# Weight of the Default Component of CDS Spreads: Avoiding Procyclicality in Credit Loss Provisioning Framework

Authors: Mariya Gubareva
Journal: Complexity
 (2019)

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## Abstract

The current expected loss calculations have recently attracted considerable attention in the research on credit risk modeling, impairment provisioning, and financial networks’ stability. A new CDS-based approach to estimate current expected credit loss is proposed for low default portfolios, containing credit exposures to corporate issuers covered by publicly traded CDS contracts. First, a fraction of CDS spread related to a pure default compensation for different CDS maturities is assessed. Our results contrast with previous research. Second, based on the obtained historical weights of the default risk premium, a forward-looking term structure of the probabilities of default implied by the current CDS quotes is derived. The proposed approach covers both investment and noninvestment grade debt. The resulting framework is applied to a sample of corporate bonds. The developed methodology provides a useful tool, on one hand, for credit risk managers and balance-sheet preparers and, on the other hand, for regulators of financial markets as it sheds light on how procyclicality could be avoided in provisions.


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## Body

## 1. Introduction

Financial systems, being complex networks in their nature, evolve continuously and their features undergo a never-ending process of substantial changes (see, e.g., Tabak et al. [1]). There is a vast body of recent literatures on systemic financial risk arising from interconnectedness of institutions, targeting financial systems’ stability (see, e.g., Aymann et al. [2]; Souza et al. [3]; Silva et al. [4]). One of the important domains analyzed in literature is the case of financial networks primarily linked through different types of credit contracts, portfolio contagion, or credit guarantees, (see, e.g., Li and Wen [5], Anagnostou et al. [6], and Jiang and Fan [7]).However, the major part of the studies considers interconnectedness of institutions, which is mostly due to one certain mechanism of interactions, being either credit relationship, or derivatives-linked connectivity, or foreign exchange driven linkages, or other one-dimensional factors (Li and Wen [7] and Poledna et al. [8]). Still, agents of real financial systems interact in diverse manners and through several channels. Such a situation could be duly modeled by bipartite (Huang et al. [9]) and/or by multiplex, that is, multilayer (Li and Wen [5] and Poledna et al. [8]) networks.With respect to the credit risk interconnectedness, it occurs at least at two different layers. The first one is the level of prudential regulation, at which the minimal capital requirements are established as obligatory for diverse financial institutions. The main objective to oblige financial institutions to hold capital buffers is to create resilience in the financial system by allowing banks and other lenders to withstand unexpected losses under eventuality of adverse future scenarios. The second layer is the level of impairment provisioning framework, related to the new accounting standards, recently issued by the Financial Accounting Standard Board (FASB) and by the International Accounting Standard Board (IASB), known, respectively, as CECL framework and IFRS 9 [10, 11]. Both the CECL model and IFRS 9 framework require financial institutions to abandon the solely incurred losses based accounting and estimate expected losses over the lifetime of credit exposures.On one hand, the idea of these new standards is to address some issues revealed by the global financial crisis, including those related to the incurred credit loss model. But if accounting, previously, was focused only on registering facts of the past, now a component of futurology, regarding expected credit losses, is entering into the domain of accounting, augmenting its interconnectedness with capital allocation framework and, hence, in a certain sense, potentially leading to systemic risks of other kinds, especially related to eventual procyclicality in the credit loss provisions, making both capital and provisioning frameworks interlinked [12, 13].Both CECL and IFRS 9 standards allow the use of market sensitive parameters and, henceforth, are expected to cause cyclicality in provisions. However, what represents a potentially dangerous systemic handicap is an eventual unintended procyclicality, that is, amplified cycle-related fluctuations of impairment allowances, driven by the new accounting standards implementation.Additionally, the systemic risk in the global financial system is interlinked even at a higher degree than one may perceive at the first sight, as both the capital allocation and the credit loss provisioning frameworks employ usually the same parameters of the credit risk, namely, probability of default (PD), loss given default (LGD), and exposure at default (EAD). It is worth noticing that the assessment of PDs for low default portfolios is one of the greatest hurdles for satisfying CECL and IFRS 9 requirements. Hence, financial institutions try to employ PD, derived from the same data for both capital requirements calculation, which must have through-the-cycle (T-t-C) features, and for expected loss provisioning, which must be based on the current forward-looking PDs. The perils of use of the unique risk measure across the financial system are evidenced, using the VaR metrics example by Aymann et al. [2].Hence, from the point of view of financial networks’ stability, it becomes highly desirable to use different sources of critical credit risk parameters, at least for PD. Such possibility will allow disentangling the capital requirements and the loss provisioning levels in the multiplex credit-related financial network, thus permitting diminishing procyclicality and potentially reducing overall systemic risks of the global financial system. The methodological approach presented herein is based on the use of CDS spreads as a starting point to estimate PDs and hence represents an alternative source with respect to PDs usually used by financial institutions to dimension their capital allocation processes.Apart from our aspiration to shed light on possible ways to reduce procyclicality in provisions and diminish the systemic risk related to credit exposures, our motivation resides in our goal to propose a robust approach to deal with credit risk of low default portfolios. One needs to bear in mind that rare default events characterize some sectors like sovereign, banking, insurance, and so on. In this regard, the use of market-based metrics allows us to develop and calibrate PD models. Forward-looking PDs can easily be derived from publicly traded single-name CDS as spread quotes are usually available on a daily basis. A wide literature (see, e.g., Choudhry, [14]) describes how to move from CDS spreads to PD estimates.Another feature facilitating the use of CDS spreads is their low correlation with interest rates. This circumstance makes them naturally suitable for credit impairment computation, which, at least in a pure theory, should not be affected by interest rate movements. For advanced reading on the interrelation between the credit spread and interest rates, see Gubareva and Borges [15]. While using yields and/or bond prices, they get influenced by the interest rates, as interest rates affect the time value of money but not necessarily impact the credit quality of the exposures. The use of CDS spreads makes, hence, the PD calculation sort of immune to interest rate trends as herein we are focused on creditworthiness of issuers.It is worth noting that CDS spreads are commonly used in the literature to proxy credit risk. For additional reading, related to the use of CDS quotes for economic capital management, see Gubareva and Borges [16] and the references therein. Another case for CDS use is that CDS is also a very efficient and sensitive instrument to measure credit risk. For example, Sensoy et al. [17], studying dynamics of CDS contracts in emerging markets, demonstrate that CDS can be efficient even in the crisis episodes.In accordance with the CECL and IFRS 9 accounting standards, robust and sound credit risk methodologies should not rely only on subjective, biased overly optimistic/pessimistic assumptions, or be based on purely hypothetic wishful-thinking considerations. The use of CDS spreads diminishes the importance of generating scenarios for ECL estimation, as they already reflect a certain set of market scenarios properly discounted by market participants. That is why the above-mentioned regulatory bodies, FASB and IASB, consider CDS spreads as valid market indicators of future debt performance: market price clears the battle of market participants’ perspectives.In this regard, we would like to point out that loss provisioning under CECL and IFRS 9 usually relies on a link function with macroeconomic scenarios, as PDs used by a vast majority of financial institutions for the origination, pricing, and capital adequacy assessment purposes are T-t-C measures, which lack point-in-timeliness and forward-looking aspects. To overcome these deficiencies, usually such financial institutions employ macroeconomic scenarios to transform their otherwise T-t-C PDs into current forward-looking estimates. That is why subjective scenario analysis usually becomes crucial for the entire ECL modeling.The robustness of our approach vis-à-vis competing methods is its objectivity, as no subjective assumptions are needed to be made for expected credit loss (ECL) estimation, as our PDs are derived from CDS spread data currently observed in the market. Within the proposed CDS-based methodology, at any reporting date, PDs estimates are derived from CDS spreads term structure, which represents current forward-looking measures, as the macro- and microeconomic scenarios are already properly weighted by the market, which clears the respective CDS spreads for several maturities.In order to further enhance our methodology, later on, it also could be linked to macroeconomic scenarios. Nevertheless, this topic remains outside of the scope of the current research paper. Our approach is also in line with the real economic value (REV) methodology applied by the European Commission to evaluate impaired portfolios, which is based on a long-term average risk premium; see, for instance, Heynderickx et al. [18].With respect to advancement of knowledge frontier in the domain of financial networks complexity, ECL calculation, and impairment provisioning, our paper contributes to the literature in the two following dimensions. First, we elaborate an effective approach for banks and financial institutions to optimize their modeling capacities complying with CECL and IFRS frameworks. Our approach allows estimating a truly forward-looking CECL which is free of subjective scenario analyses and thus enhances objectivity and reliability of the impairment allowances.Second, to enable unbiased estimates of forward-looking PDs, we split the CDS spread into two, default and nondefault, components by assessing default risk premium for each forward term. This allows us to go beyond the actual frontier in CDS area. To the best of our knowledge, a somewhat similar study is performed by Huang and Huang [19] for the bond markets for 1973-1998. Authors attempt to calculate the weight of credit risk observed in corporate-Treasury yield spreads.Additionally, the research paper by Arakelyan and Serrano [20], analyzing relatively recent data, assesses the fraction of the default component in CDS spreads within the period of 2004-2011. Still the main focus of this study is the liquidity component of CDS spreads. Thus, the quantification of the default-risk part of CDS spreads represents a by-product analysis of the main subject of this research, being assessed as a difference between the CDS spread and the liquidity component. However, our proposed CDS-based calibration approach to estimate the weight of the default component (WDC) is more robust and covers more recent period of 2007-2017, which is more relevant for CECL methodologies elaboration.The rest of the paper is organized as follows. In the next section, we discuss conceptual remarks of the proposed approach aimed at deriving unbiased forward-looking PDs from CDS spreads. In the third section, we detail our PD calibration methodology and introduce the technique for distilling the WDC of CDS spreads. In the fourth section, we perform the calibration of our model and calculate the WDCs for BBB+, BBB, BBB-, BB+, BB, BB-, and lower than BB- ratings ranges of corporate debt for each point in the CDS spread term structure. In the fifth section, we illustrate an application of the calibrated PD term structure to the CECL-compliant ECL calculations for a set of Investment Grade (IG) and High Yield (HY) bond positions. The sixth and final section presents our conclusions and discusses their implications.


