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Credit Risk

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Topic 14: Credit Risk

Learning Objectives Coverage

LO1: Describe credit risk and its components, probability of default and loss given default

Core Concept exam-focus credit-analysis

Credit risk is the risk of economic loss resulting from a borrower’s failure to make full and timely payments of interest and principal. It consists of two primary components: the probability of default (POD) and the loss given default (LGD). Together, these define the expected loss framework (EL = POD x LGD) that underpins all credit spread analysis. Credit risk is the dominant risk factor for most fixed-income investments, driving yield spreads above the risk-free term structure, shaping portfolio returns, and determining regulatory capital requirements. Recovery rates depend heavily on the seniority and security of the obligation, a topic explored in depth in Corporate Credit Analysis.

Formulas & Calculations

  • Expected Loss Formula:

    EL = POD × LGD

Where: LGD = EE × (1 - RR)

Therefore: EL = POD × EE × (1 - RR)

  • Credit Spread Approximation:

    Credit Spread ≈ POD × LGD

More precisely:
Credit Spread = EL + Risk Premium + Liquidity Premium

  • Recovery Rate and Loss Severity:

    Recovery Rate (RR) = Amount Recovered / Claim Amount
Loss Severity = 1 - RR
LGD = Exposure × Loss Severity

  • HP 12C Steps (Expected Loss): formula hp12c

    Example: POD = 3%, EE = $1M, RR = 40%

0.03 [ENTER]               (POD)
1000000 [×]                (× Exposure)
0.4 [ENTER] 1 [SWAP] [-]   (1 - RR = 0.6)
[×]                        (× Loss Severity)
Result: 18,000             (Expected Loss = $18,000)

  • HP 12C Steps (Credit Spread from Components):

    Example: POD = 2%, LGD = 60%

0.02 [ENTER]               (POD)
0.60 [×]                   (× LGD)
100 [×]                    (Convert to basis points)
Result: 120                (Credit spread ≈ 120 bps)

Practical Examples

  • Corporate Bond Analysis:

    BBB-rated 5-year bond:
- Face value: $10M
- POD (annual): 0.30%
- Recovery rate: 45% (senior unsecured)
- Expected exposure: $10.2M (includes accrued interest)

LGD = $10.2M × (1 - 0.45) = $5.61M
EL = 0.003 × $5.61M = $16,830 annually

Credit spread requirement: 16.83 bps minimum
Market spread: 150 bps (includes risk and liquidity premiums)

  • Secured vs Unsecured Comparison:

    Same issuer, $100M exposure:

Secured bond (collateral = $60M):
- Effective exposure: $40M
- Recovery rate: 80%
- LGD: $40M × 0.2 = $8M
- If POD = 2%: EL = $160,000

Unsecured bond:
- Exposure: $100M
- Recovery rate: 35%
- LGD: $100M × 0.65 = $65M
- If POD = 2%: EL = $1,300,000

Difference: $1.14M higher expected loss for unsecured

DeFi Application defi-application

DeFi protocols like TrueFi represent a new frontier in credit risk management by offering uncollateralized lending through on-chain credit scoring and dynamic POD estimation based on wallet transaction history. Unlike traditional lending where credit assessment relies on financial statements and rating agencies (as discussed in corporate credit analysis), DeFi credit evaluation draws on observable on-chain behaviors: repayment history, liquidation events, protocol usage patterns, and wallet age. TrueFi’s SAFU fund functions as a first-loss tranche, directly reducing effective LGD for senior lenders — a structural credit enhancement mechanism analogous to the subordination techniques used in securitization. The challenge remains limited historical data and the pseudonymous nature of DeFi borrowers.

