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The Journal of Risk FinanceCalibrating asset correlation for Indian corporate exposures: Implications for regulatorycapitalArindam Bandyopadhyay Tasneem Chherawala Asish Saha
Article information:To cite this document:Arindam Bandyopadhyay Tasneem Chherawala Asish Saha, (2007),"Calibrating asset correlation for Indiancorporate exposures", The Journal of Risk Finance, Vol. 8 Iss 4 pp. 330 - 348Permanent link to this document:http://dx.doi.org/10.1108/15265940710777298
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Calibrating asset correlation forIndian corporate exposuresImplications for regulatory capital
Arindam Bandyopadhyay, Tasneem Chherawala and Asish SahaNational Institute of Bank Management (NIBM), Pune, India
Abstract
Purpose – This paper is a first attempt to empirically calibrate the default and asset correlation forlarge companies in India and elaborate its implications for credit risk capital estimation for a bank.
Design/methodology/approach – The authors estimate default probabilities and defaultcorrelations of long-term bonds of 542 Indian corporates using rating transitions and pair-wisemigrations over ten year cohorts of firms. Further, the implicit asset correlation from the estimateddefault correlations and default thresholds are derived using the asymptotic single risk factor approach.
Findings – The authors find evidence that default correlations are time variant and vary acrossrating grades and industries. The highest correlations are observed between companies within thesame rating grades (systematic risk impact) and within the same industry (industry specific impact).More interestingly, significantly smooth monotonic relationship between the probability of default(PD) and asset correlation as prescribed by the Basel II IRB document (2006) are not found. Moreover,it is found that the asset correlation range for Indian corporates do not match with what is prescribedfor corporate exposures by BCBS.
Originality/value – The authors address the dilemma implied by the negative relationship betweenPD and asset correlation as suggested by BCBS IRB formula and other research for developedeconomies with estimates of asset correlation for and emerging market like India and demonstrate itsimplications on the estimation of credit risk capital.
Keywords Credit, Credit rating, Default, Capital, India, Risk analysis
Paper type Research paper
IntroductionManaging concentration risk in credit portfolios is an integral part of credit riskmanagement by Banks and FIs. Credit concentration risk may be of two types:
(1) Exposure concentration risk. That is concentration of credit exposure amountsto a single borrower, or a single group, industry or sector.
(2) Correlation risk. That is, concentration based on common or correlated riskfactors between different borrowers, industries or sectors which may lead tosimultaneous default.
Correlation exists between firms in the same industry because of industry specificeconomic conditions. Correlation also exists between companies in different industriesthat rely on the same production inputs and among companies that rely on the samegeographical market. Correlation may also arise due to systematic or macroeconomicconditions in the national or international economy.
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1526-5943.htm
The authors thank an anonymous referee of this journal for extremely helpful suggestions thathelped to improve this paper. They also acknowledge helpful comments from Sanjay Basu.
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The Journal of Risk FinanceVol. 8 No. 4, 2007pp. 330-348q Emerald Group Publishing Limited1526-5943DOI 10.1108/15265940710777298
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Modeling credit quality correlation and default correlation is therefore crucial forbanks to measure and manage portfolio credit risk. This would require studying therisk profile of the bank’s entire credit portfolio and developing the appropriatemethodology for the estimation of default dependence.
Measurement and management of correlation risk in the credit portfolios of bankshas also become an important area of concern for bank regulators worldwide. Indeed,the BCBS (2006) has specifically included an asset correlation factor in the computationof credit risk capital requirement by banks adopting the Internal Ratings Based (IRB)approach.
Development of analytical and empirical models for measuring default dependenceby banks is at an embryonic stage in India. Studying default correlation would requirerelevant data over a sufficiently long time period to capture the common macroeconomic factors across economic cycles. However, most Indian banks do not haveorganized and consistent historical loan rating data for more than two or three years.Thus, the major hurdle in developing an analytical model using actual historical loandefault data is the scarcity of data itself. In our study, we therefore consider long termcorporate bond ratings and default information published by an external rating agencyin India as a proxy for rating of long term loans extended by banks to such corporates.
Our study is the first attempt to empirically derive default correlation and assetcorrelation for large companies in India. We estimate:
. the average transition and default probabilities for various rating grades andindustries;
. the average default correlations across rating classes, across different bondgrades (Investment vis-a-vis Non-Investment Grades), and across variousindustries; and
. asset correlations across rating classes and across different bond grades.
Our analysis not only supports the fact that default events are correlated but alsoprovides numerical estimates of these correlations across rating classes and acrossindustries for an emerging economy like India. The default correlation values reportedin our study would be key inputs for estimating portfolio credit risk, economic capitaland risk adjusted returns on economic capital for large corporate exposures of banks.
The second important result of our paper is that default correlation between firmswithin each rating grade increases as the rating grade worsens, that is, defaultcorrelation is positively related to the default probability (PD) of firms. This result is ofsignificance for Indian banks since it implies that poor credit quality commercial loanportfolios would have to be supported by a higher level of economic capital not justbecause the default probabilities in such portfolios would be high but also because ofhigher inherent default correlations between poor credit quality borrowers.
