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CFA® Level II · Fixed Income · free lesson
Credit Analysis Models
Credit models turn three judgements, how much is at risk, how likely default is and how much would be recovered, into a price and a spread. This module builds the credit valuation adjustment for a risky bond step by step, shows how rating migration lowers expected returns, compares structural and reduced-form models, and explains the term structure of credit spreads and why securitised debt needs a different analysis from corporate debt. Level II item sets typically hand you a partly completed CVA table and ask you to finish it, so accuracy at each step is the priority.
What you will learn
1. Explain expected exposure, recovery, loss given default, probability of default and the credit valuation adjustment, and build a CVA table for a risky bond.
- Expected exposure at a date is the default-free value of the remaining cash flows at that date, including the coupon then due.
- LGD = exposure x (1 - recovery rate); expected loss = LGD x unconditional probability of default for that period.
- With a constant hazard rate h: POS_t = (1 - h)^t and POD_t = h x (1 - h)^(t-1).
- CVA = sum of expected losses discounted at default-free rates; fair value = VND - CVA.
- Market-implied (risk-neutral) default probabilities exceed actual default rates because they embed risk premiums.
2. Interpret credit scores and credit ratings, and calculate a bond's expected return when its rating may migrate over the holding period.
- Credit scores (individuals, small firms) and ratings (companies, sovereigns, structured debt) are ordinal rankings, not probabilities.
- Issue ratings are notched from the issuer rating for expected recovery, which depends on seniority and collateral.
- Ratings are stable and lag the market; spreads react immediately.
- %ΔP ≈ -ModDur x Δspread + 0.5 x Convexity x (Δspread)^2 for each rating outcome; weight by transition probabilities.
- Expected return ≈ yield + expected price change from migration; downgrade risk makes it lower than the yield.
3. Compare structural and reduced-form credit models, including their assumptions, strengths and weaknesses.
- Structural (Merton): default when assets < face value of debt at maturity; equity = call on assets, risky debt = riskless debt - put on assets.
- Structural strengths: explains why default occurs; links equity and credit. Weaknesses: asset value and volatility unobservable; simplified capital structure.
- Reduced-form: default is an exogenous event with a hazard rate driven by observable variables; recovery as a share of face value.
- Reduced-form strengths: observable inputs, calibrates to market prices, varies with the cycle. Weaknesses: no explanation of default; needs back-testing.
- Higher leverage or asset volatility raises the structural model's default probability and credit spread.
4. Value a risky bond and its credit spread from credit risk parameters, interpret changes in the spread and explain the term structure of credit spreads.
- Credit spread = yield on the risky bond at its fair value - yield on a default-free bond with the same cash flows.
- Approximation: spread ≈ hazard rate x (1 - recovery rate), the expected annual loss.
- Wider spread from higher hazard or lower recovery; price change ≈ -ModDur x Δspread.
- Spreads also reward uncertainty and illiquidity, so they exceed historical expected losses.
- Investment-grade spread curves usually slope upward; distressed curves are flat or inverted as bonds trade on recovery.
5. Contrast the credit analysis of securitised debt with that of corporate debt.
- Corporate credit analysis focuses on a going concern: business, management, leverage, cash flow and covenants.
- Securitised debt is backed by a pool held in a bankruptcy-remote SPE with no management; analyse collateral, structure, servicer and legal setup.
- Granular, homogeneous pools suit statistical analysis; concentrated, heterogeneous pools need loan-by-loan analysis.
- Tranche losses depend on attachment and detachment points; credit enhancement lets senior tranches outrank the pool's average quality.
- Correlated collateral losses create cliff risk for tranches.
Module at a glance
- Expected exposure at a date is the default-free value of the remaining cash flows, including the coupon then due.
- LGD = exposure x (1 - RR); POD_t = h(1 - h)^(t-1); CVA = sum of LGD x POD x DF; fair value = VND - CVA.
- Credit spread = risky yield at fair value - default-free yield; spread ≈ h x (1 - RR).
- Expected return ≈ yield + probability-weighted price change from rating migration, which is usually negative.
- Structural models treat equity as a call on assets and explain default; reduced-form models use an exogenous hazard rate fitted to market data.
- Investment-grade spread curves usually slope upward; distressed curves are flat or inverted.
- Securitised debt is analysed through collateral, structure, servicer and legal setup; granular pools statistically, concentrated pools loan by loan.
This free module has 5 lessons, 16 practice questions with full explanations.