This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Credit risk measurement remains a critical field of top priority in banking finance, directly implicated in the recent global financial crisis. This paper examines the dynamic linkages between credit risk migration due to rating shifts and prevailing macroeconomic conditions, reflected in alternative business cycle states. An innovative empirical methodology applies to bank internal rating data, under different economic scenarios and investigates the implications of credit risk quality shifts for risk rating transition matrices. The empirical findings are useful and critical for banks to align to Basel guidelines in relation to core capital requirements and risk-weighted assets in the underlying loan portfolio.

Credit risk is defined as “the potential that a bank borrower or counterparty will fail to meet its obligations in accordance with agreed terms” by the Basel Committee on Banking Supervision [

According to Basel II and III guidelines, banks are allowed to incorporate their own estimates of different risk exposures, adopting internal risk rating systems, in order to realistically assess their regulatory capital requirements, known as the “internal-ratings-based” (IRB) approach. Only banks meeting certain minimum conditions, disclosure requirements and approval from their national supervisor are allowed to apply this approach [

In a broader context, the assignment process of credit risk rating takes into account both qualitative and quantitative elements ([

To this end, credit ratings facilitate bank evaluation of borrower’s credit quality and worthiness. Credit rating (or scoring) transition, in specific, is the migration of a debt instrument from one rating to another rating over a period of time. This migration is the movement either as an upgrade or a downgrade from an existing rating and indicates the change in the credit quality of an entire loan portfolio as well as the potential for significant financial stress and loan default [

The core objective of the paper contributes to the empirical investigation of credit risk transition patterns in different business cycle states. More specifically, the study attempts to model corporate rating migration probabilities on bank loan portfolios, incorporating the state of real economic activity as well. The empirical approach assumes an IRB bank internal rating framework. The paper proceeds as follows.

As BCBS postulates “borrowers and facilities must have their ratings refreshed at least on an annual basis; certain credits, especially higher risk borrowers or problem exposures, must be subject to more frequent review. In addition, banks must initiate a new rating if material information on the borrower or facility comes to light” [

Past relevant studies have dealt with credit rating migration analysis taking into consideration the following issues. In case a sequence follows a first-order Markov process, the migration probability matrix can be critical in revealing transition properties. This outcome, however, may be biased towards the dependence of immediately successive events and does not contain all prior events [

Transition matrices are at the centre of modern credit risk management. A standard specification for rating transition probabilities is the first-order, time-homogeneous Markov model, which is based on the assumptions that (a) the probability of migrating from one rating class to another depends on the current rating only and (b) the probability of changing from one rating class at time

A number of studies postulate that credit ratings under the first-order Markov assumption provide a reasonable practical approximation, as long as different transition matrices are considered in booms from contraction states [

The cross-sectional and temporal homogeneity of transition intensities is critical for deriving the modeling approach to transition matrices. A number of past studies investigate transition probabilities functions of distance points in time between different rates and study whether the same transition matrix can be used for each-point-in time (PIT) independently of the date points in time. Some studies conclude that credit rating transitions can be adequately modeled as a Markov chain for typical forecast horizons (one or two years), based on in-sample datasets [

Several studies specify non-homogeneous models that incorporate the notion of cyclicality and treat credit rating migrations as a non-memory-less process [

When modeling credit rating migration over a specific time-horizon (not in infinity), time-homogeneity is a key issue. Modeling rating transition as a Markov chain process implies that default is considered to be an absorbing state, that is, in the long-term all assets are in default. Past studies based on external rating data and up to two-year forecasts, postulate that credit rating dynamics can be adequately modeled as a Markov chain [

A number of studies incorporate critical macroeconomic explanatory factors and business cycle states in modeling rating transition probabilities, in order to establish linkages between underlying economic conditions and credit risk migration. Transition probabilities are seen to depend on industry, company, location and business cycle states [

Jafry and Schuermann [

Α model of discrete-time maximum likelihood (DTML) is now discussed (quarterly intervals); it incorporates a parametric approach to account for the state of the economy by including key macroeconomic factors. The framework applied here is suitable for producing maximum likelihood (ML) estimates, whenever the exact time of movement between rating classes and the class occupancy between observation times are unknown; it also takes into account that the inter-examination periods (time-spans between successive ratings) may vary for different firms or individual borrowers.

