ERM Topics – How Much Insurance Should I Buy? CAS Ratemaking Seminar March 27-28, 2003 San Antonio, TX

What Does This Have To Do With Ratemaking? Nothing, if you believe actuarial rates calculated with precision in the home office actually get charged to large commercial risks. Everything, if you want to understand the challenges faced by commercial insurance buyers and how they view retentions, limits and premiums.

Analytical Considerations Explore actuarial and analytical approaches to evaluating the question of how much insurance a commercial enterprise should purchase Christopher (Kip) Bohn, ACAS, MAAA Assistant Director and Actuary Aon Risk Consultants, Inc.  Filling in for: Barry Franklin, FCAS, MAAA Managing Director & Actuary Aon Risk Consultants, Inc.

Retain/Finance/Transfer The answer to the question “How much insurance should I buy? depends on the answers to other questions:  How much risk is inherent in my operations?  How much risk can I afford to retain?  How much risk can I efficiently finance?  What are the retain/finance/insure cost/benefit trade-offs?

Quantifying Risk in the Enterprise Identify the major risks  Choose your battles wisely Gather data/solicit information  Objective, subjective, interpretive Develop parameters & distributions  Actuarial precision is laudable, but avoid “paralysis through analysis”  A cloudy crystal ball is better than no crystal ball Simulate results, derive distributions  Correlation – measure, guess, etc.

Quantifying Risk in the Enterprise

How Much Risk to Retain Benchmark ratio analysis  Where did those ratios come from?  Do they reflect key aspects of the organization?  Could be considered a starting point Peer comparisons  Risk appetite varies  Just because your friend jumps of a cliff…

Beyond Benchmarks Develop framework for decision analysis What are the company’s financial and operational boundaries?  Debt covenants and debt/equity rating rationale  What has the company promised shareholders, analysts, etc.?  Examine both objective and subjective boundaries

Beyond Benchmarks What are the company’s key indicators?  Financial ratios  Internal targets Incorporate risk modeling analysis  What is the company’s “comfort level” for the financial/operational boundaries and key indicators?

ABC Corporation Debt Coverage 75.0% 85.0% 95.0% 105.0% 115.0% 125.0% 135.0% 145.0% 155.0% 165.0% 0%20%40%60%80%100% Probability Debt Coverage Ratio Model Target Debt Coverage Example ABC’s debt ratings are based on a number of factors, the most prominent of which in the ratings analyses we have reviewed is Debt Service Coverage. Based on our understanding of the rating agency analyses we reviewed, ABC’s rating would likely be lowered if the Debt Service Coverage Ratio drops below 125%. Our simulation analysis suggests that the likelihood of the Debt Service Coverage Ratio dropping below 125%, as a result of the risk areas analyzed herein, is approximately 5%; that is to say ABC can be 95% confident that its rating will not be lowered due to contingencies associated with the risks analyzed. Reading the graph: The vertical axis represents ABC’s Debt Service Coverage Ratio. The horizontal axis represents the probability of the ratio being at or below the indicated level. For example, the point indicated by the arrow suggests that in 80% of simulated years, the ratio is projected to be 155% or less.

Choosing a Program Based on your analysis up to this point select retention/limit combinations that appear to satisfy risk bearing guidelines  Most likely, you will have identified a range of acceptable retentions  Be open to nonstandard retention structures (e.g. corridors)  Consider the limits of liability the that the company requires

Market The Risk Communicate range of retentions company is willing to consider  Be prepared to be flexible Steer clear of carriers who are outside “reasonable” price ballpark  Could indicate lack of knowledge of coverage and/or client  One-time savings could be less valuable than long term partnership

Market Risk Make sure you understand not only cost and structure differences but policy provisions as well Understand and quantify other costs  Claims handling  Premium payment terms  Collateral requirements

Evaluate Options At this stage, carrier costs are considered fixed  Theoretically, could build in load for financial health of carrier Need to somehow put all options on an apples-to-apples basis Goal is to determine total cost of risk to the company

Evaluate Options With fixed carrier costs and expected retained losses under the various programs (based on our prior analysis) known, we can accomplish this However, this does not reflect the risk associated with the retained exposure

Efficient Frontier To incorporate the risk component, we can take an idea from portfolio theory The efficient frontier brings together risk and reward It also allows us the ability to throw out carriers and options that are not on the efficient frontier

Efficient Frontier Define risk as the difference between retained loss at the expected level and at a higher confidence level Define reward as total coast savings at expected loss levels over a guaranteed cost program  This is just a base line - lots of ways to define reward

Efficient Frontier EXPECTED REWARD Various risk financing options from the market Current Program Optimal Risk Financing Structure Risk Bearing Capacity RISK Guaranteed Cost Program { Expected Savings Over Current Program The Efficient Frontier Expected Reward is measured in terms of the expected savings of the risk financing structure being considered as compared to a no-risk guaranteed cost program. Risk is measured in terms of variability from expected levels. Optimal Risk Financing Structure falls at the intersection of efficient frontier and risk-bearing capacity lines.

Efficient Frontier Now the question to answer is which risk/reward combination on the efficient frontier is the best fit for the company Make sure selected option fits into  Financial/operational boundaries  Risk Appetite  etc.

Efficient Frontier This exercise provides a framework for RELATIVE risk/reward tradeoffs  Does not optimize risk/return in absolute sense  Suggests direction to move but limited by risk transfer options & costs actually available  Doesn’t magically derive the “right” answer