LO2: Describe the uses of ratings from credit rating agencies and their limitations

Core Concept

  • Definition: Credit ratings are forward-looking assessments of an issuer’s creditworthiness, providing standardized risk measures across securities and enabling regulatory compliance and investment policy implementation.
  • Why it matters: Ratings influence bond pricing, portfolio construction, regulatory capital requirements, and market access. However, over-reliance on ratings without independent analysis can lead to significant losses.
  • Key components:
    • Rating scales (investment grade vs high yield)
    • Rating methodologies and criteria
    • Split ratings and rating watches
    • Limitations and biases

Formulas & Calculations

  • Rating Migration Probabilities:

    One-year transition matrix example:
From BBB to:
- AAA: 0.00%
- AA: 0.02%
- A: 4.10%
- BBB: 89.45% (remain)
- BB: 5.30%
- B: 0.88%
- CCC: 0.12%
- Default: 0.13%

  • Rating-Based Spread Calculation:

    Spread = Base Rate + Rating Spread + Sector Adjustment

Example:
BBB Industrial: 120 bps base + 30 bps sector = 150 bps
BB Industrial: 350 bps base + 50 bps sector = 400 bps

  • Fallen Angel Impact:

    Price Impact = -Duration × Spread Widening + Forced Selling

Example: BBB to BB downgrade
Spread widening: 250 bps
Duration: 6 years
Base impact: -15%
Forced selling: -3% additional
Total: -18%

Practical Examples

  • Rating Scale Comparison:

    Investment Grade:
Moody's: Aaa, Aa1-Aa3, A1-A3, Baa1-Baa3
S&P/Fitch: AAA, AA+/AA/AA-, A+/A/A-, BBB+/BBB/BBB-

High Yield:
Moody's: Ba1-Ba3, B1-B3, Caa1-Caa3, Ca, C
S&P/Fitch: BB+/BB/BB-, B+/B/B-, CCC+/CCC/CCC-, CC, C, D

Regulatory threshold: Baa3/BBB- (lowest investment grade)

  • Split Rating Example:

    Corporate issuer ratings:
- Moody's: Baa3 (lowest IG)
- S&P: BB+ (highest HY)
- Fitch: BBB- (lowest IG)

Market treatment: "Crossover credit"
Pricing: Between IG and HY spreads
Index inclusion: Depends on index provider rules

DeFi Application

  • Protocol example: Credora decentralized credit ratings
  • Implementation: On-chain reputation scoring, DAO-governed rating criteria
  • Advantages/Challenges:
    • Advantages: Real-time updates, transparent methodology, no issuer-pays conflict
    • Challenges: Limited track record, gaming risks, oracle dependencies
    • Example: Goldfinch uses “Backers” as decentralized credit analysts for emerging markets

LO3: Describe macroeconomic, market, and issuer-specific factors that influence the level and volatility of yield spreads

Core Concept

  • Definition: Yield spreads are determined by the interaction of macroeconomic conditions (credit cycle), market factors (liquidity and supply/demand), and issuer-specific characteristics (leverage and profitability).
  • Why it matters: Understanding spread drivers enables tactical portfolio positioning, risk management, and relative value identification across credit markets.
  • Key components:
    • Credit cycle dynamics
    • Flight-to-quality episodes
    • Market liquidity effects
    • Fundamental credit metrics

Formulas & Calculations

  • Spread Decomposition:

    Total Yield Spread = Credit Spread + Liquidity Spread

Credit Spread = Default Risk Premium + Downgrade Risk Premium
Liquidity Spread = Bid-Ask Spread + Market Depth Premium

  • Credit Metrics (Corporate):

    Key Ratios:
- EBIT Margin = EBIT / Revenue
- Interest Coverage = EBIT / Interest Expense
- Leverage = Debt / EBITDA
- FCF to Debt = Free Cash Flow / Total Debt

  • Spread Volatility Drivers:

    Spread Volatility = f(Credit Quality, Duration, Liquidity, Sector)

Empirical relationship:
HY Spread Vol ≈ 2-3× IG Spread Vol
Long Duration Vol ≈ 1.5× Short Duration Vol

