CFA Level II Exam · Credit Analysis Models

Credit Spreads, Term Structure and Credit Measures

Updated 7 October 2026 · Fact-checked

A credit spread is the extra yield a risky bond pays over a benchmark bond of similar maturity. It compensates for expected loss (default probability × loss given default) plus a risk premium. To solve questions, split the spread into those two parts, then adjust for maturity, rating changes and market conditions.

Understand Credit Spreads, Term Structure and Credit Measures

A credit spread is the yield on a risky bond minus the yield on a comparable default-free or benchmark bond. It is what investors demand for bearing credit risk. The benchmark is usually a government bond or a swap rate, so read the vignette to see which one is used.

The spread has two main parts. The first is expected loss, which is the average loss you expect from default. It equals the probability of default × loss given default (LGD). LGD = 1 − recovery rate. The second is a credit risk premium, extra yield for bearing uncertainty about defaults, which may occur in bad times when investors most need cash. A spread can also include a liquidity component. In a simple one-period approximation, spread ≈ PD × LGD + risk premium.

The term structure of credit spreads shows spreads across maturities for one issuer or rating. For investment-grade issuers it is usually upward sloping, because uncertainty about the issuer's future grows with time. For weak or distressed issuers it can be flat or inverted. Near-term default risk is high, and an issuer that survives the near term is expected to be healthier. Spreads also tend to widen in recessions and narrow in expansions, and the effect is larger for lower-rated bonds.

Rating migration is the move of an issuer to a different rating. A transition matrix gives the probabilities of moving between ratings over a period. The bond price effect of a migration is roughly: price change ≈ −modified (spread) duration × change in spread. A downgrade widens the spread and cuts the price. An upgrade does the opposite. Because of positive convexity, the price loss from a spread widening is smaller than the price gain from an equal-sized narrowing. In practice, downgrades tend to bring larger spread jumps than upgrades bring spread falls. Investors also care about credit migration risk (also called downgrade risk) and spread risk (the market-wide change in spreads) in addition to default risk.

Key formulas to remember

Expected loss: EL = PD × LGD × exposure; Use the same horizon for PD and the spread. Exposure is the amount at risk at default.
Loss given default: LGD = 1 − recovery rate; If the recovery rate is 40%, LGD is 60%.
Approximate credit spread: Spread ≈ PD × LGD + risk premium; A one-year, annualized approximation. The premium is what remains after expected loss.
Price change from spread change: %ΔPrice ≈ −Duration × ΔSpread + ½ × Convexity × (ΔSpread)²; Use spread duration. Express ΔSpread in decimals, so 25 bps is 0.0025.
Excess return over the benchmark: EXR ≈ (Spread × t) − (ΔSpread × EffSpreadDur) − (t × PD × LGD); Spread is the spread at the start of the period, t is the holding period in years, and PD is the annual default probability. The three terms are spread income, the price effect of the spread change, and expected credit loss. This is an excess return over the benchmark, not a total return.
Survival probability: Survival = 1 − PD; For multiple periods, multiply the conditional survival probabilities.

How to solve Credit Spreads, Term Structure and Credit Measures questions

Use this order for any credit spread, term structure or migration question in an item set.

1Identify the benchmark and the horizon in the vignette. Note whether the spread is quoted in basis points and whether the numbers are annual.
2Pull out PD, recovery rate or LGD, and any spread or duration data from the exhibits.
3Compute expected loss as PD × LGD, converting recovery to LGD first.
4Find the risk premium as the spread minus expected loss. If asked for a spread, add expected loss and premium.
5For migration or spread-change questions, use price change ≈ −spread duration × ΔSpread, adding the convexity term if convexity is given.
6For term structure questions, compare spreads across maturities and link the shape to the issuer's credit quality and the market cycle.
7Check units and the direction of your answer. Wider spread means lower price. Downgrade means wider spread.

Quickest way: Split, then shift

When to use it: Use it when the question gives PD, recovery and a spread, or asks about a rating change and price.

Write LGD = 1 − recovery in the margin.
Compute PD × LGD and compare it with the spread.
The gap is the risk premium, so no further work is needed for most spread-component questions.
For migration, multiply spread duration by the spread change in decimals, flip the sign, and pick the closest option.
Eliminate options with the wrong sign before calculating more.