Initially, certain critical differences between discrete and continuous-time frameworks are discussed. For that, a first-order time-homogenous Markov chain _{t}_{o}_{1}_{j}_{jn}_{j}_{j}_{j−1} = _{n}_{D}_{D−1} correspond to decreasing levels of creditworthiness and _{D}_{D}_{D}^{th} element, namely _{ll’}_{ll’}

In case that observation time points are not identical and equally spaced, the cohort estimator remains “poor” as it does not correspond to the ML estimator of _{ll’}

In the continuous-time maximum likelihood (CTML) framework, the Markov chain applies transition intensities _{ll’}_{ll’}_{D−1} transition intensities _{ll’}_{ij}_{ij}_{t}_{D}_{D}^{Qs}

In this case, the ML estimator of the transition intensity is given by Equation (3):

Based on earlier empirical studies [_{ll’}_{ll’}_{0} is a _{D}_{D}^{th} column is the right eigenvector for _{l}_{i0}_{i1},…,_{i0},_{i1},…,_{D}

Assuming that the exact time of default is known but the rating class before the default is not known, the censored observations (in the set _{D}_{D−1}

The non-censored observations (firms _{ij}_{D−1}

The total likelihood function is the product of the likelihood contributions over all _{i0}

Considering the discrete-time framework (quarterly intervals), by transforming Equation (2):
_{quarter}

The total likelihood function is the outcome of the likelihood contribution over firm _{ll’}_{quarter}

Thus, the log-likelihood function is given in Equation (13) as:

Equation (13) indicates that the quarterly transition matrix is evaluated within every observation available, where only the exact time of default is known but the previous rating class (prior to default) is unknown. Hence, an attractive feature of DTML against CTML relates to the issue that the former approach does not require iterative eigenvalue calculations to produce an outcome. In order to obtain a ML outcome in the general case of _{D}

The incorporation of business cycles and the state of the economy into a time-homogenous Markov chain in a DTML framework is now discussed. As past studies postulate, the approach to estimate matrices conditioned on the business cycle remains a critical issue [_{i,j}^{th}

Two separate time-homogenous rating migration matrices can be estimated, conditioned on the boom and contraction state of the economy, respectively. The total transition matrix (estimated on all available observations) is used to construct the average transition probabilities. The transition matrix is anticipated to shift between upward or downward market phases, depicted by the explanatory macroeconomic variables (such as GDP per capita; GDP growth; inflation rate; external debt/exports, fiscal/external balance; [_{quarter}_{average}_{boom}_{contraction}_{ll’}_{j}^{(tij+1−tij)} is the ^{th} element of:
_{j}_{ij}

In case of inclusion of

A number of past studies examine the issue of business cycles and states of the economy in the context of credit risk [

Past studies incorporate a variety of statistical approaches, models and measurements to deal with the empirical analysis of rating migration matrices. The next sections discuss briefly the singular value decomposition metric and bootstrapping approaches. The latter are frequently incorporated in transition matrix analysis, as they arguably bear attractive properties and flexibility [

The singular value decomposition (SVD) is a generalization of the eigen-decomposition which can be used to analyze rectangular matrices. The main idea of the SVD is to decompose a rectangular matrix into three simple matrices: two orthogonal matrices and one diagonal matrix. Because it gives a least square estimate of a given matrix by lower rank matrix of same dimensions, the SVD is equivalent to principal component analysis (PCA) and metric multidimensional scaling (MDS) and is, therefore, an essential tool for multivariate analysis [_{SVD}_{D}_{D}_{j}^{th} eigenvalue of a _{D}_{D}_{SVD}_{SVD}_{I}_{II}_{SVD}_{I}_{II}_{SVD}_{I}_{SVD}_{II}

The bootstrap procedure involves choosing random samples with replacement from a data set and analyzing each sample in the same way, with each observation selected separately in random from the original dataset [

The bootstrap approach applied in this study involves the following steps: first, selection of a number of firms in random out of the sample under study along with their rating histories; subsequent replacement until the number of firms is the same as in the original sample; second, incorporation of a cohort and a DTML estimation approach; third, repetition (B-1) times of the two previous steps, with computation of the comparative metric _{SVD}

The dataset of the study is based on the entire loan portfolio and internal rating system of a major Austrian bank (anonymity preserved for confidentiality reasons). An initial empirical step relates to defining the segmentation of business sectors; this is based on the respective Standard & Poor’s (S&P) segregation, including: financial institutions; insurance; consumer/services; energy and national resources; real estate; leisure time/media; and transportation. Critical issues include also the specification of a rating system with credit quality classes, grades and probabilities of migration from one class to another over the credit risk horizon. Rating agencies, such as Moody’s [

Past studies on internal rating systems [

A critical step relates to the specification of the risk horizon. The study sample includes both large and “small and medium-sized enterprise” (SME) obligors with an annual turnover of at least €2.5 million and firms originating from a diversity of business sectors and countries of origin. These borrowers are classified according to their rating history over a 10-year horizon. The rating history of all borrowers (not defaulted by that year-end) in the reference (data-provider) bank’s loan portfolio is obtained, as of 31 December 2008. In addition, rating information for all borrowers that defaulted during 1995–2008 is collected. Legal bankruptcy proceedings and loan loss provisions are used as proxies for default. The observation period is eventually restricted to 1998–2008, in order to avoid survivorship bias and to overcome information constraints.