  • HP 12C Steps (Coverage Ratio):

    Example: EBIT = $500M, Interest = $75M

500 [ENTER]                (EBIT)
75 [÷]                     (Divide by interest)
Result: 6.67               (Coverage ratio)

Practical Examples

  • Credit Cycle Impact:

    Economic Phase → Spread Behavior:

Recovery:
- IG spreads: 100 → 80 bps
- HY spreads: 500 → 350 bps
- Relative tightening: HY outperforms

Late Cycle:
- IG spreads: 80 → 100 bps
- HY spreads: 350 → 450 bps
- Relative widening: IG outperforms

Recession:
- IG spreads: 100 → 200 bps
- HY spreads: 450 → 1000 bps
- Flight-to-quality: Massive HY underperformance

  • Issuer-Specific Example:

    Company A (improving credit):
- Leverage: 4.0× → 2.5×
- Coverage: 3.0× → 5.0×
- FCF/Debt: 5% → 12%
- Spread: 300 bps → 150 bps

Company B (deteriorating credit):
- Leverage: 3.0× → 5.5×
- Coverage: 4.0× → 2.0×
- FCF/Debt: 10% → 2%
- Spread: 200 bps → 500 bps

DeFi Application

  • Protocol example: Maker DAO stability fees
  • Implementation: Dynamic spread adjustment based on collateral quality and system parameters
  • Advantages/Challenges:
    • Advantages: Algorithmic spread setting, transparent factors, real-time adjustment
    • Challenges: Limited macro data integration, governance attack risks
    • Example: DAI savings rate spreads adjust based on protocol surplus and peg stability

Core Concepts Summary (80/20 Principle)

Essential Knowledge (80% of value)

  1. EL = POD × LGD: Foundation of credit risk measurement
  2. Credit spreads compensate for expected loss plus risk premiums
  3. Ratings provide standardization but have significant limitations
  4. Spreads driven by macro (cycle), market (liquidity), and micro (issuer) factors

Advanced Concepts (20% remaining)

  1. Credit migration risk and transition matrices
  2. Structural vs reduced-form credit models
  3. CDS-bond basis and synthetic credit
  4. Factor models for spread changes

Comprehensive Formula Sheet formula

Primary Formulas

1. Expected Loss:
   EL = POD × LGD
   where LGD = EE × (1 - RR)

2. Credit Spread Approximation:
   Spread ≈ POD × LGD + Risk Premium

3. Price Impact (Small Changes):
   %ΔPV = -ModDur × ΔSpread

4. Price Impact (Large Changes):
   %ΔPV = -ModDur × ΔSpread + ½ × Convexity × (ΔSpread)²

5. Recovery Rate:
   RR = Recovered Amount / Claim Amount

6. Interest Coverage:
   Coverage = EBIT / Interest Expense

7. Leverage Ratio:
   Leverage = Debt / EBITDA

8. Free Cash Flow to Debt:
   FCF/Debt = (CFO - CapEx) / Total Debt

Variable Definitions

  • POD: Probability of Default (annualized)
  • LGD: Loss Given Default (dollar or percentage)
  • EE: Expected Exposure at default
  • RR: Recovery Rate (percentage)
  • EBIT: Earnings Before Interest and Taxes
  • EBITDA: EBIT + Depreciation + Amortization
  • CFO: Cash Flow from Operations
  • CapEx: Capital Expenditures

HP 12C Calculator Sequences

Expected Loss Calculation

Given: POD = 2.5%, Exposure = $5M, Recovery = 35%

0.025 [ENTER]              (POD)
5000000 [×]                (× Exposure)
0.35 [ENTER] 1 [SWAP] [-]  (1 - RR = 0.65)
[×]                        (× Loss Severity)
Result: 81,250             (EL = $81,250)

