CR 5 – Introduction to Credit Risk Modeling and Assessment

Credit risk is the chance that a borrower, also called the obligor, fails to pay what it owes on the schedule that was agreed when the lender extended the funds. Every loan, bond, trade receivable or credit card balance carries it, because the lender hands over money today against a promise about tomorrow. Banks are the obvious holders of this risk, since lending to companies and households is their core business, but the exposure reaches well beyond the banking system. A manufacturer that sells on 60-day terms is lending to its customers, and the same manufacturer is borrowing from its suppliers whenever it pays them late. If a key customer or supplier collapses, a perfectly sound firm can be dragged into financial and operating trouble through those trade links.

Credit matters because it lets households and firms spend today against income they expect to earn later. Without it, a company could not fund a new plant before the plant produced revenue, and a family could not buy a home before saving its full price. That liquidity supports daily operations as well as long-term investment, which is why the volume of credit in an economy is watched so closely.

The scale of private non-financial credit, 2000 to 2016

Data from the Bank for International Settlements show how quickly credit to the private non-financial sector (non-financial corporations plus households) expanded between the start of 2000 and the end of 2016. The table below sets out the absolute amounts. The final column is derived here to show what share of all private credit came from banks.

Source: Bank for International Settlements data as reported by Doumpos et al. (2019). HHs means households; Corp. means non-financial corporations.

Total credit in the Eurozone roughly doubled, rising by 105.5% to 17,481 billion euros, while in the USA it grew by 123.5% from $12,627 billion to $28,227 billion. The corporate and household columns add up to the total in every row, which is a useful check on the figures. Measured against the size of each economy the picture is calmer, because output also grew over the period.

Relative to GDP, private credit rose by 27.8% in the Eurozone and by 16.3% in the USA, yet both regions ended the period with private non-financial debt above 150% of GDP. The mix differs sharply between them. In the Eurozone, companies dominate: corporate credit reached 11,187 billion euros, or 104.2% of GDP, and it made up 64.0% of total private credit in 2016 (11,187 divided by 17,481). In the USA, households hold the larger share, with $14,756 billion, which is about 52% of the total. Banks also play very different roles. Eurozone banks supplied 9864 billion euros in 2016, but their share of total credit slipped from 63% to 56.4% because other lenders grew faster. In the USA, banks provided $9749 billion, only around 35% of the total, so capital markets and non-bank lenders carry most of the load there.

Two further changes widened the field. Credit derivatives such as credit default swaps and collateralized debt obligations are bilateral, mostly over-the-counter contracts that let parties transfer credit exposure, and they spread credit risk into places where it is harder to see. More recently, peer-to-peer lending, social lending and crowdfunding platforms have opened new channels for credit that sit partly outside traditional supervision. Credit risk management is therefore a broad discipline that combines regulatory, methodological and technical work on the analysis, assessment and monitoring of exposures.

Two forces turned credit risk management from an art practised by individual loan officers into a structured, model-based discipline: regulation and analytics. Each pushed the other along, and together they explain why modern banks devote so much effort to measurement.

From Basel I to Basel III

In 1988 the Basel Committee on Banking Supervision published the first international rules on how much capital banks must hold. Basel I used a simple scheme in which each class of asset received a fixed risk weight, so a bank’s capital requirement depended on how much it held in each bucket rather than on the actual quality of individual borrowers. In 2004 the Basel II Accord replaced that blunt structure with a far more refined framework. Basel II covered operational and market risk as well as credit risk, and it added rules on the role of supervisors and on public reporting and market discipline. Basel III followed with stricter capital requirements and with new provisions on liquidity and on leverage, which compares a bank’s equity capital with its total exposure. The common thread is that credit risk has become one of the most heavily regulated activities in financial services, with detailed requirements on how measurement systems are designed, implemented and monitored.

The CAMEL system and why it was not enough

Before analytical models took hold, the dominant tool for judging a bank’s condition was CAMEL, an empirical system that combines five groups of factors into an overall view. The letters stand for capital adequacy, asset quality, management, earnings and liquidity. Capital adequacy asks whether the institution has enough own funds to absorb losses. Asset quality looks at the soundness of its loans and other holdings, since weak assets eventually turn into losses. Management captures the competence of the people running the institution and the strength of its controls. Earnings measure whether the business generates enough profit to sustain itself and rebuild capital, and liquidity asks whether it can meet cash demands as they fall due. A supervisor or analyst scores each dimension and combines the results.

