Quantifying Credit Risk Drivers - The Global Treasurer (2024)

Part 3 in Transforming the Credit Risk Management Process

Measuring Exposure at Default

Most of the time, exposure at default (EAD) is not the same as exposure otherwise. Often credit quality does not change to default; it changes over a period of time. There is a lapse time before the market, lender and others note credit quality changes. Meanwhile, the obligor withdraws the lines of credits and commitments (on balance sheet) and off-balance sheet items such as contingent facilities.

Off-balance sheet items like derivatives are exposed to pre-settlement risk. Derivative contracts keep fluctuating from a state of “in money” to “out of money”. There are two elements in derivative contracts – current exposures and potential exposures. Empirical results show correlation between probability of default (PD) and the magnitude of EAD, which results in an increase in EAD.

Measuring Potential Exposures

Calibration Standards for EAD as prescribed by Basel Accord:

• Must identify and consider all the drivers for EAD
• EAD vs. EAD – empirical evidence also shows that EAD estimation is volatile over the economic cycle.
• PD vs. EAD – Empirical results show correlation between PD and the magnitude of EAD; this results in an increase in EAD.
• Cannot be less than current drawn amount.
• Must consider on-balance sheet netting.
• Should reflect the possibility of additional drawings by the borrower up to and after the time a default event is triggered.
• EAD differs for each facility type (within the same portfolio).
• It must be an estimate of the long-run default-weighted average EAD for similar facilities and borrowers over a sufficiently long period of time, but with a margin of conservatism appropriate to the likely range of errors in the estimate.
• Cyclic nature, economic downturn conditions and EAD volatility need to be considered, if necessary, instead of only the long run average.
• Impact of accounting and payment-processing policies must also be considered.
• Estimates of EAD must be based on a time period that must ideally cover a complete economic cycle but must in any case be no shorter than a period of seven years (this can be five years for retail).

Measuring PD

A key element in almost all approaches to credit risk measurement is a credit ratings system. Broadly, these systems are similar but vary considerably in detail. These systems are generally recognized as being reasonably successful at distinguishing the relative risks of different borrowers at a given point in time. A lot of work in the form of calibration and validation or back testing needs to be done to convert them as a system for absolute risk measurement. Further, there is not much agreement still on how to measure the changes in risk through time or how to measure correlation among the risks.

Take Note: Basel Accord II – The Basel Committee has not been prescriptive as to how ratings are assigned however, it has prescribed the following best practices:

• Borrowers should be rated or reviewed, at least annually, or whenever new information about the borrower comes to light.
• In assigning borrowers to grades, banks must assess risk factors for the future horizon based on current information.
• For risk quantification purposes, the bank must assign to each grade a probability of default over the next year.

Measuring PD makes an assumption that macro economic factors and idiosyncratic factors can predict the default. These factors are measured in different ways – quantitative and judgmental. Factors are also measured in terms of financial and non-financial ones. This system is called a credit rating system. Credit rating system has credit scoring/quantitative model and judgmental factors in varying degrees of importance.

Take Note: Risk Architecture and Best Practices – Other risk factors, like loss volatility, or the correlation of risk factors, are generally not taken into account in assigning ratings. Maturity is not explicitly cited as a consideration in the assignment of ratings. However, maturity is generally considered for exposure and credit approval. Under a two-tier rating architecture, LGD or collaterals are considered as a part of the facility rating or credit approval.

Architecture of Credit Rating

A credit rating system is not new, but as part of Basel II, it will become much more important for banks to get it right. Most credit scoring models use a combination of financial and non-financial factors. Measuring the PD is a four-step process:

1. Risk underlying the ratings – loss concept.
2. Absolute measure/calibration – point-in-time vs. through a cycle.
3. The degree of risk differentiation sought – number of grades.
4. Segregation of obligor rating and facility rating – a minimum number of pass and problem grades and no more than 20-25 per cent exposure in any of the grades.

Take Note: Risk Architecture Best Practices – No simple and direct relation (say, linear or log linear, or any other) between rating notches and probability of default can be defined. However, empirical studies using studies of S&P and Moody’s have found an exponential relation between the PD and rating notch. Therefore, the best practice is to ensure that the relationship among the notches is exponential.

Building the Credit Rating System

• Identify the factors (macro economic and idiosyncratic) which have explanatory power.
• Build the models:
• Model Selection
• Construction and Evaluation
• Model-to-decision tools
• Validation or back-testing models

Take Note: Different rating systems for different portfolios – There are significant differences across business lines or portfolios:

• Key Risk Indicators include rating criteria, business risk, financial risk, macroeconomic impact, cash flow generation and allocation among different claimants and asset allocation among different claimants.
• Historical loss characteristics.

