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This article proposes a method of modeling realized losses given default (LGDs) as a function of macroeconomic drivers for stress testing purposes. Due to the spotty and procyclical nature of defaults, realized LGD data present significant – but surmountable – challenges for economic modelers. In our solution, we employ a principal component regression approach in the context of a two-step procedure for projecting stressed realized LGDs. The use of principal components allows us to accommodate rich multivariate scenarios despite the limitations of LGD data. Our stressed realized LGD methodology is able to achieve several key objectives, including: (a) a replication of sector average differences between the LGDs of senior and subordinate debt; and (b) reasonable responses to baseline, adverse, and severely adverse scenarios across major economic sectors.

Introduction

In our recent Risk Perspectives™ article, we unveiled and tested a framework for forecasting loss given default (LGD) metrics under different macroeconomic scenarios (Malone and Wurm, 2017). That framework relied on sector-level LGD estimates that are consistent with observed bond spreads, given the prevailing market price of risk and firms' default probabilities. While such a setup has many practical benefits, including easy-to-interpret stress behavior and attractive in-sample properties, its chief drawback is that it does not use realized recovery rates for defaulted bonds to compute LGDs.

The use of market-implied LGDs in our framework creates a source of model risk for stress testers: Market-implied LGDs and realized LGDs could differ. If this is the case, then the conditional market-implied LGD forecasts from our model will be noisy and potentially biased predictors of realized LGDs under conditions of macroeconomic stress. To address this issue head-on, we decided to model realized LGDs sourced from Moody's Analytics Default and Recovery Database (DRD) directly by adapting some of the techniques we used for stressing market-implied LGDs. This article presents the results of those modeling efforts.

Our model is not meant to replace the existing Moody's Analytics Stressed LGD model, which is documented in Dwyer, Rathore, and Russell (2014) and shares several useful features with the unconditional LGD model documented in Zhuang and Dwyer (2016). Those models, like the one we present here, are based on realized LGDs calculated using the DRD. Rather, we focus primarily on demonstrating how principal component regressions can be used to capture parsimoniously the influence of a fairly rich set of macro drivers on LGDs. It is our hope that these results will be useful to fellow model-builders who face similar econometric problems when building stressed credit risk models for regulatory and other purposes.

In making our modeling choices, we were guided by two primary practical objectives:

  1. The model should capture the effects of macroeconomic variables on LGDs (i.e., recovery rates) in as robust and flexible a manner as possible.
  2. The model should replicate basic cross-sectional and time series regularities in the realized LGD data in its forecasts without asking more of the LGD data than they can bear.

The use of a principal component regression satisfies objective (1), whereas our focus on sector-level analysis, at the quarterly frequency, for only two debt seniority levels satisfies objective (2). With these points in mind, we discuss some features of the realized LGD data before presenting our empirical results.

The Realized LGD Data

The realized default data are more difficult to work with than the calibrated LGD data in our previous article. The reason for this is simple: Realized LGD estimates are only available when actual defaults occur. While Moody's Analytics DRD covers a total of about 24,000 security defaults since 1900 worldwide, more recent data for North America from 2000 onward contain a little more than 1,000 observations across 11 industrial sector classifications and various types of debt (senior secured, senior, subordinated, etc.).

In practice, this poses two obstacles for forecasting. First, data points tend to cluster around economic events. For instance, coverage for most industries is solid in the aftermath of the global financial crisis but has become sparser in the recent expansion years. Second, coverage varies by industry. Certain sectors, most notably banking and the state and local government sector, rarely experience conventional defaults on their debt securities, either because they do not rely heavily on such instruments or because they have bailout or restructuring options available that other commercial sectors do not have. For instance, the last bank registered in our dataset to file for default, in this particular case through Chapter 11, was Doral Financial in 2015, for which we do not have LGD data. Prior to this, the most up-to-date information on bank instrument default stems from a distressed exchange of Citizens Bank subordinate debt in September 2009. Needless to say, bank coverage is abundant from 2007 to 2009, but it would be difficult to align such "rare event default" data in a very systematic manner to macroeconomic variables over the business cycle. While realized default data are patchy, note that (a) this is not a problem in every single industry, and (b) the data still behave in systematic ways across industries and their debt seniority ranking.

Data Coverage: Modest Causes for Optimism

Figure 1 reports average LGD estimates by industry for all categories of debt seniority in the left column. Addressing point (a) from above, firms falling under broad industry definitions, such as capital and consumer industries, clearly experience default over the entire business cycle. While coverage tends to be better during recessions and the data are volatile, quarterly coverage suffices to make some predictions. For instance, both capital and consumer industries witnessed an uptick in their LGDs in the context of the Great Recession. LGDs subsequently remained more elevated for consumer industries in some quarters. Further, it isn't just banks and governments whose LGD coverage is systematically related to macroeconomic events. As an important example, coverage of energy producer LGDs is dramatically better after 2014, related to the collapse in energy prices. Such a simple observation underlines the importance of sector-specific LGD estimates in the context of macroeconomic stress testing.