The weakness of CAMEL lies in how the scores are combined. The weighting rests on experience and judgment rather than on a tested statistical relationship with failure, so it could not give an objective and repeatable basis for managing credit risk. That gap created demand for more rigorous methods. The first bankruptcy prediction models appeared in the 1960s and 1970s, beginning with the Altman (1968) Z-score, and the late 1980s brought the first widely used consumer credit score from Fair Isaac Co. in the USA, the FICO score.

Regulation as an accelerator

Tighter rules sped up the adoption of these models because regulators offered a reward for using them: institutions with sophisticated, validated models could hold less capital than those relying on simpler methods. Rapid progress in mathematical finance, data science and operations research supplied the tools. Analytical modeling now works at two levels. At the level of a single loan, credit scoring and rating systems estimate the borrower’s creditworthiness and the expected loss from lending. Those loan-level outputs then feed portfolio analysis, which estimates losses across all loans and guides decisions on capital targets, diversification and internal and external reporting.

The global credit crisis of 2007 to 2008 brought heavy criticism. Credit models had helped expand credit by lowering risk premiums, which made borrowing cheaper for companies and consumers, and some of them missed the true scale of risk badly. The fair response is that models describe complex social and economic behaviour and cannot be perfectly accurate. Even so, strategic planning, supervision and the design of new lending products would be impossible without them, so the practical task is to use them with a clear view of their limits.

For a long time, banks ran their credit books business line by business line. The corporate lending desk, the mortgage unit and the card business each had their own rating scales, their own ways of estimating parameters, their own limits and their own reporting metrics. The consequence was predictable: nobody could add up the bank’s total credit risk with any confidence, and comparing the riskiness of one business with another was close to impossible because the measures did not share a common basis.

Economic capital models and the Basel II and Basel III requirements changed that habit. Market risk had already been brought under a central function, and the same logic applies to credit. A central view gives the institution one consistent approach to measuring, monitoring and controlling credit exposures, so a BBB borrower in one division means the same thing as a BBB borrower in another and the totals can be aggregated meaningfully.

Central oversight does not mean that business units lose their voice. Most institutions build a hybrid structure in which the central portfolio function sets enterprise-wide goals, such as the bank’s risk appetite, how it handles very large borrowers and how it treats borrowers in default, while each business unit still handles the tactical questions of its own customers and products. The two perspectives complement one another rather than compete.

In practice, nobody can bring every exposure under portfolio management at once. Institutions usually start with their bulkiest exposures, which tend to be large loans to corporate borrowers, because those positions move the overall risk most. Once the methods and governance for those exposures are working, the same resources can be turned to the smaller pockets of credit risk elsewhere in the organization. In this setting, a borrower in default typically means one with debt more than 90 days overdue, and such borrowers form an important category for central monitoring because they concentrate both risk and management effort.

Consistent portfolio practices also make better use of scarce capital. When every unit measures risk the same way, the bank can see where capital earns an adequate return for the risk it carries and redirect it from areas where it does not, a theme that returns later with RAROC.

Lenders know before they open their doors that some customers will struggle to repay and that some will not repay at all. What they cannot know in advance is which ones. That uncertainty comes from three distinct sources, and each calls for a different response.

Strategic uncertainty: adverse selection and moral hazard

Strategic uncertainty arises because the lender cannot see the borrower’s true intentions and character. Economic theory captures it through two mechanisms. The first is adverse selection, which the source calls unfavorable choice. Suppose a lender charges one fixed interest rate to every borrower in a given credit category. Within that group, the careful borrowers with strong credit characteristics pay more than their true risk warrants, while the weaker borrowers pay less than they should. So, borrowing is a better deal for the people least likely to repay. The careful borrowers drift away, the average quality of the remaining pool falls, the lender raises rates to compensate, and the higher rate drives away still more good borrowers. Credit cards suffer from this problem in a strong form, because the line is granted for general use rather than for a particular purchase or a fixed term.

The second mechanism is moral hazard, which concerns behaviour after the loan is made. A borrower who accepts harsh terms carries a heavier burden, and that burden itself raises the chance of default: a higher interest rate pushes the borrower closer to insolvency and can lead the borrower to pile up other sources of credit. Card lending again shows the effect clearly, because people in financial difficulty tend to fall back on their card balances, turning the card issuer into a lender of last resort exactly when the borrower is weakest.

