GCorr™ Emerging Markets - Moody's Analytics · This section explores correlation patterns in developed and emerging countries. Specifically, we explore the relationship between

MODELING METHODOLOGY

QUANTITATIVE RESEARCH GROUPJULY 2015

GCorr™ Emerging Markets

Abstract

Moody’s Analytics GCorr™ Corporate model provides asset correlations of corporate borrowers for credit portfolio analysis. The GCorr Corporate model is based on 49 country factors. This paper introduces a new model, GCorr Emerging Markets, designed with more than 200 country-factors including emerging markets worldwide. The methodology expands GCorr Corporate’s 49 country factors to 200+ factors, each representing individual countries to better measure country concentration and diversification effects. The expanded factors cover predominately emerging market countries where we lack firm-level asset return data. For this reason, we refer to the extension as the GCorr Emerging Markets model. This model allows financial institutions with commercial exposures to smaller and emerging countries to better describe correlations across these countries, as well as to better capture diversification effects when investing in a wide cross-section of these countries.

In addition to a discussion on the empirical patterns observed in emerging market correlations, the methodology employed to model the emerging market factors and their correlations, validation of the model, this paper also assesses the impact of using the model for portfolio analysis.

Authors Jimmy Huang Libor Pospisil Noelle Hong

Acknowledgements We are extremely grateful to Amnon Levy, Nihil Patel, Christopher Crossen, and Ankit Rambhia for their help.

Contact Us Americas +1.212.553.1653 [email protected]

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QUANTITATIVE RESEARCH GROUP

2 JULY 2015 GCORR EMERGING MARKETS

Table of Contents

1. Introduction 3

2. Empirical Patterns in Emerging Markets 5 2.1 Data 5 2.2 Relationships Between Correlations and Country Characteristics 5

3. Creating a Factor Table 9 3.1 Overview of the GCorr Framework 9 3.2 Model Estimation 10 3.3 Modeled Correlations 12

4. Validation 15 4.1 Comparison with Empirical Patterns 15 4.2 Comparison with Empirical Asset Correlations 16

5. Portfolio Impact Analysis 19

6. Conclusion 21

Appendix Across-Region Correlations 22

References 24



1. Introduction

Credit portfolio management is a crucial area of focus for financial institutions. Though all credit portfolios are subject to the risk of losses, the uncertainty can be reduced, e.g. via diversification. However, in order to accurately capture the uncertainty of a credit portfolio’s losses and diversification effects, it is imperative to accurately model diversification sources and pockets of risk concentration within a portfolio. This problem is typically addressed by estimating a granular correlation model that captures the magnitude and dependency structure among the borrowers within a portfolio.

A granular correlation model should be based on the data and economic patterns relevant for the asset classes included in the portfolio. This paper addresses the question of how to model correlations for corporate exposures in countries — emerging and smaller countries — where firm-level data may not suffice. The existing literature suggests that emerging markets have relatively low correlations with one another and can have domestic and country-specific factors that impact correlations.1

Moody’s Analytics GCorr Corporate model can estimate correlations between the credit quality changes of corporate obligors in a credit portfolio.2 The GCorr Corporate model provides correlation estimates between publicly traded firms using firm-level asset return data. The basic framework models a firm’s asset returns as a combination of a systematic component and an idiosyncratic component:

1

With this structure, correlation between two firms can be described as follows:

, ,

Correlation between two firms depends on the asset R-squared of each firm, , as well as the correlation between their systematic factors, , . Interestingly, the R-squared values of firms in developed countries exhibit similar behavior to those in emerging countries. We see a strong relationship between a firm R-squared and its size. Large firms tend to be more sensitive to the state of the economy and often have a larger systematic exposure, so we observe higher R-squared values. After controlling for size, there is still some variation by country and industry, but we do not find a relationship between the country variations and the macroeconomic factors, such as development. We recommend using the Modeled R-squared3 to model the R-squared of a firm without asset return data. The remainder of the paper focuses on modeling the systematic factors.

A firm’s systematic component, , is further decomposed into a country and industry component: ( is the country of firm , and is the industry of ). The correlation between two firms then depends on the degree to which the country and industry components are correlated.

We estimate country and industry factors using time series of firm-level asset returns. Asset returns are a byproduct of Moody’s Analytics Public Firm EDF™ (Expected Default Frequency) model’s credit measures and rely upon firms’ equity data and financial statements.4 For countries with developed equity markets and a large number of publicly-traded firms, the correlation between the country components can be modeled with a high degree of confidence. However, for countries with fewer firms, estimates can be subject to statistical errors. To reduce the noise within GCorr Corporate, some country factors represent a broader region consisting of several individual countries, in order to increase the number of firms represented within the country factor. Two examples: the Middle East country factor and the Eastern Europe country factor.

1 See “Correlations in Emerging Market Bonds,” Bunda (2009) and “Stock Market Correlations Between China and Its Emerging Market Neighbors,” Jayasuriya (2011).

2 We refer to these correlations as “asset correlations” throughout this paper. 3 See “Modeling Credit Correlations: An Overview of the Moody’s Analytics GCorr Model.” Huang, et al., (2012). 4 See “Credit Risk Modeling of Public Firms: EDF9.” Nazeran, et al., (2015).



