Economy published by Central Statistical Organization (CSO).

Logistic regression results

One may be interested to know the significance of risk neutral distance to default ratio
(DD) on actual default outcomes. The basic empirical question is whether default is
triggered by low asset values or by liquidity shortages? The question finally boils
JRF down into whether the market value of firm’s assets and volatility of assets obtained
8,1 from the stock market information is the powerful default predictor. Default may be
triggered by both low asset values and by liquidity shortages, and the importance of
liquidity varies across firms depending on the costs of outside financing. More
interestingly, the performance evaluation of a model should be comparative rather than
absolute. Accordingly, we first test only the balance sheet ratios in predicting corporate
50 default of our sample firms. However, these ratios are quite different from Altman’s
(1968) z-score ratios but suits better with the emerging market condition
(Bandyopadhyay, 2006). Next, we use the market value of asset (MVA) scaled by
the default point (DP) and risk neutral distance to default along with financial and non
financial firm specific factors to check whether it improves the model’s explanatory
and predictive power. The idea is to check whether inclusion of inputs obtained from
BSM option model as explanatory variable can improve the predictive power of
ratio-based model. Simultaneously, we also want to develop a hybrid kind of corporate
default model which captures the benefit of market-based approach and statistical
model based on empirical analysis of historical data.
To be precise, the model is trying to predict a binary dependent variable. The
variable is zero if the company has not failed at that point in time (say t þ 1) and one if
the company has failed. We have used logit model with panel data because simple
linear models are inappropriate when the dependent variable is a probability. In logit
regressions, we have applied maximum likelihood estimation (MLE) for estimation of
model parameters. The error term is assumed logistically distributed. The descriptive
statistics for the retained variables are presented in Table I. The analysis covers the
period of 1998 to 2005. It is understandable that solvent firms, on average, have much
better financial ratios than the defaulted ones. Moreover, they are also relatively bigger
in size. One can also notice from the same table that the average distance to default is
significantly lower for defaulted firms than its solvent counterparts (0.72 in
comparison to 2.87). However, there is lot of variations in DD ratio among firms
because of their different industry affiliations.
Table II reports results of three sets of logistic regression estimates of the default
decision of three models. The dependent variable is a dummy (DDEF1) which takes the
value one if the company’s bond defaults in the following year (as published by
CRISIL’s rating) and zero otherwise.

All firms Solvent firms Defaulted firms z-statistics

Median Std dev. Median Std dev. Median Std dev. for difference

MVA_DP 1.90 19736.11 2.72 23141.21 1.043 0.70 19.29 * * *

Distance to Default (DD) 2.19 3.81 2.87 4.05 0.72 1.2 18.82 * * *
NWK_TA 0.09 1.27 0.13 0.15 2 0.025 0.39 14.19 * * *
CASHPROF_TA 0.07 0.11 0.087 0.07 2 0.002 0.13 18.07 * * *
MVE_BVL 0.41 5.87 0.65 6.85 0.07 0.23 20.03 * * *
Table I. SALES_TA 0.76 0.57 0.81 0.60 0.59 0.34 9.90 * * *
Descriptive statistics for LNASSETS 6.48 1.65 6.67 1.52 5.45 1.46 10.25 * * *
logit model: comparison
between defaulted bonds Notes: z-statistic denotes the outcome of a Wilcoxon rank-sum (Mann-Whitney) test of equality of
and solvent bonds median between series; * * *denotes significance at 1% or better level
 Drift towards
Variables Ratio-based model MVA model DD model
default. Part 2
MVA_DP – 21.48 * * * (2 7.41) –
Distance to Default (DD) – – 20.59 * * * (2 3.45)
NWK_TA 2 3.63 * * * (24.63) 25.49 * * * (2 5.00) 24.68 * * * (2 4.16)
CASHPROF_TA 2 9.15 * * * (24.78) 28.32 * * * (2 3.91) 26.12 * * * (2 2.64)
MVE_BVL 2 3.94 * * * (27.19) – 23.66 * * * (2 5.26) 51
SALES_TA 2 1.15 * * * (23.54) 21.79 * * * (2 4.05) 21.7 * * * (2 3.69)
LNASSETS 2 0.45 * * * (25.42) 20.54 * * * (2 4.72) 20.26 * (2 1.88)
DUMTOP50 – 20.87 * * * (2 2.7) 21.17 * * * (2 3.22)
GNPGRRCP – 20.22 * * * (2 4.21) 20.25 * * * (2 4.49)
Intercept 4.47 * * * (7.08) 6.84 * * * (5.73) 4.7 * * * (3.7)

