unearned premium reserves change is in the wind

Unearned Premium ReservesUnearned Premium ReservesChange is in the WindChange is in the Wind

byby

Roger M. HayneRoger M. Hayne

Milliman & Robertson, Inc.Milliman & Robertson, Inc.

1999 CLRS1999 CLRS

How Easy We Had ItHow Easy We Had It

““Unearned premium reserves are substantial Unearned premium reserves are substantial liabilities on the financial statements of liabilities on the financial statements of property-liability insurance companies. property-liability insurance companies. However, they represent one liability that However, they represent one liability that should be easily determined in amount, should be easily determined in amount, without subjectivity and based on the system without subjectivity and based on the system and method the company elects to use.”and method the company elects to use.”

Property-Casualty Insurance Accounting, 1994Property-Casualty Insurance Accounting, 1994

Why Worry?Why Worry?

1997 Reserve UEP toLoss & LAE UEP Loss

American Bankers of Fl Grp $171,707 $340,653 2.0Heritage Indemnity Co 10,707 133,545 12.5American Road Insurance Co 46,207 195,436 4.2Lyndon Property Ins Co 10,462 34,847 3.3Toyota Motor Ins Co 2,740 28,348 10.3Virginia Surety Co Inc 163,561 707,767 4.3Warranty Underwriters Ins Co 2,048 12,080 5.9Western Diversified Casualty Ins Co 2,828 44,457 15.7Western General Ins Co 2,706 29,460 10.9

Total (000) 412,966 1,526,593 3.7

Industry Aggregate (000,000) 389,531 116,011 0.3

Why the Difference?Why the Difference?

Selected companies not representative of Selected companies not representative of industry (to quote the kids … “Duh!”)industry (to quote the kids … “Duh!”)

Companies have relatively large proportion Companies have relatively large proportion of multiple year businessof multiple year business

Much warranty with short payment tails but Much warranty with short payment tails but long emergence tailslong emergence tails

Result: Increased NAIC attention in recent Result: Increased NAIC attention in recent pastpast

NAIC ReactionNAIC Reaction

First separate UEPR treatment for First separate UEPR treatment for “warranty” coverage (1994)“warranty” coverage (1994)

Next more complex, 3-part calculation for Next more complex, 3-part calculation for longer-term covers (1995)longer-term covers (1995)

Finally inclusion in statement of opinion (in Finally inclusion in statement of opinion (in “practices” 1997 & “instructions” 1998)“practices” 1997 & “instructions” 1998)

Warranty RulesWarranty Rules

UEPR based on written premiumUEPR based on written premium UEPR is percentage of written premium UEPR is percentage of written premium

that losses that losses and expensesand expenses arising after the arising after the valuation date bear to the totalvaluation date bear to the total

No longer “equity” in the UEPR for prepaid No longer “equity” in the UEPR for prepaid acquisition expensesacquisition expenses

Applies to all “warranty” coveragesApplies to all “warranty” coverages

Long-Term ContractsLong-Term Contracts

Special rules for “long-term” contractsSpecial rules for “long-term” contracts Excludes:Excludes:

– financial guaranty contractsfinancial guaranty contracts– mortgage guaranty policiesmortgage guaranty policies– surety contractssurety contracts

Includes:Includes:– terms of 13 months or longerterms of 13 months or longer– if insurer cannot cancel or change premiumif insurer cannot cancel or change premium

The RulesThe Rules

Three tests:Three tests:– Amount refundable on cancellationAmount refundable on cancellation– Percent losses & expenses to happen in futurePercent losses & expenses to happen in future– Present value of future obligations (net of future Present value of future obligations (net of future

premium)premium) Individually largest for latest 3 policy yearsIndividually largest for latest 3 policy years Aggregate largest for all prior policy yearsAggregate largest for all prior policy years Based on most recent dataBased on most recent data

Test 1Test 1

Amount refundable (at valuation date) on Amount refundable (at valuation date) on cancellationcancellation

Often pro-rataOften pro-rata Parallels earning pattern for other coveragesParallels earning pattern for other coverages May end up dominating calculation at May end up dominating calculation at

unexpected timesunexpected times

Test 2Test 2

Written premiums times “a” divided by “b”Written premiums times “a” divided by “b” Terms defined by:Terms defined by:

– a is losses and expenses expected to emerge after a is losses and expenses expected to emerge after the valuation datethe valuation date

– b is estimated ultimate losses and expensesb is estimated ultimate losses and expenses Note, expenses includedNote, expenses included Designed to match premium inflow (earning) Designed to match premium inflow (earning)

with loss and expense outflowwith loss and expense outflow

Test 3Test 3

Present value of:Present value of:– Expected losses and expenses after valuation Expected losses and expenses after valuation

date minusdate minus– Guaranteed future premiumsGuaranteed future premiums

Discounted from date of emergence Discounted from date of emergence notnot date date of paymentof payment

Some specification of interest rate usedSome specification of interest rate used No reference to premiums writtenNo reference to premiums written

Some DetailsSome Details

All based on direct losses and expenses, All based on direct losses and expenses, reinsurance “later”reinsurance “later”

