Quantitative Methods & RiskRisk Measures: Volatility, Drawdown, VaR & CVaR
Stress Testing: Scenarios that Break VaR
Where probabilistic risk ends, scenarios begin
VaR and Expected Shortfall are both estimated from a history. They cannot price a shock that is not in that history, or one bigger than anything the lookback contains. Stress testing fills the gap by asking a different question entirely: not 'what is the 99th percentile?' but 'if this specific event repeated, what would the portfolio lose?' You don't need a probability — you need a coherent, concrete scenario and the discipline to run it.
| Scenario | Date | Headline shocks |
|---|---|---|
| Lehman default | Sep 15 2008 | S&P −4.7% on the day, −18% in the week to Oct 10; IG credit spreads +200bp |
| COVID lockdown | Feb 19–Mar 23 2020 | S&P −34% in 23 trading days, VIX > 80 |
| SNB unpeg | Jan 15 2015 | EUR/CHF −30% in minutes, FX vol +400% |
| 1987 Black Monday | Oct 19 1987 | S&P −20.5% in a single day |
| 2010 Flash Crash | May 6 2010 | Dow −9% intraday, most of it recovered within about 20 minutes; closed −3.2% |
Scenario stress test
A deterministic 'what-if': apply a specific set of market shocks (historical or hypothetical) to the current portfolio and compute the loss, with no probability attached. It complements VaR/ES by capturing event risk and far-tail moves that no estimated distribution contains.
A
What VaR / ES do well
- Summarize routine, day-to-day downside
- Update automatically as data arrives
- Comparable across desks and books
- Give a probability of exceedance
B
What only stress tests do
- Capture shocks larger than any in the lookback
- Model correlations snapping to +1 in a panic
- Price a never-before-seen hypothetical
- Expose concentration the average doesn't show
Build your own scenario library
The standard historical playbook is a starting point; every shop adds its own. For a Markitel paper account a useful bespoke scenario is 'a flash crash in the single asset I'm most concentrated in, with correlations forced to +1 across the rest of the book.' Run it monthly, and run it again whenever your largest position changes.
Reverse stress testing
Most stress tests start with a shock and compute the loss. Reverse stress testing starts with the loss that would break you — the one that wipes out the account or trips a margin call — and asks what scenario produces it. It is uncomfortable by design, and it is the test most likely to reveal a hidden concentration before the market does.
Knowledge check
Why is scenario stress testing a necessary complement to VaR and Expected Shortfall?