Reserving for Long-Duration Policies

Presented byRoger M. Hayne, FCAS, MAAA

CLRS, San Diego, CASeptember 10-11, 2007

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What We Are Used To

Usual P&C Products– Term of 1 year of less– Loss emergence usually uniform over term

(though some seasonality can exist)– Often “long” lag from claim occurrence to

settlement• Weeks to months for auto physical damage

• Many years for workers comp., med. mal., etc.

As a result– Loss & LAE reserve a principle focus– Unearned premium not usually an issue

Paradigm Shift

Service Contracts, GAP and related products– Terms can be multiple years– Losses cannot be expected to emerge

uniformly over the life of the contract– Usually (though not always) a reasonably

short lag from loss incident to payment As a result– Loss & LAE reserve not often an issue– Unearned premium reserve is the key to both

the balance sheet and income statement

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Briefly Some Products Considered

Service Contracts on– Vehicles – Appliances – Electronics – Etc.

Home Warranties F&I Related Products– GAP – Tire & Wheel– Etching – Etc.

Manufacturer warranties

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Loss & LAE Reserves

Can treat as other lines Usual triangles work well

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Acc. Qtr. 3 Mos. 6 Mos. 9 Mos. 12 Mos.

2006-3Q Pd 9/06 Pd 12/06 Pd 3/07 Pd 6/07

2006-4Q Pd 12/06 Pd 3/07 Pd 6/07

2007-1Q Pd 3/07 Pd 6/07

2007-2Q Pd 6/07

Often case reserves not set so incurred not available

Count data often useful

Loss & LAE Reserve Methods

Short tail, but chain ladder can be volatile for most recent quarter(s)

Good idea to also use an incremental severity method (see Berquist/Sherman)– Chain ladder can be used to estimate claims– Be sure underlying severity trends appear

reasonable As usual, look for changes that could affect the

accuracy of the forecasts such as changes in settlement practices, may need to use Berquiest/Sherman again

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Unearned Premium

Accounting treatment varies GAAP– Generally time premium recognition to match loss

and expense flows– Usually recognizes “up-front” expenses– May require separate premium deficiency reserve

(PDR) Statutory– Differs for less than 13 month duration and longer– 3-way test for long-duration

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First Find the Beans Before Counting Recommended first step: Figure out your true

position Use that information to figure appropriate Stat

and GAAP unearned premium booking Step 1: Get estimates of ultimate losses for

contracts on the books Step 2: Use the result from step 1 to assess

loss and expense emergence during contract lives

Step 3: Use results from steps 1 and 2 along with accounting rules to “count the beans”

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Getting Organized

“Know thyself.” Understand the critical characteristics of the contacts you are about to analyze

Make sure that the data organization and methods will recognize those characteristics

Simple Example: Appliance Warranty at POS– Covers failure during fixed time after contract

purchase– Secondary to manufacturer warranty– Only available at point of sale (POS)

Suggests policy period organization by term

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Appliance Example

Note can only purchase at time of sale, no selection issues

One organization – policy quarter triangles

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Pol. Qtr. 3 Mos. 6 Mos. 9 Mos. 12 Mos.

2006-3Q Pd 9/06 Pd 12/06 Pd 3/07 Pd 6/07

2006-4Q Pd 12/06 Pd 3/07 Pd 6/07

2007-1Q Pd 3/07 Pd 6/07

2007-2Q Pd 6/07

Straight forward but– Not directly usable for emergence– Length of tail not known with certainty

Appliance Example

Consider different organization, by policy quarter and occurrence quarter

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Pol. Qtr. 3 Mos. 6 Mos. 9 Mos. 12 Mos.

2006-3Q OQ 06-3 OQ 06-4 OQ 07-1 OQ 07-2

2006-4Q OQ 06-4 OQ 07-1 OQ 07-2

2007-1Q OQ 07-1 OQ 07-2

2007-2Q OQ 07-2

Directly captures emergence with known tail

Different cells are at different maturities

Appliance Example

First use reserve analysis to estimate ultimate losses for each policy quarter, occurrence quarter cell

One way – use development implied by final selections and paid (incurred) to date to get factors by occurrence quarter age

Apply factors to each cell:– UQ 07-2 = OQ 07-2 x 3-to-ult. factor – UQ 07-1 = OQ 07-1 x 6-to-ult. factor– Etc.