Occasional uncertainty

Occasional uncertainty covers events outside the borrower’s control. Job loss, an unexpected large expense, a regional or national recession, sudden political upheaval of the kind more common in emerging markets, and major natural disasters can all turn a sound borrower into a defaulter. The borrower did nothing wrong and may have been perfectly honest; the shock simply removed the ability to pay.

Cognitive uncertainty

Cognitive uncertainty stems from borrowers misjudging their own position. Consumers often spend beyond what their income can support, accept very high interest rates and juggle balances between cards near the end of each billing cycle. Where this kind of uncertainty cannot be measured well, lenders lean on trust built up with the client, including the client’s competence, accountability and shared interest in the relationship. Trust is hard to quantify, but it shapes important qualitative features of the bond between borrower and lender, and it sits alongside the formal risk assessment rather than replacing it.

Factors that create risk in a lending decision

Against this background, several specific factors raise the risk of a credit decision:

• falling values of the collateral, securities and other guarantees that back the loan;
• over-indebtedness, where the borrower already owes more than can realistically be repaid;
• weak monitoring of the borrower’s solvency, liquidity and qualitative characteristics;
• inconsistent application of approved policies on collateral and guarantees relative to the exposure at default;
• different approval standards for small loans across branches, because of local practice or special authorization routes;
• poor management practices and weak budgetary control;
• use of loan proceeds for purposes other than those approved;
• longer loan duration, since short-term lending is generally less risky than long-term lending because uncertainty widens with the horizon;
• legal problems, omissions, misunderstandings and errors;
• missing insurance against events that could damage the borrower’s finances.

The central output of any credit risk system is the expected loss on a loan over a stated period. That period is usually one year, matching the cycle of financial reporting, although longer horizons are used for some purposes. Expected loss multiplies three components together.

Probability of default (PD)

PD is the likelihood that the obligor misses scheduled payments during the analysis period. The standard trigger for default is a payment that is at least 90 days late, although lenders can use richer definitions that also consider how much is overdue. PD depends mainly on the borrower, and it is normally estimated with credit scoring or rating models that combine many factors about the obligor’s condition. Because it is the most fundamental element of credit analysis, most of the modeling effort in the field goes into estimating PD.

Exposure at default (EAD)

EAD is the amount the lender stands to lose at the moment of default, before any recovery, meaning the capital still owed. Unlike PD, it depends mostly on the loan rather than the borrower. For a plain term loan or a bond, the payment dates and amounts are fixed, so EAD is easy to pin down. For revolving products such as credit cards the balance moves around over time, and borrowers in trouble often draw more just before they default, so estimating EAD takes more work.

Loss given default (LGD) and the recovery rate

LGD is the share of EAD that is actually lost once default happens, normally a figure between 0 and 100%. It is often expressed through its complement, the recovery rate.

LGD depends on how a default is resolved, and therefore on features of the borrower, the loan and the economy. For a corporate loan, the firm’s size, sector and financial health matter, and on the loan side collateral and seniority are the big drivers. The simplest approach sets LGD from historical averages for each loan type. Since Basel II, institutions more often use statistical models that estimate LGD from loan and borrower characteristics.

Expected loss for each loan is the building block of portfolio risk analysis. Summing expected losses tells the bank what it should provision for on average, while the variability of losses around that average, which later sections call unexpected loss, is what capital must absorb.

Regulators require every bank to hold enough capital to cover the risk of its assets. The test is the capital adequacy ratio (CAR), which compares regulatory capital with risk-weighted assets and must exceed a minimum level set by the supervisor.

Capital here means tier 1 plus tier 2 capital. Tier 1 capital is the core: equity and reserves, the funds a bank can most readily use to absorb unexpected losses. Tier 2 capital consists of supplementary sources that are less secure than tier 1. Risk-weighted assets (RWA) are a weighted sum of the bank’s assets, where each asset is scaled by a weight that reflects its riskiness, so a safe government bond contributes little or nothing and an unsecured corporate loan contributes its full amount or more.

Standardized approach versus internal ratings-based approach

Basel II gives banks two ways to calculate RWA. Under the standardized approach, the supervisor prescribes the risk weights, and they apply uniformly without tailoring to particular loans, portfolios or institutions. Risk assessment relies on external sources such as agency ratings. Because these weights are generic, they are set conservatively to cover the uncertainty they leave, so the standardized approach usually produces higher capital requirements and is costlier for the bank.