Credit Spread from Components

Given: POD = 1.5%, LGD = 70%

0.015 [ENTER]              (POD)
0.70 [×]                   (× LGD)
10000 [×]                  (Convert to bps)
Result: 105                (Spread ≈ 105 bps)

Coverage Ratio Analysis

Given: EBITDA = $800M, D&A = $100M, Interest = $120M

800 [ENTER] 100 [-]        (EBIT = 700)
120 [÷]                    (÷ Interest)
Result: 5.83               (Coverage ratio)

Leverage Calculation

Given: Debt = $2.4B, EBITDA = $600M

2400 [ENTER]               (Debt in millions)
600 [÷]                    (÷ EBITDA)
Result: 4.0                (4.0× leveraged)

Practice Problems

Basic Level

  1. Expected Loss: Bond with POD = 1%, Recovery = 40%. Calculate LGD percentage and expected loss.

    • Answer: LGD = 60%, EL = 0.6%

  2. Credit Spread: If EL = 50 bps and risk premium = 100 bps, what is the fair credit spread?

    • Answer: 150 bps minimum

  3. Recovery Rate: Default on 45M recovery. Calculate recovery rate and loss severity.

    • Answer: RR = 45%, Loss Severity = 55%

Intermediate Level

  1. Secured vs Unsecured:

    $50M loan, POD = 3%
Secured: Collateral = $30M, Recovery on unsecured portion = 50%
Unsecured: Recovery = 30%

Calculate EL for each:
Secured: EL = 0.03 × $20M × 0.5 = $300,000
Unsecured: EL = 0.03 × $50M × 0.7 = $1,050,000
Difference: $750,000

  2. Rating Migration Impact:

    A-rated bond downgrades to BBB
Duration = 7 years
Spread widening = 40 bps

Price impact = -7 × 0.004 = -2.8%

  3. Credit Metrics Analysis:

    Company financials:
Revenue: $5B, EBIT: $750M, Interest: $150M
Debt: $3B, EBITDA: $900M

EBIT Margin = 15%
Coverage = 5.0×
Leverage = 3.33×

Credit assessment: Moderate risk, BBB range

Advanced Level

  1. Portfolio Expected Loss:

    Three-bond portfolio:
Bond A: $30M, POD = 0.5%, LGD = 40%
Bond B: $50M, POD = 1.5%, LGD = 60%
Bond C: $20M, POD = 5%, LGD = 75%

Portfolio EL = $60,000 + $450,000 + $750,000 = $1,260,000
Portfolio EL % = 1.26%

  2. Spread Decomposition:

    Corporate bond trading at 250 bps over Treasuries
Estimated POD = 1.2%, LGD = 65%
Bid-ask spread = 0.5%

Expected loss = 78 bps
Liquidity premium = 50 bps
Risk premium = 122 bps

Is bond fairly priced?

  3. DeFi Protocol Credit Risk:

    Lending pool: $100M TVL
Historical defaults: 2% annually
Average recovery: 20% (liquidations)
Protocol insurance: Covers first $1M losses

User EL = 0.02 × $100M × 0.8 - $1M = $600,000
Required spread above risk-free: 60 bps minimum

DeFi Applications & Real-World Examples

Undercollateralized Lending Protocols

Maple Finance:

  • Institutional borrowers with off-chain credit assessment
  • Pool delegates perform due diligence (similar to rating agencies)
  • Default coverage: Combination of pool cover and staking incentives
  • Historical POD: <1% for institutional pools
  • Recovery mechanisms: Legal enforcement + on-chain reputation

Credit Delegation

Aave Credit Delegation:

Process:
1. Depositor approves credit line to borrower
2. Borrower draws uncollateralized up to limit
3. Interest split between depositor and protocol

Risk Assessment:
- POD based on borrower's on-chain history
- LGD = 100% (no collateral)
- Required premium = POD × 100% + risk compensation

Decentralized Credit Scoring

ARCx Credit:

