A Portfolio View of Credit Risk

Part 5: Measuring Correlation Across the Firms – Portfolio Impact

Until recently, the bulk of the credit risk literature mainly concentrated on assessing credit risk in isolation at an individual exposure level i.e. without taking into account the potential for credit quality co-movements and defaults. More recently, a portfolio view on credit losses has emerged by recognizing that changes in credit quality tend to co-move over a business cycle, and that one can diversify part of the credit risk by a clever composition of the loan portfolio across regions, industries and countries. Thus in order to assess credit risk of a loan portfolio, a bank must not only investigate the creditworthiness of its clients, but also identify the concentration risks and possible co-movements of risk factors in the portfolio.

For appropriate risk/return on the exposure, we need to accurately measure the credit loss volatility. Only then can we price an exposure appropriately. The loss volatility is optimum when the portfolio is diversified.

Correlations are of two types:

• Skewed (asymmetrical returns)
• Kurtosis (tail thickness)

Take Note: Transformation Process

Correlation is a measure for volatility. Why is correlation more important in credit risk than in market risk? On the absolute terms, the risk between equity price (20 per cent) and AAA default (0.2 per cent) is different to the order of 100 times. Obviously, volatility on a larger base is always smaller while on a very small base it is exponential. A volatility of 1 per cent has a totally different meaning for credit risk compared to market risk. The classical linear correlation coefficient that we know from the analysis of share prices, exchange rates and interest rates, is an inadequate measure of dependence between defaults in a portfolio.

Take Note: Next-level Risk Practices

Correlation is of two types – correlation across the borrowers on credit loss or credit drivers, and correlation of credit drivers with each other. While research has been done on default correlation of firms and their impact on credit losses (also measured in terms of volatility of loss or UL), not many studies have been done on correlation of credit drivers with each other. Studies of correlation of PD (probability of default) vs LGD (loss given default) are emerging now. While the first is an issue of portfolio impact and portfolio creation, the latter is an issue of calibration. Basel II neither requires measurement or modelling of correlation nor recognizes correlation as a risk driver.

Take Note – Transformation Process- Risk Measurement

In this section, we shall dwell on portfolio impacts of correlation.

Firms are correlated with each other due to the macroeconomic factors. However, it should be noted that macroeconomic indicators are the broad and aggregate indicators, and their complex relationship is not yet understood by economists. Being aggregate indicators, the data quality, and data definition play an important role. Further, it is not necessary that they follow the same equation all the time. In a nutshell, macroeconomic indicators are extremely difficult to measure and model and link to the ability (cash flow) and willingness (assets value) to pay of firms. Therefore, only broad indicators of credit risk i.e. PDs, are modelled across the firms.

Clear understanding of correlation helps in:

• Designing the portfolio according to the loss volatility and linking loss volatility with the risk taking capabilities, available capital and return on capital,
• Setting limits on each sector and exposure to build the required portfolio,
• Expected returns.

Correlation of Credit Loss Among Borrowers

The following list of empirical findings on default correlation across the borrowers/firms is not complete.

Modelling Default Correlation

Due to the paucity of data, it is very difficult to measure correlation of ability and willingness to pay across the firms with macroeconomic indicators. Various models proposed and available are actually an attempt to solve the correlation measurement problem. Several approaches have been developed in order to determine the credit loss distribution at the portfolio level for example: CreditMetrics, CreditRisk+, KMV, and Kamakura. Despite their apparent differences, they exhibit a common underlying framework.

Treatment of correlations among credit exposures determines how well risk concentrations within credit portfolios are identified. Correlations are difficult to estimate accurately.

Over a period of time these correlations are likely to be modelled and factored into the credit risk measurement and management.

Take Note: Risk Template

Banks that use bottom-up modelling techniques typically assume zero correlation among most of the risk factors recognized in their models.

Use of correlation other than in portfolio management

• Default correlation with respect to two obligors arises in the context of letter of credit-backed debt, credit guarantees, and counterparty risk (particularly in credit derivatives).
• Default correlation with respect to multiple counterparties is highly relevant for the pricing and risk management of collateralized debt obligations.

