How is Credit VaR calculated for a bond portfolio and what does it represent?

Question

AcadiFi · Accepted Answer

Credit VaR measures the potential unexpected credit loss on a bond portfolio at a specified confidence level over a given time horizon. It is the difference between the worst-case credit loss at the chosen confidence level and the expected loss.

**Framework:**

> Credit VaR = Unexpected Loss at Confidence Level - Expected Loss

Or equivalently:

> Credit VaR = Loss at Xth Percentile - Expected Loss

```mermaid
graph LR
    A["Loss Distribution"] --> B["Expected Loss
(Mean)"] 
    A --> C["VaR Loss
(99th Percentile)"]
    B -->|"Credit VaR"| C
    style B fill:#f59e0b,color:#000
    style C fill:#ef4444,color:#fff
```

**Step-by-Step Calculation — Alderton Fixed Income Fund (fictional):**

**Portfolio:** $100M corporate bond portfolio

**Step 1: Expected Loss (EL)**
EL = Probability of Default (PD) x Loss Given Default (LGD) x Exposure at Default (EAD)

For the portfolio:
- Average PD = 2.0%
- Average LGD = 40%
- EAD = $100M
- **EL = 0.02 x 0.40 x $100M = $800,000**

**Step 2: Unexpected Loss (UL) at 99% Confidence**
Using a credit loss distribution model (e.g., CreditMetrics or simulated), the 99th percentile loss is determined to be $4.5M.

**Step 3: Credit VaR**
> Credit VaR = $4.5M - $0.8M = **$3.7M**

This means: there is a 1% chance that credit losses will exceed expected losses by more than $3.7M.

**Interpretation:**

| Metric | Amount | Meaning |
|---|---|---|
| Expected Loss | $800K | Average loss provisioned for (priced into spread) |
| Credit VaR (99%) | $3.7M | Capital needed to cover unexpected losses |
| Worst case (99%) | $4.5M | Total loss at 99% confidence |

**Why Credit VaR Is Different from Market VaR:**

1. **Asymmetric distribution:** Credit losses have a fat left tail (many small gains, rare large losses)
2. **Correlation matters:** Default correlation between issuers dramatically affects portfolio Credit VaR
3. **Discrete events:** Defaults are binary, not continuous price movements
4. **Longer horizon:** Typically 1 year for credit (vs. 1-10 days for market VaR)

**Exam Tip:** CFA Level II tests the decomposition of credit loss into expected and unexpected components. Remember that EL is covered by the credit spread (priced in), while Credit VaR represents the capital buffer for unexpected losses.

Practice credit risk quantification in our CFA Level II bank.

How is Credit VaR calculated for a bond portfolio and what does it represent?

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Practice Questions

Metric	Amount	Meaning
Expected Loss	$800K	Average loss provisioned for (priced into spread)
Credit VaR (99%)	$3.7M	Capital needed to cover unexpected losses
Worst case (99%)	$4.5M	Total loss at 99% confidence