Result, ultimate emergence to date estimate

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Appliance Example

Should have separate analyses by term length and appliance type if thought important

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Pol. Qtr. 3 Mos. 6 Mos. 9 Mos. 12 Mos.

2006-3Q UQ 06-3 UQ 06-4 UQ 07-1 UQ 07-2

2006-4Q UQ 06-4 UQ 07-1 UQ 07-2

2007-1Q UQ 07-1 UQ 07-2

2007-2Q UQ 07-2

(PQ 06-3, OQ 07-2) x 3-to-Ult.(PQ 06-3, OQ 07-2) x 3-to-Ult.(PQ 06-4, OQ 06-4) x 9-to-Ult(PQ 06-4, OQ 06-4) x 9-to-Ult

(PQ 07-1, OQ 07-2) x 3-to-Ult.(PQ 07-1, OQ 07-2) x 3-to-Ult.

Appliance Example - Analysis

Separates emergence from development. Development focuses more on internal effects on claims settlement and processes– Might be consistent across a range of different

contract terms and maybe even contract types– Thus higher level summarization, e.g.

appliance all terms, may be useful and likely to be more stable than by term

Should look at claim counts – provides valuable information and allows separate severity analysis

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Appliance Example – Analysis

Now the data is organized some methods come to mind:– Chain ladder applied to

• “Traditional” policy quarter data

• Policy quarter by occurrence quarter data

– Incremental average methods averages per• Forecast claim

• Forecast contract

– Bornhuetter-Ferguson– Other

Then select ultimate estimate

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Appliance Example – Considerations Exposures and premium written may develop,

even for “point of sale” contracts due to cancellations

Since cancellations affect exposure basis, probably better to use estimated ultimate contracts (net of cancellations) in an average pure premium forecast method

For ratemaking interest is more on ultimate loss per initial contract written with a recognition of average return premium

Can do LAE separately if desired

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Appliance Example – UEPR

GAAP (simplified) – UEPR is portion of written premium relating to future losses and expenses to emerge– Divide the cumulative adjusted losses & LAE by

policy quarter and occurrence quarter triangle by forecast ultimate loss & LAE to get a triangle of emergence factors

– Select representative emergence by quarter– Reflect other expenses and apply resulting factor to

written premium. Compare expected future loss, expense &

refunds to UEPR for PDR

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Appliance Example – GAAP UEPR

Sample cumulative loss & LAE emergence

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Pol. Qtr. 3 Mos. 6 Mos. 9 Mos. 12 Mos.

2006-3Q 3% 9% 17% 25%

2006-4Q 4% 10% 14%

2007-1Q 2% 8%

2007-2Q 3%

Select 3% 9% 16% 25%

Assume expenses are 35% or premium, 25% at policy issue and 10% during life, UEPR for 2007-1Q:

WP2007-1Q x 0.75 x (1 - 0.09)

Appliance Example – GAAP PDR

Premium deficiency reserve to cover losses and expenses expected in the future in excess of the UEPR

Easy to obtain from this analysis– Future losses & LAE directly from analysis– Future overhead can be modeled separately or

applied as a load on losses & LAE– Return premium from cancellations probably

should be considered too – can be taken as premiums to date minus estimated ultimate premiums

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Appliance Example – Statutory UEPR A bit of schizophrenia– Less than 13 months duration (no special

rules):• “Earn pro-rata”

• No allowance for acquisition expenses

• Separate PDR

– 13 months or more, by formula (minimum): The UEPR should be large enough to provide for all future losses and expenses, even if all policies are cancelled at the valuation date, but should release profits no faster than losses and expenses are expected to emerge over the life of the contract

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Appliance Example – Statutory UEPR Statutory formula, 3 calculations at the UEPR

valuation date that can be based on analysis above– Calc. 1 – amount refunded if all policies are

cancelled at valuation date. Most service contracts cancel pro-rata, but check!!

– Calc. 2 – percent unemerged, parallels the GAAP UEPR calculation above

– Calc. 3 – present value of future losses and expenses, similar to GAAP PDR above, but allows discount to incurral date.