Concentration risk and diversification opportunities can be identified by means of calculating marginal risk contributions of individual exposures to the overall portfolio risk.

Take Note: Risk Template- Portfolio Creation

All correlations are estimated for assets within the same portfolio and yet no cross portfolio correlation is estimated. It means that the correlation across the portfolio is assumed to be perfect.

Portfolio Management

Portfolio management is like investment management, while loan origination is like a fee-based activity. Portfolio management economics depends upon the effective and efficient use of credit risk information, effective assets pricing and diversification. The goal of a portfolio risk manager should be to invest in technology to reduce the cost of processing (in the origination), replace traditional loan accounting with mark-to-market, encourage selling of homogenous loan products with uniform documentation (this is actually possible with consumer and SMEs) and implement credit risk measurement systems.

Banks have superior access to corporations due to various relations they have with them. Utilizing this relationship, they may be able to generate loans in the most efficient way. However, they are not the most efficient holders of the loan/credit assets, since risk increases with the amount of exposure. This phenomenon is also called credit paradox. Credit spreads increase exponentially after a certain cut off as exposure to the same obligor increases.

Although the impact of default correlation (and, in MTM models, correlation among other credit rating changes) is typically estimated in order to introduce portfolio diversification effects more realistically into the models, the zeroing out of other correlation effects ignores the tendency for default probabilities, LGD rates and credit spreads, all to increase together during economic downturns.

Portfolio management means:

• Prediction of default
  1) Default probability: internal ratings, external ratings, various approaches, homogeneity issues
  2) Transition matrices
  3) Standard & Poor’s Insight: a practical look at default probability model development
• Default Correlation
• Calculating the diversification effect
• Correlation, dependence and contagion
• Standard & Poor’s Insight: Risk Solutions
• Empirical findings on correlations
• Recovery Rates
  1) Loss Given Default (LGD)
  2) LGD – beyond mean, variance, and beta distribution
  3) Standard & Poor’s Insight: LGD empirical results; trading prices vs. ultimate recovery
• Comparison of Traditional Portfolio Models
  1) Leading alternative approaches
  2) Strengths and weaknesses of competing models
• Focus: a measurement of the impact of the choice of transition and correlation matrices in a ratings-based model

Factor Model

Step I – Measure Correlation: The model will measure default correlation among the assets in the portfolio due to changes in systematic factors (the models are likely to be a single factor model initially or, going forward, these factors will increase to two, three, multi- factors, etc. (More factors are likely to make the model complex because then correlation inter-se factors need to be considered).

Step II measures loss volatility for a given correlation. Correlation can be proved only if loss volatility increases with correlation. (However, this relationship is unlikely to be linear and may have some break points). So, the factor model should provide the loss volatility. Going forward, factor models for each portfolio are likely to emerge.

Managing Risks at Portfolio Level

The two-step treatment for portfolio risks is as follows:

Portfolio/correlation risks

Step I: Identify risk concentration at the portfolio level (as a first level to recognize correlation)

• Use of securitization
• Use of credit derivatives

Step II: Measure concentration risks

How to incorporate default correlation:

• Assume, either explicitly or implicitly, average correlations across the whole or large parts of their credit portfolios. While this approach is sensitive to large, single obligor exposures, it is insensitive to the build-up of industry and geographic risk concentrations.
• Estimate credit quality correlations based on a multi-factor analysis of equity market prices. The problem here is averaging out of correlation over a period of time.