The Reserve Bank of India (RBI, 2007) has recently (March 20, 2007) releasedrevised draft guidelines for the implementation of Basel II norms by banks in India[1].To facilitate the process of estimating credit risk capital requirements as per the IRBapproach, RBI has suggested that Indian banks should develop their internal ratingmethodology, create the default history and estimate default probabilities (PD) andLoss Given Default (LGD). Two crucial elements that need to be calibrated by the RBIbefore the IRB capital computation formula can be formally prescribed for Indianbanks are: the appropriate asset correlation values; and the relationship between PDand asset correlation in the Indian context.
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To calibrate the appropriate asset correlation values for the regulatory IRB capitalrequirement formula as prescribed by BCBS (2006), we derive asset correlations from ourempirically derived default correlations using the asymptotic single risk factor model. Ourresults show that across IG NIG grades, asset correlation decreases with increasing PD,which is in line with Basel II IRB specifications. However, the decrease in asset correlationwith increase in PD across grades is not smoothly monotonic as it is assumed in the BaselII The asset correlation range is also different in comparison to what is prescribed forcorporate exposures by BCBS (0.12 minimum to 0.24 maximum). As far as within ratinggrades are concerned, we again do not observe any significant difference in assetcorrelation as credit quality deteriorates except between AA-AA v. A-A rating categories.Here also, the asset correlation range is quite different from the BCBS prescription. Thiscorrelation comparison makes sense because asset correlation would be the key inputs toconstructing the IRB regulatory capital risk weights for banks in India.
The rest of the paper is organized as follows. In the following section we review theexisting literature on default correlations. In the next section, we describe the data, thevariables used in our empirical analysis and the methodology for estimating defaultcorrelation and corresponding implicit asset correlation. In the subsequent sections, wediscuss the major empirical findings of our paper. The final section highlights the mainconclusions.
Literature reviewInternationally, several methodologies have been developed to estimate defaultcorrelation and several authors have documented the relationship between the initialcredit quality of the portfolio and the default and asset correlation for commercialportfolios. The structural model approach uses equity correlation as a proxy for assetcorrelation. This approach is based on the seminal work by Merton (1974), according towhich loan default occurs when the market value of the firm’s assets falls below thebook value of debt. Thus, the default correlation between two borrowers is constructedwith the use of correlation of the borrower’s asset returns (derived from equity returns)and the normal inverse of their distance to default. Although intuitive, the saidapproach has not been supported by strong empirical analysis that establishes the linkbetween equity correlation and default correlation. De Servigny and Renault (2002) usea sample of 1,101 firms from S&P’s 12 industry categories and calculate average equitycorrelations across and within industries over the period 1980-2001. They find thatequity correlation is a very noisy indicator of default correlation. In a recent paper,Lopez (2004) has used the structural model framework to empirically derive assetcorrelations for portfolios of USA, Japanese and European firms. His paperdemonstrates that asset correlation for relatively highly rated, large sized companiesis high. According to his explanation, this relationship arises because high creditquality firms are more likely to be influenced by common macro economic conditions.On the other hand, asset correlations for poor credit quality, large sized companies arelow because defaults of such firms are subject to firm-specific problems. This is alsothe relationship which is highlighted by BCBS (2006) wherein, in the credit risk capitalestimation formula for large corporate exposures, asset correlation is a decreasingfunction of probability of default.
Zhou (1997) uses the first-passage-time model within the structural modelframework to derive an analytical formula for calculating default correlations. Hisanalytical framework is substantiated by empirical results using Moody’s default
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database. He concludes that default correlations and underlying asset correlationshave the same sign; the higher the underlying asset correlation, ceteris paribus, thehigher is the default correlation; generally default correlation is lower than the assetcorrelation and, the high credit quality of firms (proxied by the leverage) not onlygenerates a low default probability of each firm but also implies a low defaultcorrelation between firms. Further, high credit quality firms take a longer time to reachthe peak default correlation.
Das et al. (2002) use Moody’s database of USA public non-financial firms toempirically derive the default correlation structure using the framework of reducedform, hazard rate models in which the probability of default is determined byexogenously specified instantaneous default intensity. Their findings partiallycomplement those of Zhou (1997) in that they too find that default probabilities ofissuers are positively correlated. They further observe that default correlationsincrease with the level of default risk in the economy, implying a business cycle effecton default correlations. However, as opposed to Zhou (1997), they conclude that thehighest credit quality issuers have higher default correlation than medium grade firms.
The third approach, used extensively to approximate default correlation, is toestimate the bivariate transition probabilities and default correlations from actualhistorical default data. Lucas (1995), Nagpal and Bahar (2001) and De Servigny andRenault (2002, 2003) extract information about the joint behavior of rating migrationsand defaults directly from historical bond data to calculate joint default probabilities.They note that historical rates of default support the idea that credit events arecorrelated. However, contradictory to the findings of Das et al. (2002), they observe thatdefault correlation increases with the credit risk of firms.
One can clearly see that there are two opposing lines of arguments on therelationship between PD and default correlation as highlighted above. This thereforeimplies that any prior assumption regarding such a relationship for any country wouldresult in a misspecification of the capital requirement to cushion risk inherent in acredit portfolio. In the context of these opposing view points, we have made an attemptto investigate the actual relationship between PD and default correlations (and theimplied asset correlation) for corporates in India.