Number of observations 1,004 948 948

Chi2 statistics (d.f) 598.65 (5) 662 (22) 696.32 (23)
Prob . Chi2 0.00 0.00 0.00
Pseudo R 2 0.50 0.58 0.61
Accuracy ratio 86% 90% 92%
Notes: The dependent variable equals one if the firm defaults on long-term bonds in the following
year, and zero otherwise. MVA_DP is the market value of asset (MVA) normalized by the default point
(DP). Default point is the book value of short-term debt plus half of long-term debt. DD is the distance
to default = MVA2DP
MVA£sA ; where sA is the asset volatility. NWK_TA is the net working capital over total
assets. CASHPROF_TA is the cash profits over total assets. MVE_BVL is the market value of equity
as proportion to book value of liabilities. Book value of liability (BVL) is the total liabilities less total Table II.
net worth. SALES_TA is the ratio of total sales to total assets. DUMTOP50 is a dummy representing Logit model: bond default
top 50 business groups. LNASSETS is the natural logarithm of total assets which proxy for the firm prediction models and the
size. GNPGRRCP is the annual GNP factor growth rate at current price that controls for time specific importance of market
component. The regressions include 18 industry dummies that have not been reported to conserve value of assets (MVA)
space. Figures in parentheses are the z-values; * * *, * *, and * denotes significance at 1% or better, and distance to
1%-5% and 5%-10% level respectively default (DD)

