FRM Exam Part II · Credit Derivatives

CDX and iTraxx Indices and Multi-Name Credit Products

Updated 11 October 2026 · Fact-checked

A CDS index such as CDX or iTraxx is a standardised, equally weighted portfolio of single-name CDS traded as one contract. Its spread sits close to the average of its constituent spreads. A basket swap pays on the first or nth default in a basket. Its value depends mainly on default correlation.

Understand Credit Indices and Multi-Name Products

A single-name CDS protects against default of one reference entity. A CDS index bundles many single-name CDS into one contract. CDX covers North American names (CDX.NA.IG for investment grade, CDX.NA.HY for high yield). iTraxx covers European and Asian names (iTraxx Europe, iTraxx Crossover). Each name has an equal weight, so a 125-name index puts 1/125 of the notional on each name.

Indices are standardised. They have fixed coupons (typically 100 bp for investment grade and 500 bp for high yield or crossover), fixed maturities, and a new series roughly every six months (a roll). Because the coupon is fixed, the market spread usually differs from it. The difference is settled through an upfront payment: upfront ≈ (market spread − coupon) × risky duration × notional. If the market spread is above the coupon, the protection buyer pays upfront.

When a name in the index defaults, that name is settled like a single-name CDS, its weight is removed, and the index carries on with a smaller notional. The index spread is roughly a weighted average of constituent spreads. The gap between the index spread and the average of the single-name spreads is the index basis. It reflects liquidity, supply and demand, and the contract's standard terms. A negative basis means the index trades tighter than its names.

A basket default swap covers a small basket, often 5 to 10 names. In a first-to-default (FTD) swap, the seller pays on the first default only, then the contract ends. In an nth-to-default swap, the seller pays only on the nth default. The driver is default correlation. If defaults are independent, an FTD is very likely to be triggered. If they are perfectly correlated, one default means all default, so an FTD is no riskier than the riskiest single name.

This gives the key bounds. The FTD spread is at least the largest single-name spread and at most the sum of the single-name spreads. Higher correlation lowers the FTD spread. For a high-order nth-to-default, higher correlation raises the spread, because many defaults together become more likely. This is the same logic as the equity and senior tranches of a CDO.

Key formulas to remember

Credit triangle: spread ≈ λ × (1 − R); λ is the annual hazard rate and R the recovery rate. Use it as an approximation for flat curves.
Index upfront payment: Upfront ≈ (market spread − fixed coupon) × risky duration × notional; Positive means the protection buyer pays the seller. Risky duration is also called RPV01.
Loss per name in an equal-weighted index: Payout = (Notional ÷ N) × (1 − R); N is the number of names in the original index. After the default, notional falls by Notional ÷ N.
Index basis: Basis = index spread − weighted average of constituent spreads; Typically small. It is driven by liquidity and supply and demand.
FTD spread bounds: max(si) ≤ FTD spread ≤ Σ si; The lower bound applies at perfect correlation. The upper bound applies at zero correlation: with independence and flat hazard rates, the credit-triangle FTD spread equals the sum of the spreads. In practice it is at or slightly below the sum once discounting and payment timing are considered.
Correlation effect on nth-to-default: FTD spread falls as correlation rises; high-n spread rises as correlation rises; The effect for middle n depends on the portfolio. Do not assume a single direction.

How to solve Credit Indices and Multi-Name Products questions

Use this order for almost any question on indices or baskets.

1Identify the product: single-name CDS, index, FTD or nth-to-default.
2For an index, note the number of names, the fixed coupon, the market spread, the risky duration and the recovery rate.
3For an upfront question, compute (market spread − coupon) × risky duration × notional. Check the sign: spread above coupon means the buyer pays.
4For a default event, compute the defaulted name's notional as Notional ÷ N, then the payout with (1 − R), then the new notional.
5For a basket, apply the bounds: largest single spread at the bottom, sum of spreads at the top.
6Decide the correlation direction. Rising correlation lowers the FTD spread and raises the spread on high-order nth-to-default.
7State the interpretation in one sentence, such as who gains and why.

Quickest way: Bounds and direction check

When to use it: Use for multiple-choice questions on baskets and index comparisons when you do not need a full calculation.

Eliminate any FTD spread below the largest single-name spread or above the sum of the spreads.
Zero correlation points to the sum. Perfect correlation points to the maximum.
For a high-n nth-to-default, rising correlation means a higher spread.
For an index upfront, multiply the spread gap by risky duration, then by notional. Check the sign last.
For an index default, divide notional by N first, then multiply by (1 − R).