The alternative is the internal ratings-based (IRB) approach, which gives more flexibility but demands sophisticated models built on the bank’s own historical data. Internal rating and scoring systems estimate PD. Under foundation IRB, the bank supplies its own PD while supervisors prescribe LGD; under advanced IRB, the bank also estimates LGD with its own statistical models. The next section shows how IRB turns these inputs into capital.

The example shows the two levers a bank controls. It can raise the numerator by issuing equity or retaining profits, or it can lower the denominator by shifting toward assets with lower risk weights. Regulators care about the denominator precisely because the same balance sheet total can hide very different levels of risk.

Under IRB, the capital for unexpected losses comes from risk weight functions built on the asymptotic single risk factor (ASRF) model. The model assumes a fully diversified loan book, so the idiosyncratic risks of individual borrowers cancel out and only systematic risk, the common exposure to the state of the economy, moves portfolio losses. That assumption is what lets a bank compute capital loan by loan and simply add the results. For a corporate exposure, risk-weighted assets are:

K is the capital requirement per unit of exposure. It depends on PD, LGD, the loan’s effective maturity M and the asset correlation parameter R:

The term N(z) is the default rate the borrower would experience in a severe downturn, one so bad that it is exceeded only once in a thousand years at the 0.999 confidence level. Multiplying by LGD gives the downturn loss, and subtracting PD times LGD removes the expected loss, which is meant to be covered by provisions and pricing rather than by capital.

Asset correlation

R measures how strongly a borrower’s fortunes move with the general economy, and the Basel Committee prescribes a formula for it. That formula reflects two observations. Correlation falls as PD rises, because the default of a weak borrower is driven more by its own problems. Correlation rises with firm size, because large companies track the economy closely while small firms more often fail for reasons of their own.

Maturity adjustment

Maturity enters for two reasons. Longer loans are riskier because there is more time for a downgrade, so K should rise with M. And a borrower with a low PD has more room to fall than one that is already weak, so the maturity effect should be stronger for low-PD borrowers. The figure shows how β shrinks as PD rises.

Granularity adjustment and Basel III

Real portfolios are never perfectly diversified, so some idiosyncratic risk always remains. Ignoring it understates the true capital need, so the Basel Committee proposed a portfolio-level granularity adjustment. Granularity measures concentration risk, the extra risk from large exposures to one obligor or to groups of correlated obligors, and the adjustment can be positive or negative depending on how diversified the portfolio is. Basel III then tightened the framework: a higher capital adequacy standard (CAR of at least 10.5%), new leverage and liquidity requirements, more attention to counterparty credit risk in derivatives and securitizations, and a broader programme of stress tests and model validation to check how extreme markets and high volatility would affect both exposures and the bank’s own credit rating.

Methods for estimating the likelihood of default fall into three broad families: judgmental approaches, data-driven empirical models and financial models. They differ in the data they need, in their scope and in the range of borrowers they can handle. Judgmental approaches are the oldest and the least analytically sophisticated. They are also called qualitative approaches or expert systems because the assessment rests entirely on the judgment of credit analysts, who weigh both qualitative and quantitative information about the borrower.

The five Cs of credit

The best-known judgmental scheme is 5C analysis (printed in the source as “SC analysis”), which assesses five dimensions of creditworthiness:

1. Character: the personality and integrity of the borrower.
2. Capacity: whether the borrower can repay, given current income, expenses and other debts.
3. Capital: the borrower’s own money at stake in the business or purchase.
4. Collateral: the security pledged to support repayment.
5. Conditions: the wider business environment and the terms of the loan itself, such as its interest rate.

For a corporate borrower, analysts feed these dimensions with published financial statements, the business plan that often accompanies the loan request, and information on the firm’s sector, region, market and the general economic outlook. A small loan may be reviewed by a single analyst or a small team, whereas a large loan goes through deeper analysis and a credit committee.

Limitations

Even a carefully structured judgmental process rests on expertise rather than on theory or tested data, which creates real difficulties. It is hard to validate the quality of the results, hard to update the process when conditions or available information change, and hard to run scenarios on how events would affect one borrower or a whole portfolio. Transparency and consistency can also suffer when there are no clear rules for applying and monitoring the process.

During the 1980s and early 1990s, lenders tried to add analytical power through expert systems technology, which offered structured reasoning, often combined with database management. These systems can be seen as an early step toward the artificial intelligence methods that attract so much interest today.