The dataset contains initially 210,000 observations on 51,000 borrowers, at quarterly intervals [

Following the initial discussion of

Since the sample under study consists of heterogeneous firms that cannot be treated as a homogenous group, a single macroeconomic variable for the sample as a whole is rendered inappropriate. As a result, a smaller sample, consisting only of domestic (Austrian) firms/obligors, is finally undertaken; this results in 22,000 observations of 5000 firms (76.5% of the sub-sample exhibits an inter-examination frequency of one year; 16% of less than one year; and, 7.5% of more than one year). This sample is subsequently further divided into two sub-samples that correspond into a “boom” and a “contraction” economic state, respectively, in line with past relevant studies [

A number of studies propose different approaches in order to assess threshold values for macroeconomic variables, such as, for instance, calculation of average or median values of the factor under study; the best performing part is assumed to reflect the boom state and the worst performing part the contraction state, respectively ([

Average transition matrices in time-homogeneity for boom and contraction phases are now estimated. The estimation of a one-quarter transition matrix proceeds on the basis of the full sample of the bank loan portfolio under study, consisting of 185,000 observation pairs and targeting to maximize the log-likelihood function as stated in Equation (13).

The value of Δ_{SVD}_{SVD}_{SVD}_{SVD}_{SVD}

The cohort transition matrix is seen to be significantly more diagonal-dominant (meaning that most of the probability mass resides along the diagonal) compared with the ML transition matrix, indicating that the latter matrix captures mobility (shifts) more efficiently. The two methods generate different probabilities of default. The one-year cohort estimator incorporates only yearly noted migrations and, in general, it is seen to typically underestimate default risk along all rating grades. Broadly, past studies conclude mixed empirical findings on the cohort method, indicating over- or under-estimated PDs [

Transition probabilities in time-homogeneity: Full sample.

