What is the Incremental Risk Charge (IRC), and how does it capture default and migration risk in the trading book?

Question

AcadiFi · Accepted Answer

The **Incremental Risk Charge (IRC)** was introduced by Basel 2.5 to capture **default and credit migration risk** for credit-sensitive positions in the trading book that VaR's 10-day horizon could not adequately measure.

**Why IRC Was Needed**

Standard VaR with a 10-day horizon captures spread volatility but misses:
- **Default risk** — the jump-to-zero (or recovery value) when an issuer defaults
- **Migration risk** — the P&L impact from rating downgrades/upgrades over longer horizons
- These events are rare but devastating — the 2007-2008 crisis showed that credit positions in trading books suffered losses far beyond VaR estimates

**IRC Parameters**

| Parameter | Value | Rationale |
|---|---|---|
| Confidence level | 99.9% | Consistent with banking book capital |
| Horizon | 1 year | Full credit cycle horizon |
| Assumption | **Constant level of risk** | Positions that mature or default are replaced with equivalent risk |
| Covered positions | Bonds, CDS, CLO tranches, loan trading | Credit-sensitive trading book positions |

**Constant Level of Risk**

This is the most confusing aspect. The IRC assumes the bank maintains a constant risk profile over the 1-year horizon by rebalancing every **liquidity horizon** period (typically 3 months for IG, 1 month for HY). If a bond defaults, the model assumes it is replaced with a new bond of similar quality.

This differs from a "buy and hold" assumption and tends to produce higher capital charges because the portfolio is repeatedly exposed to default risk.

```mermaid
flowchart LR
    A["Q1: Hold portfolio"] --> B["Q2: Rebalance — replace any defaults/maturities"]
    B --> C["Q3: Rebalance again"]
    C --> D["Q4: Rebalance again"]
    D --> E["Year-end: Measure cumulative loss at 99.9%"]
    style A fill:#3b82f6,color:#fff
    style E fill:#ef4444,color:#fff
```

**Worked Example**

Blackridge Capital's credit trading desk holds:
- $500M notional in IG corporate bonds (average PD = 0.3%, average LGD = 40%)
- $200M notional in HY corporate bonds (average PD = 3.5%, average LGD = 55%)
- $150M notional in CDS protection sold (average PD = 2.0%, average LGD = 60%)

The IRC model (Monte Carlo simulation with correlated defaults and migrations) produces:

| Percentile | Annual P&L |
|---|---|
| Mean | -$5.2M (expected loss) |
| 99.0% | -$48M |
| **99.9%** | **-$89M** |

**IRC = $89M - $5.2M = $83.8M** (unexpected loss at 99.9%)

**IRC Under FRTB**

Under FRTB, the IRC is replaced by the **Default Risk Charge (DRC)**, which has a similar 99.9%/1-year framework but:
- Uses a buy-and-hold assumption (no constant level of risk)
- Covers only default risk (migration risk is captured by the ES component's longer liquidity horizons)
- Can be netted across long and short positions more explicitly

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What is the Incremental Risk Charge (IRC), and how does it capture default and migration risk in the trading book?

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