Book 2. Credit Risk

FRM Part 2

CR 5. Introduction to Credit Risk Modeling and Assessment

Presented by: Sudhanshu

Module 1. Credit Risk Modeling and Regulatory Framework

Module 2. Credit Risk Assessment Approaches

Module 1. Credit Risk Modeling and Regulatory Framework

Topic 1. CAMEL System

Topic 2. Credit Risk Factors

Topic 3. Capital Adequacy Ratio

Topic 4. IRB Approach

Topic 5. Basel III Enhancements

Topic 1. CAMEL System

• A bank's financial condition is often evaluated using the CAMEL (capital, assets, management, earnings and liquidity) rating system.

  • Capital Adequacy: Measures a bank's ability to absorb losses and maintain operations. It ensures the bank has enough capital to withstand financial shocks.

  • Asset Quality: Assesses the credit risk in a bank's loan and investment portfolios. It evaluates the performance of a bank's assets, with a focus on problem loans and other-than-performing assets.

  • Management: Determines the quality of the bank's management team and their ability to react to financial stress, manage risks, and comply with regulations.

  • Earnings: Analyzes the bank's profitability and its ability to sustain activities and expand.

  • Liquidity: Evaluates a bank's capacity to meet its short-term obligations and its ability to convert assets into cash.

Practice Questions: Q1

Q1. Which subcomponent of the CAMEL analysis tool is focused on delinquent loans?

A. Liquidity.

B. Earnings.

C. Asset quality.

D. Capital adequacy.

Practice Questions: Q1 Answer

Explanation: C is correct.

Asset quality focuses on bank assets that are performing or showing signs of
delinquency.

Capital adequacy relates to minimum capital reserves as set by
regulation.

Earnings reviews are focused on core earnings with an emphasis on
stability, net interest margin, return on assets, and future earnings potential.

Liquidity focuses more on short-term liquidity risk than on longer-term focused interest rate risk although both are considered.

Topic 2. Credit Risk Factors

• Expected loss (EL): The primary output of a credit risk model is expected loss over a given horizon (typically one year), calculated as:

  • EL = PD × EAD × LGD

• Probability of Default (PD):

  • Measures the likelihood that a borrower fails to make scheduled payments

  • Default is typically defined as payments overdue by 90 days or more

  • Expressed as a percentage

• Exposure at Default (EAD):

  • Represents the outstanding exposure at the time of default

  • Expressed in dollar terms

  • Depends on loan structure (stable balances vs. revolving exposures like credit cards)

• Loss Given Default (LGD):

  • Percentage of exposure expected to be lost if default occurs

  • Closely related to the recovery rate (RR = 100% − LGD)

  • Influenced by borrower characteristics such as size, sector, and financial health

Practice Questions: Q2

Q2. A credit risk analyst is trying to determine the percentage of a loan that is expected to be lost if a specific borrower were to default. Which of the following metrics should he apply?

A. Loss given default.

B. Exposure at default.

C. Probability of default.

D. Recovery default rate.

Practice Questions: Q2 Answer

Explanation: A is correct.

Expected loss has three subcomponents (probability of default, exposure at default, and loss given default).

• The probability of default is the likelihood that a borrower is delinquent for more than 90 days.
• The exposure at default is the expected dollar loss if the loan defaults.
• The loss given default is the percentage of the loan that is estimated to be lost if a default occurs.

Topic 3. Capital Adequacy Ratio

• Capital adequacy Ratio (CAR): Banks are required to hold sufficient capital to match the risk of their assets, measured using the capital adequacy ratio (CAR).
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• Analysis of CAR formula:

  • In the CAR formula, capital refers to both Tier 1 and Tier 2 capital.

  • The risk-weighted assets (RWA) measure is the weighted average of the bank’s assets with the weight adjusted by risk level.

  • The regulatory minimum level for CAR is denoted by α (e.g., 8% under Basel II and 10.5% under Basel III).

• A bank's RWA is calculated using below methods:

  • Standardized approach: Supervisors assign predetermined risk weights to asset categories; the method is simple to implement but relies on external data and typically results in higher capital charges due to conservative weighting.

  • Internal ratings-based (IRB) approach: Banks use internal credit ratings and historical data to estimate PD and LGD, with RWAs calculated via an asymptotic single risk factor (ASRF) model that assumes full portfolio diversification, leaving only systematic risk.