From → To | 1 | 2 | 3 | 4 | 5 | Default |
---|---|---|---|---|---|---|

1 | 0.01821 | 0.00553 | 0.00712 | 0.00003 | 0.00000 | |

(0.00173) | (0.00152) | (0.00052) | (0.00023) | (0.00006) | (0.00000) | |

2 | 0.01272 | 0.03723 | 0.01022 | 0.00157 | 0.00036 | |

(0.00093) | (0.00218) | (0.00192) | (0.00081) | (0.00035) | (0.00012) | |

3 | 0.00024 | 0.00411 | 0.03925 | 0.00392 | 0.00051 | |

(0.00004) | (0.00021) | (0.00083) | (0.00073) | (0.00027) | (0.00005) | |

4 | 0.00024 | 0.00071 | 0.02382 | 0.01661 | 0.00381 | |

(0.00003) | (0.00011) | (0.00055) | (0.00076) | (0.00040) | (0.00029) | |

5 | 0.00020 | 0.00006 | 0.00482 | 0.05120 | 0.01920 | |

(0.00012) | (0.00004) | (0.00052) | (0.00240) | (0.00280) | (0.00156) | |

Default | 0.00000 | 0.00000 | 0.00000 | 0.00000 | 0.00000 | |

1 | 0.04672 | 0.00833 | 0.00388 | 0.00039 | ||

(0.00283) | (0.00273) | (0.00081) | (0.00052) | (0.00019) | (0.00029) | |

2 | 0.03066 | 0.08177 | 0.02993 | 0.00283 | 0.00038 | |

(0.00188) | (0.00293) | (0.00239) | (0.00193) | (0.00039) | (0.00133) | |

3 | 0.00122 | 0.01982 | 0.09555 | 0.00611 | 0.00122 | |

(0.00017) | (0.00044) | (0.00152) | (0.00121) | (0.00025) | (0.00015) | |

4 | 0.00067 | 0.00261 | 0.07211 | 0.04122 | 0.00633 | |

(0.00007) | (0.00002) | (0.00084) | (0.00249) | (0.00082) | (0.00018) | |

5 | 0.00052 | 0.00054 | 0.01883 | 0.13331 | 0.06241 | |

(0.00026) | (0.00027) | (0.00073) | (0.00422) | (0.00467) | (0.00390) | |

Default | 0.00000 | 0.00000 | 0.00000 | 0.00000 | 0.00000 |

Both transition matrices are estimated for 1998–2008. The DTML transition matrix is based on all observation pairs with an inter-examination time of less than or equal to five years. Standard errors (in parentheses) are based on a non-parametric bootstrap approach with B = 1,000 replications. The 99% confidence interval is calculated at 0.0721–0.0824 by non-parametric bootstrapping. The diagonal entries are in bold for convenience.

Prior to investigating transition matrices in time-dependence, average transition matrices in time-homogeneity are initially estimated, on the basis of the bank loan portfolio under study, focusing only on the sub-sample of the domestic obligors. The one-year average cohort and the DTML estimations are summarized in _{SVD}

Transition probabilities in time-homogeneity: Sub-sample—domestic obligors only.

From → To | 1 | 2 | 3 | 4 | 5 | Default |
---|---|---|---|---|---|---|

1 | 0.03771 | 0.03112 | 0.00411 | 0.00000 | 0.00000 | |

(0.019662) | (0.01233) | (0.01781) | (0.00406) | (0.00000) | (0.00000) | |

2 | 0.00281 | 0.04612 | 0.01273 | 0.00166 | 0.00000 | |

(0.00199) | (0.00590) | (0.00441) | (0.00231) | (0.00088) | (0.00000) | |

3 | 0.00044 | 0.00551 | 0.04113 | 0.00482 | 0.00004 | |

(0.00021) | (0.00084) | (0.00272) | (0.00233) | (0.00071) | (0.00022) | |

4 | 0.00000 | 0.00022 | 0.02572 | 0.01322 | 0.00103 | |

(0.00000) | (0.00021) | (0.00162) | (0.00217) | (0.00188) | (0.00044) | |

5 | 0.00000 | 0.00000 | 0.00492 | 0.07111 | 0.00833 | |

(0.00000) | (0.00000) | 0.00182 | 0.00729 | 0.00833 | 0.00281 | |

Default | 0.00000 | 0.00000 | 0.00000 | 0.00000 | 0.00000 | |

1 | 0.12773 | 0.01222 | 0.02378 | 0.00042 | 0.00004 | |

(0.02773) | (0.02114) | (0.00722) | (0.00872) | (0.00019) | (0.00001) | |

2 | 0.00668 | 0.11729 | 0.02871 | 0.00255 | 0.00019 | |

(0.00198) | (0.00626) | (0.00551) | (0.00277) | (0.00715) | (0.00002) | |

3 | 0.00154 | 0.01622 | 0.12521 | 0.00810 | 0.00055 | |

(0.00048) | (0.00152) | (0.00303) | (0.00322) | (0.00082) | (0.00027) | |

4 | 0.00051 | 0.00177 | 0.08221 | 0.03198 | 0.00470 | |

(0.00021) | (0.00031) | (0.00372) | (0.00333) | (0.00278) | (0.00069) | |

5 | 0.00005 | 0.00062 | 0.00923 | 0.13302 | 0.05221 | |

(0.00002) | (0.00061) | (0.00140) | (0.01662) | (0.01442) | (0.00523) | |

Default | 0.00000 | 0.00000 | 0.00000 | 0.00000 | 0.00000 |

Both transition matrices are estimated for 1998–2008. The DTML transition matrix is based on all observation pairs with an inter-examination time of less than or equal to five years. Standard errors (in parentheses) are based on a non-parametric bootstrap approach with B = 1000 replications. The 99% confidence interval is calculated at 0.0811–0.1466, obtained by non-parametric bootstrapping. The diagonal entries are in bold for convenience.

_{SVD}

Transition probabilities in time-homogeneity: Discrete-time maximum likelihood (DTML) results on business cycle states.