Data description and methodology for the studyThe results presented in our empirical paper are based on CRISIL’s (a leading creditrating agency in India now owned by Standard & Poor) annual ratings of long-termbonds issued by 542 companies from July 1992 to January 2005[2]. Our data basecomprises of large corporates (those which have issued long term bonds in the debtmarket). The data on defaulted bonds are, however, available only since January 1995and hence has restricted the time period of our study. Our analysis focuses on thedefault correlations across all rating categories as well as across different industries.Accordingly, we have studied the rating movements of corporate bonds from1995-1996 to 2004-2005. The original CRISIL rating scale is divided into fifteencategories (AAA, AA þ , . . . , C). We have, however, used seven rating grades (AAA,AA, A, BBB, BB, B and C) for our analysis. Notches (“ þ ” and “ 2 ”) have beencombined into the main rating grades (e.g. all companies with rating grade AA þ orAA 2 have been assigned the grade AA) to ensure adequate sample size of firms ineach grade. The grade D represents Default which is defined as a credit event wherethe underlying firm has missed payments (a single day’s delay or a short fall of even a
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single rupee in terms of the promised repayment schedule) on a rated instrument. Anypost default recovery is not factored in by CRISIL’s ratings.
In order to ensure adequate sample size of firms in each industry category, we havedivided the CRISIL corporate bond rating data into 11 industry groups based on theirmajor economic activities. In classifying firms into different industry categories, wehave harmonized the Prowess CMIE industry categories with NIC 2 digit industrycategories (Table I)[3]. In calculating within industry default correlations, instead ofusing seven grades, we have chosen to divide the rated universe into twocategories-investment grade (IG) and non investment grade (IG). Investment graderatings correspond to ratings from AAA to BBB, while non investment grade ratings(NIG) are from BB to C. Again, this has been done to ensure adequate sample size foreach rating grade in each industry.
Our methodology for determining default correlations is based on the approachdeveloped by Lucas (1995), Nagpal and Bahar (2001) and De Servigny and Renault (2002,
Industry name Industry typeNo. offirms
Auto/parts Manufacture of transport equipments and parts: ships and boats,railway, commercial vehicles, passenger cars, automobile ancillaries,two and three wheelers, bicycles, aircrafts 37
Chemical Manufacture of organic and inorganic chemicals and chemicalproducts, paints, dyes, photographic goods, rubber, plastic, tubes,petroleum and coal products 116
Diverse Diversified 16
Food products/sugar/tea/tobacco/beverages
Manufacture of dairy products, sugar, tea. Coffee, vegetable oils andfats, bakery and food products, beverages, breweries, tobacco andrelated products 21
Machine/electrical/computers
Manufacture of machinery and equipments other than transportequipments: electronics, electrical, computers, engineering, insulatedwires and cables, fire protection equipments, industrial machineryfor food and textile industries, construction 76
Metal/non-metal Basic metal and alloys industries: iron and steel, Ferro alloys,aluminum, casting of metals, copper, steel tubes, transmissiontowers, non metallic mineral products like cement, mica stone, glassand glass products, ceramic and refractory etc. 65
Other manufacturing Other manufacturing includes optical goods, trade in electricalmachinery, trade in beverages and tobacco, plywood, trade inminerals and energy sources, trade in textiles, shoe uppers etc. 16
Paper Manufacture of paper and paper products, newsprint and printing,publishing and allied 15
Power Power generation and electricity generation and transmission 15
Service Hotel, banking, insurance and financial services 126
Textile Manufacture of cotton textiles, wool, silk and man-made fibertextiles, jute and textile products 39
Total 542
Table I.Industry categories ofsample firms
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2003). As a first step, we have done mortality rate analysis of ten one-year cohorts ofcompanies to find the number of firms in each rating class in each cohort movingtowards default category (D). Each cohort comprises of all the companies which have arating outstanding at the start of the cohort year. From these cohorts, we calculateyear-wise default probabilities for different rating grades and for different industries.Say there are Ti,D number of firms migrating to Default category out of Ni number offirms in the ith rating grade (or industry) over a one year period, where the subscript irepresents the rating grade (or industry) at the start of the period and the subscript Drepresents Default. The one-year probability (PD) of the ith rating grade (or industry) isestimated by counting the frequencies: Ti;D=Ni . The average one-year defaultprobability for the ith rating grade or industry (PDi) is obtained by weighted average,where the weights are the number of firms in the ith rating class (or industry) in aparticular year divided by the total number of firms in all the years:
PDi ¼Xn
t¼1
wti
Tti;D
Nti
ð1Þ
where wti is the weight representing the relative importance of a given year:
wti ¼
Nti
Xn
s¼1
Nsi
: ð1aÞ
In the second step, we compare the pairs of defaulting firms at the end of the periodwith the total number of pairs of firms at the start of the period to count the jointdefault frequency for each year from our data. Here we first consider the jointmigration of two obligors from the same rating grade (say AAA rating) to defaultD. Say there are Ti,D number of firms migrating to Default category out of Ni
number of firms in the ith rating grade, where the subscript i represents the ratinggrade at the start of the period and the subscript D represents Default. The one-yearwithin-grade joint default probability would be: ðTi;DÞ
2=ðNiÞ2. If obligors are moving
from different rating grades (say AA and B) towards default (D), we should beinterested in pairs of number of firms Ti,D and Tj,D migrating respectively tocategory D. The one-year between grade joint default probability (JDP) in such acase would be: Ti;DTj;D=NiNj. The one-year joint default probabilities are arrived atby assuming that the defaulting pair of bonds is drawn with replacement. Thisassumption is important to ensure that we avoid spurious negative defaultcorrelations in cases where only one default event is observed for a particular ratingcategory (or industry).
