Ch2. FRM Financial Risk Manager — Credit Risk Management
What Is Credit Risk?
Credit risk is the risk that a borrower or counterparty will fail to meet its contractual obligations, resulting in financial loss. It is the largest single risk category for most banks and financial institutions and commands roughly 20% of the FRM Part II exam.
Credit risk encompasses:
- Default risk: Will the counterparty default?
- Spread risk: Will the credit spread widen, reducing market value?
- Recovery risk: If default occurs, how much will be recovered?
- Concentration risk: Is the portfolio overly exposed to a single borrower or sector?
The Credit Risk Trinity: PD, LGD, EAD
Every credit risk model revolves around three parameters:
Probability of Default (PD)
The likelihood that a borrower defaults over a given time horizon (typically 1 year).
- Through-the-cycle (TTC): Long-run average default rate, used for regulatory capital
- Point-in-time (PIT): Current economic cycle estimate, used in IFRS 9 provisioning
Loss Given Default (LGD)
The fraction of exposure lost when a default occurs.
LGD = 1 − Recovery Rate
Typical recovery rates by seniority:
| Seniority | Recovery Rate | LGD |
|---|---|---|
| Senior Secured | 60–70% | 30–40% |
| Senior Unsecured | 40–50% | 50–60% |
| Subordinated | 20–30% | 70–80% |
Exposure at Default (EAD)
The amount outstanding at the moment of default.
- For term loans: EAD ≈ outstanding balance
- For revolving credit/derivatives: EAD includes potential future exposure (PFE)
Expected Loss (EL) and Unexpected Loss (UL)
Expected Loss (EL) = PD × LGD × EAD
EL is the average loss the bank anticipates and should price into the loan rate (credit spread). It is NOT held as capital.
Unexpected Loss (UL) is the volatility of losses around EL. This is the driver of regulatory and economic capital requirements.
The IRB Approach: Basel III Internal Ratings-Based
Under Basel III, sophisticated banks may use internal models (IRB) to estimate risk-weighted assets (RWA):
Foundation IRB (F-IRB): Banks estimate PD internally; regulators provide LGD and EAD.
Advanced IRB (A-IRB): Banks estimate all three parameters internally.
The IRB capital formula uses the Vasicek single-factor model to derive a capital requirement that covers unexpected losses at a 99.9% confidence level over 1 year:
K = LGD × [N(G(PD)/√(1−ρ) + √(ρ/(1−ρ)) × G(0.999)) − PD]
Where ρ is the asset correlation (Basel-specified) and N/G are the normal CDF and inverse CDF.
Credit Derivatives
Credit derivatives allow banks to transfer credit risk without selling the underlying loan.
Credit Default Swap (CDS)
- Protection buyer pays a periodic premium (spread)
- Protection seller pays the notional if a credit event occurs
- Credit events: bankruptcy, failure to pay, restructuring
CDS spreads reflect market perception of default probability:
CDS spread ≈ PD × LGD (for small PD)
CDO (Collateralized Debt Obligation)
- Pools loans/bonds and tranches cash flows by risk priority
- Senior tranches: low yield, first to receive payments
- Equity tranche: highest yield, first to absorb losses (called the “first loss” piece)
- Correlation between underlying assets is the key risk driver
Counterparty Credit Risk (CCR) and CVA
Counterparty Credit Risk arises from OTC derivatives where the counterparty may default before contract maturity.
Credit Valuation Adjustment (CVA) is the market price of counterparty credit risk:
CVA ≈ (1 − Recovery) × ∑[PD(t) × Discount(t) × EPE(t)]
Where EPE = Expected Positive Exposure at time t.
Post-2008 regulatory changes:
- Basel III CVA capital charge: Banks must hold capital for CVA volatility
- Central clearing mandate: Most standardized derivatives now cleared through CCPs (Central Counterparties)
- Initial margin requirements: Bilateral OTC trades must post initial margin (ISDA SIMM)
Scoring Strategy for FRM Credit Risk
| Topic | Exam Weight | Action |
|---|---|---|
| PD/LGD/EAD/EL | High | Memorize formulas cold |
| IRB approach | High | Understand conceptually; formula given |
| CDS mechanics | High | Be able to price and describe cash flows |
| CVA/DVA/FVA | Medium-High | Know the concept and direction of adjustment |
| Securitization/CDO | Medium | Focus on tranche structure and correlation |
| Basel capital formulas | Medium | Know capital = f(UL, confidence 99.9%) |
Summary
| Concept | Formula / Key Point |
|---|---|
| Expected Loss | PD × LGD × EAD |
| LGD | 1 − Recovery Rate |
| CDS spread | ≈ PD × LGD |
| CVA | Mark-to-market of counterparty default risk |
| Basel capital | Protects to 99.9% confidence, covers UL not EL |
Chapter 3 covers Operational Risk & Quantitative Analysis — the final pillar of the FRM foundation.
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