## 2. Model Set-Up: Forward-Looking PD Projection Based on CDS Spreads

### 2.1. Conceptual Remarks

Under CECL and IFRS 9 frameworks, the use of PD/LGD DCF method in the ECL calculations implies a necessity of the forward-looking projections of PD and LGD parameters. However, estimation of forward-looking PDs is in fact a major hurdle, especially for low-default portfolios. However, CECL and IFRS 9 frameworks are principal-based and impose only few specific requirements on methodology. They do not provide a particular methodology for calculating allowances, stating just that the loss allowances must reflect ECL based on past loss experiences, current economic situations, and “reasonable and supportable” forecasts of future economic conditions. Therefore, the modeling choices may generate variations in impairment allowances across institutions.Hence, employing current CDS spreads for deduction of default term structure potentially helps to address the challenge of estimation of forward-looking PDs, because such market data incorporate both current information and forward-looking perspective. So, on one hand, CDS spreads contain information regarding credit quality of obligors available at the current point in the economic cycle. On the other hand, the term structure of CDS spreads permits deriving the respective term structure of spread-implied cumulative and then marginal PDs.ECL methodologies and their implementation issues have recently attracted great attention of the academia researchers and practitioners; see McPhail and McPhail [21], Chawla et al. [22], Skoglund [23], and Zhang [24], among others. However, to the best of our knowledge, no methodology for credit loss impairment provisioning based on CDS spread quotes has been presented until now. Our paper fills this gap.In addition, there are no sufficient internal data on low-default fixed-income portfolios to be used for the development of accurate internal models for ECL calculation. This could be explained by the rarity of the observed default events. At the same time, a considerable amount of external information on bonds, credit-linked notes, and alike instruments, including CDS, is available by many providers through the Bloomberg, Thomson-Reuters DataStream, and other data platforms. Therefore, we become motivated to design an easy-to-implement and easy-to-use methodology for ECL calculation in low-default bond portfolios based on public, readily available market data.In line with the “guidelines on credit risk and accounting for expected credit losses” by the Basel Committee on Banking Supervision [25], sound credit risk methodologies should not merely rely on subjective, inherently biased assumptions or on purely hypothetic scenario constructions. Employing CDS spreads allows dedicating fewer efforts to scenario analyses, as traded CDS spreads by their proper nature represent an outcome of a set of scenarios properly discounted by market players.Thus, CDS-based methodology allows preserving point-in-timeliness and forward-looking features of risk parameters as it relies on current projections of forward-looking PDs in a form of a PD term structure. Nevertheless, a methodological adjustment is needed as resulting PDs are inflated due to the nondefault component present in CDS spreads. We need to purge it out to allow for accurate PDs and, therefore, ECL estimates.Note that a neutral character of ECL estimations is a goal of CECL framework, meaning that neither PDs nor ECL must be overoptimistic or overprudential. They just need to be precise and accurate to the maximum extent possible.


### 2.2. Through-the-Cycle Observed Default Rates versus Forward-Looking PD Projections

Two different but complementary P-i-T and T-t-C concepts are usually employed by financial entities to describe the behavior of the PD. No exact definitions exist, but normally it is assumed that P-i-T PD is mostly based on current micro- and macroeconomic situations, while the T-t-C metrics PD is almost unaffected by economic conditions. It is also worth noting that many hybrid approaches are developed and used by lenders, rating agencies, and other institutions.Alternatively, one can say that P-i-T measures seek to incorporate all the information available up to the current date and, hence, these measures change with the fluctuation of economic conjuncture. On the contrary, T-t-C measures are constant throughout the business cycle.Figure1 illustrates this dichotomy in the case of historical global corporate default studies. Figure 1 depicts the global corporate default rate, calculated as the average between the observed default rates (ODR) reported by the two major rating agencies; see S&P Global [26] and Moody’s Investors Services [27]. The data incorporate the totality of default occurring across all the rating categories of the rated universes along the calendar years.Figure 1
Global Corporate Default Rates (1994–2016).As can be seen from Figure1, the annual default rate changes with time, climbing above and dropping below its average T-t-C level according to either good or bad shape of global economy. This is well evidenced looking backward, as this is what the ODR measure is all about.The PD projection considerations differ from this mindset, as now we need to look forward into the future from the current point in the economic cycle. As the global corporate default rate changes along the time, it is reasonable to assume that such changes will be present in forward-looking PD projections, too. It is also expectable that the forward-looking PD for a chosen corporate entity may vary with fluctuations in micro- and macroeconomic conditions. The CDS spread quotes for any chosen reference entity and for any maturity point will not remain constant as time advances, indicating uninterrupted changes in its creditworthiness. So the future PD will also fluctuate around its average T-t-C value.Figure2 schematically visualizes the projected future behavior of the selected default related metrics for a hypothetical corporate entity. This figure does not pretend to suggest any concrete shape of a time dynamics of the parameters, but it is somehow inspired by the historically observed trends as per Figure 1.Figure 2
Illustrative 1Y PD projections.Although the sole purpose of Figure2 is to serve as a visual aid for a better comprehension of conceptual foundation of the proposed methodology, it is important to underline that the proportions of the chart correctly represent the relative values of the calibrated 1Y PD projections and the average T-t-C 1Y PD, as the latter is but the time average of the former.In this way, Figure2 allows perceiving the basic principal of the proposed approach. We project forward-looking PDs into the future in such a manner that the mean PD value of a sample, composed by the entities of the similar creditworthiness and averaged along the projection horizon, becomes equal to the historical ODR corresponding to the credit quality of the sample. In fact, the historically observed ODR is somewhat extrapolated into the future in a form of the average T-t-C PD. In other words, the projected forward-looking PDs become anchored to the historical ODRs.Figure2 shows what happens for just one point in the forward-looking PD term structure, namely, 1Y point. The same rational is also applied to cumulative PDs for diverse future horizons. Figure 3 schematically represents how the shape of a hypothetical PD term structure would vary in accordance with changes in the economic scenario.Figure 3
Schematic projections of a scenario-dependent PD term structure.Figure3 shows that, under the T-t-C approach, a projected cumulative PD term structure does not vary with the cycle, since the T-t-C PDs are but the long-run ODRs. However, the corporate creditworthiness depends upon the state of economy and is expected to fluctuate in the years subjacent to projection horizon. Hence, a realistic projected cumulative PD term structure must be adjusted to reflect current and future economic conditions subjacent to a chosen macroeconomic scenario.As a borrower default risk moves up or down through the economic cycle, the conditions-sensitive PD projection models are supposed to incorporate currently available information on the state of economy and assess default risk at each point within the cycle. So realistic moment-sensitive projections of a chosen PD term structure ought to be used as a base for ECL allowance calculations under CECL framework.In addition, when estimating lifetime ECL, the conditions-sensitive PD term structure must cover the entire loss projection horizon up to the contractual maturity of a financial instrument. A realistic forecast of the forward-looking PD term structure projects the cash flows and calculates the ECL allowance, among other metrics.At this point, it is worth making a special comment, back regarding Exhibit 2. It is easy to see that the depicted CDS-implied PDs are inflated relative to the calibrated PD projection, anchored to the T-t-C PD, or the ODR. The next subsection discusses this issue in a major detail and focuses on the default and nondefault components present in CDS spreads.