The next step is to calculate the average joint default probabilities (JDP) over time.For joint default migrations of firms within the same starting rating grade, thefollowing equation is used:
JDPi;i ¼Xn
t¼1
wti
Tti;D
� �2
Nti
� �2ð2Þ
where wti is the weight representing the relative importance of a given year:
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wti ¼
Nti
Xn
s¼1
Nsi
: ð2aÞ
For joint default migration of firms from different starting rating grades, we use thefollowing equation:
JDPi;j ¼Xn
t¼1
wtij
Tti;DT
tj;D
NtiN
tj
: ð3Þ
Where, the weight is given as:
wtij ¼
Nti þ Nt
j
Xn
s¼1
ðNsi þ Ns
j Þ
: ð3aÞ
Once we obtain the estimates of average joint default probabilities (JDP) and averagedefault probabilities (PD), we can calculate the one-year expected default correlationsusing the following formula:
rD;Di;j ¼
JDPi;j 2 PDiPDjffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPDið1 2 PDiÞPDjð1 2 PDjÞ
p : ð4Þ
The above formula (equation 4) is based on the assumption that there is a constantprobability of default (as given by the expected default probability) for a firm or anindustry over time and a constant joint default probability (as given by the average jointdefault probability) over time. However, this does not imply that default probabilities orjoint default probabilities are time invariant. It is the limitation of this method.
Empirical resultsBusiness cycle effects on rating transitionsTo investigate fluctuations of rating transitions over time, we report the Inverse CR(Inv-CR) in Table II. “Inv-CR” is the ratio of number of downgrades to number ofupgrades estimated for each year. The rating revisions are visually better captured bythe bars shown in Figure 1 that depict the number of companies whose long-term debtinstruments were upgraded or downgraded between 1995-1996 and 2004-2005. It canbe seen that Inverse CR ratio is increasing from 1995-1996 to 1998-1999 implying thatthe number of downgrades to number of upgrades were increasing during this period.This coincides with a recessionary period in the Indian economy during which therewere a larger number of downgrades than upgrades. The lower Inv-CR during2000-2001, 2003-2004 and 2004-2005 reflects a period of relative macro economicstability of the Indian economy (Government of India, 2004-2005).
Business cycle effects on default probabilitiesIn Tables III to V, we analyze the rating transition probabilities and defaultprobabilities for various rating grades. In Table III, we present a one-year averagetransition matrix for the entire sample period (1995-1996 to 2004-2005). We find that as
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the credit quality worsens (i.e. rating grades decline) the default probability (PD)increases. One can see from said table that PD jumps sharply from 5.17 per cent forBBB to 28.93 per cent for BB. This justifies our classification of bonds in BB grade andbelow as Non Investment Grade (NIG) and AAA to BBB grades as Investment Grade(IG)[4]. We also find that the rating stability declines as the credit quality worsens[5]. Itis worthwhile to mention that our produced transition matrix also looks similar toCRISIL except the data sample since we are studying the performance of a balancedsample of corporates over the eleven years. CRISIL has not done any study on defaultcorrelation. They also do not report industry wise PDs. Interestingly, ours or CRISIL’stransition matrix and PDs across rating grades is markedly different from Standardand Poor’s transition matrix specially for non investment grades (NIG) companies. Onecompare that our below BBB firms are as risky as S&P CCC firms are.
Year Inv-CR Upgrades Downgrades
1995-1996 1.09 11 121996-1997 4.22 9 381997-1998 18.00 4 721998-1999 19.00 5 951999-2000 9.40 5 472000-2001 1.33 18 242001-2002 20.00 1 202002-2003 6.00 3 182003-2004 0.56 9 52004-2005 0.22 9 2
Table II.Downgrades v. upgrades
Figure 1.
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In Table IV and Table V we present two average one-year transition matrices forthe periods 1995-1996 to 1999-2000 and 2000-2001 to 2004-2005. Except for therating grade BBB and C, the one year PDs for all rating grades are higher for thefirst period as compared to the second period. This is consistent with the results ofthe Inverse CR analysis. This result indicates that default probabilities vary overtime and on an average, PDs are higher during the recessionary period of the IndianEconomy.