Coverage Patterns by Sector and Seniority

Now we shift to the right column of Figure 1, which reports average LGD estimates for each industry broken down by "senior" debt, defined in this context as senior secured debt, and "junior" debt, which in this context means "everything else."1 Speaking to point (b) above, the debt structure across sectors shares two common aspects. First, subordinate default coverage is better, following from the rather straightforward observation that riskier assets fail more frequently. Second, subordinate LGDs are systematically higher than their senior counterparts, mirrored by the behavior of calibrated sector LGDs. The latter point even holds true in smaller industries with smaller sample coverage, such as the media and publishing sector.

Figure 1. Average realized LGD estimates by selected industries from 2000 to 2017. Senior debt includes all secured senior claims. Subordinate debt includes all other categories of debt.
Figure 1. Average realized LGD estimates by selected industries from 2000 to 2017. Senior debt includes all secured senior claims. Subordinate debt includes all other categories of debt.
Source: Moody's Analytics

Empirical Results

With the additional restrictions of realized default data in mind, we test the feasibility of the approach presented in our last article. Here, we allow a large number of macroeconomic variables to drive our scenario forecasts, condensing them through their principal component scores. We make three minor modifications in relation to our previous work:

  1. We reduce the frequency from monthly to quarterly. Given the patchy and volatile coverage of realized default data, this step is necessary to identify sufficient signal.
  2. We reduce the number of principal components from our original five to two in order to address the restrictions implied by smaller sample coverage and to not blindly overfit the model.2
  3. Rather than forecasting both senior and subordinate LGDs individually, we first forecast the overall sector average using the principal component approach. In a second step, we run two auxiliary regressions of the senior and subordinate sector LGDs against the average forecast. This two-step approach helps us to obtain a smoother, easier-to-forecast series in a first step, while then restoring the historical relationship between different debt categories in a second step.

Figure 2 presents stressed LGD forecasts across selected industries from step 1 of item 3 above, without differentiating across levels of debt seniority. We interpolate missing observations in history linearly for the purpose of this exercise. The forecast ordering behaves along expected lines: LGDs for the average sector tend to increase during downturns, with the qualified exception of the energy sector, for which the baseline scenario LGD is higher than the LGD under the adverse and severely adverse scenarios. This points to the relevance of idiosyncrasies across sectors. While the financial crisis of 2007-2009 had a somewhat muted effect on energy sector LGDs, the fall in global energy prices at the end of 2014, depleted energy firm revenues and had a significant and positive effect on LGDs, as we would expect based on standard finance theory.

Figure 2. Stressed sector LGD forecasts for selected sectors. Average LGD indicates the average across all defaults in the sector at any given point in time, without differentiating between degrees of debt seniority.
Figure 2. Stressed sector LGD forecasts for selected sectors. Average LGD indicates the average across all defaults in the sector at any given point in time, without differentiating between degrees of debt seniority.
Source: Moody's Analytics

Figure 3 displays stressed sector LGDs by sector and debt category, with our Comprehensive Capital Analysis and Review (CCAR) baseline forecasts in the left column and our severely adverse forecasts in the right column . As expected, LGD forecasts under the severely adverse scenario are more responsive than under the baseline scenario, where they tend to track their historical averages more closely.

Figure 3. LGD projections by sector, seniority, and economic scenario.
Figure 3. LGD projections by sector, seniority, and economic scenario.
Source: Moody's Analytics

Importantly, we see that projecting the average sector experience to the individual debt category by means of linear regression generates well-behaved forecasts. The clear historical difference between LGDs in junior and senior debt categories drives this result.

Coefficients of Principal Component Regressions of Macro Components on Realized LGDs

Figure 4 summarizes the coefficients of the principal component regression models behind the LGD projections shown in Figure 3. Principal component 1 is roughly an interest rate (i.e., yield curve) level factor, whereas principal component 2 is roughly a measure of real economic activity, in particular real GDP growth. As can be surmised from the model coefficients, LGDs in most sectors fall when growth increases. This is plausible. The exception is the energy sector, in which LGDs rise in higher interest rate environments. Since interest rate increases typically predict a fall in inflation and/or moderation of aggregate demand growth from current levels, and both of these outcomes are bad for the revenue of many energy firms, we regard the result as plausible as well.

Figure 4. Coefficient estimates for macro components.
Figure 4. Coefficient estimates for macro components.
Source: Moody's Analytics

The full list of macroeconomic drivers we consider when estimating the principal components is identical to that used in Malone and Wurm (2017), with the exception of the stressed sector Expected Default Frequencies (EDFs), which do not exist for the Moody's Investors Service industry classification. The first principal component score accounts for about 62% of the variation in our macro drivers. The second principal component captures about 17% of the joint variation of macro drivers.

The bottom of each industry panel of Figure 4 summarizes the regressions used to project LGDs for different seniorities from the average LGD. Subordinate-level LGDs follow the average more closely thanks to a higher count of default events compared with the senior level.