Where judgment still wins

Judgmental approaches remain the right tool where historical data are too thin to build a model. Project finance is the classic case: large, long-lived infrastructure projects each have unique features, so past projects say little about the next one, and the financing needs careful structuring by several groups of experts. Shipping finance, start-ups and small and medium-sized enterprises (SMEs) are other examples. Beyond these special cases, experienced analysts can extract insight from unstructured information in ways a model cannot, and that skill is valuable in complex situations.

Empirical models learn from history. They are built on records of past loans, covering applications accepted and rejected, loans repaid as agreed and loans that defaulted. Banks’ internal databases, rating agencies and data vendors supply the information, and the approach works for corporate and consumer lending alike wherever enough history exists. The raw inputs resemble those an expert would use, namely borrower characteristics, loan status and external risk factors. The difference is in how they are combined. Rather than weighting factors by experience, an empirical model searches the data for patterns and produces an explicit relationship between the probability of default and the input variables.

The idea dates back to the late 1960s, when academics built the first statistical bankruptcy prediction models. Two trends have driven the field since. Statistical, machine learning and operations research techniques now let analysts fit complex non-linear relationships efficiently even on very large datasets. And research, regulation and practice have uncovered new risk factors beyond traditional financial ratios, including corporate governance features such as business ethics, governance structure and internal audit, information from social networks and news analytics, and real-time market data for listed firms.

Advantages

Empirical models bring transparency and consistency to both their outputs and the way they are built and maintained. Their predictive power can be validated against actual outcomes, which gives a clear test of quality. They support formal hypothesis testing, scenario analysis and stress tests. They can be refreshed as new information arrives, and they can be tailored to segments, for example separate models for large companies and SMEs, for particular sectors, or for credit cards and mortgages.

Weaknesses

The main weakness is the dependence on history. Business and financial conditions are deeply uncertain and volatile, so past data may not describe future risk well, especially around crises whose scale is hard to anticipate. The data are often incomplete and imperfect. They also tend to be backward looking and static: a firm’s financial statements or a person’s income describe the borrower at one point in time. Expert judgment during model building and careful data handling can soften these problems but cannot remove them. Finally, the inputs are not updated in real time. Quarterly financial statements arrive regularly, yet they can miss the latest developments in the borrower’s condition.

Because empirical scoring and rating models are so widely used, they form the backbone of retail and much corporate credit assessment, and their design and validation are studied in depth as a separate topic.

Financial models start from theory rather than from data mining. Where empirical models describe and predict, financial models take a normative stance: they derive default from basic economic and financial principles and so describe the mechanism that produces it. They are also called market models because they draw their inputs from financial markets, and for that reason they apply mainly to corporate debt issued by firms whose securities trade.

There are two main types. Structural models treat default as an endogenous event tied to the firm’s own balance sheet, specifically the value of its assets relative to its debt. Default happens when assets are no longer worth enough to cover what the firm owes. Reduced form models take a different view. They do not try to explain why a firm defaults; instead they treat default as a random event that can strike at any moment, triggered by a jump in an exogenous random variable, usually modelled as a Poisson jump process. Their main information comes from market prices of bonds and credit derivatives, from which the implied intensity of default can be extracted.

What the evidence says

Structural models trace back to the Black and Scholes (1973) option pricing model and Merton’s (1974) work on pricing corporate debt. Tests of their predictive power give mixed results. Hillegeist et al. (2004) found that a structural market model predicted bankruptcy significantly better than popular accounting-based models, and Bharath and Shumway (2008) found a very simple structural model useful when combined with other predictors. On the other side, Agarwal and Taffler (2008) concluded from UK data that a structural model added little beyond empirical models, and Campbell et al. (2008) reached a similar conclusion for US bankruptcies. Reduced form models were pioneered by Jarrow and Turnbull (1992, 1995), with Duffie and Singleton (1999) among the best known later versions, and studies fitting hazard models to historical data have generally found reduced form approaches to outperform structural ones.

An option gives its buyer the right, but not the obligation, to buy or sell an underlying asset at an agreed price, while the writer must honour the deal if the buyer exercises. Merton’s insight was that a firm’s capital structure has exactly this shape. The shareholders hold a call option on the firm’s assets, written by the creditors. By lending, creditors in effect hold the assets until the debt is repaid, and the shareholders can reclaim them by paying off the debt, which they will do only if keeping the firm alive makes economic sense.