### 2.3. Default versus Nondefault Spread Component

Default risk is only one of the factors contributing towards the CDS spread. Other factors include protection seller premium related to the future uncertainty, compensations for eventual illiquidity of CDS instruments, and political and disaster risk among many other aspects of nondefault origin.That is why the average historically observed default rates (ODRs) for corporate obligors are typically much smaller in comparison to the average would-be hypothetical default rates as implied by nonadjusted CDS spreads. The default component hence is only a fraction of CDS spreads for the whole specter of corporate credit ratings.Still, this fact alone does not allow making a conclusion regarding fairness of the total width of CDS spread, because, even in absence of other risks, the default component is meant to be only a part of the total CDS spread as the other part is a premium demanded by credit protection seller.Protection sellers require such premium because the uncertainty of default presents systematic features, as default losses are more likely to negatively affect protection seller precisely when economy is in bad shape. It is worth noting that exactly because of the tendency for default events to cluster around economy downturns, the credit protection seller premium can be potentially very large.To assure an unbiased estimation of PDs, we calibrate the spread-implied PDs by anchoring them to the long-run ODRs. Such calibration guarantees that our final P-i-T PDs estimates are commensurate in scale with historically verified ODRs.In recent times, the process of deriving PDs and ratings from CDS spreads has been widely discussed in the literature; see Heynderickx et al. [18] and Jansen and Fabozzi [28] and references therein. Another research by Gubareva and Borges [16] is also related to our work, where CDS spreads are used as a proxy for credit risk metrics while addressing economic capital optimization strategies.Herein we discuss the conceptual aspects of the above-mentioned PD calibration aimed at distilling the pure default compensation part from CDS spread, as CDS spreads contain considerable nondefault component. We recommend for additional reading papers by Longstaff et al. [29], Tang and Yan [30], Bongaerts et al. [31], and Arakelyan and Serrano [20], which provide liquidity studies focused on the CDS market.An uncertainty-related risk premium of CDS spreads is also worth mentioning; that is, CDS spreads contain an additional premium demanded by credit protection sellers, which is related to the unpredictable distress changes in the default risk environment. See Berndt et al. [32] and references therein.Furthermore, the paper by Bekaert et al. [33] alerts on another nondefault risk component present in CDS spreads, which has its origins in political risk.In addition to the above-mentioned components of CDS spreads, one needs to also consider a component destined to compensate the cost of capital, allocated for CDS instruments. These CDS instruments, even though recognized off balance sheet, still result in capital consumption incurred by financial institutions. Consequently, the necessity to hold a capital affects CDS prices and spreads; see Gubareva and Borges [16].Thus, if CDS spreads are employed unadjusted to derive the implied PD metrics, the nondefault component in spreads would result in an inflationary bias during the assessment of PDs, due to the presence of the nondefault component of CDS spreads.Therefore, although CDS spread quotes are frequently available in the market for many corporate reference entities, they must undergo a process of adjustment as diverse nondefault risks explain a relevant part of CDS spreads.The question is how to calibrate inflated P-i-T PDs, implied by unadjusted CDS-spread, in order to receive unbiased PDs, commensurate in scale with historically verified ODRs, while preserving specific individual entity information incorporated in CDS spread quotes.It is not a simple issue as a P-i-T forward-looking PD is an individual measure, while the long-run through-the-cycle (T-t-C) ODRs are by their nature the aggregate measures. It is like comparing apple to oranges. Thus, to allow for meaningful comparison between P-i-T PDs and T-t-C ODRs, the P-i-T forward-looking individual PDs ought to be subjected to a two-fold averaging procedure: over the long run and across the sample of the obligors characterized by a credit quality similar to the analyzed obligor. This will allow comparing comparable measures, that is, to have a sort of oranges-to-oranges comparison.


## 2.1. Conceptual Remarks

Under CECL and IFRS 9 frameworks, the use of PD/LGD DCF method in the ECL calculations implies a necessity of the forward-looking projections of PD and LGD parameters. However, estimation of forward-looking PDs is in fact a major hurdle, especially for low-default portfolios. However, CECL and IFRS 9 frameworks are principal-based and impose only few specific requirements on methodology. They do not provide a particular methodology for calculating allowances, stating just that the loss allowances must reflect ECL based on past loss experiences, current economic situations, and “reasonable and supportable” forecasts of future economic conditions. Therefore, the modeling choices may generate variations in impairment allowances across institutions.Hence, employing current CDS spreads for deduction of default term structure potentially helps to address the challenge of estimation of forward-looking PDs, because such market data incorporate both current information and forward-looking perspective. So, on one hand, CDS spreads contain information regarding credit quality of obligors available at the current point in the economic cycle. On the other hand, the term structure of CDS spreads permits deriving the respective term structure of spread-implied cumulative and then marginal PDs.ECL methodologies and their implementation issues have recently attracted great attention of the academia researchers and practitioners; see McPhail and McPhail [21], Chawla et al. [22], Skoglund [23], and Zhang [24], among others. However, to the best of our knowledge, no methodology for credit loss impairment provisioning based on CDS spread quotes has been presented until now. Our paper fills this gap.In addition, there are no sufficient internal data on low-default fixed-income portfolios to be used for the development of accurate internal models for ECL calculation. This could be explained by the rarity of the observed default events. At the same time, a considerable amount of external information on bonds, credit-linked notes, and alike instruments, including CDS, is available by many providers through the Bloomberg, Thomson-Reuters DataStream, and other data platforms. Therefore, we become motivated to design an easy-to-implement and easy-to-use methodology for ECL calculation in low-default bond portfolios based on public, readily available market data.In line with the “guidelines on credit risk and accounting for expected credit losses” by the Basel Committee on Banking Supervision [25], sound credit risk methodologies should not merely rely on subjective, inherently biased assumptions or on purely hypothetic scenario constructions. Employing CDS spreads allows dedicating fewer efforts to scenario analyses, as traded CDS spreads by their proper nature represent an outcome of a set of scenarios properly discounted by market players.Thus, CDS-based methodology allows preserving point-in-timeliness and forward-looking features of risk parameters as it relies on current projections of forward-looking PDs in a form of a PD term structure. Nevertheless, a methodological adjustment is needed as resulting PDs are inflated due to the nondefault component present in CDS spreads. We need to purge it out to allow for accurate PDs and, therefore, ECL estimates.Note that a neutral character of ECL estimations is a goal of CECL framework, meaning that neither PDs nor ECL must be overoptimistic or overprudential. They just need to be precise and accurate to the maximum extent possible.


## 2.2. Through-the-Cycle Observed Default Rates versus Forward-Looking PD Projections

Two different but complementary P-i-T and T-t-C concepts are usually employed by financial entities to describe the behavior of the PD. No exact definitions exist, but normally it is assumed that P-i-T PD is mostly based on current micro- and macroeconomic situations, while the T-t-C metrics PD is almost unaffected by economic conditions. It is also worth noting that many hybrid approaches are developed and used by lenders, rating agencies, and other institutions.Alternatively, one can say that P-i-T measures seek to incorporate all the information available up to the current date and, hence, these measures change with the fluctuation of economic conjuncture. On the contrary, T-t-C measures are constant throughout the business cycle.Figure1 illustrates this dichotomy in the case of historical global corporate default studies. Figure 1 depicts the global corporate default rate, calculated as the average between the observed default rates (ODR) reported by the two major rating agencies; see S&P Global [26] and Moody’s Investors Services [27]. The data incorporate the totality of default occurring across all the rating categories of the rated universes along the calendar years.Figure 1
Global Corporate Default Rates (1994–2016).As can be seen from Figure1, the annual default rate changes with time, climbing above and dropping below its average T-t-C level according to either good or bad shape of global economy. This is well evidenced looking backward, as this is what the ODR measure is all about.The PD projection considerations differ from this mindset, as now we need to look forward into the future from the current point in the economic cycle. As the global corporate default rate changes along the time, it is reasonable to assume that such changes will be present in forward-looking PD projections, too. It is also expectable that the forward-looking PD for a chosen corporate entity may vary with fluctuations in micro- and macroeconomic conditions. The CDS spread quotes for any chosen reference entity and for any maturity point will not remain constant as time advances, indicating uninterrupted changes in its creditworthiness. So the future PD will also fluctuate around its average T-t-C value.Figure2 schematically visualizes the projected future behavior of the selected default related metrics for a hypothetical corporate entity. This figure does not pretend to suggest any concrete shape of a time dynamics of the parameters, but it is somehow inspired by the historically observed trends as per Figure 1.Figure 2
Illustrative 1Y PD projections.Although the sole purpose of Figure2 is to serve as a visual aid for a better comprehension of conceptual foundation of the proposed methodology, it is important to underline that the proportions of the chart correctly represent the relative values of the calibrated 1Y PD projections and the average T-t-C 1Y PD, as the latter is but the time average of the former.In this way, Figure2 allows perceiving the basic principal of the proposed approach. We project forward-looking PDs into the future in such a manner that the mean PD value of a sample, composed by the entities of the similar creditworthiness and averaged along the projection horizon, becomes equal to the historical ODR corresponding to the credit quality of the sample. In fact, the historically observed ODR is somewhat extrapolated into the future in a form of the average T-t-C PD. In other words, the projected forward-looking PDs become anchored to the historical ODRs.Figure2 shows what happens for just one point in the forward-looking PD term structure, namely, 1Y point. The same rational is also applied to cumulative PDs for diverse future horizons. Figure 3 schematically represents how the shape of a hypothetical PD term structure would vary in accordance with changes in the economic scenario.Figure 3
Schematic projections of a scenario-dependent PD term structure.Figure3 shows that, under the T-t-C approach, a projected cumulative PD term structure does not vary with the cycle, since the T-t-C PDs are but the long-run ODRs. However, the corporate creditworthiness depends upon the state of economy and is expected to fluctuate in the years subjacent to projection horizon. Hence, a realistic projected cumulative PD term structure must be adjusted to reflect current and future economic conditions subjacent to a chosen macroeconomic scenario.As a borrower default risk moves up or down through the economic cycle, the conditions-sensitive PD projection models are supposed to incorporate currently available information on the state of economy and assess default risk at each point within the cycle. So realistic moment-sensitive projections of a chosen PD term structure ought to be used as a base for ECL allowance calculations under CECL framework.In addition, when estimating lifetime ECL, the conditions-sensitive PD term structure must cover the entire loss projection horizon up to the contractual maturity of a financial instrument. A realistic forecast of the forward-looking PD term structure projects the cash flows and calculates the ECL allowance, among other metrics.At this point, it is worth making a special comment, back regarding Exhibit 2. It is easy to see that the depicted CDS-implied PDs are inflated relative to the calibrated PD projection, anchored to the T-t-C PD, or the ODR. The next subsection discusses this issue in a major detail and focuses on the default and nondefault components present in CDS spreads.