Topic 4. IRB Approach

• ASFR Model: The ASFR model allows capital charges to be calculated on a loan-by-loan basis and then aggregated up to the portfolio level;​
• In above formula, K is the capital required, which is a function of PD, LGD, loan maturity (M), an asset correlation parameter (R), and a maturity adjustment (β):
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  • β is calculated as:
    • ​
• Asset Correlation Parameter (R): Set by the Basel Committee, $R$ captures a borrower’s sensitivity to the overall economic environment.

  • Effect of PD: Asset correlations decrease as probability of default (PD) increases, implying greater idiosyncratic risk for higher-PD borrowers.

  • Effect of firm size: Asset correlations increase with firm size, as larger firms are more influenced by macroeconomic conditions, while smaller firms default more due to idiosyncratic factors.

• Maturity Parameter (β): β depends on both loan maturity and PD.

  • Effect of maturity: Longer-maturity borrowers are riskier than short-term borrowers due to a higher likelihood of downgrades, implying higher capital requirements for longer maturities.

  • Effect of PD: Borrowers with lower PDs have greater downgrade potential than high-PD borrowers, so maturity adjustments should be larger for low-PD exposures.

Practice Questions: Q3

Q3. The internal ratings-based (IRB) approach for calculating a bank’s capital adequacy ratio (CAR) has several underlying elements. Which of the following statements relates to the IRB approach?

A. Idiosyncratic risk is explicitly factored into the model.

B. Estimates of probability of default are made by regulators.

C. Maturity adjustments should be higher for borrowers with high probabilities of default.

D. The maturity parameter reflects that capital requirements should increase with maturity.

Practice Questions: Q3 Answer

Explanation: D is correct.

The IRB approach considers several elements based on the bank’s customized historical record. The parameters do not reflect regulatory norms because they are customized to each bank. This approach assumes that the credit portfolio is well diversified and that no idiosyncratic risk remains. The maturity adjustment has two components. First, capital requirements should increase with maturity because the risk of default increases as maturity increases. Second, borrowers with low probabilities of default (PD) should have higher adjustments than high PD borrowers. A borrower with a high PD already has a higher instance of default factored into their estimates.

Topic 5. Basel III Enhancements

• Higher capital requirements: Basel III raised the minimum capital adequacy ratio (CAR) from 8% under Basel II to 10.5%.

• New liquidity and leverage standards: The accord introduced explicit liquidity and leverage requirements to strengthen bank resilience.

• Greater focus on counterparty risk: Enhanced treatment of counterparty risk, particularly for derivatives and securitized products.

• Stronger risk management framework: Introduced stress testing for extreme market volatility, along with model validation and ongoing testing to improve robustness under stressed conditions.

Module 2. Credit Risk Assessment Approaches

Topic 1. Predicting Default in Credit Risk Models

Topic 2. Judgemental Approach

Topic 3. Empirical Models

Topic 4. Financial Models

Topic 5. Default Probability Using the Merton Model

Topic 6. Moody's KMV Model 

Topic 7. CreditMetrics Model

Topic 8. CreditRisk+ Model

Topic 9. Risk-Adjusted Return on Capital

Topic 1. Predicting Default in Credit Risk Models

• There are three primary approaches to assessing the probability of default:

  • Judgmental Approach: These models rely on the perspective of internal experts. They are based on a qualitative assessment of the borrower.

  • Empirical Models: These are data-driven models that use historical data to predict future outcomes.

  • Financial Models: These are quantitative models, such as Merton model, that use financial data and theoretical frameworks to assess the probability of default.

• ​The differences between these methods involve the input data required, their scope, and the range of application.

Practice Questions: Q1

Q1. A financial analyst and a risk manager are discussing ways to derive the probability of default for a bank’s loan portfolio. The analyst says that he prefers models that rely on the perspective of internal experts. The manager adds that while internal experts have good perspectives in the risk management process, she prefers a model that is data-driven and one that can assess loans for both consumer and corporate customers. The analyst and manager are referring to which type of credit risk assessment?

Practice Questions: Q1 Answer

Explanation: C is correct.

