Concurrent Session REI2 Impact of Reinsurance and Reinsurers on your Financials Evaluating Reinsurance: Different Metrics, Different Perspectives Casualty Actuarial Society Loss Reserving Seminar Washington, D.C. September 18-19, 2008

2 A Typical Reinsurance Analysis Company entering a new product line Considering a reinsurance program on the new business to mitigate risk Used a simulation model to quantify distribution of outcomes –Benefits of these models include: Ability to consider several metrics Easy ability to do multiple what-if’s

3 Projected Combined Ratios Gross and Net

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5 Measures of Risk – Reflect the Mean or Not? Measures of pure volatility, independent of mean –Standard deviation –Percentile-based (VaR or TVar) relative to the mean Measures that reflect level of mean as well –Percentile-based on absolute result (e.g., underwriting profit or combined ratio) –Probability of ruin or capital impairment

6 Standard Deviation and Percentiles of Underwriting Result Average Outcome – Reinsurance Costs Money Standard Deviation – Reinsurance Reduces Downside Percentile (10%) – About the same across options

7 Risk/Reward Plot – Standard Deviation

8 Risk Reward Plot – Downside Percentiles

9 Measures That Integrate Risk and Reward When risk/reward plots slope up to the right, they usually do not clearly indicate a “best” option Economic Value Added (EVA), Return on Risk Adjusted Capital (RORAC), etc. translate the risk measure into a cost of capital, which is measured in the same units as the average outcome, so they can be netted against each other EVA = Avg. Rtn. – (Capital Rqd. x Cost of Capital), where Capital Required is function of risk

10 Sample EVA Calculation Note that with EVA, zero is a good outcome Answer often depends crucially on how capital requirement is calculated (could do many sessions on this alone)

11 How to Make a Decision? Typically several metrics should be considered, as they will emphasize different aspects of risk Management needs to articulate nature of risk it is most concerned with –Glenn’s PML curve regions gets at this directly –Sensitivity to “middle of distribution” volatility, or extreme downsides? –Willingness to accept greater volatility in pursuit of higher gains? –Focus on company level impact or segment level?

12 Zooming Out - Marginal Impact on Book of Business in Total Average Outcome – Same Marginal Effect Standard Deviation – Reinsurance still reduces, but not as much Downside Percentile (1%) – Marginal impact smaller (Product-level underwriting results from earlier page, for reference)

13 EVA for Whole Book of Business Bottom line: 1.Much less clear that this reinsurance helps 2.Final answer requires management to be clear on risk tolerance Capital Based on 1% Downside Capital Based on 0.1% Downside

14 Effects of Volume If some is good, more is not always better…..

15 Summary Multiple perspectives, depending on management priorities –Absolute downside –Earnings stability –Appetite for higher reward/aversion to higher risk Need to consider marginal impact on whole company