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Reserving for Long-Duration Policies Presented by Roger M. Hayne, FCAS, MAAA CLRS, San Diego, CA September 10-11, 2007 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)

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reserving for long duration policies

Reserving for Long-Duration Policies

Presented by

Roger M. Hayne, FCAS, MAAA

CLRS, San Diego, CA

September 10-11, 2007

what we are used to
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
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
briefly some products considered
Briefly Some Products Considered
  • Service Contracts on
    • Vehicles – Appliances
    • Electronics – Etc.
  • Home Warranties
  • F&I Related Products
    • GAP – Tire & Wheel
    • Etching – Etc.
  • Manufacturer warranties
loss lae reserves
Loss & LAE Reserves
  • Can treat as other lines
  • Usual triangles work well
  • Often case reserves not set so incurred not available
  • Count data often useful
loss lae reserve methods
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
unearned premium
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
first find the beans before counting
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”
getting organized
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
appliance example
Appliance Example
  • Note can only purchase at time of sale, no selection issues
  • One organization – policy quarter triangles
  • Straight forward but
    • Not directly usable for emergence
    • Length of tail not known with certainty
appliance example11
Appliance Example
  • Consider different organization, by policy quarter and occurrence quarter
  • Directly captures emergence with known tail
  • Different cells are at different maturities
appliance example12
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
appliance example13
Appliance Example
  • Should have separate analyses by term length and appliance type if thought important

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

(PQ 06-4, OQ 06-4) x 9-to-Ult

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

appliance example analysis
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
appliance example analysis15
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
appliance example considerations
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
appliance example uepr
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
appliance example gaap uepr
Appliance Example – GAAP UEPR
  • Sample cumulative loss & LAE emergence
  • 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
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
appliance example statutory uepr
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

appliance example statutory uepr21
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
know thyself
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
some complications in real life
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
vehicle service contracts
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
vehicle service contracts25
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
pos new car contracts
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
pos new car contracts considerations
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
traditional new car contracts
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
vehicle contract characteristics
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
  • 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
trust accounts
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
trust account insurance
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!!!
  • 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