Table 1

Examples of GCorr Corporate Regional Factors: Middle East and Eastern Europe

GCORR CORPORATE

COUNTRY FACTOR COUNTRY NAME

GCORR CORPORATE

COUNTRY FACTORCOUNTRY NAME

C45 UNITED ARAB EMIRATES C32 ALBANIAC45 BAHRAIN C32 BULGARIAC45 IRAN (ISLAMIC REPUBLIC OF) C32 BOSNIA AND HERZEGOVINAC45 JORDAN C32 CZECH REPUBLICC45 KUWAIT C32 ESTONIAC45 LEBANON C32 CROATIAC45 OMAN C32 HUNGARYC45 … C32 …

We collapse a cluster of countries into regional factors. Two effects result from this process. Suppose a portfolio has exposures to the Middle East. The first implication is that the systematic factor of a Middle Eastern firm does not depend on the specific Middle Eastern country. A Jordanian construction firm’s systematic factor is the same as that of a construction firm in Kuwait ( and thus ). Therefore, the systematic factor of a U.S. firm is equally correlated to the Middle Eastern firm’s systematic factor, regardless of the specific country. The second and more impactful implication is that all the firms within the Middle East have perfectly correlated country components ( ), causing the systematic factors to be highly correlated. In reality, the different countries in the Middle East have different economies and may be exposed to different economic and political shocks, which should be reflected in the systematic factor correlations. However, it is challenging to model these effects without sufficient data.

Our objective is to add new country factors into the model. These new factors represent the individual countries for which we do not have sufficient firm-level data. In order to overcome the lack of data issue, we model these factors by leveraging country-level characteristics and economic indicators, more widely available than firm-level data. We refer to the model with these new country factors as GCorr Emerging Markets.

By leveraging country-level data, GCorr Emerging Markets expands the GCorr Corporate framework to model the correlation parameters of individual countries. Instead of the regional country factors, each individual country becomes its own country factor. For example, the Middle East country factor in GCorr Corporate now becomes more than 10 individual countries within GCorr Emerging Markets. This expansion allows us to better capture concentration and diversification effects. We can now determine which individual countries contribute the most toward overall portfolio risk. Exposures within the same region but different countries will also show more diversification, since their systematic factors will no longer share the same country component. For most portfolios, these two results will generally (but not in all cases) lead to lower portfolio risk statistics.

We organize the remainder of this paper as follows:

Section 2 explores the empirical correlation patterns in emerging economies.

Section 3 details the GCorr Emerging Markets methodology.

Section 4 discusses various validation exercises.

Section 5 shows portfolio impact when using GCorr Emerging Markets.

Section 6 concludes.



2. Empirical Patterns in Emerging Markets

This section explores correlation patterns in developed and emerging countries. Specifically, we explore the relationship between the level of correlations exhibited in a country and the observable macroeconomic variables, such as unemployment rates and oil production.

2.1 Data For many countries, we obtain different types of data, as of 2014. Data types range from:

» Overall economic indicators: GDP, unemployment rate, industrial production, etc.

» Financial indicators: debt, interest rates, etc.

» Activity in various sectors of the economy: oil production, electricity production, etc.

» Geographical: area, population, etc.

To obtain a sense of the correlations between different emerging countries, we collect 15 years of quarterly time series (1999 –2014) of the following data, shown in Table 1.

Table 2

Data Sources DATA SOURCE NUMBER OF COUNTRIES

Real GDP IMF 82

Industrial Production Index IMF 62

Equity Index MSCI 53

Asset Return Index GCorr 73

We then apply stationary transformations of the data by using log-returns. We also apply seasonality adjustments, since the presence of seasonality can greatly distort the correlation estimates.

2.2 Relationships Between Correlations and Country Characteristics We analyze the relationships between correlation levels and various economic variables and highlight some key findings.

Figure 1 presents the relationship between GDP per Capita and the level of correlation between countries. We sort countries into 10 groups, based on their GDP per Capita. p10 represents the group of countries with the lowest GDP per Capita, while p100 represents the group of countries with the highest GDP per Capita. Each box represents the average correlation across groups of countries when the countries are grouped by GDP per Capita. The average GDP correlation between the group of countries with the lowest GDP per Capita is 8%, while the average GDP correlation between the group of countries with the highest GDP per Capita is 42%. The upper left graphic shows the correlations computed using GDP growth time series, while the graphic on the upper right shows the correlations computed using industrial production indexes. The bottom left graphic shows correlations computed using equity indexes, and the bottom right shows correlations computed using asset return indexes. The correlation measures can be noisy, given that some of the time series do not contain a large number of observations, and, for some countries, the data may be less reliable, but the general pattern is clear — countries with high GDP per Capita tend to be highly correlated with one another, while countries with low GDP per Capita have lower correlations with one another. In other words, developed countries show more systematic risk and are more sensitive to the global economy. This finding is true when looking at either GDP growth correlations, industrial production correlations, or equity correlations. Figure 1 shows full results.



