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| Reference overview of Collateralized Debt Obligation (CDO) mechanics, tranche structure, mark-to-market valuation, spread pricing, and risky duration — the foundational concepts for all CDO trading strategies. |
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CDO Generalities: Collateralized Debt Obligations
Section: 11.1 | Asset Class: Structured Assets | Type: Reference / Foundational
Overview
A CDO is an asset-backed security consisting of a basket of assets (bonds, loans, credit default swaps, etc.) divided into tranches with different credit ratings and interest rates. Each tranche has an attachment point a and a detachment point d. When cumulative portfolio losses exceed a, the tranche begins to lose value; when losses exceed d, the tranche is completely wiped out. Understanding CDO valuation is the foundation for all CDO carry and curve trading strategies (Sections 11.2–11.7).
Construction / Mechanics
Tranche Structure
- Attachment point a: portfolio loss level at which the tranche begins to absorb losses
- Detachment point d: portfolio loss level at which the tranche is fully wiped out
- Example: a 3–8% tranche loses value when portfolio losses exceed 3% and is fully wiped at 8%
- Typical tranche hierarchy (decreasing default risk, decreasing premium rate):
- Equity: 0–3%
- Junior mezzanine: 3–7%
- Senior mezzanine: 7–10%
- Senior: 10–15%
- Super senior: 15–30%
Buyer/Seller Roles
- Buyer (long tranche, protection seller): receives periodic premium payments; obligated to cover defaults up to the tranche size in the event of a default.
- Seller (short tranche, protection buyer): makes periodic premium payments; receives a payment in the event of a default.
Synthetic CDOs
Synthetic CDOs are constructed using credit default swaps (CDS) on a reference pool. Exchange-traded single-tranche CDOs reference CDS indexes such as CDX or iTraxx.
Expected Loss Computation
Let t_i (i = 1,...,n) be the periodic premium payment dates. Let H(t) be the set of possible default scenarios ℓ_α (α = 1,...,K) with probabilities p_α(t). The expected loss is:
L(t) = Σ p_α(t) × max(min(ℓ_α, L_d) - L_a, 0) (481)
where L_a = a × M_CDO and L_d = d × M_CDO, and M_CDO is the CDO notional in dollars.
Mark-to-Market (MTM) Valuation
The MTM value M of the tranche (from the long investor's perspective) is:
M = P - C (482)
The premium leg (what the long investor receives):
P = S × Σ D_i Δ_i [M_tr - L(t_i)] (483)
The contingent (default) leg (what the long investor pays):
C = Σ D_i [L(t_i) - L(t_{i-1})] (484)
where:
- S = spread (annual premium rate)
- D_i = risk-free discount factor for payment date t_i
- Δ_i = t_i - t_{i-1} (time between payment dates)
- M_tr = L_d - L_a (tranche notional)
- L(t_0) = 0
Fair Spread and Risky Duration
Setting M = 0 fixes the fair spread S = S*. The risky duration D of the tranche is the first derivative of M w.r.t. the spread:
M(S) = (S - S*) × Σ D_i Δ_i [M_tr - L(t_i)] (485)
D = ∂M/∂S = Σ D_i Δ_i [M_tr - L(t_i)] (486)
The risky duration D_ix can also be defined analogously for a CDS index.
Return Profile
The long tranche position earns carry (spread income) when no defaults occur. The contingent leg represents the tail-risk cost: large losses materialise only when portfolio losses exceed the attachment point. Junior tranches have higher spreads but greater default exposure; senior tranches have lower spreads but protection from defaults up to the attachment point.
Key Parameters / Signals
| Parameter | Description |
|---|---|
| a, d | Attachment and detachment points (%) |
| M_CDO | CDO notional in dollars |
| S | Tranche spread (annual premium rate) |
| D (risky duration) | Sensitivity of MTM to spread change; Eq. (486) |
| L(t) | Expected loss at time t; Eq. (481) |
Notes
- The expected loss L(t) and the probabilities p_α(t) are model-dependent; different models (Gaussian copula, etc.) give different valuations.
- Risky duration is the primary hedging metric for CDO tranche positions (used in Sections 11.2–11.5).
- CDS indexes (CDX, iTraxx) provide liquid reference points for both outright hedging and relative-value trades.
- Convexity of tranche value w.r.t. spread means that hedging ratios change as spreads move; dynamic rehedging is required.