## 2.3. Default versus Nondefault Spread Component

Default risk is only one of the factors contributing towards the CDS spread. Other factors include protection seller premium related to the future uncertainty, compensations for eventual illiquidity of CDS instruments, and political and disaster risk among many other aspects of nondefault origin.That is why the average historically observed default rates (ODRs) for corporate obligors are typically much smaller in comparison to the average would-be hypothetical default rates as implied by nonadjusted CDS spreads. The default component hence is only a fraction of CDS spreads for the whole specter of corporate credit ratings.Still, this fact alone does not allow making a conclusion regarding fairness of the total width of CDS spread, because, even in absence of other risks, the default component is meant to be only a part of the total CDS spread as the other part is a premium demanded by credit protection seller.Protection sellers require such premium because the uncertainty of default presents systematic features, as default losses are more likely to negatively affect protection seller precisely when economy is in bad shape. It is worth noting that exactly because of the tendency for default events to cluster around economy downturns, the credit protection seller premium can be potentially very large.To assure an unbiased estimation of PDs, we calibrate the spread-implied PDs by anchoring them to the long-run ODRs. Such calibration guarantees that our final P-i-T PDs estimates are commensurate in scale with historically verified ODRs.In recent times, the process of deriving PDs and ratings from CDS spreads has been widely discussed in the literature; see Heynderickx et al. [18] and Jansen and Fabozzi [28] and references therein. Another research by Gubareva and Borges [16] is also related to our work, where CDS spreads are used as a proxy for credit risk metrics while addressing economic capital optimization strategies.Herein we discuss the conceptual aspects of the above-mentioned PD calibration aimed at distilling the pure default compensation part from CDS spread, as CDS spreads contain considerable nondefault component. We recommend for additional reading papers by Longstaff et al. [29], Tang and Yan [30], Bongaerts et al. [31], and Arakelyan and Serrano [20], which provide liquidity studies focused on the CDS market.An uncertainty-related risk premium of CDS spreads is also worth mentioning; that is, CDS spreads contain an additional premium demanded by credit protection sellers, which is related to the unpredictable distress changes in the default risk environment. See Berndt et al. [32] and references therein.Furthermore, the paper by Bekaert et al. [33] alerts on another nondefault risk component present in CDS spreads, which has its origins in political risk.In addition to the above-mentioned components of CDS spreads, one needs to also consider a component destined to compensate the cost of capital, allocated for CDS instruments. These CDS instruments, even though recognized off balance sheet, still result in capital consumption incurred by financial institutions. Consequently, the necessity to hold a capital affects CDS prices and spreads; see Gubareva and Borges [16].Thus, if CDS spreads are employed unadjusted to derive the implied PD metrics, the nondefault component in spreads would result in an inflationary bias during the assessment of PDs, due to the presence of the nondefault component of CDS spreads.Therefore, although CDS spread quotes are frequently available in the market for many corporate reference entities, they must undergo a process of adjustment as diverse nondefault risks explain a relevant part of CDS spreads.The question is how to calibrate inflated P-i-T PDs, implied by unadjusted CDS-spread, in order to receive unbiased PDs, commensurate in scale with historically verified ODRs, while preserving specific individual entity information incorporated in CDS spread quotes.It is not a simple issue as a P-i-T forward-looking PD is an individual measure, while the long-run through-the-cycle (T-t-C) ODRs are by their nature the aggregate measures. It is like comparing apple to oranges. Thus, to allow for meaningful comparison between P-i-T PDs and T-t-C ODRs, the P-i-T forward-looking individual PDs ought to be subjected to a two-fold averaging procedure: over the long run and across the sample of the obligors characterized by a credit quality similar to the analyzed obligor. This will allow comparing comparable measures, that is, to have a sort of oranges-to-oranges comparison.


## 3. Calibration Methodology

In this section, we present a new calibration approach for forward-looking PD projections, which anchors the projected means of PDs to the T-t-C ODRs, reported by the major rating agencies for different ratings and time horizons.The proposed method is based on historical default data. It is capable of providing consistent estimates of the default component of CDS spreads. We examine in detail the relationship between the average historical levels of CDS spreads, based on daily quotes data series, and the historically observed long-run ODRs. This methodological feature guarantees a neutral character of the resulting forward-looking PD projections.To obtain our results, we separately work with seven large samples, consisting of reference entities, grouped according to similarity in the credit quality of sample constituents, in our case, BBB+, BBB, BBB-, BB+, BB, BB-, and those with credit ratings below BB-. For each sample and for each time horizon, we calculate the long-run historical average of the sample’s mean “would-be” cumulative PD derived from single-name CDS spreads of the sample’s constituents. Then we calibrate these cumulative PDs by normalizing them to the levels consistent with data on the respective historical ODR.For a chosen sample, to reach the calibration target, we gauge the WDC of CDS spreads for each time horizon of the analyzed PD term structure. The debt seniority of the analyzed CDS contracts is of senior unsecured type. Additionally, we use an assumption that each reference entity has a senior unsecured bond outstanding and that the bonds issued by our reference entities have, on average, across the sample and along the time, the same probability of default as the historical ODRs for bonds of the same seniority and credit rating. The LGD parameter for the senior unsecured debt is assumed to be equal to the market consensus figure of 60%, which is close to the historical LGD values for such type of bonds.The mechanics of our calibration is based on the widely used formula, which establishes relationship between CDS spread, maturity, and loss given default (see, e.g., Choudhry [14], page 155):(1)
P
D
c
u
m
T
=
1
–
exp
⁡
-
S
p
r
e
a
d
×
T
L
G
Dwhere P
D
c
u
m
(
T
) stands for cumulative PD,Spread represents CDS spread for the maturityT, and LGD stands for loss given default.Hence, having a CDS spread for a maturityT, we can calculate the implied cumulativePD
cum(T) for the respective time horizon, and vice versa. But this is in theory, as (1) is valid only ifSpread is a pure default spread or the default component of CDS spread. Now, the main question we need to answer is how to distill solely the default component of CDS spreads.At this stage, we need a help of the reverse financial engineering. The long-run average of the mean default frequency observed for a chosen sample of issuers with similar creditworthiness defines the average default spread or the default component of across-the-sample mean CDS spread, averaged along the corresponding data history. Henceforth, the expression for long-run average of mean, hypothetical exclusively default-compensating spread of a selected sample of obligors, is(2)
S
p
r
e
a
d
L
R
_
D
T
=
-
ln
⁡
1
-
O
D
R
c
u
m
T
×
O
L
G
D
Twhere spread S
p
r
e
a
d
L
R
_
D stands for a would-be long-run default spread,ODR
cum(T) stands forT-years cumulative long-run ODR, andOLGD stands for the time-average of the observed LGDs.On the other hand, the long-run average of mean observed credit spread for a sample of obligors may be found by double averaging procedure: across-the-sample and along the analyzed long-run interval. That is,(3)
S
p
r
e
a
d
L
R
_
A
V
G
T
=
A
V
E
R
A
G
E
L
R
A
V
E
R
A
G
E
S
a
m
p
l
e
S
p
r
e
a
d
i
d
,
Twhere S
p
r
e
a
d
L
R
_
A
V
G stands for long-run across-the-sample average of individual credit spreads (Spread
i(d,T)) for maturity T historically observed at each available date d within the long-run interval. But, as already discussed, this S
p
r
e
a
d
L
R
_
A
V
G represents a sum of the components, being the default and the nondefault parts.Now we arrive at the corner stone of the proposed methodology and can empirically filter out the nondefault component of CDS spreads and stay with the pure default compensation part. On average, for the ratioW
D
C
S
a
m
p
l
e(T) of CDS spread, we can write the following expression:(4)
W
D
C
S
a
m
p
l
e
T
=
S
p
r
e
a
d
L
R
_
D
T
S
p
r
e
a
d
L
R
_
A
V
G
TThus, we are able to perform calibration of a current value of CDS spread in order to distil solely the default component. We just need to multiply a forward-looking current CDSSpread
i (current date,T) of an issuer i from a chosen sample by W
D
C
S
a
m
p
l
e(T) calculated for the sample to which the selected issuer belongs. Thus, at any current date for the pure default compensation S
p
r
e
a
d
i
_
D (current date,T), we have(5)
S
p
r
e
a
d
i
_
D
c
u
r
r
e
n
t
d
a
t
e
,
T
=
S
p
r
e
a
d
i
c
u
r
r
e
n
t
d
a
t
e
,
T
x
W
D
C
S
a
m
p
l
e
TThis default component, S
p
r
e
a
d
i
_
D (current date,T), ought to be used for projecting forward-looking cumulative P
D
c
u
m(T) by means of (1).The next section presents the result of our analyses in a form of the term structures ofW
D
C
S
a
m
p
l
e(T) for diverse categories of credit quality of corporate entities.


