An Actuarial Evaluation of the Insurance Limits Buying Decision Joe Wieligman Client Executive VP Hylant Travis J. Grulkowski Principal & Consulting Actuary Milliman, Inc. WWW.CHICAGOLANDRISKFORUM.ORG
Overview Risk profile survey A fresh perspective? How do Corporations currently look at risk? Survey characteristics & findings Actuarial examples 2 approaches Small privately held and large public company Comparison to current benchmarking techniques Next steps 2
Risk Profile Survey Consisted of 10 questions Focus was on four main areas: Exposure Current considerations Large losses Current risk philosophy 3
Risk Profile Survey Exposure: U.S. vs. Worldwide $ of Payroll, number of employees Revenues / sales Number of vehicles 4
Risk Profile Survey Current considerations: Current/historical limits purchased Budgetary constraints Impact on earnings/stock price (i.e. balance sheet) Peer benchmarking Corporate structure 5
Risk Profile Survey Current Considerations: 6
Risk Profile Survey Large losses: Historical loss review Your own Industry (similar sized) peers Jurisdictional differences Industry s largest loss Driver of claim Likelihood of occurring to your Company Statistical analysis Variability of total loss / large loss Mitigation of loss severity drivers 7
Risk Profile Survey Large Losses: 8
Risk Profile Survey Risk Philosophy: Retentions and/or large deductibles Risk transfer Annual review of TCOR (total cost of risk) Tolerance for loss 9
Risk Profile Survey Current risk philosophy: 10
Additional Findings Risk Manager s definition of a successful year: 11
Actuarial Example 1 - Privately Held Company - Product Liability Aggregate Umbrella Worldwide exposure (U.S. figures only provided below): Approximately 1.0 million in annual unit sales Revenue of $700 million Payroll of approximately $80 million for 2,000 employees Largest claim to date is $16 million 12
Actuarial Example 1 - A Basic Claims Simulation Model Based on historical claims information & actuarial judgement, select: Average Severity per Claim Average Claims per Year Estimated Variability on Individual Claims Frequency and Severity Distributions are selected Lognormal for Severity (selected by actuary) Poisson for Frequency (industry standard) Simulate GROUND UP future claims (counts and dollars), and apply theoretical reinsurance structures to simulated losses 13
Actuarial Example 1 Parameters Including Excluding Scenario 1 - Parameters Large Claim Large Claim Selected Ultimate Incurred Claims 20 19 Average Loss & ALAE Severity 700,000 600,000 Coefficient Of Variation (CV) 4.000 4.000 Illustrative Reinsurance Structure: $5M Limit $25M Aggregate Annual Limit 14
Actuarial Example 1 - Results 15
Actuarial Example 1 - Results Single product liability aggregate limit exercise Mean loss = approx. $14M (any given year) = 1.0 on chart 90% confidence level loss is $26.5M (factor or risk load of about 2.0) 9 out of every 10 years, $25M limit is adequate In other words, 10% of time annual aggregate of $25 million is exceeded Purchase depends on availability, affordability and Company s risk appetite 16
Actuarial Example 2 - Fortune 1000 Company - Product Liability Aggregate Umbrella Worldwide exposure (U.S. figures only provided below): Revenue of $6.8 billion Payroll of approximately $1.2 billion for 27,000 employees Largest claim to date is $20.0 million Largest industry loss is $50.0 million 17
Actuarial Example 2 A More Robust Claims Simulation Model Based on historical claims information, select assumptions related to Basic Claims Claims under SIR or Deductible Limit, Normal claims Shock Claims Large Losses Extreme Claims (i.e. Black Swans ) Frequency and Severity Distributions are parameterized for each type of claim: Future claims based on models that best fit historical data Can be adjusted for management expectations or incorporation of industry benchmarks Simulate GROUND UP future claims (counts and dollars), and apply theoretical reinsurance structures to simulated losses 18
Actuarial Example 2 Ground Up Losses Trials out of 1e+05 0 1000 2000 3000 4000 5000 6000 Ground Up Losses The Loss Distribution SHAPE matters! Picking a single distribution could underestimate tail risks. 19
Actuarial Example 2 Model Output Sample Diagnostics from the Robust Model: Probability of Breaching Excess Loss Layers Ground Up Losses and/or Retained Losses Expected Values, Percentiles, or Completed Probability Distributions In all Scenarios; or Isolated to Scenarios where Excess Layer is breached Since ALL data is retained, any conceivable metric is calculable Potential Uses of Robust Model Output Testing self-insured limits Testing aggregate limits Testing aggregate umbrella quotes Calibrate 1 in 100 year shock loss 20
Actuarial Example 2 Testing 3 Aggregate Limit Options Item Option A Option B Option C Self Insured Retention $1 Million Aggregate Limit $50 Million $75 Million $100 Million Expected Ground Up Losses $64.3 Million Expected Retained Losses $28.6 Million $18.5 Million $18.1 Million Options B & C appear very close, Selection may depend on excess quote Looking at the full distribution can provide more information. 21
Actuarial Example 2 Comparing Options When comparing alternatives, it s important to look beyond the mean estimate! Retained Loss Diagnostics as Percent of Mean Item Option A - $50M Option B - $75M Option C - $100M Mean ($M) $28.6 Million $18.5 Million $18.1 Million Median 0.78 0.97 0.99 75 th Percentile 0.92 1.01 1.05 90 th Percentile 1.74 1.09 1.10 95 th Percentile 2.26 1.22 1.13 97.5 th Percentile 2.66 1.72 1.16 99 th Percentile 3.14 2.32 1.20 22
Potential Further Enhancements to the Robust Model Incorporation of multiple loss distributions simultaneously Building in different lines of business each with different tail risks Incorporation of Correlation/Diversification benefit between lines and years Build in additional common reinsurance components: Multiple umbrella layers (aggregate XS) Multiple self insured retention scenarios Flexible Framework allows for limitless iterations and assumptions to be tested and reviewed quickly Goal is to help user make an informed buying decision! 23
Comparison to Other Metrics 24
Comparison to Other Metrics Many sources of competitor benchmarking Rely on large amounts of underlying data Based on publicly available data of large event claims Includes large events, lawsuits, and regulatory actions, not necessarily insured losses or final settlements Current benchmarking products provide a limited view of a Corporate insured s specific risk profile 25
Next Steps Organizations are faced with more risk than ever: Legal climate Economic / financial volatility Global competition Adding new points of discussion Understand what measures are most important to your Company when making this decision Involve your broker / actuary / risk & finance teams 26
Thank You! travis.grulkowski@milliman.com 262.796.3319 joe.wieligman@hylant.com 419.259.2788 WWW.CHICAGOLANDRISKFORUM.ORG