Provision for Adverse Deviations : Using a probabilistic stochastic approach Andr é L’Esp érance

1. Provision for Adverse Deviations : Using a probabilistic stochastic approach André L’Espérance Canadian Institute of Actuaries 18 September 2009

2. Contents • CMPA Background information • Organization • Actuarial liabilities • Characteristics • The valuation process • Calculation of PfAD components • Comments • PfAD – CIA Standard of Practice

3. CMPA Background information - Organization • Mutual Defense Association – Not for Profit organization • Monoline : medical malpractice • No insurance policy or contract • Annual membership • Services to membership • Occurrence-based protection with no limit on costs for compensation, legal and expert costs • Education and Risk Management Assistance • “Quasi insurer” according to CIA Standards of Practice

4. CMPA Background information – Actuarial liabilities • Cost components • Damages (awards and settlements) • Legal fees and disbursements • Expert fees • Administrative / operational expenses • Only claim liabilities – annual valuation at year-end for financial reporting purposes • Estimates of expected unpaid claims not yet available for individual cases • Deterministic and probabilistic approaches using historical dollarpayments data on a regional basis

5. Background information - Characteristics • Exempt from regulation • Tax exempt • No reinsurance • Excess assets returned over time to membership in the form of credits against annual fees

6. The Valuation Process • Deterministic approach • Adjustment of historical data • Paid loss development techniques • Probabilistic approach • Fitting of distributions to unadjusted historical data cells => estimation models reproducing historical data • Projected values from selected future trends applied to estimation models • Distribution of potential estimates from simulations based on distribution’s mean and S.D.

7. The Valuation Process • Criteria applied for selection of estimation models for each cost component and for all cost components combined • Best estimates validated through frequency-severity models and runoff exhibits • Multiple scenarios applied to each estimation model • Future trends • Selected Estimates = Weighting of Scenarios’ Estimates • PfAD calculated from margins based on volatility of estimation models and on structure of assets portfolio • Actuarial provision = Selected estimates + PfAD

8. Calculation of PfAD components • Margin for Claim Development (MfCD) • Considerations described in current and priorCIA Standards of Practice • Additional information : Volatility in mean / selected estimates can be used to determine the margin needed achieve given confidence level • Subject to CIA’s low and high margin limits • No Reinsurance • Margin for Interest Rate (MfIR) • Considerations described in CIA Standards of Practice • Subject to CIA’s low and high margin limits • PfAD = MfCD + MfIR

9. Calculation of PfAD components => MfCD • Typically skewed, long tail distributions • Volatility of each estimation model measured using the information from the standard deviation of its distribution and from the simulated values at each confidence level • Standard deviation and simulated values calculated • for each cost component • for an all cost components combined estimation model to recognize the correlation between eachcase’s cost components

10. Calculation of PfAD components => MfCD • MfCD can be calculated from the measures of volatility for each cost component and for all cost components combined recognizing that such measure • Includes normal fluctuations around mean • Excludes ‘model risk’

11. Calculation of PfAD components => MfCD • Potential MfCD =Standard Deviation (S.D.) of estimation model’s distribution • represents the S.D. of the ‘population’ • includes most potential outcomes • Potential MfCD = Simulated value at a given confidence level - Mean estimate • Issue : simulated values include a wide range of potential outcomes but unlikely all potential outcomes covered by the S.D. of the ‘population’ • Issue : selection of confidence level

12. Calculation of PfAD components => MfCD • A VaR approach is used to provide statistical support for the selected confidence level • i.e. The confidence level at which the expected gain from a more than sufficient MfCD is approximately equal to the expected loss from an inadequate MfCD • Empirical testing indicates an 85% confidence level • Slightly below the required level for the damages cost component • Some conservatism for other cost components

13. Calculation of PfAD components => MfCD • Selected MfCD = one S.D. of the All Cost Components model subject to • minimum = S.D. of the DAMAGES cost component • maximum = sum of S.D. of each cost component • within range defined by CIA Standards of Practice • Takes into account the correlation between the cost components of a case • Takes into account the higher volatility of the damages cost component

14. Calculation of PfAD components => MfIR • Recognizes the characteristics and structure of the assets portfolio • Fixed income (bonds) instruments • Equity (stocks) • Private assets and alternate arrangements (infrastructure,…) • Selected margin = 200 basis points • MfIR = provision discounted @ expected long-term earned rate minus 2% - provision discounted @ expected long-term earned rate • Calculated for each cost component

15. Comments • Volatility • Varies among the estimation models of the cost components • Materially higher for the damages cost component than any other cost component => beyond the maximum allowed by CIA Standards of Practice • Difficult to justify a single percentage confidence level as a standard of practice for MFCD • Range of confidence level would be more appropriate

16. PfAD - CIA Standard of Practice • Definition of ‘adverse deviations’ should be revisited • Differences between Deterministic/traditional and Probabilistic methodologies may support separate treatment of the margin for claims development based on each methodology and resulting values should be comparable. • For the calculation of the margin for claims development, guidance about a range rather than a single confidence level would likely more appropriately recognize the uncertainty inherent in the calculated expected costs

17. QUESTIONS