## 4. Results: Weights of the Default Component of CDS Spreads

It is worth recalling that the proposed approach is based on the two-dimensional time-ensemble average of daily historical CDS market data observed through the complete economic cycle, to the T-t-C metrics ofODR, derived from the observed default frequencies reported by the credit rating agencies. Hence, it is possible to determine the WDC in market-quoted CDS spreads for all points of the CDS spread term structure.Our extensive decade-long data panel on 250 IG names and 75 HY entities comprises the end-of-the-day mid-spread single-name CDS spread quotes as per CMAN provider (New York office of CMA Datavision) on a daily basis, for 1-, 3-, 5-, 7-, and 10-year tenors. We exclude sovereign reference entities from our analysis in order to have the panel data compatible with the reports on corporate issuers’ T-t-C ODRs published by Standard & Poor’s and Moody’s rating agencies; see S&P Global [26] and Moody’s Investors Service [27]. Our ODR master scale is constructed as a mean value of the respective S&P and Moody’s ODR figures. For S&P default rates, we use Table 26, from S&P Global [26], presenting Global Corporate Average Cumulative Default Rates by Rating Modifier (1981-2016). For Moody’s default rates, we operate with the data from Exhibit 35 providing Average Cumulative Issuer-Weighted Global Default Rates by Alphanumeric Rating, 1983-2016.The time history of the CDS spread data series employed for averaging of historically observed daily quotes covers the 10-year period, from July 2007 to June 2017.As already mentioned, to estimate the WDCs of CDS spreads, we separately work with seven large samples, consisting of reference entities, grouped according to similarity in the credit quality of sample constituents, in our case, BBB+, BBB, BBB-, BB+, BB, BB-, and those with credit ratings below BB-. The selection of the sample is automatically defined by the two main criteria, which restrict eligibility of constituents for a sample of a chosen rating quality, with exception of the below BB- sample for which a different methodology, explained later, is used.First, for each eligible reference entity to be a part of a sample, the CDS quotes history must cover all the analyzed 10-year period.Second, we also eliminate from the sample all those names, whose Basel rating, the second best, fluctuated more than within one notch up and one notch down with respect to the targeted credit rating of the sample within the considered 10-year-long observation window.Such double data cleansing has the purpose of averaging only spreads corresponding to a chosen credit quality, for which the historical ODR data were computed by the rating agencies.The lists of the companies considered for BBB+, BBB, BBB-, BB+, BB, and BB- samples in order to assess the WDCs are presented in AppendicesA–F, respectively. The details of calculations involved are detailed in Appendix G. The methodology based on a second-degree calibration, developed for below BB- rating, is explained in Appendix H, which also provides details of the considered corporate entities and their securities.Table1 presents the term structures of the WDCs of CDS spreads for several different categories of the credit quality of the CDS reference entities.Table 1
Term structures of CDS WDCs for selected rating categories.
Credit Rating Grade
Number of entities in the sample
Maturity(years)
1
3
5
7
10
BBB+
76
11.0%
12.0%
10.9%
10.9%
10.9%
BBB
86
20.7%
18.0%
16.1%
15.0%
14.7%
BBB-
54
24.0%
23.8%
20.9%
19.2%
17.9%
BB+
38
20.2%
27.9%
25.3%
23.3%
21.0%
BB
17
34.3%
35.2%
28.7%
24.9%
23.1%
BB-
20
53.3%
53.0%
43.1%
38.7%
34.8%
below BB-
16
57.0%
56.6%
46.1%
41.3%
37.2%Table1 shows that the default risk for IG BBB range represents only a small part, varying between 10% and 24%. For HY BBB range, it remains within 21% to 54% interval, while for ratings below BB- it varies from 37% to 57% depending on the considered maturity, representing on average roughly a half of a CDS spread.For all the maturities, the WDC grows as credit quality drops, with the only exception observed for BB+ rating at 1Y point, perhaps due to liquidity related chock at the crossover from IG to HY range.For all the considered rating categories, from 3Y point towards the long end of the term structure, the WDC diminishes reflecting augmenting uncertainty concerns. For longer than 5Y maturities, such behavior is further enforced by the diminishing liquidity of the CDS instruments, as the most liquid point, at which a major part of trading occurs around 5-year maturity contracts.From qualitative point of view, our results are in line with outcomes of other researches on CDS spread components (Longstaff et al. [29], Lin et al. [34], Chen H. et al., and Arakelyan and Serrano [20]).On the quantitative side, our findings contrast the outcomes of Arakelyan and Serrano [20] for the period of 2004-2011, as authors find that, on average, the default risk premium accounts for 40% of CDS spreads. Our empirical data suggests that the default risk premium for BBB entities, on average, is below 20% of CDS spreads, as per the three top rows of Table 1.From a quantitative point of view, our numerical results represent a fundamental contribution to the existing literature on this subject. They reach beyond the current frontier in the empirical research on the matter in a sense that our figures are based on daily empirical data subjacent to a decade-long time window from 2007 to 2017, comprising distinct phases of the business cycle. The fact that the analyzed data history spreads over both distress and normal economic conditions assures robustness of the outcomes, especially for being employed in calculating life-long ECL.In the next chapter, we provide several examples shedding light on how theWDCs could be used to calibrate PDs, implied by CDS spread quotes. We exemplify an application of our ready-to-use methodology to calculate CECL-compliant ECL for a selected set of IG and HY exposures.


## 5. Application: Examples of WDC Use in CDS-Based ECL Calculations

In order to illustrate the applicability of our approach to low default portfolios, we select five different investments in corporate bonds. The chosen debt issues are the following: CBS Corp bond with maturity, February 15, 2023 (ISIN US124857AS26); Goodyear Tire & Rubber company bond with maturity, November 15, 2023 (ISIN US382550BE09); and Windstream Services LLC bond with maturity, August 01, 2023 (ISIN US97381WAZ77). The end date of the reporting period, used as a reference date for ECL calculation, is chosen to be March 30, 2018.In accordance with CECL framework, see FABS (2016), if an entity estimates expected credit losses using methods that project future principal and interest cash flows, that is, DCF–PD/LGD method, the entity shall discount expected cash flows at the financial asset’s effective interest rate. When a discounted cash flow method is applied, the allowance for credit losses shall reflect the difference between the amortized cost basis and the net present value of the expected cash flows. Hence, we calculate the ECL as follows for the requirements established by IFRS 9:(6)
E
C
L
=
∑
t
=
1
T
P
D
t
×
L
G
D
×
E
A
D
t
1
+
E
I
R
twherePD(t) is a marginal forward-looking PD, subjacent to the current point in the economic cycle,EAD(t) is an exposure at default relative to a time intervalt,LGD is a loss given default, andEIR stands for original effective interest rate when the asset was first recognized.In the considered examples herein, for simplicity reasons, we useLGD value of 60%, which is a market consensus for senior unsecured debt. We also assume that the bond assets were purchased at their issue date, allowing us to use the initial yield at issue as a proxy forEIR. As our work is not focused on the finest details of the accounting algorithms of CECL-compliantEAD calculations, we employ an assumption that the assets used in our examples were originally recognized at par, and hence we calculateEAD as a sum of the nominal value of the position and the coupon due to be paid during the periodt.


### 5.1. IG BBB-Rated Exposure to CBS Corp

As of March 30, 2018, the major credit rating agencies, namely, S&P, Fitch, and Moody’s, rate the senior unsecured debt of the CBS Corp as BBB/BBB/Baa2, respectively. Hence, in our ECL calculations, we use the WDC for BBB rating category, as per Table1. Our results are compiled in Table 2.Table 2
Lifetime ECL for the bond of CBS Corp as of March 30, 2018.
Lifetime ECL for CBS Corp exposure as of March 30, 2018
Date (mm.yyyy)
09.2018
03.2019
03.2020
03.2021
03.2022
02.2023
Maturity horizon (years) (A)
0.5
1
2
3
4
4.9
Spread quotes (bps)
12.8
16.1
28.6
44.7
63.1
83.0
WDC of BBB-rated CDS
20.7%
20.7%
19.4%
18.0%
17.1%
16.2%
Default component (bps)
2.7
3.3
5.5
8.1
10.8
13.5
Current cumulative PD projection (see (1))
0.02%
0.06%
0.18%
0.40%
0.72%
1.09%
Current marginal PD projection (B)
0.02%
0.03%
0.13%
0.22%
0.31%
0.37%
Coupon
2.50%
2.50%
2.50%
2.50%
2.50%
2.50%
Initial Yield (C)
2.50%
2.50%
2.50%
2.50%
2.50%
2.50%
LGD (D)
60%
60%
60%
60%
60%
60%
EAD/Nominal (p.p.) (E)
101.25
101.25
102.50
102.50
102.50
102.20
Marginal ECL (p.p.) (F= B×D×E / (1+C) ∧
A)
0.01
0.02
0.08
0.12
0.17
0.20
ECL lifetime (p.p.)
0.61For the presented calculations in Table2 we use the CDS spread quotes of March 30, 2018, and calibrate them by using the WDC from Table 1. For 0.5-year maturity point, we apply the 1-year WDC. The spreads and the WDC for the maturity point are obtained by the linear interpolation of 4-year and 5-year tenor figures. The purely default compensation parts of the CDS spreads are transformed in current marginal forward-looking PD projections. The coupon of 2,50% results inEAD per half-year period of 101,25 and for yearly periods of 102,50. Finally, summing marginal ECL we arrive at lifetime ECL of 0,61 percentage points.In Figures4 and 5 we present two charts, which shed further light on the method to project forward-looking PDs, as implied by CDS market information. Figure 4 presents the term structure of the CBS Corp CDS spreads along with the default spread component for each point of the term structure, as of March 30, 2018.Figure 4
CBS Corp term structures: CDS spread and default component.Figure 5
CBS Corp default risk structure: current PD projections.As per Figure4, we conclude that the default component grows with time up to the 7-year point and then further remains almost constant although it continues to slightly increase with time. In Figure 4, the presented term structure of the default component is used to derive, by means of (1), the term structures of current cumulative and marginal PD projections, depicted in Figure 5.In Figure5, we see that the current forward-looking PD projections augment up to the 7-year point and then moderately decay forward into the future. While an exact interpretation of the factors behind the depicted dynamics of annual marginal PD is rather difficult, the chart supports the following insight. The market, through the CDS quotes, implicitly considers that the most difficult years for CBS Corp. to cope with its liabilities will be from the 6th to the 8th year into the future. Seemingly, as of March 30, 2018, market participants do not envisage any other significant stress for the long end of the term structure. Hence, we find the description of future creditworthiness of CBS Corp. presented by the term structure of the annual marginal forward-looking PD as plausible and convincing to be used in ECL calculations.As could be seen in this example, the ECL calculations were performed using the points of the PD term structure, located within the positive slope of the curve, which means that the issuer, although somewhat stressed, is not at an imminence of default.


