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March 12th, 2013Experience StudiesMichael Chen, FCAS MAAA
Experience StudiesProperty & Casualty InsuranceThe goal of a ratemaking analysis is to set the rates such that the premium charged will be appropriate to cover the losses and expenses while achieving the targeted profit for policies that will be written during a future time period. Premium = Losses + Loss Adjustment Expenses + Underwriting Expenses + Underwriting Profit.
Note:Source: CAS Basic Ratemaking Manual
Experience StudiesHow do we as Actuaries accomplish this goal?
There are two basic approaches for determining an overall rate level need:
1. Pure premium methodThe pure premium method determines an indicated average rate, not an indicated change to the current average rate. The pure premium method is generally used to determine rates of a new product where there is not internal historical experience.
2. Loss ratio methodThe loss ratio method is the more widely used of the two rate level indication approaches. The loss ratio method compares the estimated percentage of each premium dollar needed to cover future losses, loss adjustment expenses, and other fixed expenses to the amount of each premium dollar that is available to pay for such costs.
Experience StudiesRate Indication Example:
Indicated Rate Change = ( Projected Loss Ratio / Permissible Loss Ratio ) -1
AccidentTotalProjectedProjectedIndicatedYearAdjustedUltimateLossRateEndingPremiumLossesRatioWeightsChange12/31/20083,000,000 2,000,000 66.7%0.10011.1%12/31/20098,000,000 5,000,000 62.5%0.1504.2%12/31/201012,000,000 7,000,000 58.3%0.200-2.8%12/31/201114,000,000 9,000,000 64.3%0.2507.1%12/31/201215,000,000 9,500,000 63.3%0.3005.6%
Total52,000,000 32,500,000 62.5%4.2%Weighted62.8%4.6%
Permissible Loss Ratio = 60.0%
Experience StudiesRate Indication Premium Adjustments Adjustment of Premium to Current RatesParallelogram MethodExtension of Exposures
Premium TrendCompanys Own TrendsIndustry Trend [Insurance Services Office (ISO), National Council on Compensation Insurance (NCCI), etc.]Other Sources (Bureau of Labor and Statistics, fitting distributions)
Other Premium Adjustments Basic Limits Indications?
Experience StudiesRate Indication Loss Adjustments
Loss DevelopmentLoss Development based on Case Incurred Loss Development MethodLoss Development from other methods example: Bornhuetter-Ferguson method
Loss TrendCompanys Own TrendsIndustry Trend (Fast Track, ISO, NCCI, etc.)Other Sources (Bureau of Labor and Statistics, fitting distributions, ?)
Large Loss Adjustments
Storm (Catastrophic) Loss Adjustments
Experience StudiesRate Indication Other Adjustments / Assumptions Credibility StandardComplement of CredibilityAnnual WeightsExample of possible alternative to (10%, 15%, 20%, 25%, 30%) weights
(1)(2)(3)(4)Accident Year% Distribution of AdjustedEndingWeightsTotal PremiumWeights12/31/200810.0%5.8%2.5%=(10.0% * 5.8%) / 22.9%12/31/200915.0%15.4%10.1%12/31/201020.0%23.1%20.2%12/31/201125.0%26.9%29.4%12/31/201230.0%28.8%37.8%Total100.0%100.0%100.0%
Sumproduct of column (2) & (3)22.9%
Besides changing rates to the full indicated rate change, what other initiatives may be used to effect the overall rate level? UnderwritingClaimsExpensesOther
Michael Chen, FCAS MAAAActuary PC PricingMichael.Chen@fbfs.com Contact Information
Experience StudiesGlen Reineke, FSA MAAA FRMMarch 12th, 2013
Experience StudiesLife & AnnuityMortality (including a Cause of Death)Premium Persistency (Flexible Premium Universal Life)Surrender (and involuntary Lapse), including modifications for Dynamic Surrender formulaPartial Withdrawal (and Policy Loan Utilization)Other policyholder characteristicsRider utilizationInvestment Type of activities
Experience Study & Assumptions Setting ProcessThe root of the question: What should we assume in the future?While there are other purposes, this is my primary focus.One approach: Take a look at the past and adjust accordingly (Actual to Expected = A/E ratios)
Assumption Setting Must be coordinated with modeling effortsEven if you create the best (most accurate) assumption possible, you must be able to implement it in your actuarial projection models.
If your model cant implement it, have you really accomplished your objective?
For example, financial credit scores (and other 3rd party data obtained through Predictive Modeling) may provide excellent insight in to surrender behavior but may not be implementable in to your actuarial projection models.
Assumptions SettingIs the past always the best predictor of the future?Could it ever lead you in the wrong direction?Must ask yourself if the past really is the best indicator of YOUR companys future. Are there any outliers that should be thrown-out?
One example of modifying past experienceLife Mortality Improvement modification example:If your company has recently adopted a mortality improvement assumption, you may want to modify your experience study to reflect your newest outlook on mortality.
Contact Information:Glen Reineke, FSA MAAA FRMVice President Product Reportingglen.email@example.com
*For example, lets say you determine that a policy is 25x more likely to surrender if his/her credit-score drops by 150 points within one years time. Thats impressive that you found the correlation but do you model credit-scores and, in particular, do you model them stochastically? If your company doesnt model that component/input, while you have created an accurate assumption unfortunately, it is currently useless in your actuarial projection model.