Year 2Percentages
Year 1 AAA AA A BBB BB B C D
AAA 97.08 2.92 0.00 0.00 0.00 0.00 0.00 0.00AA 2.54 87.57 7.93 1.05 0.60 0.15 0.00 0.15A 0.00 4.35 79.97 9.14 3.48 0.44 0.73 1.89BBB 0.00 0.74 5.90 67.53 14.76 2.21 3.69 5.17BB 0.00 0.83 0.00 1.65 57.02 4.13 7.44 28.93B 0.00 0.00 0.00 7.41 0.00 55.56 7.41 29.63C 0.00 0.00 0.00 2.33 0.00 0.00 51.16 46.51D 0.00 0.00 0.31 0.31 0.92 0.00 0.00 98.46
Table III.One-year averagetransition matrix(1995-1996 to 2004-2005)
Year 2Percentages
Year 1 AAA AA A BBB BB B C D
AAA 97.50 2.50 0.00 0.00 0.00 0.00 0.00 0.00AA 3.34 92.10 3.95 0.61 0.00 0.00 0.00 0.00A 0.00 9.46 80.41 6.08 0.68 0.00 2.03 1.35BBB 0.00 1.69 8.47 69.49 6.78 5.08 0.00 8.47BB 0.00 3.23 0.00 6.45 74.19 3.23 0.00 12.90B 0.00 0.00 0.00 13.33 0.00 53.33 6.67 26.67C 0.00 0.00 0.00 4.35 0.00 0.00 47.83 47.83D 0.00 0.00 0.41 0.41 1.22 0.00 0.00 97.97
Table V.One-year averagetransition matrix(2000-2001 to 2004-2005)
Year 2Percentages
Year 1 AAA AA A BBB BB B C D
AAA 96.12 3.88 0.00 0.00 0.00 0.00 0.00 0.00AA 1.77 83.19 11.80 1.47 1.18 0.29 0.00 0.29A 0.00 3.48 93.91 11.74 5.00 0.65 0.43 2.39BBB 0.00 0.47 5.19 66.98 16.98 1.42 4.72 4.25BB 0.00 0.00 0.00 0.00 51.11 4.44 10.00 34.44B 0.00 0.00 0.00 0.00 0.00 58.33 8.33 33.33C 0.00 0.00 0.00 0.00 0.00 0.00 55.00 45.00D 0.00 0.00 0.00 0.00 0.00 0.00 0.00 100.00
Table IV.One-year averagetransition matrix(1995-1996 to 1999-2000)
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Business cycle effects on joint default frequenciesIn Figure 2, we plot the joint default frequency over the period of ten years betweenIG-IG, NIG-NIG and IG-IG bonds. It is quite clear from these diagrams that joint defaultfrequencies within the NIG group have a more pronounced co-movement with theeconomic cycle. The year 1998-1999 has witnessed a slight increase in correlated defaultbetween the IG-NIG grades and even within the IG group. The joint default movements,in general, are lower during the economic recovery period (2002-2003 to 2003-2004).
It is clear from the findings in the above three sections that rating transitions,default probabilities and joint default frequencies vary over the business cycle. Thisclearly indicates that default correlations are time varying and would tend to increaseduring the recessionary phase. Further, the business cycle impact on the defaultcorrelation would be higher for the low credit quality (NIG-NIG) firms as compared tothe IG-IG group or IG-NIG group.
Industry wise default probabilitiesTable VI presents the average default probabilities for each of the 11 industries. Aswould be expected, the PD for each industry is higher for the NIG class as compared tothe IG class. The PD for the NIG class as a whole (all industries) is 3.30 per cent and thePD for the IG class as a whole is 1.42 per cent. The highest default probabilities areobserved for Machine/Electrical/Computers industry (7.51 per cent) followed by FoodProducts industry (7.41 per cent)
Default correlation across rating gradesTable VII reports the one-year average joint default probabilities across rating classes.To derive the numerical estimates of default correlation and to have a betterunderstanding of the relationship between default correlation and the default risk ofborrowers, we calculate the average default correlation across rating grades usingequation (4). The results are presented in Table VIII.
In Table VIII, we report the estimates of default correlation across rating classes.We have also tested whether the correlation coefficients are statistically different fromzero for validating these figures. The significance of the correlation coefficient iscomputed by testing the hypothesis that the correlation is zero by using the followingformula:
t ¼r
ffiffiffiffiffiffiffiffiffiffiffin2 2
p
ffiffiffiffiffiffiffiffiffiffiffiffiffi1 2 r 2
p
where r is the correlation coefficient and n is sample size, and where one looks up the tvalue in a table of the distribution of t, for (n 2 2) degrees of freedom. If the computed tvalue is as high or higher than the table t value, then the researcher concludes thecorrelation is significant (that is, significantly different from 0). The t values and thedegrees of freedom of the default correlation coefficients are reported in theparentheses below each coefficient in Table VIII.
The first important conclusion that we draw from Table VIII is with regard to theestimated values of the default correlations. The values of significant positive defaultcorrelations are much higher than those quoted for developing economies. On the otherhand, we also report a significant negative default correlation between medium andlow credit quality grades. For comparison, we show in Tables IX and X, across rating
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Figure 2.Joint default frequency
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category default correlation matrices derived by De Servigny and Renault (2004) andLucas (1995) respectively.
The second important conclusion that we draw from Table VIII is that withdeclining credit quality, default correlation increases within the same rating grade (forexample, the default correlation within AA rating grade is 1.222 per cent and itincreases up to 24.55 per cent within B rating grade). Most of the within grade defaultcorrelations are positive and significantly different from zero (Table VIII). This tablealso shows that there is relatively lower default correlation between the lower gradecategories than between the higher rating grades (for example, default correlationbetween A and AA is 1.71 per cent vis-a-vis default correlation of 0.32 per cent betweenB and BBB). Further, default correlation is low and in some cases, negative, betweenthe low rating grades (B and C) and higher rating grades (A and AA). As far asnegative correlations are concerned, we find that except for default correlation betweenA and B (26.65 per cent), all other negative default correlations are marginal. Thismay be a result of low sample size of defaulted bonds in these categories.