From → To | 1 | 2 | 3 | 4 | 5 | Default |
---|---|---|---|---|---|---|

1 | 0.11443 | 0.00634 | 0.02877 | 0.00066 | ||

(0.02555) | (0.02288) | (0.00421) | (0.01729) | (0.00027) | (0.0000) | |

2 | 0.00524 | 0.11960 | 0.03175 | 0.00351 | ||

(0.00143) | (0.00911) | (0.00832) | (0.00420) | (0.00165) | (0.00002) | |

3 | 0.00087 | 0.01332 | 0.12778 | 0.00582 | ||

(0.00038) | (0.00144) | (0.00525) | (0.00425) | (0.00096) | (0.00004) | |

4 | 0.00053 | 0.00177 | 0.08465 | 0.04230 | 0.00147 | |

(0.00024) | (0.00048) | (0.00363) | (0.00488) | (0.00264) | (0.00049) | |

5 | 0.00133 | 0.00843 | 0.27555 | 0.03559 | ||

(0.00002) | (0.00096) | (0.00061) | (0.01664) | (0.01773) | (0.00521) | |

Default | 0.00000 | 0.00000 | 0.00000 | 0.00000 | 0.00000 | |

1 | 0.18223 | 0.01223 | 0.01188 | 0.00048 | ||

(0.03882) | (0.03216) | (0.008150) | (0.01929) | (0.00028) | (0.00001) | |

2 | 0.00799 | 0.12833 | 0.02811 | 0.00126 | ||

(0.00221) | (0.00836) | (0.00825) | (0.00372) | (0.00182) | (0.00003) | |

3 | 0.00187 | 0.01722 | 0.10277 | 0.01322 | 0.00172 | |

(0.00056) | (0.00177) | (0.00523) | (0.00449) | (0.00142) | (0.00033) | |

4 | 0.00032 | 0.00066 | 0.08280 | 0.04221 | 0.00488 | |

(0.00028) | (0.00015) | (0.00427) | (0.00522) | (0.00303) | (0.00161) | |

5 | 0.01722 | 0.27731 | 0.05208 | |||

(0.00002) | (0.00003) | (0.00466) | (0.01662) | (0.01734) | (0.00911) | |

Default | 0.00000 | 0.00000 | 0.00000 | 0.00000 | 0.00000 |

Both transition matrices are estimated for 1998–2008. Both DTML transition matrices are based on all observation pairs with an inter-examination time of less than or equal to five years. Standard errors (in parentheses) are based on a non-parametric bootstrap approach with B = 1000 replications. The 99% confidence interval is calculated at 0.0006–0.0311, obtained by non-parametric bootstrapping. The diagonal entries are in bold for convenience.

The log-likelihood function (Equation (16)) is now implemented to determine the time-dependent one-quarter transition matrix (as in Equation (17)). All available observation pairs are incorporated to estimate _{quarter}_{average}_{expansion}_{recession}

_{SVD}

The default probabilities for risk-grades 1, 2, and 3 are seen to be lower in the “average state” panel than in the “mixed state” panel. More frequently, the largest part of data for defaults corresponds to risk grade 5 surpassing any other risk-grade. This implies that default transition comparisons could be restricted to the transition from risk-grade 5 to default. When comparing migration probabilities from risk-grade 5 into default in all four matrices on different business cycle scenarios, PDs increase from the lowest in the boom state, followed by the average and mixed states and ending, finally, into the highest in the contraction state. As anticipated, the worse (more unstable) the state of the economy is, the higher the respective PDs are.

Past studies argue that PDs should be preferably overestimated in boom states rather than underestimated in contraction states [

Transition probabilities in time-dependence: DTML results on different business cycle scenarios.

