Building on our series exploring risk measurement tools, let’s dive deep into stress testing and scenario analysis. While Value at Risk (VaR) has its place, it’s insufficient alone (and some would say outright deficient). Here we explore complementary tools that can provide richer insights into risk.

Understanding the Distinction: Stress Tests vs Scenarios

Stress tests examine specific risk factor movements – like a 20% equity fall or 10% increase in claims frequency. They’re precise, quantifiable, and comparable across time and entities.

Scenarios tell richer stories about how multiple factors might interact. Consider a pandemic scenario: market crash leads to mass unemployment, which triggers changes in interest rates and inflation. This cascades into less distance driven (reducing motor premiums), increased disability claims with reduced claim terminations, increased policy fraud, lower business volumes, and higher unit expenses. Each element interacts with and amplifies others.

Applications Across Insurance

These tools serve multiple crucial functions:

1. Regulatory Requirements – Regular ongoing reporting requirements – Acute period testing (like liquidity testing during GFC and COVID) – Demonstration of risk understanding and management capability
2. Own Risk and Solvency Assessments (ORSA), ICAAP, and Financial Condition Reports – Forward-looking stressed assessments – Demonstration of ability to handle adverse experience – More sophisticated versions incorporate complex interactions
3. Product Design and Pricing – Testing beyond expected experience – Examining portfolio resilience to mortality shocks – Understanding impacts of severe interest rate dislocations
4. Asset-Liability and Balance Sheet Management – Testing hedging programs against market jumps – Examining impacts of negative real rates – Analyzing effects of negative nominal rates – Considering hyperinflation scenarios – Assessing impact of government defaults – Understanding policyholder option exercise patterns under stress

Creating Meaningful Scenarios: A Toolkit

Statistical Approaches

Start with the familiar – scaling standard regulatory stresses (like Solvency II’s 99.5th percentile) up or down. But distribution choice matters critically:

• Normal distributions are easy but often wrong
• Student-t, lognormal, or Pareto distributions might better reflect reality
• Counter-intuitive insight: heavier-tailed distributions often give milder 1-in-10 year stresses despite more severe extremes

Fitting to Historical Data

Modern statistical tools (R is particularly powerful) allow sophisticated distribution fitting, but several considerations matter:

• Maximum Likelihood vs Method of Moments – different approaches suit different situations
• Testing fit across multiple moments (mean, variance, skewness, kurtosis)
• Avoiding over-fitting through sensible distribution selection
• Bootstrapping for empirical estimation when theoretical distributions fail

Learning from History

Major events provide ready-made scenarios that demonstrate how risks manifest and interact:

• 1987 Market Crash (20% single day equity fall)
• 1998 Russian Crisis (Ruble collapse, LTCM near-failure threatening market stability)
• 2001 Tech Bubble (80% NASDAQ decline, telecoms collapse)
• 2007-2009 GFC (housing crash, bank failures, liquidity freeze)
• 2020 COVID (30%+ market falls, business interruption, mortality shock)
• 2021 South African riots (property damage, business interruption, supply chain failure)
• Regional lessons (Latin American hyperinflation, Japanese 30-year equity bear market and zero rates)

Beyond Pure Statistics

• Catastrophe modeling combining data with physics (particularly relevant for climate risk)
• Expert judgment through structured approaches: – Delphi method – Brain-writing – Pre-mortems – Structured scenario workshops
• Bayesian Belief Networks explicitly modeling risk interactions and combining qualitative insights with quantitative calibration

The Severity Spectrum

Different severities serve different purposes:

• Mild stresses (1-in-10 year events) help with business planning
• Severe stresses (1-in-200) align with capital requirements
• Extreme scenarios (1-in-400+) reveal system vulnerabilities

Critics often ask “How can you know what a 1-in-200 event looks like?” But this misses the point. While we use statistical methods and historical data to inform calibration, the real value lies in understanding how your business might respond to severe, unimaginable shocks. (Large, graceful, and unimaginably coloured birds anyone?)

When Long-Term Capital Management’s models suggested their 1998 losses were a 1-in-several-universe event, it revealed more about their model failings than the markets.

The Magic of Interactions

The real value emerges when examining interactions:

• Policyholder behavior changes (surrenders spike with rates)
• Competitors react and markets adapt
• Management responds (though be skeptical of assumed actions that haven’t been tested)
• Market liquidity can disappear precisely when needed most
• Correlations often break down in stress scenarios

Final Thoughts

Being explicit about estimated severities provides useful context and drives calibration discipline. But don’t let perfect be the enemy of good – often at least half the value lies in the discussion itself. Understanding how different parts of your business interact under stress often matters more than precise probability estimates.

The next crisis won’t look exactly like your stress tests – but the insights gained might just help you navigate it.