Stress Testing and Scenario Analysis
advancedPublished: 2026-01-01
Stress Testing and Scenario Analysis
Stress testing evaluates portfolio performance under extreme but plausible market conditions, complementing VaR by examining scenarios that statistical models may underweight. Effective stress testing combines historical events, hypothetical shocks, and reverse stress tests to identify vulnerabilities.
Definition and Key Concepts
Types of Stress Tests
| Type | Description | Use Case |
|---|---|---|
| Historical | Replay actual market events | Known crisis impacts |
| Hypothetical | Construct plausible shocks | Forward-looking scenarios |
| Sensitivity | Single-factor moves | Understand risk drivers |
| Reverse | Find scenarios causing failure | Identify vulnerabilities |
Stress Test vs. VaR
| Attribute | VaR | Stress Test |
|---|---|---|
| Probability-based | Yes | No (plausibility judgment) |
| Scenario-specific | No (aggregate) | Yes (named scenarios) |
| Extreme events | Underweighted | Explicitly examined |
| Regulatory use | Market risk capital | Comprehensive capital |
Scenario Library
Historical scenarios:
| Event | Date | Key Shocks |
|---|---|---|
| Black Monday | Oct 1987 | Equity -22%, vol +400 bps |
| LTCM/Russia | Aug 1998 | Credit spreads +200 bps |
| Tech Crash | Mar 2000 | NASDAQ -40%, growth →value |
| GFC | Oct 2008 | Equity -40%, vol +500 bps |
| Volmageddon | Feb 2018 | VIX +400%, vol products liquidate |
| COVID Crash | Mar 2020 | Equity -35%, vol +600 bps |
How It Works in Practice
Scenario Construction
Historical scenario replay:
- Select event period
- Extract actual market moves
- Apply to current portfolio
- Calculate P/L
Hypothetical scenario design:
| Step | Activity |
|---|---|
| 1 | Define narrative (e.g., "Fed rate shock") |
| 2 | Specify risk factor moves |
| 3 | Ensure internal consistency |
| 4 | Apply to portfolio |
| 5 | Analyze results |
Risk Factor Shocks
Standard shock magnitudes:
| Risk Factor | Moderate | Severe | Extreme |
|---|---|---|---|
| Equity spot | -15% | -25% | -40% |
| Equity vol | +50% | +100% | +200% |
| Interest rates | +100 bps | +200 bps | +400 bps |
| Credit spreads | +100 bps | +250 bps | +500 bps |
| FX | +/- 10% | +/- 20% | +/- 30% |
Correlation Assumptions
Normal markets: Correlations as observed historically.
Stress markets: Correlations typically move toward +1 for risk assets.
| Pair | Normal Correlation | Stress Correlation |
|---|---|---|
| Stocks / Credit | 0.4 | 0.8 |
| Stocks / Vol | -0.6 | -0.9 |
| EM / DM equities | 0.7 | 0.9 |
| USD / Risk assets | -0.3 | -0.7 |
Worked Example
Portfolio:
- Long $100M equities (S&P 500)
- Long 1,000 SPX puts (4,000 strike, 3-month)
- Short 500 SPX calls (5,500 strike, 3-month)
Current Greeks:
- Delta: +85,000 shares
- Gamma: +50 deltas per $1
- Vega: +$200,000
Scenario 1: 2008-Style Crisis
Shocks:
- S&P 500: -40% (5,000 → 3,000)
- Implied vol: +200% (20% → 60%)
- Rates: -150 bps
P/L Calculation:
| Component | Calculation | P/L |
|---|---|---|
| Equity position | -40% × $100M | -$40,000,000 |
| Delta on options | 85,000 × (-2,000) × 50% | -$85,000,000 |
| Gamma benefit | ½ × 50 × (2,000)² | +$100,000,000 |
| Put payoff (intrinsic) | 1,000 × 100 × ($4,000-$3,000) | +$100,000,000 |
| Vega gain | $200,000 × 40% | +$8,000,000 |
| Call liability | 500 × 100 × $0 | $0 |
| Net P/L | +$83,000,000 |
The protective puts and long vega more than offset equity losses.
