# Modeling Stressed LGDs for Macroeconomic Scenarios

New accounting standards, which place increased emphasis on the ability of banks to calculate current expected credit losses, also make clear the importance of using models that appropriately link probabilities of default (PDs) and losses given default (LGDs) to macroeconomic drivers. At the same time, calculating conditional expected credit losses under Fed-supervised stress tests requires stressed PDs and LGDs as inputs. While validated stressed PD models are already on offer, efforts to properly model LGDs as a function of macroeconomic drivers are still in their infancy. In this article, we develop and validate a model for stressed LGDs aimed at meeting this need. Empirically, we find that LGDs sometimes lead PDs by several months during crisis periods. At the sector level, our stressed LGDs provide reasonably accurate forecasts out-of-sample for most sectors and exhibit attractive qualities under the Fed’s baseline, adverse, and severely adverse Comprehensive Capital Analysis and Review (CCAR) scenarios for all 13 sectors studied.

## Introduction

Recent regulatory trends have forced banks to develop new probability of default (PD), loss given default (LGD), and exposure at default (EAD) models. Such developments are driven by the expansion of regulatory stress testing, as well as novel current expected credit loss (CECL) and international financial reporting (IFRS 9) standards. The literature on PDs is ample, and practitioners typically have access to both internal modeling approaches as well as industry-wide estimates; however, LGDs and EADs lack similar treatment. The Bank for International Settlements, for instance, has long remarked upon the fact that banks have more difficulties in establishing estimates of their own LGDs vis-à-vis PDs.^{1}

As a step toward closing this gap, we first develop metrics of stressed LGDs for North America. Our LGDs are calculated at the industry level from Moody’s Analytics CreditEdge™ database and are similar in nature to existing point-in-time (PIT), stressed EDF measures based on the same source.^{2} Such information provides practitioners with an important baseline for the establishment of firm-level estimates. We further demonstrate that historical sector LGDs Granger-cause average EDFs for several industries in Moody’s Analytics CreditEdge data. This finding is important because it suggests that the early warning value of well-calibrated PIT LGD measures may have been somewhat underestimated by risk and investment practitioners. Second, we discuss the interpretation of our stressed LGD model for the financial sector. Finally, we show that the out-of-sample accuracy and behavior under stress scenarios of our sector LGD models are generally quite good.

Before proceeding, a caveat is in order. The work underlying this article relies on calibrated sector LGDs from the Moody’s Analytics fair value spread (FVS) model, rather than realized LGD data at the issuer level. There are good reasons for this: Calibrated sector LGDs are consistent by design with both bond spread data and issuer-level Expected Default Frequency (EDF) data. By extension, they are consistent with the stressed EDFs already used in stress testing work. Further, well-behaved sector-level LGD data – as opposed to more granular data – facilitates the initial development of econometric models in which LGDs respond in an intuitive and appropriate way to macroeconomic drivers under stress. These advantages notwithstanding, a first-best stressed LGD model must ultimately take into account issuer-level, realized LGD data, rather than calibrated sector LGDs alone.

Fortunately, realized LGDs by issuer and instrument seniority level can be constructed using Moody’s Analytics Default and Recovery Database (DRD), and such data will directly inform our forthcoming research on stressed realized LGD models.^{3} In that context, the present article primarily offers a proof-of-concept: It is possible to produce reliable, validated estimates of LGD for a wide variety of North American issuers under conditions of macroeconomic stress. We believe this finding alone is a positive development from a regulatory compliance and risk management perspective.

## Sector LGDs and Sector EDFs

For our stressed LGD model, we employ the expansive CreditEdge dataset. Our analysis is limited here to the approximately 12,000 firms in the US and Canada. Average sector LGDs for senior and subordinate debt are already available for 13 TPM industry sectors^{4} at the monthly frequency, with data beginning in December 2005. To obtain corresponding metrics of sector EDFs, we take the equally-weighted average across the individual firm EDFs within a given sector in each month.

For ease of exposition, we will primarily display graphical results for the banking and services sectors only, with notes on other sectors in the text. Figure 1 charts the history for the senior and subordinate sector LGDs and these sector EDFs for the available sample period. Several patterns stand out clearly for these and other sectors. First, senior LGDs are generally lower and less volatile than their subordinate counterparts. Second, LGDs – more so than EDFs – co-vary differently with the state of the economy across sectors. LGDs in some sectors, such as the telecommunication sector (TPM sector 10), are broadly countercyclical; LGDs for other sectors, such as banks (TPM sector 1), appear more cyclical, with higher LGDs occurring during the period defining the Great Recession.