From → To | 1 | 2 | 3 | 4 | 5 | Default |
---|---|---|---|---|---|---|

1 | 0.11701 | 0.01752 | 0.02505 | 0.00051 | 0.00004 | |

2 | 0.00611 | 0.11761 | 0.02551 | 0.00276 | 0.00016 | |

3 | 0.00177 | 0.01882 | 0.11662 | 0.00623 | 0.00074 | |

4 | 0.00063 | 0.00152 | 0.08339 | 0.03119 | 0.00361 | |

5 | 0.00005 | 0.00094 | 0.00735 | 0.29901 | 0.05218 | |

Default | 0.00000 | 0.00000 | 0.00000 | 0.00000 | 0.00000 | |

_{i} = 89.81 ( |
||||||

1 | 0.17772 | 0.02881 | 0.01455 | 0.00038 | 0.00004 | |

2 | 0.00731 | 0.12673 | 0.02117 | 0.00166 | 0.00018 | |

3 | 0.00155 | 0.01773 | 0.11732 | 0.01282 | 0.00172 | |

4 | 0.00038 | 0.00722 | 0.08221 | 0.03661 | 0.00618 | |

5 | 0.00003 | 0.00009 | 0.01662 | 0.17629 | 0.07209 | |

Default | 0.00000 | 0.00000 | 0.00000 | 0.00000 | 0.00000 | |

_{i} = 69.23 ( |
||||||

1 | 0.14422 | 0.01442 | 0.02884 | 0.00044 | 0.00004 | |

2 | 0.00644 | 0.14802 | 0.02319 | 0.00211 | 0.00014 | |

3 | 0.00141 | 0.01622 | 0.14290 | 0.00711 | 0.00092 | |

4 | 0.00052 | 0.00162 | 0.08518 | 0.03981 | 0.00485 | |

5 | 0.00005 | 0.00070 | 0.00852 | 0.16619 | 0.05282 | |

Default | 0.00000 | 0.00000 | 0.00000 | 0.00000 | 0.00000 | |

_{i} = 74.33 ( |
||||||

1 | 0.12773 | 0.01883 | 0.02771 | 0.00044 | 0.00005 | |

2 | 0.00641 | 0.11662 | 0.02188 | 0.00275 | 0.00017 | |

3 | 0.00177 | 0.01622 | 0.10031 | 0.00851 | 0.00134 | |

4 | 0.00057 | 0.00166 | 0.08510 | 0.03287 | 0.00442 | |

5 | 0.00004 | 0.00056 | 0.00955 | 0.17739 | 0.05296 | |

Default | 0.00000 | 0.00000 | 0.00000 | 0.00000 | 0.00000 | |

_{1} = 89.81; _{2} = 74.33; _{3} = 74.33; _{4} = 69.23 |

The DTML transition matrices are estimated for 1998–2008 and are based on all observation pairs with an inter-examination time of less than or equal to five years. The _{i}_{SVD}_{SVD}_{SVD}_{SVD}_{SVD}_{SVD}

To sum up, this study contributes certain interesting and useful empirical findings to the relevant empirical literature. First, comparing different estimation methods on time-homogenous average transition probabilities, the ML transition matrix is found to have a better capture rating transition mobility relative to the more diagonal-dominant cohort estimated transition matrix. Second, the application of the DTML method to business cycle states (in order to examine time-homogenous average transition probabilities) indicates that most transition probabilities reflecting risk-grade improvement are, conceivably, higher during the boom state. Third, there appears to be significant differences in default probabilities but all of them are seen to be lower in the boom state. Forth, empirical evidence supports the robustness of CUI index as a key macroeconomic variable that can adequately contribute to transition matrices that incorporate different states in the economy. Finally, comparing probability migrations from risk-grade 5 to default in different business cycle scenarios, the DTML approach indicates that the PDs increase from the lowest in the boom state, followed by the average and mixed states and ending in the highest in the contraction state, justifying that the worse the state of the economy is, the higher the respective PDs are. The discrete-time (

A focal issue in Basel directives emphasizes on the intensified sensitivity banks should pay to capital requirements in correspondence to the risk exposures of the bank’s assets. In other words, the level of capital a bank should hold is to be directly related to the riskiness of its underlying assets portfolio. Nevertheless, business cycle fluctuations can exert an impact on bank capital adequacy requirements. Under Basel guidelines, banks are allowed to incorporate own estimates to critical risk parameters in order to calculate regulatory capital.

Given that regulatory measures of financial robustness (such as the Tier-1 capital ratio) refer to core bank capital and risk-weighted assets, the empirical estimation of convenient credit risk migration matrices remains a critical exercise for bank capital requirements against unexpected losses in the loan portfolio as well as for efficient risk control. This paper enriches and expands past empirical literature by examining the linkages between credit risk management and macroeconomic states. This appears to be one of the first studies to empirically estimate and compare the DTML and CTML approaches and then apply the DTML approach to four different business cycle scenarios (boom, contraction, average and mixed economic states) to produce risk transition matrices. Further empirical research in this field remains useful and timely.

Dimitris Gavalas and Theodore Syriopoulos have written the paper jointly contributing to its theoretical foundations and empirical applications. This paper relates to initial output from D. Gavalas’ doctoral research, supervised by T. Syriopoulos.

The authors declare no conflict of interest.

Whereas “credit rating migration probabilities” characterize the probability of a credit rating being upgraded, downgraded or remaining unchanged within a specific time period, “credit migration matrices” characterize the evolution of credit quality for issuers with the same approximate likelihood of default; they are constructed by mapping the rating history of the entities into transition probabilities.

Similar to a probability transition matrix, an intensity matrix, Q, can be constructed, containing all possible intensities between various states. An outcome containing K states, for instance, would have the following intensity matrix, _{ij}_{ij}