Figure 1 Country Correlations by GDP per Capita

Of the variables explored, GDP per Capita, which can be considered a proxy for development level, has the strongest relationship with the general level of correlations. Said another way, developed economies tend to move more closely with the global environment, while less-developed countries are subject to more country-specific risk. Other variables that may seem intuitive, such as unemployment rate or oil production, do not show strong relationships, as seen in Figures 2 and 3. When we repeat the same exercise using the unemployment rate, we do not observe a clear relationship.

p10 p20 p30 p40 p50 p60 p70 p80 p90 p100

p10 8% 19% 13% 27% 20% 23% 15% 12% 12% 17%

p20 19% 18% 22% 28% 21% 20% 21% 11% 10% 10%

p30 13% 22% 25% 36% 39% 39% 37% 38% 36% 27%

p40 27% 28% 36% 44% 35% 48% 47% 34% 37% 30%

p50 20% 21% 39% 35% 43% 41% 36% 38% 45% 37%

p60 23% 20% 39% 48% 41% 57% 47% 49% 55% 45%

p70 15% 21% 37% 47% 36% 47% 59% 49% 56% 45%

p80 12% 11% 38% 34% 38% 49% 49% 53% 61% 53%

p90 12% 10% 36% 37% 45% 55% 56% 61% 58% 53%

p100 17% 10% 27% 30% 37% 45% 45% 53% 53% 42%

GDP Growth Correlation by GDP per Capita

p10 p20 p30 p40 p50 p60 p70 p80 p90 p100

p10 ‐4% 5% 6% ‐2% 11% 2% 6% 2% ‐3% 6%

p20 5% 6% 15% 11% 12% 9% 15% 12% 8% 9%

p30 6% 15% 17% 16% 17% 15% 24% 20% 15% 14%

p40 ‐2% 11% 16% 21% 24% 24% 39% 40% 28% 23%

p50 11% 12% 17% 24% 12% 18% 28% 38% 21% 21%

p60 2% 9% 15% 24% 18% 22% 26% 34% 19% 23%

p70 6% 15% 24% 39% 28% 26% 44% 49% 30% 35%

p80 2% 12% 20% 40% 38% 34% 49% 53% 43% 41%

p90 ‐3% 8% 15% 28% 21% 19% 30% 43% 30% 24%

p100 6% 9% 14% 23% 21% 23% 35% 41% 24% 24%

Industrial Production Correlation by GDP per Capita

p10 p20 p30 p40 p50 p60 p70 p80 p90 p100

p10 19% 22% 37% 31% 32% 27% 32% 38% 33% 36%

p20 22% 29% 40% 34% 34% 33% 33% 41% 36% 39%

p30 37% 40% 56% 50% 50% 37% 46% 50% 55% 55%

p40 31% 34% 50% 43% 46% 36% 43% 49% 47% 50%

p50 32% 34% 50% 46% 57% 34% 46% 54% 56% 54%

p60 27% 33% 37% 36% 34% 38% 39% 38% 39% 39%

p70 32% 33% 46% 43% 46% 39% 51% 50% 49% 51%

p80 38% 41% 50% 49% 54% 38% 50% 66% 66% 61%

p90 33% 36% 55% 47% 56% 39% 49% 66% 64% 62%

p100 36% 39% 55% 50% 54% 39% 51% 61% 62% 59%

Equity Correlation by GDP per Capita

p10 p20 p30 p40 p50 p60 p70 p80 p90 p100

p10 22% 12% 14% 18% 17% 12% 18% 16% 15% 16%

p20 12% 32% 13% 21% 17% 18% 17% 15% 17% 17%

p30 14% 13% 32% 28% 25% 18% 24% 26% 25% 27%

p40 18% 21% 28% 50% 34% 25% 34% 36% 35% 37%

p50 17% 17% 25% 34% 41% 23% 32% 36% 32% 33%

p60 12% 18% 18% 25% 23% 31% 25% 24% 24% 25%

p70 18% 17% 24% 34% 32% 25% 45% 41% 36% 38%

p80 16% 15% 26% 36% 36% 24% 41% 56% 41% 45%

p90 15% 17% 25% 35% 32% 24% 36% 41% 43% 40%

p100 16% 17% 27% 37% 33% 25% 38% 45% 40% 49%

Asset Correlation by GDP per Capita



Figure 2 Country Correlations by Unemployment Rate

Looking at the various correlation measures, there is also no clear pattern between the amount of oil a country exports and the correlation level. We look at dozens of other economic variables, but GDP per Capita shows the strongest relationship with correlation.