###### Figure 1 Sector LGDs and EDFs for the banking and services sectors

###### Source: Moody's Analytics

LGDs in the raw materials and mining sector (TPM sector 9), in contrast, do not appear cyclical at all. Rather, the sector LGD appears to be in almost secular decline from 2006 to 2014, after which subordinate LGDs shoot up in response to the 2014 plunge in energy prices.

In contrast to the case of LGDs, virtually all sectors experienced an increase in their average EDF levels in the aftermath of the global financial crisis, with slight variations in timing and degree, followed by a subsequent period of relative calm. The most noticeable exceptions to this rule are the raw materials and the mining and energy sectors, which both saw an increase in EDFs after 2014. Consequently, the contemporaneous relationship between EDFs and LGDs varies in subtle ways across industries. Figure 2 summarizes the Pearson correlation coefficients, by sector, between the three pairs of variables drawn from the set of senior sector LGDs, subordinate sector LGDs, and sector EDFs.

###### Figure 2 Pearson correlation coefficients: LGDs and EDFs

###### Source: Moody's Analytics

Across sectors, correlation coefficients between senior and subordinate LGDs are positive and typically quite high, as expected. The main stylized fact of note that emerges from Figure 2, rather, is that “financial services sectors are special.” In particular, whereas LGD-EDF correlations are almost uniformly negative for non-financial sectors, the correlations for financial sectors (1, 7, and 13) are positive.

The reason for this finding likely originates in the forces of valuation and interdependence at work amongst financial institutions. The PDs of financial institutions depend on the value of their collateral, which is linked to their LGDs, and the value of their collateral often depends upon the PDs of the counterparties that owe them claims; therefore, financial institutions’ PDs and LGDs are endogenous. This is one reason for which the cross-ownership of liabilities across financial institutions can make them more vulnerable to contagion.^{5}

In practice, the positive correlation between PDs and LGDs for financial institutions works to increase the variance of their time-varying expected credit losses. This results in increased model risk. It may also cause more cyclical reserve requirements under new IFRS 9 and CECL standards if banks do not pay careful attention to both LGD and PD modeling as well as the natural dependence between these two activities.

### In practice, the positive correlation between PDs and LGDs for financial institutions works to increase the variance of their time-varying expected credit losses. This results in increased model risk.

As a first step to thinking about how to model sector LGDs, therefore, we examine whether they exhibit lead-lag relationships with EDFs. Specifically, we test for the presence of Granger causality between senior and subordinate LGDs for each sector, respectively, with the corresponding sector EDF. These results are presented in Figure 3.^{6}

###### Figure 3 Granger causality tests: EDFs and LGDs

###### Source: Moody's Analytics

From Figure 3, we find that in 39% of instances, LGDs Granger-cause EDFs, while the reverse is true in 50% of cases. Sector EDFs tend to Granger-cause senior LGDs more reliably (in 62% of cases), whereas they hold less predictive power for subordinate EDFs (39% of sectors).

### In 39% of instances, LGDs Granger-cause EDFs, while the reverse is true in 50% of cases.

Notably, in the case of depository institutions (sector 1) we find that both senior and subordinate sector LGD measures Granger-cause the sector EDF, whereas the reverse is not true. While banks’ PDs may help forecast growth,^{7} it turns out that the early spike in banks’ LGDs provided an even better early warning indicator during the crisis. The measured spike in bank LGDs prior to the crisis is consistent with a deterioration in the value of their real estate-linked collateral.

## Stressed Sector EDFs and LGDs

Let’s proceed to model-building. To obtain good conditional stressed LGD forecasts, one needs to identify a set of suitable macroeconomic drivers. “Realism” in this context does not refer only to “forecast accuracy,” although that is also obviously desirable. The objective of a stress forecast is rather to replicate the behavior of a variable under particular macroeconomic assumptions. For instance, if senior LGDs in transportation tend to drop in an economic downturn, a good scenario forecast needs to approximate the direction and magnitude of such behavior given a shock of similar severity. This is different from the approach of standard time-series forecasting methodologies, such as vector-autoregressive models, where the objective is to minimize the forecast error of any given series based on observed history. In stress testing applications, certain in-sample properties such as goodness of fit or serial correlation share the stage with the need to produce realistic scenario forecasts for the dependent variable under stress.

### The objective of a stress forecast is to replicate the behavior of a variable under particular macroeconomic assumptions.

