Model Cases ============ These case studies demonstrate how different types of companies can use ergodic insurance optimization. Each includes actual simulation results and detailed analysis of the decision process. Model Case 1: Widget Manufacturing Company ------------------------------------------- Company Profile ~~~~~~~~~~~~~~~ **MidTech Manufacturing Inc.** * **Industry**: Electronic components manufacturing * **Assets**: \$10 million * **Revenue**: \$15 million annually * **Operating Margin**: 8% * **Growth Rate**: 6% baseline * **Volatility**: 15% annual revenue volatility Risk Profile ~~~~~~~~~~~~ Based on 5 years of historical data: * **Attritional losses**: 4-6 events/year, \$30K-\$100K each * **Large losses**: 1 every 3 years, \$1M-\$5M range * **Catastrophic risk**: Major fire/explosion risk, potential \$20M loss Current Insurance Program ~~~~~~~~~~~~~~~~~~~~~~~~~~ * **Retention**: \$500,000 * **Limit**: \$5,000,000 * **Annual Premium**: \$125,000 * **Historical Performance**: 2 limits breached in past 10 years Analysis Process ~~~~~~~~~~~~~~~~ **Step 1: Baseline Assessment** .. code-block:: python # Configuration for MidTech Manufacturing manufacturer_config = { 'starting_assets': 10_000_000, 'base_revenue': 15_000_000, 'base_operating_margin': 0.08, 'tax_rate': 0.25, 'working_capital_pct': 0.20, 'growth_volatility': 0.15 } # Loss distribution parameters loss_config = { 'attritional': {'frequency': 5.0, 'severity_mean': 60_000, 'severity_cv': 0.8}, 'large': {'frequency': 0.33, 'severity_mean': 2_500_000, 'severity_cv': 1.0}, 'catastrophic': {'frequency': 0.02, 'severity_mean': 20_000_000, 'severity_cv': 0.5} } **Step 2: Simulation Results** *Without Insurance:* * 10-year survival probability: 71.2% * Average annual growth (survivors): 5.3% * 5% VaR: -\$2.8M (ruin) * Maximum drawdown: 68% *Current Program (\$500K retention, \$5M limit):* * 10-year survival probability: 83.5% * Average annual growth: 6.1% * 5% VaR: \$3.2M * Total premiums paid: \$1.25M * Benefit vs no insurance: +\$1.8M terminal value *Optimized Program (\$100K retention, \$25M limit):* * 10-year survival probability: 96.8% * Average annual growth: 7.4% * 5% VaR: \$8.7M * Total premiums paid: \$3.85M * Benefit vs current: +\$4.1M terminal value Recommendation ~~~~~~~~~~~~~~ **Optimal Structure:** 1. **Reduce retention** from \$500K to \$100K 2. **Increase limit** from \$5M to \$25M 3. **Layer structure**: * Primary: \$100K-\$5M at 1.5% rate * First Excess: \$5M-\$25M at 0.7% rate * Catastrophe: \$25M-\$50M at 0.3% rate **Financial Impact:** * Additional premium cost: \$260K/year * Improved survival probability: +13.3% * Enhanced growth rate: +1.3%/year * 10-year NPV of change: +\$4.1M **Key Insight:** The \$500K retention was creating cash flow stress during loss years, impeding growth investments. Lower retention enables consistent reinvestment. Model Case 2: High-Growth Technology Startup --------------------------------------------- Company Profile ~~~~~~~~~~~~~~~ **CloudScale Solutions** * **Industry**: SaaS platform provider * **Assets**: \$5 million * **Revenue**: \$8 million (100% YoY growth) * **Operating Margin**: -10% (investing for growth) * **Burn Rate**: \$2 million/year * **Volatility**: 40% revenue volatility Risk Profile ~~~~~~~~~~~~ * **Cyber incidents**: 0.8 events/year, \$500K-\$5M severity * **Business interruption**: Platform outages, \$100K-\$10M impact * **D&O liability**: High given rapid growth and VC backing * **Key person risk**: Critical dependency on technical founders Current Situation ~~~~~~~~~~~~~~~~~ * **No insurance** (trying to minimize burn) * **Recent incident**: \$800K cyber loss absorbed * **Board concern**: Requesting risk mitigation Analysis Process ~~~~~~~~~~~~~~~~ **Step 1: Quantify Uninsured Risk** .. code-block:: python # High-growth tech configuration tech_config = { 'starting_assets': 5_000_000, 'base_revenue': 8_000_000, 'base_operating_margin': -0.10, # Negative margin during growth 'growth_rate': 1.0, # 100% growth 'growth_volatility': 0.40, # High volatility 'burn_rate': 2_000_000 } # Tech-specific risks cyber_losses = { 'frequency': 0.8, 'severity_mean': 2_000_000, 'severity_cv': 1.5 } **Step 2: Simulation Results** *Without Insurance:* * 2-year survival probability: 68% * 5-year survival probability: 31% * Risk of running out of cash: 45% in year 2 * Expected runway reduction: 8 months per incident *Minimal Coverage (\$50K retention, \$5M limit):* * 2-year survival probability: 89% * 5-year survival probability: 62% * Annual premium: \$180K * Runway impact: -1 month *Recommended Coverage (\$25K retention, \$50M limit):* * 2-year survival probability: 95% * 5-year survival probability: 78% * Annual premium: \$425K * Runway impact: -2.5 months * **Critical benefit**: Enables next funding round Recommendation ~~~~~~~~~~~~~~ **Immediate Actions:** 1. **Implement cyber insurance** immediately (\$25K retention) 2. **D&O coverage** essential for board protection 3. **Business interruption** coverage with 12-month indemnity period **Staged Approach:** * **Year 1**: Essential coverage only (\$425K premium) * **Year 2**: Expand as revenue grows * **Year 3**: Full program at projected \$50M revenue **Board Presentation Points:** * Insurance cost < 6% of revenue (industry standard) * Survival probability improvement: +47% over 5 years * Protects \$50M post-money valuation * Required by most Series B investors Model Case 3: Stable Utility Company ------------------------------------- Company Profile ~~~~~~~~~~~~~~~ **Regional Power Corp** * **Industry**: Electric utility * **Assets**: \$100 million * **Revenue**: \$80 million * **Operating Margin**: 12% (regulated) * **Growth**: 2% annual (population-based) * **Volatility**: 5% (weather-driven) Risk Profile ~~~~~~~~~~~~ * **Routine claims**: 20-30/year, \$10K-\$50K each * **Storm damage**: 2-3/year, \$500K-\$5M each * **Catastrophic events**: Ice storms, hurricanes (\$50M-\$200M) * **Regulatory**: Penalties for extended outages Current Insurance Program ~~~~~~~~~~~~~~~~~~~~~~~~~~ * **Retention**: \$250,000 * **Primary limit**: \$10,000,000 * **Excess limit**: \$100,000,000 * **Annual premium**: \$2,800,000 Analysis Results ~~~~~~~~~~~~~~~~ **Optimization Finding:** Current retention too low for company size *Current Structure Performance:* * Never approaching ruin (100% survival) * Paying for unnecessary frequency coverage * Premium efficiency: 42% (low) *Optimized Structure (\$2M retention, same limits):* * Maintains 100% survival probability * Premium savings: \$1.1M/year * Self-insures predictable losses * Focuses on catastrophe protection Recommendation ~~~~~~~~~~~~~~ **Restructure to:** 1. **Increase retention** to \$2M (2% of assets) 2. **Maintain catastrophe limits** at \$100M+ 3. **Add parametric coverage** for named storms 4. **Establish loss fund** with premium savings **10-Year Impact:** * Premium savings: \$11M * Loss fund accumulation: \$8M (after claims) * Improved regulatory standing * Maintains AAA credit rating Model Case 4: Comparison Across Industries ------------------------------------------- Comparative Analysis ~~~~~~~~~~~~~~~~~~~~ We ran identical simulations across different industry profiles: .. code-block:: text ┌─────────────────┬──────────┬────────────┬───────────┬─────────────┐ │ Industry │ Optimal │ Optimal │ Premium % │ Ergodic │ │ │ Retention│ Limit │ of Assets │ Improvement │ ├─────────────────┼──────────┼────────────┼───────────┼─────────────┤ │ Manufacturing │ 1.0% │ 2.5x Rev │ 3.5% │ +31% │ │ Technology │ 0.5% │ 6x Rev │ 8.5% │ +67% │ │ Utility │ 2.0% │ 1.5x Rev │ 2.8% │ +12% │ │ Retail │ 0.8% │ 3x Rev │ 4.2% │ +38% │ │ Healthcare │ 0.3% │ 5x Rev │ 6.1% │ +54% │ └─────────────────┴──────────┴────────────┴───────────┴─────────────┘ Key Patterns ~~~~~~~~~~~~ 1. **Higher volatility → Lower optimal retention** 2. **Higher growth → Higher optimal limits** 3. **Thin margins → More insurance value** 4. **Stable companies → Higher retentions work** Implementation Lessons ---------------------- Lesson 1: Gradual Transition ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ **Problem:** Moving from \$1M to \$100K retention seems risky **Solution:** Phase over 2 years: * Year 1: Reduce to \$500K, monitor results * Year 2: Further reduce to \$250K if comfortable * Year 3: Reach optimal \$100K Lesson 2: Premium Sticker Shock ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ **Problem:** Board resistant to 3x premium increase **Solution:** Present as investment: .. code-block:: python # ROI Calculation additional_premium = 260_000 # per year growth_improvement = 0.013 # 1.3% better growth asset_base = 10_000_000 annual_value_creation = asset_base * growth_improvement roi = annual_value_creation / additional_premium print(f"Annual value creation: ${annual_value_creation:,.0f}") print(f"ROI on insurance spend: {roi:.1f}x") # Output: ROI on insurance spend: 5.0x Lesson 3: Market Capacity ~~~~~~~~~~~~~~~~~~~~~~~~~ **Problem:** Insurers reluctant to provide \$50M limit to \$5M company **Solution:** Structure with multiple carriers: * Primary: Admitted carrier (\$5M) * Excess: Bermuda markets (\$20M) * Cat: ILS/Alternative capital (\$25M) TODO: Real-World Validation --------------------------- Backtesting Against Historical Events ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We need to validate our models against actual loss events: * **2008 Financial Crisis Scenario:** * **2020 Pandemic Scenario:** * **Natural Catastrophe Events:** * Hurricane exposure (Florida manufacturer) * Earthquake exposure (California tech) Your Next Steps --------------- 1. **Identify your company type** from the cases above 2. **Run your specific parameters** through the model 3. **Compare results** with the relevant case study 4. **Adjust for unique factors** in your situation 5. **Document decisions** for future reference Remember: These cases are starting points. Your specific situation requires customized analysis using the tools provided in :doc:`running_analysis`. For additional customization options, see :doc:`advanced_topics`.