A judgmental model uses the perspectives of experts to assess the probability of default. It can be applied to both consumer and corporate loans. An empirical model uses historical data to estimate relationships between variables and risk outcomes. This can also be applied to both consumer and corporate customers. The financial model uses market data to detect trends and risk estimates. Because financial market data is the primary input, this method can only be used for corporate customers.

Topic 2. Judgemental Apprpoach

• Judgmental approach: Also called the qualitative approach or expert system, this method relies primarily on qualitative inputs and expert judgment (e.g., credit risk officers).

• 5C analysis: A commonly used judgmental framework that evaluates a borrower’s creditworthiness across five core dimensions.

  1. Character: The personality of the borrower.

  2. Capacity: The ability of the borrower to repay in a timely manner.

  3. Capital: The amount of the borrower’s own capital that is at risk in the transaction.

  4. Collateral: Any secondary sources that are guaranteeing the loan.

  5. Conditions: The business environment and any loan-specific characteristics.

• Broad data inputs: Judgmental credit approaches draw on diverse inputs such as financial statements, business plans, industry and regional factors, market conditions, and macroeconomic trends, making them applicable to both consumer and corporate lending.

• Value when data is scarce: These approaches are particularly useful when historical data is limited or unavailable, such as in project finance, where unique deal structures limit meaningful comparisons and analyst experience adds significant value.

• Key drawbacks: Because judgmental methods rely on expert opinion rather than empirical models, outputs are harder to validate, update for changing conditions, or aggregate consistently at the portfolio level.

• Appropriate use cases: Despite limited transparency and consistency, judgmental approaches remain suitable for highly customized or unique loan types.

Topic 3. Empirical Models

• Data-driven default modeling: Empirical models use historical loan data (accepted, rejected, performing, defaulted) to identify patterns linking default likelihood to borrower, loan, and external risk factors.

• Sources of data: Inputs are drawn from internal databases, credit rating agencies, and other external data providers.

• Use of machine learning: ML techniques enable detection of complex, nonlinear relationships and the identification of new risk factors.

• Risk factors: Modern empirical models may incorporate factors such as corporate governance quality, social network data, and real-time market information.

• Advantages of empirical approach:

  1. Relative to the judgmental approach, it adds transparency and consistency to the process.

  2. Both the underlying structure of the model and its predictive power can be

     empirically validated.

  3. A hypothesized relationship can be analytically explored.

  4. Market data can be updated in real-time to better adjust to changing conditions.

  5. Adjustments can be made for specific sectors of the market.

  6. The breadth of data inputs enables this approach to be used for both consumer and corporate loans.

Topic 3. Empirical Models

• Weaknesses of empirical approach:

  • ​Reliance on historical data: Empirical methods depend on historical data, which may fail to predict future outcomes, particularly during periods of high uncertainty and volatility.

  • Data timeliness limits: While some market inputs update in real time, other inputs such as financial statement data are available only quarterly, delaying model updates and potentially providing risk information more slowly than judgment-based approaches.

Topic 4. Financial Models

• Nature of financial models: Financial (market) models are grounded in normative economic and financial theory and rely on market data, which limits their use primarily to corporate borrowers rather than consumer loans.

  • Structural models: Treat default as an endogenous outcome driven by a firm’s internal characteristics, such as asset value and leverage (e.g., the Merton model).

  • Reduced-form models: Treat default as an exogenous, random event, often modeled using processes like Poisson jumps, with key inputs derived from market data on bonds and credit derivatives.

Topic 5. Default Probability Using the Merton Model

• Option-based view of credit risk: The Merton model treats a firm’s capital structure as a call option on the firm’s assets.

• Roles of stakeholders: Shareholders are analogous to call option buyers, while creditors act as option writers.

• Economic intuition: Creditors effectively “own” part of the firm until debt maturity, while shareholders retain the right to reclaim full ownership by repaying or refinancing the debt.

• Single-loan setup: The firm has one loan with face value $L$ maturing at time $T$.

  • Shareholder decision rule: Shareholders will repay the debt only if the firm’s market value at maturity (ATA_TAT​) exceeds the debt obligation.

  • Default intuition: If AT<LA_T < LAT​<L, repaying the debt would result in negative net value, making default economically rational. Accordingly,

    • Net worth of firm = max (AT​-L, 0)

• ​Call option payoff: The above formula represents the terminal payoff of a call option with strike price $L$ and underlying asset price ATA_TAT​ at expiration.