As a benchmark estimation approach, we employ a principal component regression^{8} (PCR) using as explanatory variables Moody’s Analytics stressed EDF forecasts as well as other drivers obtained from Moody’s Analytics macro model.

Sector EDFs are natural inputs to sector LGD models based on conceptual considerations and, at least for some sectors, based on the presence of observed nonzero historical correlations. The CreditEdge software already contains estimates on stressed firm EDFs based on both the Fed’s regulatory Comprehensive Capital Analysis and Review (CCAR) scenarios, as well as some of Moody’s Analytics own macroeconomic scenarios.^{9} To establish stressed sector EDF forecasts, we simply compute the equally-weighted average of firm-level scenario forecasts at every point of the forecast horizon across all firms in a sector.^{10}

The varying strength in correlation between the variables in Figure 2 implies that some sector EDFs are insufficient on their own to adequately predict sector LGDs. We therefore extend the pool of potential drivers to include variables from the Fed’s CCAR scenarios and Moody’s Analytics own macro model forecast. For our full set of variables, we obtain the first five principal component scores, which we use as forecast drivers. The full set of variables is listed in Figure 4 and corresponds roughly to a similar list in Poi (2016).

###### Figure 4 Drivers

###### Source: Moody's Analytics

The choice of the PCR modeling approach is based on two considerations. First, the limited sample size prevents us from including more than only a handful of macro drivers before running into multicollinearity problems. Principal component analysis (PCA) allows us to largely overcome this issue. Second, while the original 28 variables used in the last CCAR cycle yield plausible results for certain sectors (such as transportation), they do not generate enough stress for others (such as depository institutions). The specific purpose of PCA is to select a small set of variables whose variation explains the maximal amount of the variation present in the full set of macroeconomic drivers. Given our goal of modeling sector LGDs, we construct a dataset of macroeconomic drivers, such as GDP, along with measures of housing and labor market performance, equity market performance, and various interest rates.^{11}

With principal component estimates in hand, we next regress each sector’s senior LGD against the principal components, and use forecasts under the regulatory scenarios to obtain estimates for stressed senior LGDs. The factor loadings for the PCA for sector 1 (depository institutions) are displayed in Figure 5a.^{12} Basic cutoff criteria such as the Kaiser criterion suggest using five principal components to capture the joint variation of our set of drivers. The explained variation for the banking sector is about 92%. Figure 5b reports the results of regressing the component scores on the senior sector LGD.

From Figure 5a, we see that component 1 is essentially an interest rate level factor, component 2 is (approximately) a GDP growth and employment macro factor, component 3 is a market and oil price factor, component 4 is a housing activity-to-disposable income factor, and component 5 is a real disposable income growth factor. Components 2, 3, and 5 also give nontrivial weight to the sector EDF for depository institutions.

###### Figure 5a Principal component factor loadings – banking sector

###### Source: Moody's Analytics

In Figure 5b, components 2, 3, and 5 are also the most consistently statistically significant drivers of both senior and subordinate sector LGDs. The coefficient for component 1 is statistically significant at the 5% level in the subordinate sector LGD model, but not in the model for the senior LGD. Based on adjusted R-squared figures of 69% and 65% for the subordinate and senior LGD models, respectively, we can surmise that the five principal components describe the fluctuations in the depository institution sector LGDs reasonably well.

###### Figure 5b Linear regression result

###### Source: Moody's Analytics

Summary statistics for the in-sample performance of the five-component PCR for each sector are reported in Figure 6. R-squared values for the senior LGD models range from 36% to 81%, indicating significant variability in the explanatory power of the five components across sectors. Also, the explanatory power of the five components for senior LGDs is somewhat better than for subordinate LGDs.

###### Figure 6 In-sample fit

###### Source: Moody's Analytics

We now examine the out-of-sample performance of our models. For this purpose, we estimate the model coefficients using data from January 2006 to August 2013, and then forecast LGDs based on the realized values of model drivers (hence components) from September 2013 until early 2016, when our sample ends. The graphical forecast results are shown in Figure 7 for the case of the banking and services sectors for both senior and subordinate LGDs. Overall, the model performs quite well for some sectors (and parts of the capital structure) and less well for others.

###### Figure 7 Out-of-sample results for the banking and services sectors

###### Source: Moody's Analytics

Figure 8 reports root-mean-square errors (RMSEs) and mean absolute errors (MAEs) for the out-of-sample exercise. There is clearly scope for additional research to improve the performance of the models for some sectors, such as sector 3 (aeronautics). However, for financial sectors, the models perform well out-of-sample, with RMSEs in the range of 2% to 4%.