Common mistakes in Credit Indices and Multi-Name Products

Saying higher correlation raises every basket spread.
Students remember that correlation increases risk and apply it to all products.
Fix: For FTD, higher correlation lowers the spread because defaults cluster. For high-n nth-to-default, it raises the spread.
Treating the index as a single entity that ends after one default.
Confusing the index with an FTD basket.
Fix: An index continues after a default. Only that name's weight is removed and settled. An FTD ends after the first default.
Getting the sign of the upfront payment wrong.
Students forget that the fixed coupon differs from the market spread.
Fix: Spread above coupon means the protection buyer pays upfront. Spread below coupon means the buyer receives it.
Applying the full notional loss to a defaulted index name.
Forgetting equal weighting.
Fix: Payout = (Notional ÷ N) × (1 − R).
Assuming the index spread must equal the average of the single-name spreads.
Students read 'related to' as 'equal to'.
Fix: The two are close but not equal. The difference is the index basis, driven by liquidity and market conditions.

Worked examples

Example 1

You buy protection on USD 50 million of a CDX IG index with a fixed coupon of 100 bp. The market spread is 130 bp, risky duration is 4.5, N = 125 and recovery is 40%. (a) What upfront payment do you make? (b) One name defaults. What is the payout and the new notional?

Show the solution

(a) Spread gap = 130 − 100 = 30 bp = 0.30% = 0.0030.
Upfront rate = 0.0030 × 4.5 = 0.0135 = 1.35%.
Upfront = 1.35% × USD 50,000,000 = USD 675,000. The market spread is above the coupon, so you, as buyer, pay it.
(b) Notional on the defaulted name = 50,000,000 ÷ 125 = USD 400,000.
Payout = 400,000 × (1 − 0.40) = USD 240,000.
New index notional = 50,000,000 − 400,000 = USD 49,600,000.

Answer: (a) You pay USD 675,000 upfront. (b) You receive USD 240,000 and the index notional falls to USD 49,600,000.

Example 2

A first-to-default swap covers 5 independent reference entities. Each has a 5-year CDS spread of 100 bp and recovery of 40%. Using the credit triangle and flat hazard rates, estimate the FTD spread if defaults are independent. Compare it with the case of perfect correlation.

Show the solution

Single-name hazard rate: λ = spread ÷ (1 − R) = 0.0100 ÷ 0.60 = 1.667% per year.
With independence and flat hazard rates, the first-default intensity is exactly the sum of the hazard rates: 5 × 1.667% = 8.333%.
FTD spread = 8.333% × (1 − 0.40) = 5.00% = 500 bp, using the credit triangle.
This equals the sum of the single-name spreads: 5 × 100 bp = 500 bp. So under independence and flat hazard rates the credit-triangle FTD spread sits exactly at the upper bound. In practice, once discounting and payment timing are considered, the FTD spread is at or slightly below the sum.
With perfect correlation, all names default together, so the first default occurs at the single-name rate and the FTD spread = 100 bp, the lower bound.

Answer: 500 bp under independence, equal to the sum of the single-name spreads (in practice at or slightly below the sum once discounting and timing are included), versus about 100 bp under perfect correlation. Rising correlation lowers the FTD spread.

Exam tips

Memorise the FTD bounds: between the largest single spread and the sum of spreads.
Be clear on direction: correlation lowers FTD spreads and raises spreads on senior or high-n exposure.
For index questions, always check the sign of the upfront payment and use Notional ÷ N for defaults.
Know the difference between the index (continues after default, standardised) and a single-name CDS (bespoke terms, one entity).
Expect interpretation questions on index basis. Link it to liquidity and supply and demand, not to arbitrage that is always free.

Practice questions from Credit Derivatives

Credit Indices and Multi-Name Products: frequently asked questions

What is the difference between a CDS index and a single-name CDS?

A single-name CDS covers one reference entity and can have bespoke terms. A CDS index covers many names with equal weights and has standardised coupon, maturity and roll dates. The index continues after a default, with a reduced notional.

Why does an FTD swap spread fall as default correlation rises?

The seller pays only on the first default. When defaults cluster, the chance that at least one name defaults gets closer to the chance that a single name defaults. So the FTD spread moves toward the largest single-name spread.

How does the index spread relate to the constituent spreads?

The index spread is close to a weighted average of the constituent spreads. The difference is the index basis, which is shaped by liquidity, supply and demand, and standardised contract terms.

What happens to an nth-to-default swap when correlation rises?

For high n, such as the last-to-default, the spread rises because several names defaulting together becomes more likely. For middle n the effect depends on the portfolio, so avoid a blanket rule.