p10 p20 p30 p40 p50 p60 p70 p80 p90 p100

p10 39% 32% 30% 44% 35% 36% 23% 40% 21% 32%

p20 32% 39% 42% 42% 39% 43% 16% 41% 27% 37%

p30 30% 42% 39% 35% 45% 41% 21% 50% 21% 46%

p40 44% 42% 35% 43% 41% 45% 19% 42% 22% 39%

p50 35% 39% 45% 41% 40% 36% 20% 49% 26% 45%

p60 36% 43% 41% 45% 36% 39% 23% 45% 24% 40%

p70 23% 16% 21% 19% 20% 23% 13% 11% 14% 19%

p80 40% 41% 50% 42% 49% 45% 11% 66% 40% 57%

p90 21% 27% 21% 22% 26% 24% 14% 40% 23% 37%

p100 32% 37% 46% 39% 45% 40% 19% 57% 37% 53%

GDP Growth Correlation by Unemployment

p10 p20 p30 p40 p50 p60 p70 p80 p90 p100

p10 33% 23% 32% 17% 26% 36% 27% 40% 17% 12%

p20 23% 16% 20% 16% 14% 29% 22% 21% 23% 12%

p30 32% 20% 38% 20% 34% 44% 29% 39% 34% 15%

p40 17% 16% 20% 10% 20% 21% 21% 15% 19% 11%

p50 26% 14% 34% 20% 30% 51% 33% 41% 21% 16%

p60 36% 29% 44% 21% 51% 53% 41% 45% 39% 17%

p70 27% 22% 29% 21% 33% 41% 25% 33% 31% 15%

p80 40% 21% 39% 15% 41% 45% 33% 37% 29% 13%

p90 17% 23% 34% 19% 21% 39% 31% 29% 24% 21%

p100 12% 12% 15% 11% 16% 17% 15% 13% 21% 10%

Industrial Production Correlation by Unemployment

p10 p20 p30 p40 p50 p60 p70 p80 p90 p100

p10 41% 47% 42% 46% 47% 35% 39% 35% 42% 37%

p20 47% 39% 46% 51% 47% 42% 40% 35% 45% 37%

p30 42% 46% 47% 51% 45% 47% 45% 40% 49% 39%

p40 46% 51% 51% 63% 53% 60% 54% 45% 58% 46%

p50 47% 47% 45% 53% 45% 48% 44% 42% 46% 41%

p60 35% 42% 47% 60% 48% 49% 46% 42% 60% 43%

p70 39% 40% 45% 54% 44% 46% 42% 38% 52% 38%

p80 35% 35% 40% 45% 42% 42% 38% 36% 42% 33%

p90 42% 45% 49% 58% 46% 60% 52% 42% 63% 50%

p100 37% 37% 39% 46% 41% 43% 38% 33% 50% 32%

Equity Correlation by Unemployment

p10 p20 p30 p40 p50 p60 p70 p80 p90 p100

p10 37% 27% 26% 28% 33% 22% 26% 20% 14% 20%

p20 27% 35% 24% 28% 31% 23% 24% 20% 12% 21%

p30 26% 24% 30% 26% 30% 21% 24% 18% 12% 20%

p40 28% 28% 26% 37% 34% 26% 28% 20% 12% 21%

p50 33% 31% 30% 34% 44% 29% 32% 24% 15% 25%

p60 22% 23% 21% 26% 29% 32% 23% 19% 10% 18%

p70 26% 24% 24% 28% 32% 23% 36% 21% 11% 22%

p80 20% 20% 18% 20% 24% 19% 21% 28% 11% 14%

p90 14% 12% 12% 12% 15% 10% 11% 11% 20% 9%

p100 20% 21% 20% 21% 25% 18% 22% 14% 9% 23%

Asset Correlation by Unemployment



Figure 3 Country Correlations by Oil Exports

For each pair of countries, we compute the average empirical asset correlation between a random sample of firms in the two countries. We then segregate the country-level correlations by region. The plot in Figure 4 shows the distribution of correlations of countries within the same region (blue) and the distribution of correlations between countries in the region and countries outside of the region (red).