The result reported in column 2 of Table II is the traditional balance sheet ratio best
model which better suits with the Indian condition. We have performed a step wise
selection of variables to retain in the ratio-based model solely based on the significance
of the accounting values. These accounting ratios are: net working capital to total
assets (NWK_TA) showing the short-term liquidity position of the firm, cash profit
over total assets (CASHPROF_TA) measuring the cash flow of the firm, the equity
market value over the book value of the liabilities (MVE_BVL) capturing the solidity of
the firm, the ratio of total sales to total assets (SALES_TA) illustrating the sales
generating ability of the firm’s assets. We have taken the natural log of total assets of
the firm as control for the firm size.
In the second model (see column 3, Table II), we test the significance of market value
of firm’s assets obtained from the BSM model as exogenous variable in predicting real
bond defaults. Instead of the level, we have taken the ratio of MVA over default point
(MVA_DP). Default Point (DP) is the book value of short term debt (maturity less than
one year) plus half of long-term debt (maturity more than a year).
In column 4 of Table II, we assess the informational contribution of risk neutral
distance to default (DD) on the probability of actual bond default in the following year.
JRF As we saw earlier, the distance to default ratio measure (DD) is a combined index of
8,1 movement of firm’s asset value, asset volatility (business risk) and also leverage.
In MVA and DD models, we have included natural log of firm’s asset size
(LNASSETS) to compare the size effects in our panel regression. We have also taken
corporate governance by the type of ownership as another non-financial parameter
represented by a dummy (DUMTOP50). This dummy captures whether the firm
52 belongs to Indian top 50 business group category (equals one) or not (zero). Other
studies (Khanna and Palepu, 2000; Gangopadhyay et al., 2001; Bandyopadhyay and
Das, 2005) have observed that top business group firms have a brand reputation
advantage in the product market as well as financial market. These two models
application takes care of industry effects and time effect. The industry effects are
controlled by incorporating 18 industry intercept dummies into regressions (coefficient
results not being reported to conserve space). The time dimension of our panel
regressions is factored in by including a macro variable which is growth rate in gross
national product measured in current price (GNPGRRCP).
The ratio-based MLE results shows that all the financial ratios negatively explain
the probability of default. This result is in line with the theoretical prediction of
traditional models (see Bandyopadhyay, 2006). The results of MVA model shows as
soon as we include market value of firm’s assets as proportion to default point
(MVA_DPT), the result significantly improves in terms of pseudo R 2 (0.58 as
compared to traditional ratio’s 0.50) and accuracy power (90 percent as compared to
Ratio’s 86 percent)[4]. This is despite the fact that accounting-based model already
includes the ratio of the market value of equity to book value of total liabilities
(MVE_BVL). The coefficient of MVA_DP is negatively significant implying that
higher the market value of firm’s assets, lower is the chance of default. Model 3 results
give evidence that risk neutral distance to default (DD) contributes significantly to
explaining future default probabilities when they are included alongside the
accounting and other firm specific non-financial variables (0.61 pseudo R 2). One can
clearly see that risk neutral DD is negatively significant on the probability of default.
This means that as distance to default increases, the chance of default comes down.
This is because the firm is now able to generate better return from its underlying assets
by which it can pay out its debt. When we use DD metric as exogenous parameter
along with the profitability (CASHPROF_TA), liquidity (NWK_TA) parameters and
firm specific size (LNASSETS), reputation (DUMTOP50), industry affiliation (industry
dummies) and time specific components (GNPGRRCP), we get a more accurate
prediction of default (92 percent discriminatory power)[5].
As far as control variables are concerned, our results show that the firm size
parameter (LNASSETS) is negatively significant which means larger firms can absorb
more risk. We have also found that the likelihood of default is less if the firm belongs to
top 50 business group suggesting group firms have more sound and stable financial
health than the unaffiliated firms. This is expected as the other studies have also
shown that top business groups have stability in cash flows and show better
productivity as well as risk sharing through mutual debt guarantees than unaffiliated
firms. The negative significance of macro variable GNPGRRCP reflects the business
cycle effect on corporate default probability. It depicts that if the economy grows well
(with high growth rate of GNP); the chance of default comes down due to the
improvement in corporate performance. On the other hand, default probability Drift towards
increases in the recessionary period. default. Part 2
Conclusions
Our empirical results show that integrating information from the structural model
significantly improves the default predictive power in statistical scoring model. The
results in this paper indicate that the combination of market valuation parameters and 53
the value given in their financial statements (profitability, liquidity, solvency etc.)
along with other firm specific characteristics (like industry affiliation, management
quality, reputation, size etc.) would more meaningfully explain corporate distress
potential. Therefore, banks can no longer ignore the equity market information in their
credit risk capital estimation and risk adjusted performance. The combination of
continuous valuation by the market with the value given in their financial statements
along with the non-financial firm characteristics would benefit the banks and financial
institutions to predict corporate default more accurately and realistically. The
inclusion of BSM parameters into our hybrid default estimation model would assist
banks and financial institutions to bring market capitalization and stock volatility into
the lending equation and therefore can enhance their corporate credit appraisals and
pricing decisions.
A promising direction for future research lies in employing artificial neural network
(ANN) approach on set of market-based parameters along with financial and
non-financial factors to examine the accuracy of default prediction. Several studies in
the literature have enhanced the neural network models to appropriately predict
bankruptcy of financial and non-financial units. One can also test our model
parameters by using non-parametric approach to incorporate the entire distribution of
factors in explaining default. However, in the present study, we are interested to
determine the relationship between realized defaults and their characteristics prior to
default. For this, we applied parametric MLE technique to predict dichotomous
dependent variable (default or no default). In doing so, we could compare the
performance of Merton versus statistical scoring model empirically. We found that a
combination of accounting and market-based information would produce a richer
version of credit scoring model that would benefit the financial institution and
investment managers to understand the real picture of corporate expectations. One can
also extend our work by examining more emerging markets and compare the success
of BSM model in these markets. This article does not have space to address these
issues, but we are leaving this job for future research.

Notes
1. The far-reaching goal of the second Basel accord is aligning the capital requirements of
banks with risk sensitivity. The accord emphasizes the quantification of capital
requirements on the basis of internal rating models. The internal credit rating models of
banks are expected to produce the probability of default and loss given default to estimate
the capital requirements of credit risk.
2. CRISIL is a leading credit rating agency in India which is recently in collaboration with the
international rating agency Standard & Poor’s (S&P).
3. See historical stock price data and S&PCNX500 market price volume data at: www.nseindia.
com/
JRF 4. The accuracy power of the model is obtained by estimation of Power Curve (CAP). This is
constructed by plotting cumulative percentage of firms excluded in the horizontal axes
8,1 versus cumulative percentage of defaulted firms excluded in the vertical axis. To count the
percentage, we ranked the estimated scores in descending order (i.e. worst to best). From the
CAP, we obtain Gini coefficient that measures the accuracy of the prediction. A perfect
random model would have accuracy rate of only 50 percent that would yield a 458 line from
the origin. A better model would produce a steeper CAP such that worst scores cover greater
54 percentage of defaulted firms.
5. If we use only risk neutral default obtained from our BSM structural approach, we get
accuracy of 81 percent.

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Corresponding author
Arindam Bandyopadhyay can be contacted at: arindam@nibmindia.org

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