26 September 2005 Stephen Lowe Survey Results / Overview of Methods CAS Limited Attendance Seminar on Risk and Return in Reinsurance

2 Sixteen survey participants ACE Tempest Re AWAC Chubb Re GE GMAC Re Hannover Re Max Re Montpelier Re Odyssey Re Partner Re Platinum Re QBE Re Scor Re Signet Star Toa Re Transatlantic Re

3 Traditional approaches to pricing Measure Target Combined Ratio Target Return Approach Return on Sales Return on Capital Variations Nominal versus Discounted Fixed versus Variable Target ROE based on NPV of Internal Cash Flows versus IRR of Free Cash Flows Fixed Versus Variable Target Rating Agency Capital versus Economic Capital These methods are usually applied to deterministic (i.e., expected) cash flows

4 Stochastic pricing methods Description Required capital a fn of contract outcome distribution Tail VaR Required capital a fn of marginal impact on portfolio outcome distribution Tail VaR Calculate R2R from contract outcome distribution Price is expected outcome using modified probabilities Price is expected outcome using modified amounts Approach Standalone Tail VaR Marginal Tail VaR R2R Wang Transform Capital Consumption Measure Target Return Target R2R Adjusted Expected Value Thanks, Don

5 Typical descriptions of method Target ROE, comparing NPV of contract cash flows to equity based on leverage ratios Target underwriting profit by class of business Target ROE, using NPV model that balances to capital requirements Target IRR, based on free cash flows (capital and profits in/out) Target ROE, reflecting corporate cost of capital, based on NPV of contract cash flows and internal RBC factors Variety of methods that look at downside risk and utility metrics; game theory considered Metrics relating to simulated contract results distribution used to determine leverage required, then target ROE

6 How are profit margins set in pricing? NominalNPVIRR Return on Capital Return on Sales One company responded that they used “a variety of methods”

7 Do pricing methods vary by line? Most companies indicated that they use the same general method for all lines Exceptions: Property catastrophe, where pricing reflects the marginal impact of the contract on the portfolio Clash covers, where a bank approach is taken Property business, where volatility of individual contract and portfolio concentration is taken into account Contracts with loss sensitive features treated differently One company responded that they used “a variety of methods” that vary by line

8 How is risk reflected? At the class of business level Fixed ROC, but RBC allocates more capital to volatile classes Variable ROC, and RBC allocates more capital to volatile classes Profit margins vary with volatility of class At the individual contract level Risk loads determined by individual contract simulation Contracts with unusually high risk have target set higher than the standard target for the class Underwriters make judgmental adjustments Volatility of contract is benchmarked to other contracts in class

9 How is capital allocated? Rating agency RBC factors Leverage ratios Management allocation Internal capital model (Economic Capital) Volatility of class Individual contract simulation distribution Individual contract downside risk Contract characteristics Not allocated

10 How are pricing targets reconciled with corporate financial goals? They are the same; they are consistent No reconciliation is made Reconciliation assures that aggregate pricing return is greater than overall financial target They are expected to be similar Differences reflect actual versus rating agency capital IRR versus ROE make them different

11 What enhancements are being developed or considered? Allocation of capital to contract is being tested Researching RAROC Researching greater use of marginal portfolio impact in the allocation of capital Need to understand correlations between lines to implement marginal impact Refinements to marginal capital allocation Looking at game theoretical constructs Researching internal risk models Implementing rating agency capital formula into capital allocation

12 Additional Materials on Stochastic Pricing

13 Pricing to a Target R2R = 8.00

14 Transform the distribution amounts or probabilities? Valuex1x2…xn Probp1p2…pn ValueU(x1)U(x2)…U(xn) Probp1p2…pn Valuex1x2…xn Probp1p2…pn Valuex1x2…xn Probq1q2…qn Probability Transform or “Measure Change” modifies the Probabilities Downside penalty function modifies the amounts Either approach uses SUMPRODUCT of amounts and probabilities PENALTY FUNCTION WANG TRANSFORM

15 Downside Penalty a.k.a. Capital Consumption Risk Load = E[X*] expected value of adjusted amounts Adjustment happens by modifying the amounts using a capital consumption penalty: —Zero if positive NPV outcome —Multiple of outcome if negative NPV outcome Expected value = SUMPRODUCT of Amounts and Probabilities

16 Capital Consumption Once NPV Falls Below Zero, Penalties Assessed to Offset Consumption of Additional Capital NPV Above Zero – No Penalties

17 Capital Consumption Pricing Example Downside (Capital Consumed) Amounts Increased

18 Wang Transform Modifies the Probabilities In Excel: F* = normsdist( normsinv(F) - lambda ) Makes severe outcomes appear more likely by reducing their implied percentile For example, if lambda = 0.5, a 3 std deviation outcome becomes a 2.5 std deviation outcome

19 The Wang Transform shifts the NPV distribution, giving more weight to the tail of the distribution. Unlike TVaR and VaR, WT considers the entire distribution

20 Target adjusted ENPV Wang Pricing Transform Modifies the Probabilities Applies a Greater Weight to Downside …. By Modifying Probabilities