### 5.2. Lifetime ECL for a HY BB-Rated Exposure to Goodyear Company

As of March 30, 2018, the senior unsecured bond issued by Goodyear Tire & Rubber Company with maturity date November 15, 2023, is rated BB by S&P and by Fitch, and Ba3 by Moody’s, though the company long-term rating is Ba2. Hence, in our ECL calculations, we use the WDC for BB rating category, as per Table1. Our results are compiled in Table 3.Table 3
Lifetime ECL for the bond of the Goodyear Company as of March 30, 2018.
Lifetime ECL for Goodyear Company exposure as of March 30, 2018
Date (mm.yyyy)
09.2018
03.2019
03.2020
03.2021
03.2022
03.2023
11.2023
Maturity horizon (years) (A)
0.5
1
2
3
4
5
5.6
Spread quotes (bps)
20.7
31.5
45.4
68.9
103.9
141.3
161.5
WDC of BB-rated CDS
34.3%
34.3%
34.8%
35.2%
32.0%
28.7%
27.5%
Default component (bps)
7.1
10.8
15.8
24.3
33.2
40.6
44.4
Current cumulative PD projection (see (1))
0.06%
0.18%
0.53%
1.21%
2.20%
3.35%
4.12%
Current marginal PD projection (B)
0.06%
0.12%
0.35%
0.68%
0.99%
1.15%
0.77%
Coupon
5.125%
5.125%
5.125%
5.125%
5.125%
5.125%
5.125%
Initial Yield (C)
5.125%
5.125%
5.125%
5.125%
5.125%
5.125%
5.125%
LGD (D)
60%
60%
60%
60%
60%
60%
60%
EAD/Nominal (p.p.) (E)
102.56
102.56
105.13
105.13
105.13
105.13
103.22
Marginal ECL (F= B×D×E/ (1+C) ∧
A)
0.04
0.07
0.20
0.37
0.51
0.56
0.36
ECL lifetime (p.p.)
2.11In Table3, for the presented calculations, we use the CDS spread quotes of March 30, 2018, and calibrate them by using the WDC from Table 1. The spreads and the WDC for the maturity point are obtained by the linear interpolation of 5-year and 7-year tenor figures. The purely default compensation parts of the CDS spreads are transformed in current marginal forward-looking PD projections. Finally, summing marginal ECL until maturity, we arrive at lifetime ECL of 2,11 percentage points.In Figures6 and 7 we present two charts, which shed additional light on the method to project forward-looking PDs, as implied by CDS market information. Figure 6 presents the term structure of the Nabors Industries Inc. CDS spreads along with the default spread component for each point of the term structure, as of March 30, 2018.Figure 6
Goodyear Company term structures: CDS spread and default component.Figure 7
Goodyear Company default risk structure: current PD projections.As per Figure6, our calculations show that, for Goodyear Company, the default component grows with time up to the 7-year point and then further on remains almost perfectly constant. In Figure 6, the presented term structure of the default component is used to derive, by means of (1), the term structures of current cumulative and marginal PD projections, depicted in Figure 7.In Figure7, we see that the current forward-looking PD projections augment up to the 7-year point and then moderately decay forward into the future. Seemingly, as of March 30, 2018, market participants do not envisage any increase in credit-related stress for the long end of the term structure. We find the description of future creditworthiness of Goodyear Company presented by the term structure of the annual marginal forward-looking PD as plausible and convincing to be used in ECL calculations.As could be seen in this example, the ECL calculations were performed using the points of the PD term structure, located within the positive slope of the curve, which means that the issuer, although somewhat stressed, is not at an imminence of default.


### 5.3. Lifetime ECL for a HY below BB- Exposure to Windstream Services LLC

Next, we apply our methodology to calculate ECL for exposure to Windstream Services debt, rated B- by SP, B by Fitch, and Caa1 by Moody’s, as of March 30, 2018. We select the Windstream Services bond with maturity date August 01, 2023, on purpose to demonstrate a capacity of our approach to treat ECL of names under financial stress. In our ECL calculations, we use the WDCs for the below BB- rating category, as per Table1. Our results are compiled in Table 4.Table 4
Lifetime ECL for the bond of the Windstream Services as of March 30, 2018.
Lifetime ECL for Windstream Services LLC exposure as of March 30, 2018
Date (mm.yyyy)
09.2018
03.2019
03.2020
03.2021
03.2022
03.2023
08.2023
Maturity horizon (years) (A)
0.5
1
2
3
4
5
5.3
Spread quotes (bps)
3808.2
2980.9
2428.9
2459.5
2692.2
3035.8
3036.7
WDC of BB-rated CDS
57.0%
57.0%
56.8%
56.6%
51.4%
46.1%
45.3%
Default component (bps)
2169.6
1698.2
1379.3
1392.1
1382.5
1399.7
1375.4
Current cumulative PD projection (see (1))
17.13%
26.03%
40.18%
56.90%
70.80%
83.89%
86.70%
Current marginal PD projection (B)
17.13%
8.90%
14.15%
16.72%
13.90%
13.09%
2.81%
Coupon
6.375%
6.375%
6.375%
6.375%
6.375%
6.375%
6.375%
Initial Yield (C)
6.375%
6.375%
6.375%
6.375%
6.375%
6.375%
6.375%
LGD (D)
60%
60%
60%
60%
60%
60%
60%
EAD/Nominal (p.p.) (E)
103.19
103.19
106.38
106.38
106.38
106.38
102.17
Marginal ECL (F= B×D×E / (1+C) ∧
A)
10.29
5.18
7.98
8.87
6.93
6.13
1.24
ECL lifetime (p.p.)
46.61For the presented calculations in Table4 we use the CDS spread quotes of March 30, 2018, and calibrate them by using the WDC from Table 1. The spreads and the WDC for the maturity point are obtained by the linear interpolation of 5-year and 7-year tenor figures. The purely default compensation parts of the CDS spreads are transformed in current marginal forward-looking PD projections. Finally, summing marginal ECL until maturity, we arrive at lifetime ECL of 46,61 percentage points.In Figures8 and 9 we present two charts, which shed further light on the method to project forward-looking PDs, as implied by CDS market information. Figure 8 presents the term structure of the Windstream Services CDS spreads along with the default spread component for each point of the term structure, as of March 30, 2018.Figure 8
Windstream Services term structures: CDS spread and the default component.Figure 9
Windstream Services term structure of default risk: current PD projections.The inverted, at the short end, term structure of CDS spreads is considered to be an indication of an eventually approaching default or debt restructuring. As per Figure8, we conclude that the default component decays from the level of 2200 bps at 0.5-year point to the 2-year point below 1500 bps and then remains almost constant until the 5-year point and then continues to gradually decay towards the long end of the term structure. In Figure 8, the presented term structure of the default component is used to derive, by means of (1), the term structures of current cumulative and marginal PD projections, depicted in Figure 9.In Figure9, we see that the annual marginal forward-looking P-i-T PD within the 1st year exhibits a negative slope, reaching its local minima at 1-year point. Then it starts growing and reaches its local maximum around the end of the 3rd year into the future and then exhibits a decay tendency though quite inhomogeneous.While an exact interpretation of the factors behind the depicted dynamics of annual marginal PD is rather difficult, the chart corroborates the following explanation. The market through the CDS quotes implicitly considers that the most difficult moment for Windstream Services to cope with its liabilities lays within the next half a year. Seemingly, as of March 30, 2018, market participants also envisage another significant stress for the entity along the 2nd and the 3rd years in the term structure.We consider the description of future creditworthiness of Windstream Services presented by the term structure of the annual marginal PD to be plausible, convincing, and, hence, applicable to ECL calculations.Such a complex PD term structure results from the current March 30, 2018, CDS spread quotes for diverse points in the CDS term structure, which are representative of prices at which market had cleared on March 18, 2018. In our approach, we consider that these CDS represent all future scenarios duly weighted and discounted by market participants. The more reliable and the less speculative are the quotes, the more accurate is the result of the proposed ECL calculation methodology.


