Financial Risk Manager (FRM) Credit Risk Measurement and Management Syllabus

Credit Risk Measurement and Management syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Credit Risk Measurement and Management in Financial Risk Manager (FRM), not a summary of it.

1. 1

   Credit Risk Fundamentals and Structural Models

   4 topics

   • Components of credit risk and credit events
   • The Merton structural model
     • Equity as a call option on firm assets
     • Distance to default and default probability
   • Reduced-form and hazard-rate models
   • Credit scoring and internal rating systems
2. 2

   Counterparty Credit Risk

   4 topics

   • Exposure metrics
     • Expected exposure, potential future exposure, and peak exposure
     • Expected positive exposure and effective EPE
   • Credit Valuation Adjustment (CVA)
     • Unilateral versus bilateral CVA and DVA
     • Wrong-way and right-way risk
   • Mitigants: netting, collateral, and the CSA
   • Funding and capital valuation adjustments (FVA, KVA)
3. 3

   Credit Derivatives and Structured Credit

   4 topics

   • Single-name credit default swaps and pricing
   • Index CDS and tranched products
   • Collateralized debt obligations and the copula model
     • Gaussian copula and default correlation
     • Tranche correlation and the limits of the model
   • Securitization structures and credit enhancement
4. 4

   Portfolio Credit Risk and Capital

   4 topics

   • Default correlation and concentration risk
   • Credit portfolio models
     • CreditMetrics and the migration approach
     • CreditRisk+ and the actuarial approach
   • Economic capital and credit VaR
   • The Basel IRB approach and the asymptotic single-risk-factor model
5. 5

   Credit Risk Mitigation and Stress

   4 topics

   • Loan portfolio management and securitization as a tool
   • Recovery rate modeling and cyclicality
   • Stress testing credit portfolios
   • Sovereign default and credit spread risk

Credit Risk Measurement and Management flashcards for Financial Risk Manager (FRM)

23 of 61 cards from the Credit Risk Measurement and Management deck — real questions with worked answers.

1. What are the two fundamental components whose product (along with exposure) determines expected credit loss?

   Expected loss is $EL = PD \times LGD \times EAD$, where $PD$ is the probability of default, $LGD$ is loss given default ($=1-\text{recovery rate}$), and $EAD$ is exposure at default.

2. What is a 'credit event' under standard ISDA documentation, and name the main ISDA credit events?

   A credit event is a defined occurrence that triggers settlement of a credit derivative. The main ISDA credit events are: bankruptcy, failure to pay, restructuring, obligation acceleration, obligation default, and repudiation/moratorium (the last two mainly for sovereigns).

3. Distinguish 'default risk', 'credit spread risk', and 'downgrade (migration) risk'.

   Default risk is the chance the obligor fails to meet obligations. Credit spread risk is the risk of loss from widening credit spreads even without default. Downgrade/migration risk is the risk that a rating migration to a lower grade reduces the asset's value.

4. In the Merton structural model, how is a firm's equity interpreted in option terms?

   Equity is a European call option on the firm's assets $V$ with strike equal to the face value of debt $F$ and maturity $T$: $E_T = \max(V_T - F, 0)$. Equity holders are paid only if asset value exceeds debt at maturity.

5. In the Merton model, how is risky debt expressed in terms of a risk-free bond and an option?

   Risky debt $= $ risk-free debt $-$ put option on assets: $D_0 = F e^{-rT} - P(V,F,T)$. Equivalently, debt holders are short a put on the firm's assets struck at $F$, so they bear default risk.

6. State the Merton-model formula for the value of equity.

   $$E_0 = V_0 N(d_1) - F e^{-rT} N(d_2)$$ where $d_1 = \dfrac{\ln(V_0/F) + (r + \tfrac{1}{2}\sigma_V^{2})T}{\sigma_V \sqrt{T}}$ and $d_2 = d_1 - \sigma_V \sqrt{T}$.

7. In the Merton model, what expression gives the risk-neutral probability of default?

   The risk-neutral default probability is $PD = N(-d_2)$, where $d_2 = \dfrac{\ln(V_0/F) + (r - \tfrac{1}{2}\sigma_V^{2})T}{\sigma_V \sqrt{T}}$. Default occurs if $V_T < F$.

8. Define 'distance to default' in the Merton/KMV framework.

   Distance to default is the number of standard deviations the asset value is above the default point: $DD = \dfrac{\ln(V_0/F) + (\mu - \tfrac{1}{2}\sigma_V^{2})T}{\sigma_V \sqrt{T}}$. A larger $DD$ implies a lower expected default frequency.

9. What is the key conceptual difference between structural and reduced-form credit models?

   Structural models (e.g., Merton) derive default endogenously from the firm's asset value crossing a barrier. Reduced-form (intensity) models treat default as an exogenous, unpredictable event governed by a hazard rate calibrated to market prices, with no explicit link to firm fundamentals.

