How is factor-based VaR used in stress testing and scenario analysis?

Factor-based VaR and stress testing are complementary tools. VaR tells you what to expect under normal conditions; stress testing tells you what happens in extreme scenarios. Factor models provide the bridge between them.

From VaR to stress testing:

A factor-based portfolio model:

ΔV = Σ βᵢ × ΔFᵢ + ε

For VaR: Use the factor covariance matrix to estimate the distribution of ΔV.

For stress testing: Replace the statistical factor shocks with specific extreme scenarios.

Types of factor-based stress tests:

1. Historical scenarios (replay actual crises):

Apply these historical factor moves to current portfolio sensitivities.

2. Hypothetical scenarios (design specific shocks):

• "Fed raises rates by 200bps unexpectedly"
• "China invades Taiwan" (equity -25%, EM FX -20%, oil +40%)
• "US sovereign downgrade" (rates +100bps, credit +200bps, USD -10%)

3. Sensitivity analysis (one factor at a time):

Shock each factor independently to identify which factors matter most.

The challenge of multi-factor consistency:

When designing scenarios, factor shocks must be internally consistent. If you shock equity markets down 30%, it's unrealistic to assume credit spreads stay flat. The factor correlation structure helps:

• Use historical crisis correlations (correlations spike during stress)
• Apply PCA-based scenarios that respect the factor structure
• Use conditional distributions: "Given equity -30%, what's the expected move in credit?"

Example — Silverstone Capital stress test:

Portfolio factor sensitivities:

Compare to the 99% VaR of $8.0M — the stress scenario is 2.5x the VaR, revealing tail risk that VaR misses.

Reverse stress testing:

Start from a loss that would threaten the firm's viability (e.g., -$50M) and work backward to find which factor combinations would produce that loss. This identifies "what would have to go wrong" for the firm to face existential risk.

Exam tip: FRM Part II tests the design of consistent multi-factor stress scenarios, the relationship between VaR and stress testing, and reverse stress testing concepts. Know how to apply factor sensitivities to scenario shocks.

Explore market risk management on AcadiFi's FRM course.