What is the Default Risk Charge under FRTB and how is it calculated?

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AcadiFi · Accepted Answer

The Default Risk Charge (DRC) under FRTB captures **jump-to-default** (JTD) risk — the sudden loss when an issuer defaults. This is treated separately from credit spread risk (in the SbM) because spread movements and actual defaults are fundamentally different events.

**Why Separate from SbM Credit Spread Risk?**

Credit spread risk in the SbM covers gradual spread widening/tightening. But default is a discrete, catastrophic event where:
- Recovery is typically only 20–60% of face value
- The loss is realized immediately, not gradually
- Hedges (like CDS) pay discrete amounts at default

The SbM's sensitivity-based approach (delta, vega) doesn't capture this binary event well.

**DRC Calculation Steps**

**Step 1: Compute Jump-to-Default (JTD) Amounts**

For long positions:
JTD_long = Notional x LGD = Notional x (1 − Recovery Rate)

For short positions (e.g., bought CDS protection):
JTD_short = Notional x LGD (as a negative value)

**Example:**
Valterra Capital holds:
- Long $30M Issuer X bonds (rated BBB, recovery 40%): JTD = $30M x 0.60 = **+$18M**
- Short $20M CDS protection on Issuer X (recovery 40%): JTD = $20M x 0.60 = **−$12M**
- Long $15M Issuer Y bonds (rated BB, recovery 30%): JTD = $15M x 0.70 = **+$10.5M**

**Step 2: Net JTD Within Obligors**

For Issuer X: Net JTD = $18M − $12M = **+$6M**
For Issuer Y: Net JTD = **+$10.5M** (no offset)

**Step 3: Apply Risk Weights by Rating**

FRTB prescribes risk weights based on credit quality:

| Rating | Risk Weight |
|--------|------------|
| AAA | 0.5% |
| AA | 2.0% |
| A | 3.0% |
| BBB | 6.0% |
| BB | 15.0% |
| B | 30.0% |
| CCC | 50.0% |
| Unrated | 15.0% |
| Defaulted | 100.0% |

**Step 4: Compute Weighted JTD**

Issuer X (BBB): $6M x 6.0% = **$360,000**
Issuer Y (BB): $10.5M x 15.0% = **$1,575,000**

**Step 5: Aggregate Using Bucket Correlations**

Issuers are grouped into buckets (by sector/region), and within-bucket and across-bucket correlations are applied — similar to SbM aggregation.

Simplified total DRC ≈ sqrt($360K^2 + $1,575K^2 + 2 x rho x $360K x $1,575K)

With rho = 0.5: DRC ≈ sqrt($129,600 + $2,481,056 + $567,000) ≈ sqrt($3,177,656) ≈ **$1,783,000**

**Key Points:**
- Netting is allowed only for the **same obligor** (long bond vs. short CDS on the same name)
- Cross-obligor hedging reduces capital through correlation, not through direct netting
- The DRC replaces the old 'Incremental Risk Charge' from Basel 2.5

**Exam Tip:** Remember that JTD = Notional x LGD (not PD x LGD x EAD, which is expected loss). The DRC is about loss *given* default, not expected loss.

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What is the Default Risk Charge under FRTB and how is it calculated?

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