###### Figure 8 Out-of-sample fit

###### Source: Moody's Analytics

We now turn to the performance of our models under the Federal Reserve’s stress test scenarios. In Figure 9, we report sector LGD forecasts under the baseline, adverse, and severely adverse scenarios provided by the Fed in early 2016. The results are encouraging, and the stressed LGDs appear to exhibit very plausible patterns under each of the different scenarios. Both the direction of the shocked LGDs as well as their magnitudes under the severely adverse scenario in particular are consistent with the paths followed by LGDs during the worst part of the Great Recession.

###### Figure 9 LGD forecasts under the Fed’s 2016 baseline, adverse, and severely adverse scenarios

###### Source: Moody's Analytics

## Conclusion

The stressed LGD methodology whose results we have summarized in this article provide a practical solution for banks and other financial institutions that require public firm LGD estimates for risk management and compliance purposes. This approach complements private firm LGD estimates available through outlets such as Moody’s Analytics RiskCalc software. Going forward, we expect that further improvements in LGD modeling will help drive efforts to measure current expected credit losses more accurately. In particular, firm-specific accounting information might be matched with past records of realized losses given default in order to differentiate LGD estimates across firms within a given sector and geography.

###### Footnotes

1 See Allen and Saunders, 2003; and Basel Committee on Banking Supervision, 2005.

2 See Ferry, Hughes, and Ding, 2012a and 2012b.

3 See Malone and Wurm, forthcoming.

4 TPM industry sectors refer to the sector categories encoded in the CreditEdge sector LGD database.

5 For details about the underlying mechanisms at work, see Gray and Malone (2008).

6 The null hypothesis of the Wald test for Granger causality is that the coefficients on the p-lags of a variable of interest in a vector autoregressive equation are jointly zero, that is to say, that they do not Granger-cause the left-hand-side variable. Thus, a low p-value suggests the presence of Granger causality. We choose the lag length of each vector autoregression (VAR) by picking the lag preferred by the majority of these four criteria: the final prediction error (FPE), Akaike information criterion (AIC), Schwarz’s Bayesian information criterion (SBIC), and the Hannan-Quinn information criterion (HQIC). Where the criteria are split, we base our preference on the AIC. The presented results are not very sensitive to the reliance of one criterion over another.

7 See Hughes and Malone, 2015.

8 We alternatively considered a generalized linear model with a logit link, since LGDs are censored between 0 and 1. Based on in-sample fit, however, we prefer simple least squares.

9 For methodological details see Ferry, Hughes, and Ding, 2012.

10 Since jump-offs can occur between the sector EDFs in history and their scenario forecasts, we splice each series to smooth them.

11 Notice that some macroeconomic variables, such as GDP, are only available at a quarterly frequency. These variables are interpolated in Moody’s Analytics macro forecast, using a cubic spline.

12 Since the sector EDFs vary from industry to industry, the factor loadings are not exactly identical in across sectors. They are, however, otherwise similar. These results are not reported.

###### Sources

Allen, Linda and Anthony Saunders. “A survey of cyclical effects in credit risk measurement models.” Bank for International Settlements, working paper 126. January 2003.

Basel Committee on Banking Supervision. “Guidance on Paragraph 468 of the Framework Document.” BCBS 115. July 2005.

Ferry, Danielle H., Tony Hughes, and Min Ding. “Stressed EDF Credit Measures.” Moody’s Analytics modeling methodology. May 2012.

Ferry, Danielle H., Tony Hughes, and Min Ding. “Stressed EDF Credit Measures for Western Europe.” Moody’s Analytics modeling methodology. October 2012.

Gray, Dale and Samuel W. Malone. *Macrofinancial Risk Analysis*. John Wiley & Sons, 2008.

Hughes, Tony and Samuel W. Malone. "Systemic Risk Monitor 1.0: A Network Approach." Moody's Analytics whitepaper. July 15, 2015.

Malone, Samuel W. and Martin Wurm. “Stressed LGDs.” Moody's Analytics whitepaper. Forthcoming.

Poi, Brian. “Peer Group Analysis in Bank Call Report Forecasting.” Moody’s Analytics whitepaper. 2016.

###### SUBJECT MATTER EXPERTS

#### Dr. Samuel W. Malone

Director of Research

Sam leads the quantitative research team within the CreditEdge™ research group. In this role, he develops novel risk and forecasting solutions for financial institutions while providing thought leadership on related trends in global financial markets.

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