Identify Factors with Explanatory Power

Financial Factors – generally this is driven by two factors: the ability to generate cash flow and allocation of cash flow towards repayment. Altman (1968) built a linear discriminant model based only on financial ratios and matched samples (by year, industry, size): Z = 1.2 X1 + 1.4 X2 + 3.3 X3 +0.6 X4 + 1.0 X5

• Ability to generate cash flow:
• X1 = working capital/total assets
• X3 = earning before interest and taxes/total assets
• X5 = sales total assets
• Allocation of cash flow towards repayment:
• X2 = retained earnings total assets
• X4 = market value of equity book value of total liabilities

This model has to be refined further for each market, industry, geography and country by identifying the financial/accounting variables which have a better explanatory power. It should be noted that Z-scores-based PDs are less sensitive, volatile and timely.

Non-financial Factors – these factors help evaluate the link of the firm with macroeconomic factors and the capability of the firm to churn out cash flow in the required numbers. This includes:

• Size
• Age/ Industry experience of key managers
• Industry
• Location

Take Note – Risk Template – Factors considered for building Credit Rating tools for corporate exposures. The relative weight of each of the factor differs. In the most general terms, “all relevant information” should be considered in assigning an internal credit rating. The following is a suggested list which shows what needs to be considered for each type of exposure:

Financial Strengths

• Capability to generate revenue/cash flow – market conditions
• Claims on cash flow
• Ratios
• Debt Service Coverage Ratio
• Loan Life Coverage Ratio
• Project Life Coverage Ratio
• Stress analysis of cash flow
• Amortization schedule

Regulatory and Legal Environment

• Impact of regulatory changes
• Enforceability of contract, collateral and security
• Country risks

Transaction Characteristics

• Impact of technology used in the business (of borrower) on the business
• Completion of the project (start of cash flow for the borrowers business)
• Operational risk
• Supply risk
• Contracts for off-take or supply
• Assignment of cash flow
• Control over cash flow – assignment of cash flow
• Strength of covenants
• Availability of reserve funds
• Cash flow predictability
• Security and charges over assets
• Marketability of assets (liquidity and volatility for the assets secured in the market) including resale value
• Availability of insurance and other coverage

Management strengths

• Involvement of promoter in projects (equity + lending)
• Proven track record
• Willingness to support the purpose behind borrowings
• High quality financial disclosures

Building models and tools

(i) Model selection

Several statistical methods are used to develop credit-scoring systems, including linear probability models, logit models, probit models, and discriminant analysis models. The first three are standard statistical techniques for estimating the probability of default based on historical data on loan performance and characteristics of the borrower. These techniques differ in linearity of models. The linear probability model assumes that there is a linear relationship between the probability of default and the factors; the logit model assumes that the probability of default is logistically distributed; and, the probit model assumes that the probability of default has a (cumulative) normal distribution. Discriminant analysis differs in that instead of estimating a borrower’s probability of default, it divides borrowers into high and low default-risk classes. Two newer methods experiencing seeing increased usage in estimating default probabilities include options-pricing theory models and neural networks.

(ii) Construction and evaluation

“Field performance” of the models

• Stratification power
• Calibration
• Consistency
• Robustness
• Model evaluation: there is a battery of statistical tests, which are used to help us select from competing models and assess performance
• In-sample
• Out-of-sample (“field testing”)

Back-testing à la VaR models are extremely difficult; Lopez & Saidenberg (1998) show how hard this is and propose a simulation-based solution – there are a number of positives and negatives

(iii) From model to decision tool

• Application and usage tests
• Importance of education across the bank
• There are two schools of credit assessment and banks can choose to use either one of them.
• Unconditional (“through-the-cycle”) internal models or ratings from agencies are sluggish/insensitive.
• Conditional (“Mark-to-market): KMV’s stock price-based PDs are sensitive/volatile/timely.

Differences in Credit Rating Systems

Banks have either converted, or are in the process of converting their original credit risk rating system into a two-dimensional or ‘composite’ system. Composite systems separately assess both the likelihood of a borrower defaulting and the likely severity of loss, should default occur. Compared with the existing systems of mingling these concepts into a single rating, composite rating systems are better aligned conceptually with the banks’ portfolio credit models, and provide more useful information for general credit management purposes. Differences in the credit rating systems across the banks and across the portfolio within the same bank:

1. Relative vs. absolute measurement – the loss concept underpinning the rating differs across models and banks. Ratings often reflect counterparty default probability and/or expected loss on facilities, but may in some cases merely constitute an ordinal ranking of the banks’ exposures relative to each other.
2. Time Horizon – the time horizon for assessing the credit quality of counterparty/exposures varies.
3. The rating system may be calibrated on long-term average default/loss measures (so called “central tendency” or “through-the-cycle” approaches) or assess the point-in time quality of issuers/exposures.
4. Methodology – the methodologies used to arrive at a rating are themselves diverse: some models directly infer a default probability from market indicators (spread or equity based models), others rely on the statistical analysis of financial indicators relative to the counterparty (score cards and neural networks).
5. Qualitative vs. quantitative measurement – though banks measure credit ratings at the basis of their scoring system, they also include a qualitative assessment of management and contingencies, which can modify their initial quantitative analysis.