Portfolio Management: Basel II Context

Framework and embedded assumptions

Debt Portfolio Capital Management Tools

• Economic capital
• Splitting between components: marginal VaRs, unexpected loss etc.
• Measurement tools: RAROC

Debt Portfolio Management and Market Solutions

Structured tools for capital management (e.g., CDOs)

• Credit derivatives for capital management

Portfolio Management and Fund Management

• Difference between a banker’s and a fund manager’s approaches to credit risk
• The use of credit portfolio tools for asset managers

Factors Determining Portfolio Creation

Repayment source of the borrower

The ability to repay closely depends upon the ability to raise cash flow. Types of borrowers vary according to the source of cash flow of a borrower and to what extent that cash flow can be maintained. This will divide all borrowers into the following types:

• Borrowers with the power to tax, or guaranteed by authorities who are empowered to tax, and fiscal deficits. This borrower type is termed Sovereign.
• Borrowers who have flexibility in raising the cash flow. These are usually banks and similar firms with the flexibility to raise resources.
• Individual borrowers who have the capacity to earn (however the capacity to raise cash flow is limited, so the exposure is small).
• All other borrowers are called corporate and are those who sell or trade with or manufacture products and services. Their cash flow depends upon the realization of their cash flow.

The primary source of repayment is the returns generated by assets or from the sale of the collateral or asset. Due to developments in the markets in addition to financial instruments, liquidity and volatility are fast becoming an important factor for housing mortgage and vehicles loans. With the development of the commodities market, physical goods like primary commodities, oil and energy products, liquidity and volatility become important. There can be two types of portfolio from this: a portfolio whose repayment is driven by the income generated by the assets or, a portfolio whose repayment is driven by income generation and sale of the collateral. So, the market conditions for collaterals (for income generation or re-sale) are important, if:

1. Collateral price and/or the returns on collaterals are the primary source of returns of borrowing.
2. There is a thin dividing line between collateral as a source of repayment and collateral as a risk mitigant. This is a portfolio for collateral as a repayment source. (For example, commodity financing, where the market is quite developed and the price in the market is the source of income for the borrower and repayment for lender).

There must also be certainty in cash flow generation. Project finance which is normally a part of the corporate portfolio, may be considered separately due to high uncertainty in the cash flow (by churning or selling of collaterals).

Size of exposure

Ideally, granularity should be measured with the exposure amount. However, it can also be measured by the size of the total cash flow of the borrower. (For example, an SME is identified by the total sales of the borrower). The size of the borrower is probably a good indicator for the maximum exposure and credit analysis or availability of the borrower’s financial and other statements.

Retail loans

There are three criteria for retail loans:

• Small exposures
• Repayment is from the personal income
• Number of exposures is large.

Exposures to individuals:

• Short-term or revolving exposures – credit cards, overdrafts, and retail facilities secured by financial instruments.
• term loans and leases – instalment loans, auto loans and leases, student and educational loans, personal finance, and other exposures with similar characteristics.
• Residential mortgage loans

Loans for small business- with a limit on the exposure (€1m)

Correlation and Portfolio

Correlation plays an important role in the creation of the portfolio. Only single factors models are created to link the borrower’s performance with macroeconomic factor. Modelling borrowers’ performance for their inclusion in a portfolio is difficult based on geography, industry and credit risk.

Geography – the repayment capacity of the borrower is determined by geographical location. Country risk is the most accepted sub-portfolio.

Industry – there are various ways to group exposure on an industry basis. It is generally done on the basis of what they sell. However, it can be performed on other factors from the value addition chain of the borrower.

Credit Risk:

• Credit grades or LGD grades or loss grades or maturity are indicators of credit risk. Exposures within the same grade generally behave similarly and, therefore, are generally grouped together.
• Securitization/Purchased receivables – since the exact credit risk is difficult to measure and segregate.

Using the extreme value theory (EVT), it can be shown that the tail probabilities of portfolio credit losses declines in a polynomial manner to zero, whereas a normal distribution tail declines at an exponential rate. This means, extreme portfolio credit losses happen relatively more frequently than expected on the basis of a normally distributed random variable. As a result, normal distribution curve for calculating loss quintiles no longer apply. The 99.9 per cent quintile might be much more than three standard deviations (the number that one would expect for the normal distribution) above the distributional mean.

Creation of sub-portfolios: Portfolio can be further sub-divided by identifying the common factors impacting or forecasting their repayment cash flow capacity.

¹ Correlated Default Risk, Sanjiv R Das, Laurence Freed, Gary Geng, Nikunj Kapadia, August 2002