Take a firm with a single zero-coupon liability of face value L due at time T. At maturity the shareholders compare the market value of the assets, A_T, with L. If assets exceed the debt, they repay and keep the surplus. If assets fall short, the firm’s net worth is negative, so they walk away and hand the assets to the creditors. The equity payoff at T is:

Because equity is a call option, its current value comes from the Black-Scholes formula, with the asset value A in place of the share price and L in place of the strike:

Treating equity as a function of assets and time also links the two volatilities:

Solving for the unobservable asset value

Neither A nor σ_A can be seen directly, but everything else can. Equity value E is the firm’s market capitalization. Equity volatility σ_E is the annualized volatility of the share price estimated from history. T is the time in years until the debt is repaid, L is the face value of debt, usually taken as short-term debt from the balance sheet, and r is the yield on treasury bills or similar low-risk securities. Equations 5.1 and 5.2 are two equations in two unknowns, so a simple iterative Newton-type algorithm can solve them for A and σ_A.

Once A and σ_A are known, N(−d₂) is the risk-neutral probability of default, the chance that the shareholders decide not to repay, computed as if assets grow at the risk-free rate. The next section converts this into a real-world default probability.

The risk-neutral probability N(−d₂) assumes assets drift at the risk-free rate r, which is right for pricing but not for forecasting. To estimate the real probability that the firm fails, the expected return on assets μ replaces r:

A standard way to obtain μ is to solve equations 5.1 and 5.2 over several past periods and measure the rate at which the estimated A has changed. The fraction inside the brackets has its own name. It is the distance to default (DD), the number of standard deviations by which the expected asset value at T sits above the default point L:

So, PD = N(−DD). A larger cushion of assets over debt, a higher expected return or lower volatility all lengthen the distance and shrink the probability.

In practice the calculation runs the other way: an analyst observes E = 26.17 and σ_E = 82.2%, solves equations 5.1 and 5.2 to recover A = 120 and σ_A = 20%, and only then computes DD and PD.

The best-known commercial implementation of the structural approach is the Moody’s-KMV Expected Default Frequency (EDF) model, documented by Crosbie and Bohn (2003). It computes a distance to default in the same spirit as Merton, but it changes two things that matter in practice.

First, it does not convert DD into a probability through the normal distribution as equation 5.3 does. Instead it uses a large historical database to build an empirical mapping: firms that had a given distance to default in the past defaulted with some observed frequency, and that frequency becomes the EDF. This matters because real default experience has fatter tails than the normal curve suggests, so a normal mapping tends to understate the PD of firms that look safe. Second, it redefines the default point. Rather than using short-term debt alone, KMV sets the default point at short-term debt plus half of long-term debt, which tracks more closely the obligations that actually force a firm into default within the horizon.

Limitations of the Merton model

The structural approach is elegant, but its assumptions limit how well it works:

• Simple debt structure. The model assumes a single zero-coupon liability maturing at T. Real firms have layers of debt with different maturities, coupons and seniority, so choosing L is a judgment call, which is why KMV adjusts the default point.
• Default only at maturity. Default can occur only at T, whereas real firms can fail at any time when a payment falls due.
• Normal distribution. Mapping DD through the normal curve misprices the tail, which is why KMV substitutes an empirical distribution.
• Unobservable inputs. Asset value, asset volatility and the expected return on assets μ are never observed and must be inferred, so estimation error feeds straight into PD.
• Market data required. The model needs a traded share price, so it applies mainly to listed companies; applications to unlisted companies and consumer loans exist but require adaptation, as in Niklis et al. (2014) and Thomas (2009).
• Mixed predictive record. Some studies find that structural measures add little beyond accounting models. Chen and Hill (2013) found an empirical z-score model more closely correlated with agency ratings for UK firms than two structural models, and Doumpos et al. (2015) found that Merton PDs added information to financial data for European firms but little beyond market capitalization.

CreditMetrics looks at credit risk through ratings rather than through the balance sheet. It asks how likely a borrower is to move from its current grade to each other grade, including default, over the coming period, and what the loan would be worth in each case. Because a loan loses value when the borrower is downgraded, not only when it defaults, CreditMetrics is a mark-to-market model rather than a default mode model. Where the variables that drive default cannot be measured directly, the observed transition probabilities stand in for them.