Table XI best captures the effect of the common macroeconomic environment oncorrelated defaults. The results reflect that default correlation within IG group is lowerthan the default correlation within the NIG group over a one-year horizon for allindustries taken together. This further reinforces our earlier conclusion that as wemove from IG-IG to NIG-NIG category (i.e. credit quality is worsening and PD is
PercentagesIndustry IG NIG ALL
Auto/parts 1.79 16.67 2.87Chemical 0.88 32.00 3.98Diverse 3.70 18.75 7.14Food products/sugar/tea/tobacco/beverages 1.37 55.56 7.41Machine/electrical/computers 2.75 37.14 7.51Metal/non-metal 3.11 35.48 6.60Other manufacturing 0.00 0.00 0.00Paper 0.00 33.33 5.66Power 0.00 0.00 0.00Service 0.22 27.78 1.25Textile 1.52 40.00 5.44All 1.42 32.98
Table VI.Industry-wise average
one- year PD for IG andNIG and Pool (1995-1996:
2004-2005)
Year 2Percentages
Year 1 AAA AA A BBB BB B C
AAA 0.000AA 0.000 0.002A 0.000 0.012 0.085BBB 0.000 0.028 0.186 0.655BB 0.000 0.098 0.737 2.222 11.052B 0.000 0.000 0.146 1.563 6.751 13.898C 0.000 0.066 0.689 2.174 11.881 12.088 25.748
Table VII.One-year average joint
default probabilitiesacross rating classes
(1995-1996 to 2004-2005)
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Yea
r2
AA
AB
BB
BB
BC
Yea
r1
%t-
val
ue
(%)a
%t-
val
ue
(%)a
%t-
val
ue
(%)a
%t-
val
ue
(%)a
%t-
val
ue
(%)a
%t-
val
ue
(%)a
AA
1.22
20.
45,1
336
A1.
710.
63,1
357
2.68
1.00
,137
8B
BB
2.38
0.73
,939
2.93
0.77
,690
7.93
**
1.85
,542
BB
3.10
0.87
,789
3.10
0.88
,810
7.25
*1.
44,3
9213
.06
**
2.04
,242
B2
2.51
20.
66,6
952
6.65
**
21.
78,7
160.
320.
055,
298
28.
792
1.07
,148
24.5
5*
*1.
83,5
4C
20.
192
0.05
1,71
12
2.79
20.
75,7
322
2.08
20.
37,3
142
6.96
20.
89,1
642
7.43
20.
61,7
016
.537
*1.
54,8
6
Notes:
at-
val
ues
and
the
nu
mb
erof
obse
rvat
ion
sre
spec
tiv
ely
;*
den
otes
sig
nifi
can
ceat
5-10
%;
**
den
otes
the
sig
nifi
can
cele
vel
at5%
orb
ette
r
Table VIII.One-year defaultcorrelations across ratingclasses (1995-1996 to2004-2005)
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increasing), default correlation is increasing. We can explain this by the fact that NIGgrade firms can be considered as a portfolio of poor credit quality firms with differentrating grades including BB, B and C. Such portfolio would be relatively more sensitiveto common risks than to idiosyncratic risks. If the economy experiences a downturn, allthe firms within NIG class are more likely to experience problems leading to defaults
Default correlation across industriesWe have applied the methodology described previously to compute defaultcorrelations across industries. The results are shown in Table XII. The highestcorrelations can be observed in the diagonal of the correlation matrix, i.e. within thesame industry. This is obvious, since firms belonging to the same industry are morelikely to default simultaneously. Thus, irrespective of growth prospects, risk is high ifthe bank’s portfolio is more concentrated in a single industry. The off-diagonal
Year 2Percentages
Year 1 AA A BBB BB B CCC
AA 0.16A 0.02 0.12BBB 20.03 0.03 0.33BB 0.00 0.19 0.35 0.94B 0.10 0.22 0.30 0.84 1.55CCC 0.06 0.26 0.89 1.45 1.67 8.97
Sources: De Servigny and Renault (2004), Standard & Poor’s CreditPro
Table IX.One-year default
correlations all countries,all industries, 1981-2002
Year 2Percentages
Year 1 Aaa Aa A Baa Ba B
Aaa 0Aa 0 0A 0 0 0Baa 0 0 0 0Ba 0 0 0 0 2B 0 1 0 1 4 7
Note: Moody’s Investors Service ratings of all non-municipal issuersSource: As reported by Lucas (1995)
Table X.One-year default
correlations, 1970-1993
IG NIG% t-value (%)a % t-value (%)a
IG 2.08 * 1.31,3942NIG 1.43 0.66,2162 6.59 * 1.29,382
Notes: * Denotes significance level at 5-10%; a t-values and the degrees of freedom respectively
Table XI.One-year default
correlations across IGand NIG grades,
1995-1996 to 2004-2005
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Per
cen
tag
es
Au
to/p
arts
Ch
emic
alD
iver
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ood
/su
gar
/te
a
Mac
hin
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onic
sM
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etal
Oth
erm
anu
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2.96
Ch
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iver
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0.61
3.12
21.2
6F
ood
/su
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/tea
20.
611.
9610
.70
10.4
4M
ach
ine/
elec
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ics
1.02
2.61
12.3
75.
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77M
etal
/non
-met
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322.
404.
402.
815.
004.
38O
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man
ufa
ctu
rin
g0.
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000.
000.
000.
000.
000.
00P
aper
0.00
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0.00
0.00
0.00
0.00
0.00
0.00
Pow
er0.
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000.
000.
000.
000.
000.
000.
000.
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1.32
1.03
5.89
3.72
5.45
2.96
0.00
0.00
0.00
4.28
Tex
tile
0.24
1.62
20.
361.