p10 p20 p30 p40 p50 p60 p70 p80 p90 p100

p10 48% 49% 34% 34% 42% 53% 40% 47% 31% 43%

p20 49% 60% 35% 45% 33% 43% 46% 42% 37% 37%

p30 34% 35% 21% 25% 23% 40% 28% 31% 24% 27%

p40 34% 45% 25% 26% 28% 28% 23% 34% 29% 29%

p50 42% 33% 23% 28% 9% 35% 26% 29% 20% 27%

p60 53% 43% 40% 28% 35% 51% 36% 47% 33% 44%

p70 40% 46% 28% 23% 26% 36% 32% 32% 28% 32%

p80 47% 42% 31% 34% 29% 47% 32% 38% 31% 34%

p90 31% 37% 24% 29% 20% 33% 28% 31% 26% 24%

p100 43% 37% 27% 29% 27% 44% 32% 34% 24% 32%

GDP Growth Correlation by Oil Exports

p10 p20 p30 p40 p50 p60 p70 p80 p90 p100

p10 21% 19% 20% 25% 13% 39% 11% 26% 14% 24%

p20 19% 17% 23% 17% 13% 39% 18% 23% 6% 13%

p30 20% 23% 22% 28% 14% 30% 23% 18% 29% 16%

p40 25% 17% 28% 18% 12% 40% 14% 31% 16% 18%

p50 13% 13% 14% 12% 10% 22% 15% 14% 2% 10%

p60 39% 39% 30% 40% 22% 63% 32% 43% 21% 31%

p70 11% 18% 23% 14% 15% 32% 13% 18% 14% 15%

p80 26% 23% 18% 31% 14% 43% 18% 33% 17% 26%

p90 14% 6% 29% 16% 2% 21% 14% 17% 16% 19%

p100 24% 13% 16% 18% 10% 31% 15% 26% 19% 17%

Industrial Production Correlation by Oil Exports

p10 p20 p30 p40 p50 p60 p70 p80 p90 p100

p10 69% 55% 41% 55% 59% 54% 51% 38% 58% 45%

p20 55% 51% 39% 49% 53% 50% 51% 36% 51% 48%

p30 41% 39% 21% 31% 39% 30% 41% 31% 39% 32%

p40 55% 49% 31% 41% 51% 44% 46% 33% 47% 38%

p50 59% 53% 39% 51% 49% 50% 46% 35% 48% 45%

p60 54% 50% 30% 44% 50% 44% 45% 35% 44% 39%

p70 51% 51% 41% 46% 46% 45% 46% 36% 49% 44%

p80 38% 36% 31% 33% 35% 35% 36% 27% 40% 37%

p90 58% 51% 39% 47% 48% 44% 49% 40% 42% 45%

p100 45% 48% 32% 38% 45% 39% 44% 37% 45% 41%

Equity Correlation by Oil Exports

p10 p20 p30 p40 p50 p60 p70 p80 p90 p100

p10 31% 35% 28% 30% 28% 23% 33% 13% 30% 15%

p20 35% 60% 35% 36% 34% 26% 39% 13% 36% 15%

p30 28% 35% 45% 29% 27% 25% 32% 14% 29% 16%

p40 30% 36% 29% 49% 29% 27% 38% 14% 32% 15%

p50 28% 34% 27% 29% 42% 23% 32% 13% 30% 16%

p60 23% 26% 25% 27% 23% 40% 28% 13% 22% 15%

p70 33% 39% 32% 38% 32% 28% 52% 19% 36% 19%

p80 13% 13% 14% 14% 13% 13% 19% 39% 11% 12%

p90 30% 36% 29% 32% 30% 22% 36% 11% 48% 12%

p100 15% 15% 16% 15% 16% 15% 19% 12% 12% 31%

Asset Correlation by Oil Exports



Figure 4 Country Correlations by Region

In almost all regions, the median within-region correlation is higher than the median across-region correlations. The exception is in Africa, where the within-region correlations are lower than across-region correlations. One possible economic narrative could point to the trade patterns of African countries. Many African countries export, e.g., commodities or agricultural products, to Europe, North America, and Asia, which increases the correlations between African and non-African countries.

3. Creating a Factor Table This section describes how we use the empirical patterns presented in Section 2 to create the GCorr Emerging Markets model.

3.1 Overview of the GCorr Framework Within the GCorr framework, the covariance between any two country or industry factors, and , is determined by loadings on a set of common orthogonal factors (we refer to these loadings as a factor table). GCorr Corporate uses 14 orthogonal factors. The first orthogonal factor is a global factor, computed as a weighted-average return across all firms, weighted by their size. To create the second orthogonal factor, we construct a weighted-average return using the firms’ log-size as the weights, placing higher weights on small firms. We regress the second index onto the first orthogonal factor, and the residual becomes the second orthogonal factor. By construction, the second factor is orthogonal to the first factor. To create each additional orthogonal factor, we regress an index onto all the previously constructed orthogonal factors, and the residual becomes the next orthogonal factor. This procedure repeats, and, in the end, we create 14 orthogonal factors.

Next, we regress the time series of each country and industry factor onto the set of orthogonal factors. The beta coefficient represents the sensitivity to the orthogonal factor, while the R2 of the regression represents the proportion of a factor’s variation explained by the 14 orthogonal factors.



Table 3

GCorr Corporate Factor Table

LOADINGS TO COMMON FACTORS

FACTOR CODE COUNTRY F1 F2 …

GC

orr C

orpo

rate C01 USA/CARIBBEAN 1.50… 0.34… … 0.99… 0.01…

C02 CANADA 1.06… 0.43… … 0.88… 0.04…

… … … … … … …

C48 CHILE 0.71… 0.41… … 0.50… 0.07…

C49 MEXICO 0.88… 0.43… … 0.65… 0.06…

Using the beta coefficients and R2 from the factor regressions, we can then compute the correlations between any combination of factors.

∑ where is either a country or industry factor

,

,, ∑

∑ ∑

3.2 Model Estimation To create a model for the emerging countries, we first analyze patterns in countries with sufficient asset return data. Figure 5 plots each country factor’s beta coefficients and factor’s R2 against its GDP per Capita to see if there are any patterns. For the country factors that represent broader regions, we compute a weighted-average GDP per Capita across the countries within the region, weighted by the number of firms in the country. The following relationships appear:



Figure 5 Relationship Between the Loading to f1 and GDP per Capita

Figure 6 Relationship Between the and GDP per Capita

There are two significant results from this exercise. First, a country with a high GDP per capita tends to have a high beta coefficient with respect to the first orthogonal factor, which can be thought of as return on global credit risk factor. Countries with high GDP per capita are more-developed countries, and so the interpretation is that more-developed countries are more closely linked to the global economy. The second result is that countries with a high GDP per capita also have a high R2. This means that less-developed countries have more idiosyncratic risk. The activities of smaller and emerging countries are less linked to the global



economy. As an example, these countries are sometimes subject to political instability, which affects their firms’ credit risk, but this risk is not necessarily related to the performance of the global economy.

Using these two relationships, we apply the model to the broad set of countries that report GDP per capita. Since there is no relationship between the other 13 beta coefficients with GDP per capita, we are unable to provide a modeled value. Instead, because any given country belongs to one of the 49 regions, we use the same beta coefficients to the other 13 orthogonal factors as those of the original GCorr factor. For example, a country in the Middle East will have a modeled value for the first beta coefficient and an R2 based on its GDP per capita, but it will also have the same beta coefficients for the other orthogonal factors as in the original Middle East country factor in GCorr Corporate.

As a result, the GCorr Emerging Markets factor table appears as follows:

Table 4 TABLE 1

GCorr Emerging Markets Factor Table LOADINGS TO COMMON FACTORS

FACTOR CODE COUNTRY F1 F2 …

GC

orr

Cor

pora

te C01 USA/CARIBBEAN 1.50… 0.34… … 0.99… 0.01…

C02 CANADA 1.06… 0.43… … 0.88… 0.04… … … … … … … …

C48 CHILE 0.71… 0.41… … 0.50… 0.07… C49 MEXICO 0.88… 0.43… … 0.65… 0.06…

GC

orr

Emer

ging

M

arke

ts

C175 ANGOLA 0.74… 0.42… … 0.52… 0.07… C176 ANGUILLA 1.30… 0.34… … 0.67… 0.09…

… … … … … … … C333 ZAMBIA 0.71… 0.42… … 0.48… 0.08… C334 ZIMBABWE 0.71… 0.42… … 0.48… 0.08…

3.3 Modeled Correlations With the GCorr Emerging Markets factor table, we break up the regional country factors into individual country factors. For example, the original Middle East factor is now segmented into granular factors, where we model the loading to the global factor (f1) and the proportion of variation explained by the orthogonal factors (R2) using a country’s GDP per Capita:

