Module 29
Credit indices & tranches
A single-name CDS insures one company. A credit index insures a whole market in one trade. The two big families are CDX in North America — IG with 125 investment-grade names, HY with 100 high-yield names — and iTraxx in Europe. Each is an equal-weighted basket of single-name CDS, and a fresh series rolls every six months with an updated name list; liquidity concentrates in the on-the-run series. Together they are the liquid macro hedge of credit.
What they're used for:
- Hedging — protect a whole bond or loan book in one trade instead of shorting names one by one.
- Macro views — buy or sell credit as an asset class, the way an equity trader trades the S&P.
- Relative value — index vs its single names, or index vs cash bonds. The CDS-cash basis — the index or CDS spread against the cash bond's Z-spread — is a classic RV trade and a barometer of funding and liquidity stress: when balance sheets are scarce, cash cheapens against synthetics and the basis blows out.
Then it gets structural. Index tranches — CDX 0–3%, 3–7%, and so on — are a synthetic securitization of the index: each tranche absorbs the index's losses between its attachment and detachment points, and the equity tranche takes the first loss. The price of a tranche depends on something no single-name trade cares about: default correlation. If defaults arrive independently, a few losses are near-certain and the equity tranche is expensive while seniors are bulletproof. If defaults cluster— high correlation — the loss distribution grows a fat tail that reaches the senior tranches, while equity's expected loss profile is (relatively) spared: it was likely to be hit anyway. That correlation parameter is exactly what blew up the “correlation trade” in 2008. Options on CDX — payer and receiver swaptions — complete the toolkit: that's credit vol in one line.
On a risk platform, an index book is measured the same way a credit desk is: CS01 per name and at index level, jump-to-default per name, curve risk across the maturities, recovery risk, counterparty and wrong-way risk — buying protection from a seller whose health is correlated with the reference, the AIG lesson — and basis risk between the hedge and the position it protects.
Run defaults through the capital structure below and watch the losses climb.
🎛 Index tranche loss lab
Index loss
2.4%
of index notional
0–3% loss
80%
of tranche notional
Defaults to first loss
1
before 0–3% is hit
Capital structure (0–20% shown)
loss eats from the left ⟶
5 defaults at 40% recovery → 2.4% index loss. 0–3% at 80% loss · 3–7%, 7–10%, 10–15%, 15–100% untouched
Deterministic loss waterfall: index loss = defaults / 125 × (1 − recovery), and each tranche absorbs losses between its attachment and detachment points. A real tranche pricer works with the whole distribution of losses — which is where default correlation enters — not a single default count. Educational tool — not investment advice.
How tranche losses are computed
Each name in a 125-name index is 1/125 = 0.8% of the notional, and a default loses that slice times (1 − recovery). A tranche with attachment A and detachment D absorbs whatever part of the index loss falls between those two points:
index loss = defaults / 125 × (1 − recovery) tranche loss = clamp( (index loss − A) / (D − A), 0, 1 ) × tranche notional
Worked example — 5 defaults at 40% recovery: index loss = 5/125 × 0.60 = 2.4%. The 0–3% equity tranche has lost 2.4/3 = 80%of its notional; the 3–7% mezzanine hasn't lost a cent yet. Two more defaults push the index loss to 3.36% — equity is wiped and the mezzanine starts eating losses at default number seven.
The lab is deliberately deterministic: you choose the default count. A real tranche pricer integrates over the whole probability distribution of that count — and the shape of that distribution is set by default correlation, which is why correlation, not spread, is the quoted parameter of the tranche market.
Things to try
- • With recovery at 40%, drag defaults up one at a time — equity (0–3%) starts losing at the first default and is wiped by the seventh.
- • Select the 3–7% tranche and check “defaults to first loss” — 7 at 40% recovery. Now drop recovery to 0% and watch that cushion shrink to 4.
- • Push defaults to 40 with recovery 0% — a 32% index loss reaches the super senior. That's the fat-tail, high-correlation scenario that made “safe” seniors dangerous in 2008.
- • Raise the recovery rate at a fixed default count — every tranche's loss falls. Recovery risk is a real risk line, not a footnote.