### 5.4. Additional Considerations

In is worth mentioning that an alternative approach to assessment of default risk profile, which is widely employed by financial industry players, is a transformation of the T-t-C PDs into forward-looking PD measures sensitive to the current point in the cycle by means of hypothetic scenarios. Still it is rather impossible for the T-t-C to current forward-looking PD conversion approach to result in such a detailed description of forward-looking marginal PDs, similar to those provided by our approach.Differently from the commonly employed T-t-C to current PD conversion procedure, which starts with the T-t-C default rates and then converts them by means of scenario analyses into the forward-looking PD projections, our methodology incorporates the point-in-timeliness from the very beginning as it commences with the forward-looking term structure of quoted CDS spreads. Then, we calibrate the otherwise inflated PDs by duly treating the spread components structure and distilling solely the default compensation part.In addition, our methodology could be coupled with scenario analyses and macroeconomic considerations in order to see how ECL will behave under increased or diminished stress. However, these issues overcome the frame of the present paper and will be addressed in the future research.Although there is a vast universe of single-name CDS curves and also of CDS indices (see Gubareva [35]), it does not cover the whole specter of the bond issuers. It is worth pointing out that the herein exemplified methodology can be also applied in the case of obligors without CDS spread curves; alternatively, instead of the CDS spread, the credit spread of the individual BVAL curves over the respective risk-free rates could be employed.The applicability of the proposed approach could also be extended to the entities, for which there exists neither single-name CDS nor individual BVAL curves, as there is a wide range of generic BVAL curves for diverse economy sectors arranged according to letter rating grades. These generic BVAL yield curves are accessible through the Bloomberg terminal.In such case, the term structure of the sector BVAL curve could be employed to proxy the default risk term structure. In addition, the adjustment procedure must be performed. The ratio of the obligor’s yield to the sector’s BVAL yield to maturity should be employed as a scaling factor to rescale the BVAL curve yield at each point of the term structure. Then, the proposed methodology, exemplified in our study for obligors with the single-name CDS spread curves, becomes fully applicable for BVAL-less obligors too.Such methodology extension potentially allows for almost complete and highly accurate coverage of the entire bond domain of the fixed-income universe.


## 5.1. IG BBB-Rated Exposure to CBS Corp

As of March 30, 2018, the major credit rating agencies, namely, S&P, Fitch, and Moody’s, rate the senior unsecured debt of the CBS Corp as BBB/BBB/Baa2, respectively. Hence, in our ECL calculations, we use the WDC for BBB rating category, as per Table1. Our results are compiled in Table 2.Table 2
Lifetime ECL for the bond of CBS Corp as of March 30, 2018.
Lifetime ECL for CBS Corp exposure as of March 30, 2018
Date (mm.yyyy)
09.2018
03.2019
03.2020
03.2021
03.2022
02.2023
Maturity horizon (years) (A)
0.5
1
2
3
4
4.9
Spread quotes (bps)
12.8
16.1
28.6
44.7
63.1
83.0
WDC of BBB-rated CDS
20.7%
20.7%
19.4%
18.0%
17.1%
16.2%
Default component (bps)
2.7
3.3
5.5
8.1
10.8
13.5
Current cumulative PD projection (see (1))
0.02%
0.06%
0.18%
0.40%
0.72%
1.09%
Current marginal PD projection (B)
0.02%
0.03%
0.13%
0.22%
0.31%
0.37%
Coupon
2.50%
2.50%
2.50%
2.50%
2.50%
2.50%
Initial Yield (C)
2.50%
2.50%
2.50%
2.50%
2.50%
2.50%
LGD (D)
60%
60%
60%
60%
60%
60%
EAD/Nominal (p.p.) (E)
101.25
101.25
102.50
102.50
102.50
102.20
Marginal ECL (p.p.) (F= B×D×E / (1+C) ∧
A)
0.01
0.02
0.08
0.12
0.17
0.20
ECL lifetime (p.p.)
0.61For the presented calculations in Table2 we use the CDS spread quotes of March 30, 2018, and calibrate them by using the WDC from Table 1. For 0.5-year maturity point, we apply the 1-year WDC. The spreads and the WDC for the maturity point are obtained by the linear interpolation of 4-year and 5-year tenor figures. The purely default compensation parts of the CDS spreads are transformed in current marginal forward-looking PD projections. The coupon of 2,50% results inEAD per half-year period of 101,25 and for yearly periods of 102,50. Finally, summing marginal ECL we arrive at lifetime ECL of 0,61 percentage points.In Figures4 and 5 we present two charts, which shed further light on the method to project forward-looking PDs, as implied by CDS market information. Figure 4 presents the term structure of the CBS Corp CDS spreads along with the default spread component for each point of the term structure, as of March 30, 2018.Figure 4
CBS Corp term structures: CDS spread and default component.Figure 5
CBS Corp default risk structure: current PD projections.As per Figure4, we conclude that the default component grows with time up to the 7-year point and then further remains almost constant although it continues to slightly increase with time. In Figure 4, the presented term structure of the default component is used to derive, by means of (1), the term structures of current cumulative and marginal PD projections, depicted in Figure 5.In Figure5, we see that the current forward-looking PD projections augment up to the 7-year point and then moderately decay forward into the future. While an exact interpretation of the factors behind the depicted dynamics of annual marginal PD is rather difficult, the chart supports the following insight. The market, through the CDS quotes, implicitly considers that the most difficult years for CBS Corp. to cope with its liabilities will be from the 6th to the 8th year into the future. Seemingly, as of March 30, 2018, market participants do not envisage any other significant stress for the long end of the term structure. Hence, we find the description of future creditworthiness of CBS Corp. presented by the term structure of the annual marginal forward-looking PD as plausible and convincing to be used in ECL calculations.As could be seen in this example, the ECL calculations were performed using the points of the PD term structure, located within the positive slope of the curve, which means that the issuer, although somewhat stressed, is not at an imminence of default.


## 5.2. Lifetime ECL for a HY BB-Rated Exposure to Goodyear Company

As of March 30, 2018, the senior unsecured bond issued by Goodyear Tire & Rubber Company with maturity date November 15, 2023, is rated BB by S&P and by Fitch, and Ba3 by Moody’s, though the company long-term rating is Ba2. Hence, in our ECL calculations, we use the WDC for BB rating category, as per Table1. Our results are compiled in Table 3.Table 3
Lifetime ECL for the bond of the Goodyear Company as of March 30, 2018.
Lifetime ECL for Goodyear Company exposure as of March 30, 2018
Date (mm.yyyy)
09.2018
03.2019
03.2020
03.2021
03.2022
03.2023
11.2023
Maturity horizon (years) (A)
0.5
1
2
3
4
5
5.6
Spread quotes (bps)
20.7
31.5
45.4
68.9
103.9
141.3
161.5
WDC of BB-rated CDS
34.3%
34.3%
34.8%
35.2%
32.0%
28.7%
27.5%
Default component (bps)
7.1
10.8
15.8
24.3
33.2
40.6
44.4
Current cumulative PD projection (see (1))
0.06%
0.18%
0.53%
1.21%
2.20%
3.35%
4.12%
Current marginal PD projection (B)
0.06%
0.12%
0.35%
0.68%
0.99%
1.15%
0.77%
Coupon
5.125%
5.125%
5.125%
5.125%
5.125%
5.125%
5.125%
Initial Yield (C)
5.125%
5.125%
5.125%
5.125%
5.125%
5.125%
5.125%
LGD (D)
60%
60%
60%
60%
60%
60%
60%
EAD/Nominal (p.p.) (E)
102.56
102.56
105.13
105.13
105.13
105.13
103.22
Marginal ECL (F= B×D×E/ (1+C) ∧
A)
0.04
0.07
0.20
0.37
0.51
0.56
0.36
ECL lifetime (p.p.)
2.11In Table3, for the presented calculations, we use the CDS spread quotes of March 30, 2018, and calibrate them by using the WDC from Table 1. The spreads and the WDC for the maturity point are obtained by the linear interpolation of 5-year and 7-year tenor figures. The purely default compensation parts of the CDS spreads are transformed in current marginal forward-looking PD projections. Finally, summing marginal ECL until maturity, we arrive at lifetime ECL of 2,11 percentage points.In Figures6 and 7 we present two charts, which shed additional light on the method to project forward-looking PDs, as implied by CDS market information. Figure 6 presents the term structure of the Nabors Industries Inc. CDS spreads along with the default spread component for each point of the term structure, as of March 30, 2018.Figure 6
Goodyear Company term structures: CDS spread and default component.Figure 7
Goodyear Company default risk structure: current PD projections.As per Figure6, our calculations show that, for Goodyear Company, the default component grows with time up to the 7-year point and then further on remains almost perfectly constant. In Figure 6, the presented term structure of the default component is used to derive, by means of (1), the term structures of current cumulative and marginal PD projections, depicted in Figure 7.In Figure7, we see that the current forward-looking PD projections augment up to the 7-year point and then moderately decay forward into the future. Seemingly, as of March 30, 2018, market participants do not envisage any increase in credit-related stress for the long end of the term structure. We find the description of future creditworthiness of Goodyear Company presented by the term structure of the annual marginal forward-looking PD as plausible and convincing to be used in ECL calculations.As could be seen in this example, the ECL calculations were performed using the points of the PD term structure, located within the positive slope of the curve, which means that the issuer, although somewhat stressed, is not at an imminence of default.


