John Kerper, FSA, MAAA JHK Company 9/15/2018 Reserving for Automobile Warranty and Other Long Duration Contracts Gap & Residual Value 2001 Casualty Loss Reserve Seminar John Kerper, FSA, MAAA JHK Company

9/15/2018 Purpose Introduce Gap and Residual Value coverages and the methods of estimating unearned premium reserve for these coverages.

Topics of Discussion Description of Coverages Sellers Underwriters 9/15/2018 Topics of Discussion Description of Coverages Sellers Underwriters UEP Reserve for Residual Value UEP Reserve for Gap

Description of Coverages 9/15/2018 Description of Coverages

Description of Coverages 9/15/2018 Description of Coverages Excess of loan balance over book value: Purchase price above book value Low, zero or negative down payment Loan amortization vs. vehicle depreciation Optimistic residual values After-market extras Financed insurance coverages

Description of Coverages 9/15/2018 Description of Coverages Covered Events Gap - total loss of vehicle (e.g. theft or collision) Residual Value - maturity of loan

Description of Coverages 9/15/2018 Description of Coverages Common Additional Benefits - Gap auto insurance deductible 1 or 2 delinquent payments New car purchase bonus

9/15/2018 Sellers Auto dealers Financing source Auto insurer

Underwriters Service Contract or Credit Insurer Auto Insurer 9/15/2018 Underwriters Service Contract or Credit Insurer Auto Insurer Bank / Finance Company (Debt Cancellation)

UEP Reserve for Residual Value 9/15/2018 UEP Reserve for Residual Value No refund value Timing of losses known Probability of loss unknown at inception Base reserve on assumed combined ratio As business matures, adjust combined ratio assumption No refund value - doesn't make sense to allow refund when claim can occur only at maturity and probability of claim / no-claim is better known as maturity approaches Timing of losses known - exposure concentrated at loan maturity Probability of claim unknown at inception (except to extent residual is high or low compared to market - ALG; better known as time passes); could perform historical study on development of actual market values compared to ALG projections At issue, in absence of reliable data, could assume x% combined ratio and earn premium accordingly Adjust projected combined ratio as business matures - can compare current value projections with those embedded in business to develop probable losses in portfolio. Use to project probable losses

UEP Reserve for Gap Refund Value (Rule of 78, Pro-Rata) Other tests 9/15/2018 UEP Reserve for Gap Refund Value (Rule of 78, Pro-Rata) Other tests Refund Value – usually reserve due to heavy front-end exposure not recognized in usual methods (R78 & Pro-Rata) Claim emergence pattern and present value calculations required, but generally will not determine reserve unless premium is inadequate

9/15/2018 UEP Reserve for Gap Estimating Exposure for each month

UEP Reserve for Gap Estimating Exposure for each month - example 9/15/2018 UEP Reserve for Gap Estimating Exposure for each month - example

9/15/2018 UEP Reserve for Gap

9/15/2018 UEP Reserve for Gap

UEP Reserve for Gap Estimating Probability of Loss (frequency) 9/15/2018 UEP Reserve for Gap Estimating Probability of Loss (frequency) Experience under existing book of gap contracts Separate determination of severity (based on exposure) and frequency. Total loss data from auto insurance statistics Estimating Probability of Loss (frequency) 1. Experience under existing book of gap contracts 1.1. Separate determination of severity (based on exposure) and frequency. Use frequency, but adjust severity based on relative exposure. Should not assume composite claim pattern (severity x frequency) from existing book will hold true for projections because underlying loan practices may change (fully amortizing vs. lease or balloons, loan term lengthening / shortening, new/used mix, etc) and lead to change in exposure (severity) 2. Use total loss data from auto insurance statistics to estimate frequency

9/15/2018 Conclusion UEP Reserve for Residual Value is a guess at inception and must be adjusted as residual values develop UEP Reserve for Gap is generally determined by refund value Other tests can reveal inadequate pricing or longer exposure period