Table 5

GCorr Corporate vs. GCorr Emerging Markets for the Middle East

GCORR CORPORATE:

F1 F2 F3 … C45 (Middle East) 0.61… 0.50… 0.29… … 0.70… 0.05…

GCORR EMERGING MARKETS:

F1 F2 F3 …

UNITED ARAB EMIRATES 0.62… 0.50… 0.29… … 0.71… 0.05…

BAHRAIN 0.62… 0.50… 0.29… … 0.71… 0.05…

IRAN (ISLAMIC REPUBLIC OF) 0.61… 0.50… 0.29… … 0.59… 0.06…

JORDAN 0.61… 0.50… 0.29… … 0.55… 0.07…

KUWAIT 0.70… 0.50… 0.29… … 0.81… 0.04…

LEBANON 0.61… 0.50… 0.29… … 0.61… 0.06…

OMAN 0.62… 0.50… 0.29… … 0.71… 0.05…

QATAR 0.70… 0.50… 0.29… … 0.81… 0.04…

SAUDI ARABIA 0.63… 0.50… 0.29… … 0.72… 0.05…

Under the legacy GCorr Corporate model, the systematic factor correlations between a country in the Middle East with a country outside of the Middle East would be identical, and the systematic factor correlation between any two Middle Eastern countries



would be the same. Figure 7 shows the impact of the new GCorr Emerging Markets model on correlations. For each country, we compute the factor correlations with all other countries using the expanded emerging markets factor table. We then show the distributions of the correlations between a Middle Eastern country with all other countries within the Middle East and the distributions of the correlations with countries outside of the Middle East.

Figure 7 GCorr Emerging Markets Factor Correlations for the Middle East

Using the GCorr Emerging Markets model, there is more differentiation within the Middle East. Countries with higher GDP per Capita have stronger correlations with the rest of the world, as well as with the rest of the Middle East. This differentiation helps to identify the countries that contribute the most toward a portfolio’s risk.

Another example of an area showing increased differentiation is Africa. GCorr Corporate had three African factors: North, Central, and South Africa. Using GCorr Corporate, countries within the same regional factor have identical correlations with one another, shown in Figure 8.



Figure 8 Average GCorr Corporate African Factor Correlations

Average Factor Correlations Using GCorr Emerging Markets

Since GCorr Corporate considers Egypt and Morocco to be within the North Africa factor, they have a 93% average factor correlation with one another. They are not 100% correlated, because there is variation due to different industry factors. However, the recent political instability in Egypt, which Morocco did not experience, means that their economies, and, in turn, their corporate credit risk, are subject to specific shocks, suggesting their correlation should not be that high. GCorr Emerging Markets separates the two countries into individual factors, resulting in a lower factor correlation. There is also more differentiation in correlations between other African countries when using the GCorr Emerging Markets model.



4. Validation This section shows the results of various validation exercises we perform in order to assess how the level and rank ordering of correlations in the GCorr Emerging Markets model compares to various benchmarks. The first part examines whether the correlations resulting from the GCorr Emerging Markets factor table exhibit the empirical patterns discussed in Section 2. The second part compares the asset correlations coming from the GCorr Emerging Markets and the GCorr Corporate factor tables with empirical asset correlations.

4.1 Comparison with Empirical Patterns Empirically, we see that countries with high GDP per Capita have higher correlations with one another, regardless of whether we use GDP growth, industrial production, or equity indices to compute correlations. One of the first checks is to make sure the same pattern is observed in the GCorr Emerging Markets model. Countries are grouped by their GDP per Capita into 10 groups, and the average factor correlation is computed between all the groups. Using the factor table, the same pattern is observed:

Figure 9 Factor Correlations by GDP per Capita Under GCorr Emerging Markets

Another result from the empirical discussion: countries in the same region tend to have higher correlations with one another. Using the GCorr Emerging Markets factor table, we compute the factor correlations between each country and sort results by region. We find that this pattern is present in the correlations implied by the model. Countries within the same region tend to show higher correlations than countries in different regions.

p10 p20 p30 p40 p50 p60 p70 p80 p90 p100

p10 26% 25% 25% 23% 25% 27% 28% 30% 34% 37%

p20 25% 25% 25% 24% 25% 26% 28% 30% 33% 36%

p30 25% 25% 25% 24% 26% 26% 27% 30% 33% 36%

p40 23% 24% 24% 23% 25% 25% 26% 29% 32% 34%

p50 25% 25% 26% 25% 26% 28% 29% 31% 35% 38%

p60 27% 26% 26% 25% 28% 30% 32% 33% 37% 41%

p70 28% 28% 27% 26% 29% 32% 33% 34% 39% 43%

p80 30% 30% 30% 29% 31% 33% 34% 38% 43% 45%

p90 34% 33% 33% 32% 35% 37% 39% 43% 48% 52%

p100 37% 36% 36% 34% 38% 41% 43% 45% 52% 57%

Factor Correlation by GDP per Capita



Figure 10 Factor Correlations by Region Under GCorr Emerging Markets

4.2 Comparison with Empirical Asset Correlations We now explore whether the GCorr Emerging Markets model improves on the GCorr Corporate model when comparing performance with empirical asset correlations. For each country, we randomly select up to 200 firms. For each pair of countries, we compute the average pair-wise empirical asset correlations over a three-year period, average asset correlations using GCorr Corporate, and the average asset correlations using GCorr Emerging Markets. Since average pair-wise asset correlations can be noisy for countries with few firms, we exclude countries with fewer than five firms. Given the large number of country pairs, we present results by region. Within each region, we plot the correlations using the GCorr Corporate (blue) and GCorr Emerging Markets (green) against the empirical asset correlations.