  • The market value of equity (E) can be derived using the Black-Scholes-Merton option pricing formula as follows:

    •                                                          

    • A = current market value of the firm's assets

Topic 5. Default Probability Using the Merton Model

• In the previous formula,

  • AT<LA_T < L

  • ​

• Unknown inputs: The current value of assets $A$ and the volatility of asset returns σA\sigma_AσA​.

• Known inputs:

  • Market value of equity $(E)$: borrower’s market capitalization

  • Equity volatility (σE\sigma_EσE​): estimated from historical market data

  • Time to maturity $(T)$: time until full debt repayment

  • Face value of debt $(L)$: typically short-term debt on the balance sheet

  • Risk-free rate $(r)$: current Treasury bill yield

• ​Risk-neutral probability of default: N(−d2​), represents the likelihood that shareholders do not exercise their option to repay the loan, under the assumption that the firm’s asset value grows at the risk-free rate.
• Real-world probability of default: The expected return on the firm’s assets (μ) is substituted for the risk-free rate (r):
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Topic 5. Default Probability Using the Merton Model

• Inputs for PD estimation: Deriving a PD requires the firm’s asset return, typically obtained by first estimating the market value of equity (E) and equity volatility (σE​) from historical market data.

• Asset dynamics: The expected asset return (μ) is defined as the historical rate of change in the firm’s asset value (A).

• Distance to default: The real-world PD is then used to compute the distance to default (DD), which measures how many standard deviations the firm’s asset value is from the face value of its debt (L).

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Topic 6. Moody's KMV Model

• This model is similar to Merton model but has two key differences from the Merton model:
  1. Instead of using the standardized normal distribution, the Moody’s-KMV model uses historical data to develop the distribution of default frequencies.
  2. The default point (L) is defined as all short-term debt plus half of the long-term debt. The inclusion of some long-term debt more closely approximates the actual loan obligations of the borrower.

Topic 7. CreditMetrics Model

• PD estimation: CreditMetrics estimates PD using peer set analysis and a rating transition matrix to capture changes in credit quality over time.

• Model inputs: It is a mark-to-market model relying on borrower credit ratings, rating transition matrices, historical recovery rates, and bond market yield spreads.

• Key assumptions and horizon: Credit grades are assumed to be homogeneous, with a typical one-year horizon (sometimes extended up to 10 years).

• Model limitations: Recovery rates are treated as fixed, which ignores their historical volatility and is a key point of criticism.

• Formula:

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• The above equation calculates the value of a bond in credit grade i             where credit grade i is the assumed credit rating for the next period.

• The terms in the formulas include:

  •         ​: coupon payments at time t

  •    : risk-free rate at time t

  •    : the annual risk premium for a loan in credit grade i at time t

Topic 7. CreditMetrics Model

• Purpose and output: The CreditMetrics model estimates market values for individual nonmarketable loans and loan portfolios, producing a distribution of loan value changes over time to support systematic and transparent credit risk management.

• Scope and intent: CreditMetrics is not a rating tool; it provides risk measures that capture relationships among assets and can be applied across a wide range of financial products.

  • Stage 1 (Reporting profiles): Integrates data from diverse instruments, including fixed- and floating-rate bonds, nonperforming and non-interest-bearing loans, letters of credit, and market-based instruments such as swaps.

  • Stage 2 (Rating volatility and defaults): Uses rating transition matrices to model upgrades, downgrades, and defaults, with each transition adjusting the risk premium and loan valuation.

  • Stage 3 (Correlations): Aggregates individual loan valuations at the portfolio level and estimates correlations between portfolio value volatility and underlying asset price volatility.

Topic 8. CreditRisk+ Model

• Model overview: Developed by Credit Suisse in 1997, CreditRisk+ does not incorporate the borrower’s capital structure, unlike the Moody’s-KMV model, as it is not directly linked to default probability.

• Focus on defaults: Unlike CreditMetrics, which models full credit migration, CreditRisk+ considers only default (bankruptcy or severe credit deterioration), focusing on negative credit shocks.

• Statistical assumptions: Defaults are modeled using a Poisson distribution, assuming small, independent probabilities of default with the mean default rate equal to its variance.