## 5.3. Lifetime ECL for a HY below BB- Exposure to Windstream Services LLC

Next, we apply our methodology to calculate ECL for exposure to Windstream Services debt, rated B- by SP, B by Fitch, and Caa1 by Moody’s, as of March 30, 2018. We select the Windstream Services bond with maturity date August 01, 2023, on purpose to demonstrate a capacity of our approach to treat ECL of names under financial stress. In our ECL calculations, we use the WDCs for the below BB- rating category, as per Table1. Our results are compiled in Table 4.Table 4
Lifetime ECL for the bond of the Windstream Services as of March 30, 2018.
Lifetime ECL for Windstream Services LLC exposure as of March 30, 2018
Date (mm.yyyy)
09.2018
03.2019
03.2020
03.2021
03.2022
03.2023
08.2023
Maturity horizon (years) (A)
0.5
1
2
3
4
5
5.3
Spread quotes (bps)
3808.2
2980.9
2428.9
2459.5
2692.2
3035.8
3036.7
WDC of BB-rated CDS
57.0%
57.0%
56.8%
56.6%
51.4%
46.1%
45.3%
Default component (bps)
2169.6
1698.2
1379.3
1392.1
1382.5
1399.7
1375.4
Current cumulative PD projection (see (1))
17.13%
26.03%
40.18%
56.90%
70.80%
83.89%
86.70%
Current marginal PD projection (B)
17.13%
8.90%
14.15%
16.72%
13.90%
13.09%
2.81%
Coupon
6.375%
6.375%
6.375%
6.375%
6.375%
6.375%
6.375%
Initial Yield (C)
6.375%
6.375%
6.375%
6.375%
6.375%
6.375%
6.375%
LGD (D)
60%
60%
60%
60%
60%
60%
60%
EAD/Nominal (p.p.) (E)
103.19
103.19
106.38
106.38
106.38
106.38
102.17
Marginal ECL (F= B×D×E / (1+C) ∧
A)
10.29
5.18
7.98
8.87
6.93
6.13
1.24
ECL lifetime (p.p.)
46.61For the presented calculations in Table4 we use the CDS spread quotes of March 30, 2018, and calibrate them by using the WDC from Table 1. The spreads and the WDC for the maturity point are obtained by the linear interpolation of 5-year and 7-year tenor figures. The purely default compensation parts of the CDS spreads are transformed in current marginal forward-looking PD projections. Finally, summing marginal ECL until maturity, we arrive at lifetime ECL of 46,61 percentage points.In Figures8 and 9 we present two charts, which shed further light on the method to project forward-looking PDs, as implied by CDS market information. Figure 8 presents the term structure of the Windstream Services CDS spreads along with the default spread component for each point of the term structure, as of March 30, 2018.Figure 8
Windstream Services term structures: CDS spread and the default component.Figure 9
Windstream Services term structure of default risk: current PD projections.The inverted, at the short end, term structure of CDS spreads is considered to be an indication of an eventually approaching default or debt restructuring. As per Figure8, we conclude that the default component decays from the level of 2200 bps at 0.5-year point to the 2-year point below 1500 bps and then remains almost constant until the 5-year point and then continues to gradually decay towards the long end of the term structure. In Figure 8, the presented term structure of the default component is used to derive, by means of (1), the term structures of current cumulative and marginal PD projections, depicted in Figure 9.In Figure9, we see that the annual marginal forward-looking P-i-T PD within the 1st year exhibits a negative slope, reaching its local minima at 1-year point. Then it starts growing and reaches its local maximum around the end of the 3rd year into the future and then exhibits a decay tendency though quite inhomogeneous.While an exact interpretation of the factors behind the depicted dynamics of annual marginal PD is rather difficult, the chart corroborates the following explanation. The market through the CDS quotes implicitly considers that the most difficult moment for Windstream Services to cope with its liabilities lays within the next half a year. Seemingly, as of March 30, 2018, market participants also envisage another significant stress for the entity along the 2nd and the 3rd years in the term structure.We consider the description of future creditworthiness of Windstream Services presented by the term structure of the annual marginal PD to be plausible, convincing, and, hence, applicable to ECL calculations.Such a complex PD term structure results from the current March 30, 2018, CDS spread quotes for diverse points in the CDS term structure, which are representative of prices at which market had cleared on March 18, 2018. In our approach, we consider that these CDS represent all future scenarios duly weighted and discounted by market participants. The more reliable and the less speculative are the quotes, the more accurate is the result of the proposed ECL calculation methodology.


## 5.4. Additional Considerations

In is worth mentioning that an alternative approach to assessment of default risk profile, which is widely employed by financial industry players, is a transformation of the T-t-C PDs into forward-looking PD measures sensitive to the current point in the cycle by means of hypothetic scenarios. Still it is rather impossible for the T-t-C to current forward-looking PD conversion approach to result in such a detailed description of forward-looking marginal PDs, similar to those provided by our approach.Differently from the commonly employed T-t-C to current PD conversion procedure, which starts with the T-t-C default rates and then converts them by means of scenario analyses into the forward-looking PD projections, our methodology incorporates the point-in-timeliness from the very beginning as it commences with the forward-looking term structure of quoted CDS spreads. Then, we calibrate the otherwise inflated PDs by duly treating the spread components structure and distilling solely the default compensation part.In addition, our methodology could be coupled with scenario analyses and macroeconomic considerations in order to see how ECL will behave under increased or diminished stress. However, these issues overcome the frame of the present paper and will be addressed in the future research.Although there is a vast universe of single-name CDS curves and also of CDS indices (see Gubareva [35]), it does not cover the whole specter of the bond issuers. It is worth pointing out that the herein exemplified methodology can be also applied in the case of obligors without CDS spread curves; alternatively, instead of the CDS spread, the credit spread of the individual BVAL curves over the respective risk-free rates could be employed.The applicability of the proposed approach could also be extended to the entities, for which there exists neither single-name CDS nor individual BVAL curves, as there is a wide range of generic BVAL curves for diverse economy sectors arranged according to letter rating grades. These generic BVAL yield curves are accessible through the Bloomberg terminal.In such case, the term structure of the sector BVAL curve could be employed to proxy the default risk term structure. In addition, the adjustment procedure must be performed. The ratio of the obligor’s yield to the sector’s BVAL yield to maturity should be employed as a scaling factor to rescale the BVAL curve yield at each point of the term structure. Then, the proposed methodology, exemplified in our study for obligors with the single-name CDS spread curves, becomes fully applicable for BVAL-less obligors too.Such methodology extension potentially allows for almost complete and highly accurate coverage of the entire bond domain of the fixed-income universe.


## 6. Conclusion

We develop CECL-compliant original methodology to calibrate forward-looking PDs estimates, based on CDS market information, thus making such PDs projections employable for the ECL calculations. Our approach is based on an innovative technique suitable for distilling the pure default component in CDS spreads.To enable economic adjustment of PDs, we consider seven homogeneous samples corresponding to BBB+, BBB, BBB-, BB+, BB, BB-, and below-BB rating ranges, assuring in this manner a similarity in issuers’ creditworthiness across each sample. Then, we analyze the relationship between a long-run average of the across-the-sample mean value of the CDS spreads of a chosen maturity, on one hand, and, on the other hand, the spread, implied by the long-run average of the respective cumulative ODR.In this manner, we solve the problem of calibrating of an issuer’s current forward-looking PD, which is an individual metrics, to the cumulative default rate, which is an aggregate measure relative to the cohort-like sample of individual issuers.We provide the empirical results regarding the average WDC for each point in the CDS spread term structures derived for the seven different ranges of issuers’ creditworthiness and empirically evidence that for BBB and BB rating categories nondefault risks are responsible for a major part of a CDS spread.We evidence that the average value of the WDC for BBB reference entities represents only a small fraction, on average below 20% of CDS spread, while for BB entities this fraction is somewhat bigger, but still it predominantly remains below 40% of CDS spreads for all the tenors. Being qualitatively in line with previous research on nondefault drivers of CDS spreads, our results contrast with the quantitative findings of Arakelyan and Serrano [20], reporting that, on average, the default risk premium accounts for 40% of CDS spreads. In addition, it is important to stress that differently to previous research we provide WDC for each forward term and for several ranges of credit ratings.To overcome the limited data on the below-BB sample, we develop a second-degree calibration procedure, which allows us to obtain the WDC for this low credit quality group of reference entities. We find that the WDC for this category varies between 57% and 37%, decaying for the long end of the term structure.The performed assessment of the WDC allows for objective, that is, unconditional projections of multiperiod PDs to be used in ECL calculations. Our PDs are truly point-dependent current measures incorporating forward-looking information, as they are based on current CDS quotes, which provide a current market forecast on default risk of reference entities.Differently from commonly employed approaches, which use the T-t-C default rates and then transform them by means of scenario analyses into the forward-looking PDs, our approach incorporates the point-in-timeliness from the very beginning as it starts with current quotes of CDS spreads, which contain forward-looking information. As a next step we calibrate these CDS spreads, by distilling the pure default component.In this manner, the developed approach permits optimizing modeling efforts and avoiding waste of time, spent by financial institutions analyzing multiple scenarios in order to incorporate point-in-timeliness and forward-looking aspects into their otherwise T-t-C PDs. Another important drawdown of the scenario-based approaches is an inherent subjectivity related to scenario construction activities. Avoidance of subjective assumptions and forecasts in our methodology potentially enhances objectivity, robustness, and replicability of ECL calculations as well as their comparability among the field players.CECL framework envisages the use of market sensitive parameters and, henceforth, is expected to cause cyclicality in provisions. However, what represents a potentially dangerous systemic handicap is an eventual unintended procyclicality, that is, amplified cycle-related fluctuations of impairment allowances, driven by CECL implementation. Our approach based on PDs calibration, which anchors them to the long-run T-t-C ODRs, assures that fluctuations in provisions are hold controlled by construction.The employment of T-t-C ODRs for calibrating forward-looking PDs in our methodology marks the initial step towards better convergence between capital quantifications under Basel III/IV accord, usually tied to T-t-C metrics, and CECL-compliant accounting treatment incorporating volatility of current economic conditions through the credit risk parameters, changing with the cycle. The herein presented framework allows for better comprehension of complex ongoing interactions, on one hand, between the impairment and economic capital requirements in relation to credit losses, and, on the other hand, between credit risk management and accounting.We expect that our research will serve practical needs of many financial institutions, being at the same time of theoretical value for practitioners, regulators, and members of scientific community during and after the implementation of CECL requirements.



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*Source: 7820618-2019-07-04.xml*