We also show a 45-degree line. If the green points are closer to the 45-degree line than the blue points, the interpretation is that the GCorr Emerging Markets model produces modeled asset correlations closer to the empirical asset correlations. For many developing regions, the GCorr Corporate asset correlations are high above the 45-degree line, indicating the modeled correlations are higher than the empirical asset correlations. This result occurs because countries in some regions are modeled using the same GCorr Corporate country factor, resulting in high systematic factor correlations, leading to high asset correlations. The factor correlations are greatly reduced after applying the GCorr Emerging Markets model. In general, the GCorr Emerging Markets asset correlations are closer to the 45-degree line, although still a little above. Since many smaller countries may not have many firms with sufficient data, the GCorr Emerging Markets correlations remain on the conservative side, so that correlations are not under-estimated.

Several statistics are also shown at the top of each graph. The Mean Squared Error (MSE) shows the mean square deviation between the modeled correlation and the empirical correlation. The correlation statistic measures the correlation between the modeled correlation and the empirical correlation. Lower MSE and higher correlation represent a better fit.



Figure 11 Within-Region Correlations



In all the within-region charts, the GCorr Emerging Markets correlations show significant improvement. The Emerging Markets correlations are closer to the empirical asset correlations than the GCorr Corporate correlations. The largest improvements come from countries previously found under the same GCorr country factor, resulting in high systematic factor correlations. One region in particular is the Middle East, where all the countries were previously classified under the same country factor in GCorr Corporate. The GCorr Emerging Markets model reduces the average systematic factor correlation in the Middle East, and the resulting asset correlations are closer to the empirical asset correlation levels.

Table 6 shows a few specific examples.



Table 6

Comparison of Empirical Asset Correlations with GCorr Corporate and GCorr Emerging Markets

REGION COUNTRY1 COUNTRY2 EMPIRICAL

ASSET CORRELATION

GCORR CORPORATE

ASSET CORRELATION

GCORR EMERGING MARKETS

ASSET CORRELATION

Africa Egypt Morocco 1.4% 20.5% 3.6%

Asia India Sri Lanka 1.9% 14.1% 5.8%

Asia Vietnam Indonesia 1.0% 12.0% 5.9%

Europe Hungary Slovenia 3.6% 15.7% 9.7%

Europe Czech Republic Romania 8.9% 16.2% 9.3%

Latin America Colombia Venezuela 3.6% 18.4% 9.9%

Latin America Colombia Peru 5.5% 16.7% 7.7%

Latin America Peru Venezuela 1.2% 14.3% 7.2%

Middle East Bahrain United Arab Emirates 10.6% 21.1% 11.2%

Middle East Qatar Saudi Arabia 9.6% 20.7% 11.5%

5. Portfolio Impact Analysis To assess the impact on credit portfolios, we create a sample portfolio for each region and run the portfolios through RiskFrontier™ to show the impact on unexpected loss and economic capital. We create the portfolios by randomly selecting 100 firms from each country where we have EDF measures and GCorr correlation parameters. We then combine the firms into regional portfolios.

In order to run the results, each country requires a set of factor loadings. If a country is already represented by its own country factor in GCorr Corporate, then it uses the factor loadings from the existing GCorr Corporate country factor in both the GCorr Corporate and GCorr Emerging Markets runs in RiskFrontier. If a country does not have its own country factor in GCorr Corporate, then it uses the original GCorr Corporate factor loadings in one run and the GCorr Emerging Markets factor in the other run. For example, Bahrain would use the Middle East factor from the GCorr Corporate model in one run and use the Bahrain factor from the GCorr Emerging Markets model in the other run.

Table 7 shows results.

Table 7

Risk Statistics by Region

GCORR CORPORATE GCORR EMERGING MARKETS DIFFERENCE (%)

REGION UNEXPECTED LOSS (BPS) CAPITAL (BPS) UNEXPECTED

LOSS (BPS) CAPITAL (BPS) UNEXPECTED LOSS (BPS) CAPITAL (BPS)

North America 172.7 761 170.7 745.2 -1.16% -2.08%

Europe 136.3 579 136.4 581.8 0.07% 0.48%

Asia 102.3 466.6 101.1 463.6 -1.17% -0.64%

Latin America 192.9 1067.9 164.7 829 -14.62% -22.37%

Middle East 89.2 494.7 72.9 368.2 -18.27% -25.57%

Africa 218.6 1224.6 176.4 906.7 -19.30% -25.96%

Australia 136.8 603.1 136.8 603.1 0.00% 0.00%

Global 138.8 679.6 132 622.8 -4.90% -8.36%



The unexpected loss and capital tend to decrease when the asset correlations between the borrowers of a portfolio decrease. Latin America, the Middle East, and Africa are the regions with largest concentrations of developing countries, and so these portfolios show the largest decreases in unexpected loss and capital. Using GCorr Corporate, many of the countries in these regions are modeled using the same country factor, causing the factor correlations to be very high. By breaking up the GCorr Corporate country factors into individual countries, the factor correlations under the GCorr Emerging Markets model are significantly lower, resulting in lower asset correlations and lower risk statistics.