The main inputs are the issuer’s current credit rating, a rating transition matrix giving the probability of moving from one grade to another, recovery rates on defaulted loans, and credit spreads in the bond market. The model assumes that all borrowers within a grade are homogeneous, which has drawn criticism. The horizon is usually one year, although periods as long as 10 years can be studied. Recovery values are projected using fixed rates, which has raised concerns because rates over long periods can be quite volatile. The output is a distribution of the change in the loan’s value over the horizon.

Valuing a loan in each rating grade

For a loan or bond whose rating at the horizon is grade i, each cash flow is discounted at the risk-free rate for its period plus the credit spread for that grade:

Repeating the calculation for every possible grade gives a market value even for loans that do not trade, and because each loan can have a different risk profile, each can carry a different capital requirement.

The three stages of the methodology

CreditMetrics works at both loan and portfolio level in three stages. The first establishes each instrument’s exposure profile. It handles conventional instruments such as floating-rate bonds and loans, and it also gives a way to estimate less obvious exposures such as undrawn commitments, letters of credit and trade credit agreements, as well as market-driven instruments such as swaps and fixed-rate bonds, all placed on an equivalent basis. The second stage estimates the volatility of each instrument’s value caused by upgrades, downgrades and defaults: each possible transition produces a change in value, the changes are weighted by their probabilities, and the result is an expected value and a standard deviation, exactly as in the example. The third stage brings in correlations between credit quality changes to combine the individual value distributions into a distribution for the whole portfolio. Credit quality correlations are hard to observe directly, so practitioners use various shortcuts, the simplest being a single fixed correlation.

CreditMetrics is neither a rating tool nor a pricing model. Its purpose is to produce portfolio risk measures that reflect how each exposure relates to the rest of the book, which supports transparency in internal risk management and in supervision.

CreditRisk+ was released by Credit Suisse Financial Products in 1997, and it takes the simplest view of the three portfolio approaches. Unlike KMV, it makes no use of the firm’s capital structure, since in this framework capital structure has no direct link to the rating or the probability of default. Unlike CreditMetrics, which tracks a whole ladder of rating changes and the value effects they cause, CreditRisk+ recognizes only two states: the borrower either defaults or does not. Losses arise only from default, and the default frequency itself is treated as a continuous random variable.

The model assumes that the probability of any single borrower defaulting is small and that defaults occur independently of one another. Under those conditions, the number of defaults in a portfolio follows a Poisson distribution, whose defining property is that the mean equals the variance. If a large loan book expects 4 defaults a year, the variance of the number of defaults is also 4, so the standard deviation is 2. Because the model needs only default data and not ratings migration or market prices, its data requirements are minimal and it is particularly easy to use. The price of that simplicity is that it ignores losses from credit deterioration short of default.

Comparing the approaches

The table brings out a useful way to choose among them. Structural models suit listed companies with traded equity and give a forward-looking, market-driven PD. CreditMetrics suits portfolios where ratings migration and mark-to-market value changes matter, such as bond books. CreditRisk+ suits large portfolios of small loans where defaults are rare and independent, and where simplicity and limited data are decisive.

Scoring and rating models are judged statistically, but lending decisions are judged in money. A bank needs a financial measure that sets a loan’s return against its risk and takes account of fees, operating costs, taxes, regulatory requirements and the cost of capital. The most widely used measure is risk-adjusted return on capital (RAROC). In general it compares the income or profit generated by a bank, a product line or a single loan with the economic capital needed to produce that income, and different institutions specify the pieces in different ways.

For a single loan, the numerator is the revenue the loan generates after expenses and expected losses, and the denominator is the capital at risk, the capital the bank would need to cover its exposure if things go wrong:

The decision rule is simple: the loan is worth making if its RAROC exceeds the bank’s cost of capital.

Capital at risk from duration: the market-based approach

One way to set the denominator is to ask how much the loan’s value could fall over the period, usually one year, because of a rise in interest rates. Duration measures that sensitivity. For a loan of value L, duration D and interest rate i, a change in rates of Δi changes the loan’s value by approximately:

Capital at risk from unexpected loss

When default prediction models are available, the denominator is more often the unexpected loan loss:

Here a is a risk factor representing the unexpected default rate, set from the distribution of historical default rates for similar loans. If default rates were normally distributed, a = 2.6σ would cover the 99.5% confidence level, where σ is the standard deviation of historical default rates. Real loss distributions are skewed, with long right tails, so practitioners often use a higher multiple, for example 5 to 6.