14.4 External and Internal Credit Ratings

External and Internal Credit Ratings

Credit risk measurement begins with an assessment of default likelihood. VRM–4 covers how external agencies and internal bank models produce ratings, how those ratings link to probability of default (PD), recovery, and expected loss (EL), and why markets and history refuse to treat a letter grade as gospel.

External Rating Scales, Process, and the Default Link

Major agencies (S&P, Moody’s, Fitch) assign ordinal grades—e.g., S&P AAA, AA, A, BBB (investment grade) then BB, B, CCC, … (speculative / high yield). Moody’s uses Aaa, Aa, A, Baa, Ba, B, Caa, …. Modifiers (+/− or 1/2/3) refine ranks.

The rating process typically includes:

1. Issuer request / surveillance mandate (issuer-pays model for most corporate ratings),
2. Quantitative analysis of leverage, coverage, cash flow, liquidity,
3. Qualitative business-risk and industry assessment,
4. Management meetings and projections,
5. Rating committee decision and published rationale,
6. Ongoing surveillance and outlook / watchlist updates.

Agencies publish historical default studies: average default frequencies by rating and horizon (1-year, 5-year cumulative). These frequencies are the empirical bridge from letter → PD. Important caveats: averages mix cycles; withdrawals and transitions matter; and structured-finance ratings historically behaved differently from corporates.

*Orders of magnitude only—use the agency study table on the exam if numbers are given.

Conditional Versus Unconditional PD

Unconditional PD over horizon T is the probability that default occurs by T, measured from “now,” without further conditioning: PD(0,T) = P(τ ≤ T).

Conditional PD conditions on survival so far or on a state variable (e.g., rating, macro regime). The hazard rate (default intensity) γ(t) is the instantaneous default rate given survival to t. For a constant hazard γ,

P(τ > T) = e^{−γT}

Unconditional PD over T:

PD(0,T) = 1 − e^{−γT}

For small γT, PD ≈ γT (e.g., γ = 1% per year → 1-year PD ≈ 0.995% ≈ 1%).

Worked hazard → PD

Hazard γ = 2% per year, horizon T = 3 years:

PD = 1 − e^{−0.02 × 3} = 1 − e^{−0.06} ≈ 1 − 0.9418 = 5.82%

Linear approximation 0.02 × 3 = 6.0% is close but slightly high. If the firm has already survived 1 year and hazard stays 2%, the conditional PD over the next 2 years is 1 − e^{−0.04} ≈ 3.92%, which differs from the original 3-year unconditional PD—conditioning on survival matters.

Recovery Rates and Expected Loss

Default is not a total loss of exposure. Loss given default (LGD) = 1 − recovery rate. Exposure at default (EAD) is the amount outstanding (or drawn + expected draw for lines) at default.

Expected loss:

EL = PD × LGD × EAD

Worked EL

Facility EAD = $10 million, 1-year PD = 1.5%, expected recovery = 40% → LGD = 60%.

EL = 0.015 × 0.60 × 10m = $90,000.

Recovery varies by seniority (secured bank debt ≫ subordinated bonds), jurisdiction, collateral, and cycle (recoveries fall in recessions—downturn LGD). Ratings primarily target PD (or expected loss for some scales historically); splitting PD versus LGD is essential for modern IRB / credit VaR.

Through-the-Cycle Versus Point-in-Time

Through-the-cycle (TTC) ratings aim for stability across the economic cycle: a BBB name stays BBB unless fundamentals permanently change. Agencies historically emphasize TTC-style stability (with debate).

Point-in-time (PIT) PDs move with current conditions—higher in recessions, lower in booms—matching short-horizon default experience and market spreads more closely.

Exam trap: a stable TTC rating can look “wrong” versus soaring CDS spreads in a crisis even if the agency has not yet downgraded—markets are PIT-ish; agencies may lag.

Alternatives to Agency Ratings

Users who cannot or will not rely solely on agencies use:

• Internal rating systems (bank IRB scorecards, expert judgment),
• Market-implied PDs from bond credit spreads or CDS (after adjusting for LGD and risk premia),
• Merton / structural models (distance-to-default from equity vol and leverage),
• Credit scoring models for retail/SME (logistic, machine learning),
• Peer financial ratios and private scorecards for unrated issuers.

Each alternative trades transparency for timeliness or granularity—and injects its own model risk.

Internal Versus External Ratings

Banks build internal ratings for Basel IRB permission, underwriting, and limits. Relative to external grades:

• Internal grades can be more granular (21+ notches) and portfolio-specific.
• Internal PDs are calibrated to bank default history (PIT or hybrid).
• External ratings remain crucial for public disclosure, some regulatory maps, and investment-policy boxes (“IG only”).
• Mapping tables translate internal grades ↔ agency grades ↔ PD buckets; mismatches are a governance hotspot.

Transition Matrices

A credit transition (migration) matrix gives probabilities of moving from rating i to rating j over a horizon (usually one year), including a default absorbing column.

Uses:

• Mark-to-market credit VaR (CreditMetrics-style),
• Predicting downgrade risk for hold-to-maturity books,
• Stressing matrices (increase off-diagonal downgrade probs in recessions).

Rows sum to 1. Empirical matrices show rating stickiness (large diagonals) and more volatility in speculative grades. Multi-year matrices can be powered from one-year matrices under a Markov assumption—convenient but imperfect when migrations are serially correlated or cycle-dependent.

Ratings Versus Prices and CDS

Bond prices and CDS spreads embed market-implied compensation for default risk, liquidity, and risk premia. Roughly, for a flat hazard and constant LGD,

spread s ≈ γ × LGD = PD_approx × LGD

so implied PD ≈ s / LGD. Example: CDS spread s = 120 bp, LGD = 60% → implied hazard ≈ 0.012 / 0.60 = 2.0% per year. This risk-neutral / market PD usually exceeds physical historical PD because investors demand a credit risk premium.

When agency ratings and CDS disagree, traders ask whether the agency is slow, the market is overreacting, or LGD/liquidity assumptions differ. FRM wants you to respect both signals without equating them.

Historical Failures and Challenges

Documented challenges—high-yield for exam essays and ethics crossover:

• Issuer-pays conflicts and shopping for favorable structured-finance ratings pre-2008.
• Cliff effects: mechanical downgrades force selling by rating-constrained investors, amplifying spirals.
• Lagging downgrades in fast crises (agencies follow as well as lead).
• Structured products: tranching and correlation underestimation produced AAA defaults that corporate AAA history never foreshadowed.
• Sovereign ceiling / country risk interactions and political pressure.
• Over-reliance in regulation (hardwiring) reduced independent credit analysis.

Post-crisis reforms pushed more transparency, reduced hardwiring, and forced banks to strengthen internal ratings—yet external grades remain ubiquitous. Treat them as informed ordinal opinions calibrated to history, not as infallible PDs.