• Key advantage: The model estimates default events only (not credit ratings), requiring relatively limited data, which makes it simple and practical to implement.

Practice Questions: Q2

Q2. The Merton model is different from Moody's-KMV Expected Default Frequency approach in two key areas. Which of the following statements refers to one of those differences?

A. The Merton model factors the market value of the borrower's equity, while Moody's-KMV model uses book value.

B. The Merton model uses the risk-free rate to calculate the distance to default, while Moody'sKMV model uses a customized value.

C. Moody's-KMV model uses a default point with short-term debt and half of long-term debt, while the Merton model only uses short-term debt.

D. The Merton model uses historical data to derive a distribution of default frequencies, while Moody's-KMV model uses standardized expectations.

Practice Questions: Q2 Answer

Explanation: C is correct.

One key difference is that Merton sets the default point as only short-term debt and Moody's-KMV model adds in half of long-term debt. Another key difference is that Moody's-KMV model uses historical data to derive a personalized distribution of default probabilities, while the Merton model uses standardized normal distribution values. In the distance to default formula, the rate of change in historical assets replaces the risk-free rate, and both models use the market value of equity.

Practice Questions: Q3

Q3. A credit risk manager is looking for a method to estimate default risk that considers volatility, credit scores, and comparisons to similar borrowers to enhance predictions. Which of the following methods should this manager select?

A. Merton model.

B. CreditRisk+ model.

C. CreditMetrics model.

D. Moody's-KMV model.

Practice Questions: Q3 Answer

Explanation: C is correct.

The CreditMetrics model is the option for peer comparisons. It considers bond issuer credit ratings (unlike the CreditRisk+ model). The Merton model uses option pricing theory to calculate the default rate, but it only considers shortterm debt. Moody's-KMV model adds some long-term debt to the theory behind the Merton model, but the CreditMetrics model is the best option due to peer comparison demands.

Topic 9. Risk-Adjusted Return on Capital

• Risk-Adjusted Return on Capital (RAROC): A ratio of the income on a loan relative to the capital required to obtain the loan:
  • RAROC = (Loan Revenues)/(Capital at Risk)

• A loan is considered to be profitable if the calculated RAROC is higher than the bank’s cost of capital.

• Loan Revenues: It consists of interest and principal coming from the loan, and calculated as:

  • ​The spread (s) between the loan rate and the bank’s cost of capital

  • The fees (f) attributable to the loan

  • The estimated loan losses (l)

  • The associated operating costs (c)

  • Relevant taxation (x)

• Capital at Risk: The capital needed by a bank to cover the default risk on a loan.
  • ​Capital at risk can be quantified using change change in loan value over an observation period, which is often 1 year, to capture the impact of changing interest rates.
  • Change in a loan's value (ΔL) can be estimated as:
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Topic 9. Risk-Adjusted Return on Capital

• Alternative Approach for RAROC: This method uses historical values and not market-based metrics like expected changes in interest rates. This approach uses the unexpected loan loss in the RAROC deonominator.
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• Key components: The method incorporates loss given default (LGD), exposure at default (EAD), and an adjustment factor (α) to capture unexpected default risk.

• Derivation of α: The adjustment factor is based on the distribution of historical default rates.

• Normality assumption: If default rates are normally distributed, α is set to 2.6σ at the 99.5% confidence level.

• Skewness adjustment: As loan default distributions are often skewed, practitioners typically use higher α values (e.g., 5 or 6) depending on loan characteristics.

Practice Questions: Q4

Q4. ABC Bank has a loan with a value of $750,000. There is an associated commission of 0.15%, the spread between the loan's interest rate and the bank's cost of capital is 0.45%, the estimate of operating costs is 0.3%, and their estimated tax rate is 12 %. This loan is expected to be a performing loan with no risk of default.

Additionally, this loan has a duration of 2.85 and an interest rate of 9.5%. Interest rates are expected to increase by 1.25%. What is this loan's risk-adjusted return on capital (RAROC)?

A. 4.92 %.

B. 6.01 %.

C. 7.64 %.

D. 8.11 %.

Practice Questions: Q4 Answer

Explanation: D is correct.

The estimated loan revenue is $1,980 and the estimated capital at risk is $24,400.68. This results in a RAROC of 8.11%. As long as the bank's own interest rate is less than this value, then the loan will be profitable.