Interest rate in Test 3, smaller of:Interest rate in Test 3, smaller of:– YTM (yield to maturity) of 5-year treasury billsYTM (yield to maturity) of 5-year treasury bills– Company’s YTM on statutory invested assets Company’s YTM on statutory invested assets

less 1.5%less 1.5% Net of salvage/subrogation but Net of salvage/subrogation but notnot

deductibles (unless secured)deductibles (unless secured)

Some Basic ObservationsSome Basic Observations

Premium earning Premium earning notnot completely known completely known when you write a contractwhen you write a contract

Tests 2 and 3 consider losses Tests 2 and 3 consider losses and expensesand expenses unlike UEPR calculations for other linesunlike UEPR calculations for other lines

If earned premiums are written minus If earned premiums are written minus unearned then it is possible to have unearned then it is possible to have negativenegative earned premium in a yearearned premium in a year

Actual effects depend on nature of contractActual effects depend on nature of contract

Some Example ContractsSome Example Contracts

Contract 1 Contract 2 Contract 3Policy Issue 15.0% 15.0% 15.0%First Year 0.77$ 26.64$ 0.23$ Second Year 7.88 42.45 2.44 Third Year 20.22 10.91 7.48 Fourth Year 24.57 14.10 Fifth Year 19.16 19.46 Sixth Year 7.41 23.44 Seventh Year 12.86

The ContractsThe Contracts

Contract 1 - Similar to a five-year, limited Contract 1 - Similar to a five-year, limited mileage extended service contract on a new carmileage extended service contract on a new car

Contract 2 - Similar to a two-year, limited Contract 2 - Similar to a two-year, limited mileage extended service contract on a used carmileage extended service contract on a used car

Contract 3 - Similar to an appliance warranty Contract 3 - Similar to an appliance warranty or unlimited mileage new-car contractor unlimited mileage new-car contract

Three ScenariosThree Scenarios

Note all have $80 in expected losses and Note all have $80 in expected losses and expenses after policy issueexpenses after policy issue

Scenarios:Scenarios:– $100 price, 5.0% underwriting profit$100 price, 5.0% underwriting profit– $85 price, 9.1% underwriting loss$85 price, 9.1% underwriting loss– $60 price, 48.3% underwriting loss$60 price, 48.3% underwriting loss

All actually well within reason for “real All actually well within reason for “real world” warranty experienceworld” warranty experience

$100 Price - Contract 1$100 Price - Contract 1

Year Test 1 Test 2 Test 3 UEPR0 100.00$ 84.21$ 67.73$ 100.00$ 1 90.00 83.40 70.33 90.00 2 70.00 75.11 65.77 75.11 3 50.00 53.83 48.34 53.83 4 30.00 27.97 25.59 30.00 5 10.00 7.80 7.23 10.00


Year Test 1 Test 2 Test 3 UEPR0 100.00$ 84.21$ 75.11$ 100.00$ 1 75.00 56.17 51.57 75.00 2 25.00 11.48 10.64 25.00


Year Test 1 Test 2 Test 3 UEPR0 100.00$ 84.21$ 63.90$ 100.00$ 1 91.67 83.97 66.86 91.67 2 75.00 81.40 67.71 81.40 3 58.33 73.52 63.43 73.52 4 41.67 58.68 52.15 58.68 5 25.00 38.20 34.82 38.20 6 8.33 13.53 12.55 13.53


Year Test 1 Test 2 Test 3 UEPR0 85.00$ 73.32$ $67.73 $85.001 76.50 72.61 70.33 76.50 2 59.50 65.39 65.77 65.77 3 42.50 46.86 48.34 48.34 4 25.50 24.35 25.59 25.59 5 8.50 6.79 7.23 8.50


Year Test 1 Test 2 Test 3 UEPR0 60.00$ 53.93$ 67.73$ 67.73$ 1 54.00 53.42 70.33 70.33 2 42.00 48.11 65.77 65.77 3 30.00 34.47 48.34 48.34 4 18.00 17.91 25.59 25.59 5 6.00 5.00 7.23 7.23

Contract 1 EarnedContract 1 Earned

Price$100.00 $85.00 $60.00

Cumul- Incre- Cumul- Incre- Cumul- Incre-Year ative mental ative mental ative mental

0 -$ -$ -$ -$ (7.73)$ (7.73)$ 1 10.00 10.00 8.50 8.50 (10.33) (2.60) 2 24.89 14.89 19.23 10.73 (5.77) 4.56 3 46.17 21.28 36.66 17.43 11.66 17.43 4 70.00 23.83 59.41 22.75 34.41 22.75 5 90.00 20.00 76.50 17.09 52.77 18.35 6 100.00 10.00 85.00 8.50 60.00 7.23


Price$100.00 $85.00 $60.00


0 -$ -$ -$ -$ (15.11)$ (15.11)$ 1 25.00 25.00 21.25 21.25 8.43 23.54 2 75.00 50.00 63.75 42.50 45.00 36.57 3 100.00 25.00 85.00 21.25 60.00 15.00