Largest by PY for last 3, PY aggregate prior

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Know Thyself

It is always a good idea to know what you expect to see and why. This often helps identify issues in the data or features that might not be appropriately captured in your models

I would expect appliance loss emergence to be slow early on, and non-existent in early occurrence quarters (depending on OEM warranty)

I would expect build-up with continuing increase till the end

Deviations should be investigated

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Some Complications in Real Life

Different products have different expected patterns, different OEM warranties, different inherent tendencies to break down

Motor vehicle contracts tend to be toward the more expensive end of the spectrum, have a rather long history (since the 1970’s or so) and tend to have twists and complications. Two major ones:– Extended eligibility– Point of Sale contracts

Take them in reverse chronological order

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Vehicle Service Contracts

General features of vehicle service contracts:– Have limitation both with respect to time coverage

exists and mileage covered– Secondary to OEM warranty– May provide for items not under OEM

Traditional new car contracts:– Time measured from original vehicle in-service

date– Mileage based on odometer mileage– May be sold on cars that are actually used, with no

change in coverage provision

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Vehicle Service Contracts

Used Car Contracts– Time measured from contract purchase date– Mileage aggregate from time of contract

purchase POS New Car Contracts– Time measured from contract purchase date– Mileage based on odometer mileage– May be sold on cars that are actually used

Suggests analysis of both used and POS new contracts on policy quarter basis

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POS New Car Contracts

Typically a car must be under OEM warranty to qualify for a “new” car contract

OEM warranty depresses losses in early stages of new car contract

For “POS” new car contracts mileage at contract purchase effects both:– Length of remaining OEM warranty so delay to full

service contract coverage and– Effective length of coverage provided

For these reasons it is a good idea to subdivide POS analyses by start miles

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POS New Car Contracts – Considerations A relatively recent contract provision (last 5 or

so years, depending on carrier or administrator) Often reference is to “twin” traditional new car

contract Actually POS contracts – Provide more coverage than corresponding

traditional new car contract– Additional coverage is in “tail”

Care should be taken in using traditional contracts to price or reserve POS contracts

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Traditional New Car Contracts

In-service quarter organization instead of policy quarter due to start characteristics

Maintains known end date Should subdivide by in-service to policy lag– Affects start of possible losses– There has been considerable adverse selection for

such “extended eligibility” Possible for policy (and premium) development to

be upwards before reductions from cancellations Need to allocate results to policy quarter

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Vehicle Contract Characteristics

Improvements in vehicle quality affect loss costs and development

For vehicles– Mileage limitations eliminate vehicles as time

progresses– Repair costs tend to increase with mileage

Broadly, losses for new car contracts tend to be “back loaded” due to OEM warranty

Broadly, losses for used car contracts tend to be “front loaded” due to lack of OEM warranty

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GAP

Guaranteed Auto Protection (GAP) provides for the difference between the loan or lease balance and actual cash value of car in case vehicle is a total loss

Term equal to loan/lease term Exposure– Heavily front-ended– Loan to value affects

• Loss cost

• Loss emergence

– LTV of 150% or more not uncommon now

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Trust Accounts

Some insurance on vehicle service contract programs on a “trust” basis– Loss portion of contract cost put into “trust”– Trust earns interest– Trust pays losses and certain expenses– Insurance coverage in case trust is exhausted

Insurance coverage can cover trust:– For contracts issued in a period of time– Entire trust

Premium usually charge per contract

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Trust Account Insurance

Should look at underlying trust account(s) Policy (underwriting) period coverage– Less complicated– Loss, LAE, UEPR similar to other multiple year

coverages– Premiums correspond to exposure

Aggregate coverage (i.e. red alert)– If policy is annual arguably no loss until entire

fund is exhausted• Loss & LAE reserve $0 unless a reasonable chance for

fund to be exhausted by year end

• UEPR???? Not clear!!!

– Premiums do not match exposure!!!04/19/23 32

Conclusion

Loss reserves amenable to most reserving methods applied to accident (repair) period (month, quarter, year) data

Exposure period by occurrence period organization a powerful tool allowing separation between policy characteristics (emergence) and internal processing (loss development)

Focus first at assessing ultimate experience, then think about counting the beans

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