Common mistakes in Credit Spreads, Term Structure and Credit Measures

Using the recovery rate in place of LGD when computing expected loss.
Vignettes often give recovery, and students multiply PD by it directly.
Fix: Always convert first: LGD = 1 − recovery. Then EL = PD × LGD.
Treating the whole spread as compensation for expected loss.
Students forget the risk premium and liquidity components.
Fix: Expected loss is only part of the spread. The remainder is the risk premium, and sometimes liquidity.
Assuming every credit spread curve slopes upward.
Investment-grade curves are usually upward sloping, and students generalize.
Fix: Distressed or low-rated issuers can show flat or inverted spread curves because near-term default risk dominates.
Getting the sign wrong on price change after a downgrade.
Students focus on the spread rise and forget price moves the opposite way.
Fix: Use −duration × ΔSpread. A spread widening gives a negative price change.
Entering spread changes in basis points into the duration formula.
The quoted change is, say, 50 bps and gets used as 50.
Fix: Convert to decimals: 50 bps = 0.0050 before multiplying.
Mixing horizons, such as a five-year cumulative PD with an annual spread.
Exhibits show several horizons in one table.
Fix: Match the PD horizon to the spread horizon, or annualize before comparing.

Worked examples

Example 1

Vignette: A one-year bond from Corvane Industries yields 5.60%. The one-year government benchmark yields 3.50%. The analyst estimates a one-year probability of default of 2.0% and a recovery rate of 40%. Questions: (1) What is the credit spread? (2) What is the expected loss rate? (3) What is the risk premium?

Show the solution

Credit spread = 5.60% − 3.50% = 2.10%.
LGD = 1 − 0.40 = 0.60.
Expected loss = 2.0% × 0.60 = 1.20%.
Risk premium = spread − expected loss = 2.10% − 1.20% = 0.90%.

Answer: (1) Spread 2.10% (210 bps). (2) Expected loss 1.20%. (3) Risk premium 0.90%.

Example 2

Vignette: Halden Telecom holds a bond with a spread duration of 6.0 and a spread of 180 bps. A rating agency downgrades Halden, and the market spread widens to 240 bps. Convexity can be ignored for questions (1) and (2). Questions: (1) What is the approximate price change? (2) If the bond was priced at 100, what is the new approximate price? (3) With positive convexity included, would a 60 bp spread narrowing produce a gain larger or smaller in size than the loss from a 60 bp widening, all else equal?

Show the solution

ΔSpread = 240 − 180 = 60 bps = 0.0060.
%ΔPrice ≈ −6.0 × 0.0060 = −0.036, or −3.6%.
New price ≈ 100 × (1 − 0.036) = 96.4.
The duration term alone is linear, so a 60 bp narrowing would give +3.6%, equal in size to the loss.
Positive convexity adds ½ × Convexity × (ΔSpread)², which is positive for both widening and narrowing. It reduces the loss from widening and increases the gain from narrowing. So the gain from a 60 bp narrowing is slightly larger than 3.6%.

Answer: (1) About −3.6%. (2) About 96.4. (3) Larger: with convexity included, the gain from a 60 bp narrowing is slightly larger than the 3.6% loss from a 60 bp widening. By the linear duration approximation alone, the sizes are equal.

Exam tips

Read which benchmark the spread is measured against before using any number.
Convert recovery to LGD in your first line of working. Examiners often give recovery.
For term structure questions, link the curve shape to issuer quality: upward for strong issuers, flat or inverted for stressed ones.
Link market conditions to spreads: recessions widen spreads, and low-rated bonds widen more.
Eliminate options with the wrong sign first, then calculate only if two options remain.

Credit Spreads, Term Structure and Credit Measures in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Credit Spreads, Term Structure and Credit Measures: frequently asked questions

How do I calculate a credit spread from default probability and LGD?

Compute expected loss as PD × LGD, where LGD = 1 − recovery rate. That gives the part of the spread that covers expected default losses. Add any risk premium given in the vignette to get the full approximate spread.

What is the difference between expected loss and risk premium in a spread?

Expected loss is the average loss from default, PD × LGD. The risk premium is extra yield for bearing the uncertainty and the chance that defaults cluster in bad times. The spread is roughly the sum of the two.

Why is the credit spread curve sometimes inverted?

Distressed issuers face high near-term default risk. If they survive, their credit quality is expected to improve, so longer-maturity spreads can be lower than short-maturity spreads. Investment-grade issuers usually show an upward slope instead.

How does a rating downgrade affect bond price?

A downgrade usually widens the credit spread. Using spread duration, the price falls by roughly spread duration × the increase in spread. Convexity makes this estimate more accurate for larger moves.