Price$100.00 $85.00 $60.00


0 -$ -$ -$ -$ (3.90)$ (3.90)$ 1 8.33 8.33 7.08 7.08 (6.86) (2.96) 2 18.60 10.26 14.13 7.05 (7.71) (0.85) 3 26.48 7.88 20.99 6.86 (3.43) 4.28 4 41.32 14.84 32.85 11.86 7.85 11.28 5 61.80 20.48 50.18 17.33 25.18 17.33 6 86.47 24.67 72.45 22.28 47.45 22.28 7 100.00 13.53 85.00 12.55 60.00 12.55

Contract 1 Loss & Expense Contract 1 Loss & Expense RatiosRatios

Price$100.00 $85.00 $60.00


1 157.7% 157.7% 159.0% 159.0% -94.6% -94.6%2 95.0% 52.9% 111.3% 73.4% -305.7% 172.9%3 95.0% 95.0% 113.5% 116.0% 324.8% 116.0%4 97.8% 103.1% 111.4% 108.0% 181.4% 108.0%5 97.3% 95.8% 111.6% 112.1% 154.6% 104.4%6 95.0% 74.1% 109.1% 87.2% 148.3% 102.5%


Rate$100.00 $85.00 $60.00


1 166.6% 166.6% 185.4% 185.4% 422.6% 422.6%2 112.1% 84.9% 128.4% 99.9% 173.5% 116.1%3 95.0% 43.6% 109.1% 51.3% 148.3% 72.7%


Rate$100.00 $85.00 $60.00


1 182.8% 182.8% 183.3% 183.3% -134.5% -134.5%2 95.0% 23.7% 109.1% 34.6% -151.4% -287.7%3 95.0% 95.0% 109.1% 109.1% -559.0% 174.7%4 95.0% 95.0% 112.6% 118.9% 423.6% 125.0%5 95.0% 95.0% 112.5% 112.3% 209.3% 112.3%6 95.0% 95.0% 110.3% 105.2% 160.5% 105.2%7 95.0% 95.0% 109.1% 102.5% 148.3% 102.5%

ImplicationsImplications

Tests appear to apply to long-term contracts Tests appear to apply to long-term contracts in the aggregate, so effects of contracts 1, 2, in the aggregate, so effects of contracts 1, 2, and 3 may offsetand 3 may offset

For better or worse (better in speaker’s For better or worse (better in speaker’s opinion) requires periodic analysis of opinion) requires periodic analysis of warranty bookwarranty book

Detailed analysis may help get a better Detailed analysis may help get a better handle on the businesshandle on the business

AnalysisAnalysis

Tests make distinction between:Tests make distinction between:– Emergence lag (covered by UEPR)Emergence lag (covered by UEPR)– Payment lag (covered by Loss & LAE reserves)Payment lag (covered by Loss & LAE reserves)

Analysis of experience should then also Analysis of experience should then also consider the two separatelyconsider the two separately

Group data by policy periodGroup data by policy period Standard development still blends the twoStandard development still blends the two

Analysis Analysis (Continued)(Continued)

““Extended Service Contracts,” 1994 Extended Service Contracts,” 1994 PCASPCAS has an approachhas an approach

Group current valuation data by policy Group current valuation data by policy period and accident periodperiod and accident period

Most recent “diagonal” is most recent Most recent “diagonal” is most recent accident period and most immature, etc.accident period and most immature, etc.

Use accident period analysis to develop Use accident period analysis to develop diagonalsdiagonals

Some ConsiderationsSome Considerations

Policy period emergence depends on Policy period emergence depends on contract characteristics (term, mileage, level contract characteristics (term, mileage, level of coverage, etc.)of coverage, etc.)

Accident period lag probably more uniform Accident period lag probably more uniform across at least portions of bookacross at least portions of book

Accident period lag usually short, but Accident period lag usually short, but bewarebeware exceptions exist (processing lags exceptions exist (processing lags because of TPA batching, etc.)because of TPA batching, etc.)

Some ConsiderationsSome Considerations(Continued)(Continued)

Know your bookKnow your book Characteristics can affect analysis and Characteristics can affect analysis and

comparison with other sourcescomparison with other sources In early-to-mid 1980’s changes in In early-to-mid 1980’s changes in

manufacturer warranty plagued analysis of manufacturer warranty plagued analysis of auto warranty booksauto warranty books

““Extended Eligibility” is latest “wrinkle”Extended Eligibility” is latest “wrinkle”

ConclusionsConclusions

More work for opining actuariesMore work for opining actuaries Hopefully a better tool in managing long-Hopefully a better tool in managing long-

term exposuresterm exposures Although the UEPR may be “conservative” Although the UEPR may be “conservative”

could lead to misleading year-to-year could lead to misleading year-to-year experienceexperience

Potential accounting issues when UEPR Potential accounting issues when UEPR exceeds writtenexceeds written

unearned premium reserves change is in the wind

Documents

expected losses

date of emergence

direct losses

ultimate losses

expenses includeddesigned

valuation date bear

warranty rulesuepr

percentage of written