The other regions do not show much of a change. The European portfolio had many exposures to developed European countries, and, therefore, it does not show much change. Had we constructed the portfolio with a larger exposure to the developing European countries (namely CEE’s, Central and Eastern European countries), we would see a greater reduction in unexpected loss and capital. Many of the Asian countries are already modeled at a granular level under GCorr Corporate, and so they do not show a large change when using GCorr Emerging Markets.

To illustrate this finding in more detail, Table 8 presents the average factor correlations within each region. Each country either already exists in the GCorr Corporate model or has a new factor in the GCorr Emerging Markets model. The existing GCorr Corporate countries are usually more developed (e.g. the United States, Germany, Japan, etc.), but can also represent developing countries (e.g. Argentina, Thailand, South Africa, etc.). Within each region, we compute the average factor correlation between two emerging countries, between an emerging country and an existing country, between two existing countries, and the overall regional average.

Table 8

Factor Correlations by Region

Region Emerging vs.

Emerging Country Emerging vs.

Existing Country Existing vs.

Existing Country Region Average

Africa

GCorr Emerging Markets 48% 55% 100% 48%

GCorr Corporate 70% 60% 100% 69%

Asia



Australia

GCorr Emerging Markets 100% 100%

GCorr Corporate 100% 100%

Europe



Latin America



Middle East

GCorr Emerging Markets 75% 75%

GCorr Corporate 100% 100%

North America



We find that the correlations between two emerging countries decrease when using GCorr Emerging Markets. This occurs because, under GCorr Corporate, the countries share the same country risk, but in GCorr Emerging Markets, they no longer do. However, the correlations between an emerging country and an existing country can increase in some cases in this exercise. The increase happens due to the loading to f1 and R2, for emerging countries are modeled using the country’s GDP per Capita, and if an



emerging country has a relatively high GDP per Capita (such as certain Central and Eastern European countries), their loading to f1 and R2 are actually higher under GCorr Emerging Markets than under GCorr Corporate. As a result, the correlation between such an emerging country and an existing country increases when using GCorr Emerging Markets. Since existing countries use the same factor loadings in both runs, the correlation between existing countries is the same in both GCorr Corporate and GCorr Emerging Markets.

The regional averages are heavily dependent on the composition of emerging versus existing countries. Africa, Latin America, and the Middle East have high concentrations of emerging countries, and so the average factor correlations for these regions show the largest decrease under GCorr Emerging Markets. On the other hand, Asia and Europe have many existing countries in GCorr Corporate, and so the regional averages are similar under both models. A European portfolio with exposures to more emerging countries would see a larger decrease in factor correlations. Since the directional change in portfolio capital and unexpected loss is highly related to the directional change in the factor correlations, we see larger decreases in Africa, Latin America, and the Middle East than in Asia and Europe.

In general, global portfolios show a reduction in both unexpected loss and capital levels. The degree of reduction depends on the composition of the portfolio. Portfolios diversified in emerging markets show a greater reduction than portfolios heavily invested in developed countries.

6. Conclusion Credit portfolio managers have long used GCorr Corporate as a correlation model to help understand the extent to which their portfolios are diversified and to assess the concentration risks of their portfolios. The model uses a global dataset of publicly-traded firms. Though a rich set of data exists for developed countries, the data is scarcer for smaller and developing countries. GCorr Emerging Markets leverages country-level data rather than firm-level data in order to help estimate correlations between countries.

Empirically, we find a strong relationship between the GDP per Capita of a country and the level of correlations with other countries. Countries with higher GDP per Capita tend to have stronger correlations with other countries that have higher GDP per Capita, and vice-versa. We leverage this relationship to fit a model, utilizing the countries in which we have sufficient data and applying the relationship to countries without sufficient data. In the end, we expand the factor table to cover more than 200 countries.

GCorr Emerging Markets shows significant improvement over GCorr Corporate when comparing modeled asset correlations with empirical asset correlations. This new model preserves the patterns observed empirically. We also run a synthetic global portfolio through RiskFrontier to show portfolio impact. In general, we expect risk statistics to decrease for a portfolio invested in emerging economies, with the impact depending on the nature of the portfolio.



Appendix Across-Region Correlations

Figure 12 Across-Region Correlations

We also look at the correlations between a country within a region and a country outside of the region.



For the across-region scatterplots, there is not as much difference between GCorr Corporate and GCorr Emerging Markets when compared to within-region correlations. The MSE and correlation statistics are slightly poorer, in general, but there is no noticeable worsening in the scatterplots. The main model improvement comes from the improved modeling of correlations within a region.



References

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Huang, J., M. Lanfranconi, N. Patel, and L. Pospisil, “Modeling Credit Correlations: An Overview of the Moody’s Analytics GCorr Model.” Moody’s Analytics White Paper, 2014.

Huang, J., O. Ozkanoglu, N. Patel, L. Pospisil and M. Mitrovic, “Understanding GCorr 2014 Corporate.” Moody’s Analytics White Paper, 2014.

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GCorr™ Emerging Markets - Moody's Analytics · This section explores correlation patterns in developed and emerging countries. Specifically, we explore the relationship between