962
0.02
0.63
0.00
0.00
0.00
0.35
5.37
Table XII.One- year defaultcorrelations acrossindustries, period:1995-2006 to 2004-2005
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correlations tend to be relatively low. This would give banks ample opportunities toexploit diversification strategies across industries and thereby reduce the unexpectedlosses on their large commercial loan portfolios.
Deriving implied asset correlation from default correlationIn order to compare the results of our study to the Basel II credit risk capitalformulation, we need to derive the implicit asset correlation from our estimates ofdefault correlation. For this, we have followed the asymptotic single risk factor basedapproach. In this approach, the key risk driver is the value of the firm’s assets. It isassumed that each firm earns some random return on its assets (Ai) at the horizon(T ¼ 1 year). If the return is sufficiently negative, the value of the firm’s assets fallsbeneath the value of its fixed liabilities, and the firm defaults. The realized returns are aweighted sum of a single common risk factor (representing systematic risk) and ashock idiosyncratic to the firm (Gordy and Heitfield, 2002). Both of these followstandard normal distribution. The idiosyncratic component is uncorrelated with thesystematic component and with other firms’ idiosyncratic components.
We assume Ai , Nð0; 1Þ; when Ai falls below a critical default threshold say Ki
(popularly known as distance to default), default is triggered. Thus:
PDi ¼ Pr½Ai # Ki�
) Ki ¼ N 21ðPDi ÞÞ: ð5Þ
The Ki cut-off level is thus a function of the ith firm’s rating grade.The joint default probability can therefore be obtained by using the following
expression:
JDPij ¼ Pr½Ai # Ki;Aj # Kj� ¼ N 2ðKi;Kj; raijÞ ð6Þ
where, N2 (.) denotes the cumulative bivariate standard normal distribution, and, raijdenotes the asset correlation between firm i and firm j.
Given the values of JDPij (empirically derived), Ki and Kj (from equation 5 above),we can infer the “implied asset correlation” (raij) by inverting the joint distribution:
raij ¼ N212 ðKi;Kj; JDPijÞ: ð7Þ
The implied asset correlations within IG (raIG2IG) and NIG (raNIG2NIG) grade firms and
across IG-NIG (raIG2NIG) grade firms are estimated used the methodology described
above, presented in Table XIII.The asset correlation estimates reveal that as PD increases (credit quality worsens
from IG to NIG grade), asset correlation decreases. This relationship is the opposite ofthe relationship between PD and default correlation as observed in Table VIII. We havealso tested whether these variation in the asset correlation observed across grades isstatistically significant. A t test is used to test for the difference of two correlationsassuming independent samples. For this, we have first used Fisher’s z scoretransformation technique to convert these correlation estimates into a z-score forpurpose of our hypothesis testing. This is done by dividing the correlation plus 1, bythe same correlation minus 1; then taking the natural log of the absolute value of theresult; then divide that result by 2[6]. Next, we estimate the standard error of difference
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between the two correlations[7]. After obtaining z scores and standard errors (SE), wecompute the t value by dividing the difference between two z scores by the standarderror. The t values along with the number of observations are reported in theparentheses of the asset correlation coefficients. One can see that there is significantasset correlation difference across IG-IG v. NIG-IG and IG-IG v. NIG-NIG. However,NIG-IG v. NIG-NIG difference is not significant. Hence, the decrease in asset correlationwith increase in PD across grades is not smoothly monotonic as assumed in the Basel II(2006) document.
We also estimate implied asset correlations within each rating grade starting fromAA to C to find if there is any difference in asset correlation in a more granular way.The results from Table XIV show that there is no significant monotonic relationshipbetween PD and asset correlation within rating grades. In fact, we observe that thoughthe asset correlation within AA grade is high, the correlation value significantly fallsfor A grade and subsequently increases (though increase is statistically insignificant)as the credit quality further worsens (up to B grade). This empirically observedrelationship is in contradiction to the Basel II asset correlation formula which assumesa smooth inverse relationship between PD and asset correlation.
ConclusionsThe main aim of this paper is to derive estimates of default correlations and assetcorrelations for large companies in India. Our empirical results substantiate thepresence of default correlation due to macroeconomic factors and/or industry-specificfactors. Since default events are not independent, as is evident from our observations,the correlation effects need to be considered carefully in managing and measuringconcentration risks in credit portfolios. We also find corroborating evidence thatdefault correlations vary over time due to the business cycle effect and that default
N t-valuesa
IG-IG 0.162NIG-IG 0.035 * 4.79NIG-NIG 0.029 20.11
Notes: a t-values of the difference between the correlation coefficients; the t value for the differencebetween correlation coefficients of IG-IG v. NIG-NIG is 2.5 and is significant at 1% level; * denotes thesignificance level at 5% or better
Table XIII.Implicit asset correlationsacross IG and NIG grades
N t-valuesa
AA-AA 0.35A-A 0.19 * 4.50BBB-BBB 0.22 20.62BB-BB 0.29 20.96B-B 0.33 20.29C-C 0.28 0.31
Notes: a t-values of the difference between the correlation coefficients; * denotes the significance levelat 5% or better
Table XIV.Implicit asset correlationswithin rating grades
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correlations vary across rating grades and industries. The highest default correlationsare observed between companies within the same rating grades (systematic riskimpact) and within the same industry (industry specific impact).