Comparison of Realized LGDs with Market-Implied LGDs

In our previous article, we demonstrated the viability of building stressed LGD models using market-implied LGDs sourced from the Fair Value Spread model available via the CreditEdge™ platform. We now present some preliminary comparisons between the market-implied and realized LGD datasets.

An important caveat is in order before making this comparison: The sector classifications in the CreditEdge platform and DRD are not directly comparable. The CreditEdge tool maps the issuer of a publicly traded security to one of 13 TPM sectors, based on its broad industry. DRD, meanwhile, maps the issuing line of business associated with a particular bond or loan default to one of 11 Moody's Investors Service industry classification sectors. The debt of any given borrower may, therefore, be classified in several different sectors in DRD, while the same situation will typically not arise in the CreditEdge platform.

When compared with standard industry categorizations, such as the standard industry classification system (SIC), the TPM sectors in the CreditEdge model generally deliver a tighter match for any given borrower. Since the purpose of stress testing is to establish a relationship between broad macroeconomic events and individual borrower fortunes, we find it more instructive to rely on the TPM sector definitions. The reason for this is simple: The LGD for a given firm is conceptually more a function of its broad industry performance than an indication of whether one of its specific lines of business is classified as, say, a capital versus a consumer industry.

Despite the above caveat, some sector definitions can be reconciled between the DRD and CreditEdge datasets. The closest match is energy and environment, which corresponds to energy and utilities in the CreditEdge data. There exists a looser match between consumer industries and consumer goods, while capital industries are broken down into various TPM sectors3.

Figure 5. Average LGDs in DRD versus subordinate and senior LGD in the CreditEdge platform.
Figure 5. Average LGDs in DRD versus subordinate and senior LGD in the CreditEdge platform.
Source: Moody's Analytics

Figure 5 presents forecasts for three sectors based on the realized and market-implied LGD data. A comparison of realized versus market-implied LGD histories is instructive. For instance, both types of energy sector LGDs have increased in level and volatility since the beginning of the oil price crash. It is also obvious that the CreditEdge market-implied LGD data are smoother and behave more consistently over the business cycle, while the realized LGD data from the DRD are much more volatile.

For the energy and consumer goods sectors, market-implied LGDs are above realized LGDs on average, while for the capital goods sector they are similar on average. Realized LGDs are more volatile than market-implied LGDs for all sectors. Stressed LGDs from both models remain flat under the baseline (not shown). Under the severely adverse scenario shown above, however, realized and market-implied stressed LGD paths do not always follow similar patterns. Market-implied and realized LGDs achieve their maximums at different times for the capital industries and consumer industries sectors, for example, while the shape of the stressed LGD paths are similar in the case of the energy sector.

Realized capital and consumer goods sector stressed LGDs increase, whereas realized energy sector LGDs fall under the severely adverse scenario, mirroring what happened to these variables in 2008. Better data coverage allows us to run separate models for the senior and subordinate debt when using the CreditEdge market-implied LGD data. The distinction is most visible for consumer goods, where LGDs fell around the Great Recession in the senior category and rose in the subordinate category, a pattern reflected in our market-implied stressed LGD forecast.

Conclusion

This article proposes a method of modeling realized LGDs as a function of macroeconomic drivers for stress testing. The time-varying availability of default data poses challenges for economic modelers. In our solution, we employ a principle component regression approach in the context of a two-step procedure for projecting stressed realized LGDs for debt of different seniority levels. We believe the resulting stressed LGD scenario projections provide reasonable, immediately applicable results for forecasting conditional expected losses on portfolios with exposures to the debt of firms in North America.

An important next step in LGD research is a full reconciliation of market-implied and realized LGD levels. It will take more effort in this direction in order to determine exactly how well bond markets price in recovery rates under different states of the macroeconomy. Our preliminary evidence suggests that realized and market-implied LGDs, while volatile, are largely consistent with a few differences by sector.

Footnotes

1This definition includes senior unsecured debt as well. We follow this distinction largely based on sample-size considerations. Moving a specific category from one bucket to the other does not affect the central patterns reported, however.

2We also repeated the exercise presented here with five principal components as in our original article. The results are qualitatively identical.

3In our previous article, we presented information on depository institutions and services. The DRD data have few entries on bank defaults, but also lacks information on services, as understood by TPM, since corresponding firms are instead associated more directly with other TPM sectors such as healthcare.

References

Dwyer, Douglas, Sanjay Rathore, and Heather Russel. "Stressed LGD Model." Moody's Analytics methodology paper. January 2014.

Malone, Samuel W. and Martin A. Wurm. "Modeling Stressed LGDs for Macroeconomic Scenarios." Moody's Analytics Risk Perspectives, volume IX. July 2017.

Zhuang, Zhong and Douglas Dwyer. "Moody's Analytics RiskCalc LGD: LossCalc v4.0 Model." Moody's Analytics methodology paper. January 2016.

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