  • DeFi Credit Score (0-999) based on:
    • Repayment history
    • Liquidation events
    • Protocol usage patterns
    • Wallet age and activity
  • Higher scores → Lower collateral requirements
  • Dynamic POD estimation from score

Revenue-Based Financing

Goldfinch Protocol:

Emerging market lending:
- Senior Pool (lower risk): POD ≈ 5%, Target return = 8%
- Backer Pools (higher risk): POD ≈ 10%, Target return = 15%
- First-loss capital: Backers take initial 20% losses
- Effective Senior Pool LGD = 0% up to 20% defaults

Common Pitfalls & Exam Tips

Calculation Errors to Avoid

  1. Confusing POD with expected loss (EL = POD × LGD, not just POD)
  2. Wrong recovery rate application (LGD = EE × (1-RR), not EE × RR)
  3. Mixing basis points and decimals (100 bps = 0.01 = 1%)
  4. Forgetting duration in spread impact (Must multiply by duration)

Conceptual Traps

  1. Ratings are not probabilities: AAA doesn’t mean 0% POD
  2. Recovery rates vary by seniority: Secured > Senior Unsecured > Subordinated
  3. Credit spread ≠ Expected loss: Includes risk and liquidity premiums
  4. Split ratings common: Don’t assume single rating tells full story

Exam Strategy

  1. Know the formulas cold: EL = POD × LGD is fundamental
  2. Understand rating scales: IG/HY boundary is Baa3/BBB-
  3. Remember spread drivers: Macro, market, and micro factors
  4. Practice credit metrics: Coverage, leverage ratios are testable

Quick Recognition Patterns

  • “Economic loss from borrower failure” → Credit risk definition
  • “Forward-looking assessment” → Credit rating
  • “Conditional on default” → LGD
  • “Flight-to-quality” → Spreads widen, govts rally

Key Takeaways

Must-Know Concepts

  1. ✅ Credit risk = POD × LGD framework
  2. ✅ Ratings provide standardization but have limitations
  3. ✅ Credit spreads compensate for EL + risk + liquidity
  4. ✅ Macro/market/micro factors drive spread levels
  5. ✅ Recovery rates depend on seniority and collateral

Critical Formulas

  1. ✅ EL = POD × LGD = POD × EE × (1-RR)
  2. ✅ Credit Spread ≈ POD × LGD + Premiums
  3. ✅ %ΔPrice = -Duration × ΔSpread

Practical Applications

  1. ✅ Use multiple rating agencies, not just one
  2. ✅ Monitor credit metrics for early warning signals
  3. ✅ Consider market liquidity in spread analysis
  4. ✅ DeFi credit requires new risk frameworks

Cross-References & Additional Resources

DeFi Protocol Documentation

  • Maple Finance - Institutional undercollateralized lending
  • TrueFi - Uncollateralized lending protocol
  • Goldfinch - Emerging markets credit
  • ARCx - DeFi credit scoring

Advanced Reading

  1. Duffie & Singleton: “Credit Risk” - Academic foundation
  2. Moody’s: “Annual Default Study” - Historical default rates
  3. BIS: “Credit Risk Transfer” - Regulatory perspective
  4. Research: “DeFi Credit Markets” (Aave Governance Forum)

Online Tools & Calculators

Review Checklist

Conceptual Understanding

  • Define credit risk and its components
  • Explain rating agency roles and limitations
  • Identify spread drivers at all levels
  • Differentiate secured vs unsecured risk

Calculation Proficiency

  • Calculate expected loss from components
  • Estimate credit spreads from fundamentals
  • Compute key credit ratios
  • Apply duration to spread changes

Application Skills

  • Analyze credit quality from financials
  • Assess relative value across credits
  • Identify credit cycle positioning
  • Apply concepts to DeFi protocols

Exam Readiness

  • Master all formulas and definitions
  • Complete practice problems accurately
  • Understand rating scale nuances
  • Connect credit risk to other topics

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