Models differ in the way they incorporate the effect of contingent credit risk (e.g. country risk, credit risk mitigation).

Judgmental factors in PD

If a model is linked with macroeconomic factors, this will involve a larger complexity of modelling and measurement of macroeconomic factors. Further, banks are worried that errors in forecasting economic turning points could lead, in particular, to a shortfall in desired capital coverage just as the economy turns sharply downwards. Therefore, macroeconomic factors in PD are generally represented through Judgmental factors.

Empirically, it is found that both market and accounting variables significantly explain these corporate default probabilities. When only accounting variables are used in prediction, they provide almost as much information as a model solely based on market measures. Within the accounting variables and market variables, some have greater explanatory powers than the others. It should be empirically investigated to identify the accounting variables which have greater explanatory power. Generally, the explanatory power is market capitalization and excess returns are compared with option-based distance to default measures. The absolute value of variables has greater explanatory power than the relative changes over the year.

Transition Matrices (TMs)

There are two ways to measure credit losses Default mode and Mark-to-Market mode. Transition Matrices measure credit loss in terms of mark-to-market mode. Transition Matrices are tabular representations of credit quality migrations over a specified period of time (usually a year). For example, it would show what percentage of credits that were in the AAA credit rating bucket at the beginning of the year have stayed in the same grade and what percentage have migrated to other rating grades such as AA, A, BBB, BB, etc.

TMs are used in most of the popular quantitative credit risk modelling techniques. They can also be used as a monitoring technique to track credit migrations.

Take Note: Risk Architecture and Best Practices – Empirically, it is argued that the use of a single rating transition matrix in credit risk models might not be appropriate. A multivariate model, distinguishing obligors by domicile and industrial sectors, and taking account of the business cycle, might provide a more valid summary of migration patterns than the common practice of using simple estimates of transition probabilities based on historical averages.

Shortcomings of Transition Matrices

TMs are assumed to have developed from a portfolio that is diversified and granular, and this may not represent internally developed TMs in many banks (transitions of loans in internal bank portfolios do not behave the same way as the transitions provided by the rating agencies Moody’s or Standard and Poor’s).

Modellers of TMs need to track migrations of a large dataset of obligors across credit grades and sufficient migration data is usually unavailable for highly-rated debt (e.g. migrations to ‘Default’ grade for AAAs, may carry a probability of 0.02 per cent, which implies one default out of 5000 obligors in AAA category; although, the existence of such in-house data is rare, even in the case of averages).

Published TMs are usually annualized and unsuitable for instruments that are for much shorter durations. The rating migration behaviour of obligors may change over time and averaged transition matrices based on, say, 15 years of data may not be suitable for ‘boom’ or ‘bust’ years (due to cyclical behaviour of the economy migration matrices not being constant through time).

Take Note: Transition Process

The relationship between default probabilities and credit rating transitions: Empirically, it is found that rating downgrades may lag behind the deterioration in credit quality. While this characteristic of rating changes was well known, the magnitude of these lags (up to 18 months in some cases) suggested a serious limitation on the usefulness of ratings.

This creates divergence between ex-post and ex-ante PD. This is a serious handicap during the economic cycle. Use of rating transition models estimated from data on changes in bond ratings to be applied to loan portfolios is now being questioned. Until recently, empirical corporate default rate studies had taken into account bonds (whose prices were readily observable), rather than loans.

Measuring LGD

Measuring Loss Given Default is heavily constrained by data availability. This limitation is addressed by banks through their own and external historical data and through proper judgment from their management teams. Collateral quality, liquidity and availability, product and business lines govern measurement decisions.

LGD Measurement According to Basel II

By reverse engineering, the credit loss with Probability of Default, LGD can be estimated from credit loss. The sum of all the credit losses over a period is credit loss (good year or bad year). Due to paucity of data, loss data for a longer period is taken into account. The impact of actual loss, default-weighted average loss is considered for estimating LGD. This helps to even out the loss volatility. Credit loss is calculated as follows:

• Long run (generally more than five/seven years or a single business cycle.
• Default-weighted average loss

Under default weighted average loss, loss of all years gets the same weight. Sometimes, we argue that the recent data is more relevant than the past (due to the business cycle; for example, the cycle is going down). The losses/data of recent years can be given more weight; Basel II allows this for retail. We can argue similarly for other exposures, too. Basel II has provided an estimate of average LGD (45 per cent) under the foundation approach for an unsecured corporate loan. If collateral is provided, it can be treated in two ways.

