---
description: "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."
tags: [structured-assets, cdo, credit, tranche, abs, cds]
---

# 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.