What is Stressed VaR, how is the stress period selected, and how does it enter the market risk capital calculation?

Question

AcadiFi · Accepted Answer

**Stressed VaR (sVaR)** is a VaR estimate calibrated to a continuous 12-month period of significant financial stress relevant to the bank's portfolio. It was introduced by Basel 2.5 in 2009 to address the problem that regular VaR models, calibrated to recent (often benign) data, severely underestimated tail risk during the 2007-2008 crisis.

**Why Regular VaR Failed**

During 2004-2006, financial markets experienced abnormally low volatility. Banks' VaR models, using 1-year lookback windows, produced small risk estimates. When the crisis hit, actual losses dwarfed VaR predictions by 3-5x.

**Stress Period Selection**

Banks must identify a 12-month period that would produce the largest VaR for their **current portfolio composition**. This requires:

1. Testing multiple historical windows (2007-2008, 2000-2001 dot-com, 2011 European debt crisis, 2020 COVID)
2. Re-running the VaR model using each window's volatilities and correlations
3. Selecting the window producing the highest VaR

```mermaid
flowchart TD
    A["Current Portfolio Positions"] --> B["Apply 2008 volatilities & correlations"]
    A --> C["Apply 2020 COVID volatilities"]
    A --> D["Apply 2011 Euro crisis volatilities"]
    B --> E["sVaR = $42M"]
    C --> F["sVaR = $38M"]
    D --> G["sVaR = $29M"]
    E --> H["Select max: 2008 window, sVaR = $42M"]
```

**Worked Example**

Northfield Securities has the following market risk profile:

| Metric | Regular VaR (99%, 10-day) | Stressed VaR (99%, 10-day) |
|---|---|---|
| Interest rate risk | $12M | $31M |
| Equity risk | $8M | $24M |
| FX risk | $5M | $14M |
| Diversified total | $18M | $42M |

**Capital Charge Formula (Basel 2.5)**

**Capital = max(VaR_{t-1}, m_c x VaR_avg) + max(sVaR_{t-1}, m_s x sVaR_avg)**

where m_c and m_s are multipliers (minimum 3, increased for backtesting failures) and avg is over the previous 60 business days.

Using m_c = m_s = 3:

Capital = max($18M, 3 x $17M) + max($42M, 3 x $40M)
Capital = $51M + $120M = **$171M**

Without stressed VaR, capital would have been just $51M — the sVaR component more than triples the requirement.

**Key Exam Points:**
- The stress period must be **relevant to the current portfolio** — a bank heavy in emerging market FX might find 1997-98 or 2018 most stressful
- The stress window must be updated at least annually
- Under FRTB, stressed VaR is replaced by stressed Expected Shortfall, but the concept is the same

For more on capital calculations, explore our FRM Part I study materials.

What is Stressed VaR, how is the stress period selected, and how does it enter the market risk capital calculation?

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