• Collateral reduces exposure
• Collateral reduces LGD

The Accord has adopted the first method. Under Para 291, the following method of LGD estimation after considering collateral is given: LGD* = LGD x (E*/E), where E* indicates the exposure-less risk mitigation.

Factors Affecting LGD Estimation

• Collaterals provided reduce LGD
• Availability of ready market for collateral. Absence of such a market is the primary factor for non-recognition of collaterals by the Accord
• Type of charge could be senior or subordinated. A subordinated loan is a facility that is expressly subordinated to another facility

Ways to consider correlation or cyclic affect impact

• Measure the losses and, therefore, LGD, during periods of high credit losses (they do not average out)
• Use conservative estimates for losses and LGD

LGD models

Most credit risk models treat LGD as either a stochastic variable independent of the PD, or as a parameter that must be specified for each exposure and do not treat LGDs as a macroeconomic function. Banks generally assume that LGD distributions are well described by beta distributions.

Measuring Maturity

Banks for the time being recognize maturity as a risk driver by defining a maturity limit on the exposures and not taking exposures beyond a certain period; a periodic review of credit grades and covenants; calling back loans; and, grading the exposures for the full business cycle or exposure period are undertaken.

Due to cost benefit considerations, Basel II does not attempt at present to identify the risk indicators for maturity and, therefore, there is no question of calibration or measurement of risks. In order to avoid the regulatory capital arbitrage, the Accord has not recognized separate risk weights for different maturity and has assumed an average maturity to estimate risk weights. However, it needs to be separately considered.

Take Note: Next-level Risk Practices – Banks need to keep in mind the cost of refinement in the credit risk coming from the actual measurement of the maturity impact as compared to the maturity adjustments. Validation of maturity impact on findings may be a lot more difficult since the theoretical explanation of credit spread is not clear yet. It will be difficult to un-bundle the credit spread to measure the maturity impact.

Maturity Measurement According to Basel II

The Accord attempts to mitigate the impact of maturity as a credit risk driver in the following manner:

• The Committee has sought to develop a treatment of maturity that is feasible and risk sensitive, while avoiding perverse incentives that could distort a bank’s lending practices or encourage gaming to minimize regulatory costs without reducing economic risk.
• Time Horizon for PD – period for which PD is considered is complementary to the maturity impact.
• Seasoning of loans – Project finance and retail mortgages have seasoning effects. In the life of the exposure, for some period, the exposure has greater risks. With the seasoning effect, setting in the risk profile does not change with maturity. (After seasoning sets in, a loan of four years to maturity, eight years to maturity, 12 years to maturity, 15 years to maturity, portfolios do not have different risks due to maturity differences).
• Where the residual maturity of CRM is less than that of the underlying credit exposure, a maturity mismatch occurs and need to be recognized in the risk.
• Since maturity is one of the material drivers, it can also be a basis for portfolio creation (portfolio of 10-year mortgages, 30-year mortgages).

Take Note: Next-level Risk Practices – Never forget that measurement means additional cost and additional burdens of tracking, compiling, and validating the requisite data. This cost needs to be balanced with the additional risk measurement capabilities acquired. First of all maturity is not a correct measurement of risk. Instead, duration is measured as it is done for the interest rate risks. Extrapolating the argument that credit spread represents the credit quality. Credit spread is also a yield curve and a part of the IRR. Duration should be measured instead of the maturity.

This is after having said that maturity or duration can be measured by scenario analysis (changes in the credit spread) or sensitivity analysis or VaR for credit spread. However, none of this has yet developed either in theory or in practice.

Dispersion of maturity from the average or effective maturity

The following table shows the maturity profile of various portfolios.

Time Horizon

This is to capture Credit Loss/PD behaviour during the holding period since generally the credit loss/PD is captured for one year and this does not reflect the actual risks. Maturity risks implications differ whether the MTM models are used or default models are used. In either case, it is gauged as a part of PD.

A long-term and short-term loan may respond similarly to defaults within the chosen time horizon. However, a borrower downgrade from, say, Baa to Ba will tend to have a larger relative price effect on a 10-year loan compared with a one-year loan. Banks adopting best practices recognize the importance of more formal maturity adjustments, and more institutions are moving in this direction.

Take Note: Next-Level Risk Practices – For better quality assets, a bank’s interest will be protected if there is a clause for adjustment in the interest rates according to the credit quality. Further, the Accord assumes a linear relationship between maturity and risk for maturity between one and seven years. This may not be true (spread curve is curvature) and banks may need to find out their own curve, especially those banks dealing in infrastructure projects and housing mortgages which are typically more than 20 years maturity. This curve will also help them find out when the seasoning affect sets in.

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