Scenario 2: Rate Spike + Equity Selloff
Shocks:
- S&P 500: -20%
- Implied vol: +50% (20% → 30%)
- Rates: +200 bps
P/L Calculation:
| Component | Calculation | P/L |
|---|---|---|
| Equity position | -20% × $100M | -$20,000,000 |
| Delta on options | 85,000 × (-1,000) × 60% | -$51,000,000 |
| Gamma benefit | ½ × 50 × (1,000)² | +$25,000,000 |
| Vega gain | $200,000 × 10% | +$2,000,000 |
| Rho impact | Higher rates reduce put value | -$500,000 |
| Net P/L | -$44,500,000 |
Moderate crash hurts more than extreme crash due to less gamma convexity.
Scenario 3: Melt-Up
Shocks:
- S&P 500: +20%
- Implied vol: -30% (20% → 14%)
- Rates: +50 bps
P/L Calculation:
| Component | P/L |
|---|---|
| Equity gains | +$20,000,000 |
| Put decay | -$3,000,000 |
| Call liability | -$8,500,000 (calls go ITM) |
| Vega loss | -$1,200,000 |
| Net P/L | +$7,300,000 |
Upside capped by short calls.
VaR Comparison
| Scenario | Stress P/L | Implied by 99% VaR |
|---|---|---|
| 2008-style crash | +$83M | ~(-$15M) |
| Rate spike + selloff | -$45M | ~(-$15M) |
| Melt-up | +$7M | ~(-$15M) |
Stress tests reveal both upside potential and losses beyond VaR.
Risks, Limitations, and Tradeoffs
Scenario Design Challenges
| Challenge | Description |
|---|---|
| Correlation shifts | Hard to predict how correlations change |
| Non-linearity | Options payoffs non-linear in risk factors |
| Path dependency | Some products depend on how crisis unfolds |
| Model breakdown | Models may fail in extreme stress |
Historical Scenario Limitations
| Limitation | Example |
|---|---|
| Survivorship bias | Don't test for events that haven't happened |
| Regime change | 2008 may not repeat exactly |
| Different starting point | Current vol/valuations differ from historical |
Common Pitfalls
| Pitfall | Description | Prevention |
|---|---|---|
| Too few scenarios | Miss important risks | Comprehensive library |
| Inconsistent shocks | FX up, exports down? | Ensure economic consistency |
| Static portfolio | Ignores hedging response | Consider dynamic scenarios |
| Ignore liquidity | Can't exit positions in stress | Include liquidity stress |
Reverse Stress Testing
Process:
- Define failure threshold (e.g., -50% capital)
- Work backward to find scenarios causing failure
- Assess plausibility of those scenarios
- Develop contingency plans
Example: Failure threshold: Portfolio loss > $50 million
Scenarios causing failure:
- Equity -25% with vol flat (puts don't help enough)
- Vol crush -50% without equity move
- Counterparty default on winning positions
Regulatory Requirements
| Jurisdiction | Requirement |
|---|---|
| US (Fed) | CCAR, DFAST stress testing |
| EU (EBA) | EU-wide stress tests |
| Basel | Internal stress testing for capital |
| SEC | Registered fund stress testing |
Checklist and Next Steps
Scenario library checklist:
- Include 5+ historical scenarios
- Create 3+ hypothetical scenarios
- Define sector-specific scenarios
- Include recovery scenarios
- Document scenario rationale
Execution checklist:
- Calculate P/L for each scenario
- Compare to risk limits
- Identify largest loss scenarios
- Attribute losses to risk factors
- Present to risk committee
Follow-up checklist:
- Review scenarios quarterly
- Update for new risk factors
- Conduct reverse stress tests
- Develop action plans for severe scenarios
- Document and archive results
Related articles:
- For VaR methodology, see Measuring and Reporting Value at Risk
- For hedge effectiveness, see Hedge Effectiveness Testing for Accounting