Most interestingly, we do not find significantly smooth monotonic relationshipbetween the probability of default (PD) and asset correlation as prescribed by the BaselII IRB document (2006). Our results show that across IG NIG grades, asset correlationdecreases with increasing PD, which is in line with Basel II IRB specifications.However, the decrease in asset correlation with increase in PD across grades is notsmoothly monotonic as it is assumed in the Basel II. The asset correlation range is alsodifferent in comparison to what is prescribed for corporate exposures by BCBS (0.12minimum to 0.24 maximum). As far as within rating grades are concerned, we again donot observe any significant difference in asset correlation as credit quality deterioratesexcept between AA-AA v. A-A rating categories. Here also, the asset correlation rangeis quite different from the BCBS prescription.
These findings have serious implications for banks which will compare their IRBregulatory capital with their economic capital as in the case of economic capital therehave more flexibility. To further elaborate, this may encourage banks to arbitrage theirregulatory capital by lending to poor credit quality corporates. Moreover, since PDs oflower grades are higher in comparison to USA ratings, Basel II correlation would belower in the non-investment grade categories corporate assets in emerging market (likeIndia) than the developed market. This will further encourage capital arbitrageactivities. The Basel II correlation function (in which correlation is a declining functionof PD) is quite possibly justified more on political grounds (i.e. a desire to favor smalland medium enterprises) than with reference to empirical evidence.
Notes
1. The Reserve Bank of India has stipulated that Indian banks with overseas presence andbranches of foreign banks in India will adopt Basel II norms with effect from March 31, 2008and other banks not later than March 31, 2009. Subject to meeting some minimum qualifyingcriteria, some banks may be allowed to migrate to IRB Approach.
2. External credit rating agencies in India are: Credit Rating Information Services of IndiaLimited (CRISIL), Investment Information and Credit Rating Agency (ICRA) and CreditAnalysis and Research Limited (CARE). CRISIL began its operations in 1987. In 1992, theReserve Bank of India and the Securities and Exchange Board of India (the main regulatorsof India’s financial markets) made ratings mandatory for various classes of debtinstruments. ICRA was established in the year 1991. CARE was incorporated in April 1993.
3. CMIE and NIC are corporate databases in India. For a discussion on concordance, seeVeeramani (2001), Debroy and Santhanam (1993).
4. In our sample, a few companies which were assigned Default Grade for their long term debthave subsequently been upgraded to Non-Default Categories, thereby implying that the PDfor D grade is not 100 per cent. Thus the Default grade is not an all – absorbing state.
5. Stability of ratings implies that the probability that a company would maintain its ratinggrade at the end of the period is higher than its migration to any other rating grade duringthe period.
6. The formula for z score: z ¼ ln[j(r þ 1)/r 2 1)j ]/2 where r is the default correlationcoefficient.
7. Standard error ðSEÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1n123 þ
1n223
qwhere n1 and n2 are the sample sizes of two
independent samples.
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References
Basel Committee on Banking Supervision (BCBS) (2006), International Convergence of CapitalMeasurement and Capital Standards: A Revised Framework, Publication No. 128, Bank forInternational Settlements, Basel, June.
Das, S.R., Freed, L., Geng, G. and Kapadia, N. (2002), “Correlated default risk”, working paper,Default Risk.
De Servigny, A. and Renault, O. (2002), “Default correlation: empirical evidence”, working paper,Standard and Poor’s.
De Servigny, A. and Renault, O. (2003), “Correlations evidence”, RISK, July, pp. 90-4.
De Servigny, A. and Renault, O. (2004), Measuring and Managing Credit Risk, Chapter 5,Standard & Poor’s, McGraw-Hill Companies, Inc., New York, NY.
Debroy, B. and Santhanam, A.T. (1993), “Matching trade codes with industrial codes”, ForeignTrade Bulletin, Indian Institute of Foreign Trade.
Government of India (2004-2005), Economic Survey 2004-2005, Government of India.
Gordy, M. and Heitfield, E. (2002), “Estimating default correlations from short panels of creditrating performance data”, working paper, Federal Reserve Board, Washington DC.
Lopez, J.A. (2004), “The empirical relationship between average asset correlation, firmprobability of default, and asset size”, Journal of Financial Intermediation, Vol. 13 No. 2,pp. 265-83.
Lucas, D.J. (1995), “Default correlation and credit analysis”, Journal of Fixed Income, Vol. 4 No. 4,pp. 76-87.
Merton, R.C. (1974), “On the pricing of corporate debt: the risk structure of interest rates”, Journalof Finance, Vol. 29, pp. 449-70.
Nagpal, K. and Bahar, R. (2001), “Measuring default correlation”, RISK, Vol. 14, March,pp. 129-32.
Reserve Bank of India (2007), Revised Draft Guidelines for Implementation of the New CapitalAdequacy Framework, March 20, RBI, Mumbai.
Standard & Poor’s (n.d.), Standard & Poor’s Credit Por, McGraw-Hill, New York, NY.
Veeramani, C. (2001), “Analyzing trade flows and industrial structure of India: the question ofdata harmonization”, working paper, CDS , Thiruvanthapuram.
Zhou, C. (1997), “Default correlation: an analytical result”, Mimeo, Federal Reserve Board,Washington, DC.
Further reading
Blalock, H. (1972), Social Statistics, McGraw-Hill, New York, NY, pp. 406-7.
Corresponding authorArindam Bandyopadhyay can be contacted at: [email protected]
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