10. In a hazard-rate (intensity) model, how is the survival probability expressed for a constant hazard rate $\lambda$?

    Survival to time $t$ is $P(\tau > t) = e^{-\lambda t}$, and the probability of default by $t$ is $1 - e^{-\lambda t}$. The default time density is $\lambda e^{-\lambda t}$.

11. What is the meaning of the hazard rate $\lambda(t)$ in a reduced-form model?

    The hazard (default intensity) is the instantaneous conditional default rate: $\lambda(t) = \lim_{\Delta t \to 0} \dfrac{P(t < \tau \le t+\Delta t \mid \tau > t)}{\Delta t}$. Survival probability is $\exp\!\left(-\int_0^t \lambda(s)\,ds\right)$.

12. State the standard 'credit triangle' approximation relating spread, hazard rate, and recovery.

    $s \approx \lambda (1 - R)$, where $s$ is the credit spread, $\lambda$ is the hazard rate (default intensity), and $R$ is the recovery rate. Thus $\lambda \approx \dfrac{s}{1-R}$.

13. Contrast cumulative, marginal, and conditional (forward) default probabilities.

    Cumulative PD is the probability of default by a horizon. Marginal (unconditional) PD is the probability of defaulting during a specific period viewed from time 0. Conditional/forward PD is the probability of defaulting in a period given survival to its start.

14. What is the difference between a credit scoring model and an internal rating system?

    A credit scoring model is typically a statistical/quantitative model (e.g., logistic regression) producing a numeric score for an individual borrower. An internal rating system assigns obligors/facilities to discrete rating grades, often combining quantitative models with qualitative expert judgment, and maps grades to PD/LGD.

15. Distinguish 'through-the-cycle' (TTC) from 'point-in-time' (PIT) rating philosophies.

    PIT ratings reflect current economic conditions, so PDs move with the cycle. TTC ratings stress a borrower's resilience over a full cycle, producing more stable ratings that change less with short-term conditions. Agency ratings lean TTC; many bank PD models are PIT.

16. What is Altman's Z-score and what does it predict?

    Altman's Z-score is a discriminant-analysis model predicting corporate bankruptcy from five financial ratios (working capital/TA, retained earnings/TA, EBIT/TA, market value of equity/book liabilities, sales/TA). For public manufacturers, $Z < 1.81$ signals distress and $Z > 2.99$ signals safety.

17. Define the credit exposure metrics: Expected Exposure (EE), Potential Future Exposure (PFE), and Expected Positive Exposure (EPE).

    EE($t$) is the average of positive exposure at future time $t$. PFE is a high percentile (e.g., 95th/97.5th) of exposure at time $t$ — a worst-case measure. EPE is the time-average of EE over the horizon. Maximum PFE is the peak PFE across all dates.

18. What is the difference between current exposure and potential future exposure?

    Current exposure is today's replacement cost, $\max(V,0)$ (the loss if the counterparty defaults now). Potential future exposure captures how much exposure could grow over time due to market moves, measured at a confidence level over the contract's life.

19. Why is netting important for counterparty exposure, and how does it change exposure?

    Under a netting agreement, exposure to a counterparty is the net positive value across all trades in the netting set: $\max\!\left(\sum_i V_i, 0\right)$ rather than $\sum_i \max(V_i,0)$. Netting reduces exposure whenever positive and negative MtM positions offset.

20. Define Credit Valuation Adjustment (CVA).

    CVA is the market value of counterparty default risk — the expected discounted loss from a counterparty defaulting before contract maturity. It is the amount by which a derivative's risk-free value is reduced to account for counterparty credit risk.

21. Give the standard discretized formula for (unilateral) CVA.

    $$CVA = (1-R)\sum_{i=1}^{n} EE(t_i)\, \cdot PD(t_{i-1}, t_i)\, \cdot DF(t_i)$$ where $R$ is recovery, $EE(t_i)$ is discounted expected exposure, $PD(t_{i-1},t_i)$ is the marginal default probability in each interval, and $DF$ is the discount factor.

22. What is Debt Valuation Adjustment (DVA) and how does it relate to CVA?

    DVA is the mirror image of CVA from the entity's own default perspective — it is the expected benefit (to the entity) from its OWN potential default, based on the counterparty's exposure to it. Bilateral CVA $= CVA - DVA$. A worsening of one's own credit raises DVA, producing a counterintuitive accounting gain.

23. What is wrong-way risk (and right-way risk) in CVA?

    Wrong-way risk occurs when exposure to a counterparty is positively correlated with that counterparty's default probability (exposure rises as creditworthiness falls), increasing CVA. Right-way risk is the opposite — exposure falls as default probability rises, reducing CVA.

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