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Explore methods & approaches to risk and return in reinsurance from industry leaders. Learn about pricing variations, capital allocation, risk reflection, and more.
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Survey Results / Overview of Methods CAS Limited Attendance Seminar on Risk and Return in Reinsurance Stephen Lowe
Sixteen survey participants • Odyssey Re • Partner Re • Platinum Re • QBE Re • Scor Re • Signet Star • Toa Re • Transatlantic Re • ACE Tempest Re • AWAC • Chubb Re • GE • GMAC Re • Hannover Re • Max Re • Montpelier Re
Measure Target Combined Ratio Target Return Approach Return on Sales Return on Capital Traditional approaches to pricing 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
Stochastic pricing methods Thanks, Don Approach Standalone Tail VaR Marginal Tail VaR R2R Wang Transform Capital Consumption 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 Measure Target Return Target Return Target R2R Adjusted Expected Value Adjusted Expected Value
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
How are profit margins set in pricing? Nominal NPV IRR Return on Sales Return on Capital One company responded that they used “a variety of methods”
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
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
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
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
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
Transform the distribution amounts or probabilities? Either approach uses SUMPRODUCT of amounts and probabilities Downside penalty function modifies the amounts PENALTY FUNCTION Probability Transform or “Measure Change” modifies the Probabilities WANG TRANSFORM
Downside Penaltya.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
Capital Consumption Once NPV Falls Below Zero, Penalties Assessed to Offset Consumption of Additional Capital NPV Above Zero – No Penalties
Capital Consumption Pricing Example Downside(Capital Consumed) Amounts Increased
Wang TransformModifies 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
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
Wang Pricing Transform Modifies the Probabilities Applies a Greater Weight to Downside …. By Modifying Probabilities Target adjusted ENPV