subject3031999-2004

Faculty of Actuaries Institute of Actuaries

EXAMINATIONS

April 1999

Subject 303 — General Insurance

Time allowed: Three hours

INSTRUCTIONS TO THE CANDIDATE

1. You have 15 minutes at the start of the examination in which to read thequestions. You are strongly encouraged to use this time for reading only butnotes may be made. You then have three hours to complete the paper.

2. You must not start writing your answers in the booklet until instructed todo so by the supervisor.

3. Write your surname in full, the initials of your other names and yourCandidate’s Number on the front of the answer booklet.

4. Mark allocations are shown in brackets.

5. Attempt all 11 questions, beginning your answer to each question on aseparate sheet.

AT THE END OF THE EXAMINATION

Hand in BOTH your answer booklet and this question paper.

In addition to this paper you should have availableActuarial Tables and an electronic calculator.

Faculty of Actuaries303—A99 Institute of Actuaries

303—2

1 A small general insurance company underwrites only a single class ofbusiness, which is long tailed. Describe briefly the factors it should considerwhen deciding upon its investment policy. [7]

2 An insurance company intends to offer a product to the motion pictureindustry. The product will provide cover should the cost of producing afinalised, distributable product exceed a pre-agreed budget. List the majorperils that could be included in the cover. [4]

3 (i) Describe the assumptions behind the Bornhuetter-Ferguson method ofestimating the ultimate cost of claims of a book of business. [2]

(ii) You have been given the following information about a particular classof business.

Underwriting Initial Premium Reported claimsYear Expected cost as at

Loss ratio 31 December 1998

1995 70% 1,000,000 500,0001996 75% 1,500,000 500,0001997 80% 2,000,000 1,000,0001998 85% 2,500,000 400,000

Expected reported claims development pattern:

Development year 0 1 2 3 4Expected proportion developed 10% 50% 80% 90% 100%

Calculate the expected ultimate claims as at 31 December 1998according to the Bornhuetter-Ferguson method. [3]

(iii) Comment briefly on the reliability of the results in part (ii). [3][Total 8]

4 List, and state the purposes of, the major actuarial investigations undertakenby general insurers in relation to investment. [5]

5 (i) List the reasons why a general insurer models claims. [4]

(ii) List the steps involved in applying a deterministic modelling method.[3]

[Total 7]

303—3 PLEASE TURN OVER

6 Two general insurance companies both have a solvency margin equal to 50% ofwritten premiums. Explain why the underlying financial strengths of the twocompanies may differ. You may ignore the question of the adequacy of thetechnical reserves. [5]

7 List the main regulatory restrictions that may be encountered by a generalinsurance company when transacting insurance business. [4]

8 List the reasons why general insurance claims experience may vary from thatassumed in the premium basis. [6]

9 (i) Explain the terms “reinstatements” and “reinstatement premiums” inthe context of catastrophe excess of loss reinsurance. [4]

(ii) Define the term “rate on line”. [1]

A property catastrophe reinsurance layer with unlimited reinstatementswould have a theoretical rate on line, given a detailed actuarial assessment ofthe risk, of 5%. A prospective reinsured has asked for two quotations for coveron this layer – one with no reinstatements, and one with a singlereinstatement at 100% additional premium.

(iii) State with reasons which of the two alternative structures you wouldexpect to require the higher rate on line. [4]

[Total 9]

10 (i) List the factors that a general insurance company writing manydifferent classes of business would consider in determining appropriatereinsurance arrangements. [5]

A general insurance company A writes only commercial propertybusiness. One risk which it coinsures with three other insurers B, Cand D has a sum insured of $10 million, but an expected maximum loss(EML) of $500,000. Company A accepts 40% of this risk, with B, C andD accepting 20% each.

Company A reinsures with company X 5% of every risk under a quotashare treaty. It is agreed that A will not write business for which itsgross share of the EML exceeds $250,000.

Company A also has a three line surplus treaty with companies Y and Z,each taking 50%, which operates after the quota share, and is based oncompany X taking 5% of company A’s gross business. The surplustreaty has a maximum EML retention of $50,000.

A single large claim gives rise to a loss of $750,000.

303—4

(ii) Calculate the amount of the claim which Company A will pay, net of allreinsurance recoveries due. State any assumptions you make. [4]

(iii) Explain how your answer to (ii) would differ if, immediately prior tothis claim, companies B and Y were declared insolvent. [3]

(iv) State the information you would expect Company A to provide toCompany Z during the handling of this claim. [3]

[Total 15]

11 You are the actuary of a general insurance company with two Private Motorproducts, A and B. The monthly Gross Written Premium (GWP) of products Aand B has been £10m split equally between the two products for many years upto and including December 1998. You have been asked by the FinanceDirector to evaluate the adequacy of the Unearned Premium Reserve (UPR) of£60m in Private Motor at 30 June 1999. The UPR has been calculated gross ofDeferred Acquisition Costs (DAC) and on a 24ths basis.

In your testing of the adequacy of the Claim Reserves as at 31 December 1998,you determined an expected ultimate loss ratio for Accident Year 1997 forPrivate Motor of 90%, split 75% for product A and 105% for product B.

In the light of the emerging poor performance of Product B during 1998, thecompany imposed two rate increases to Product B’s rates, each of 6%, whichwere applied at 1 January and 1 April 1999. This had the effect of reducingProduct B’s share of the monthly GWP to 20% by June 1999. This reductionoccurred evenly over the business written in the first 6 months of 1999. Mostcustomers switched to Product A, and the total monthly GWP remained at£10M in each month. No other rate increases had been applied for a number ofyears.

Claim cost inflation has been 0.5% per month for many years. DAC is 15% ofUPR. Claims handling expenses are 2.5% of the outstanding claim amount.The present value of investment return at 30th June 1999 is 10% of theoutstanding claim amount. You may ignore reinsurance.

(i) Define the following terms:

(a) Unearned Premium Reserve(b) Deferred Acquisition Cost(c) Unexpired Risk Reserve(d) Additional Reserve for Unexpired Risks (AURR) [4]

(ii) Calculate the expected ultimate loss ratio for the total Private Motorbusiness written in July 1999. State clearly any assumptions you makein your calculation. [8]

(iii) Calculate the expected ultimate claim cost of the unexpired risks as at30 June 1999. State any additional assumptions made. [10]

303—5

(iv) Determine whether or not an AURR is required in respect of PrivateMotor business as at 30 June 1999. [4]

(v) Explain why the AURR calculated for Product A alone might differ fromthat calculated for Product B alone. [4]

[Total 30]


EXAMINATIONS

April 1999


EXAMINER’S REPORT


Subject 303 (General Insurance) — April 1999 — Examiners’ Report

Page 2

Comments on each specific question appear in italics at the end of each solution.

1 Main objective is to maximise investment return whilst meeting all itscontractual obligations.

Match characteristics of the assets with those of the liabilities by term,amount, nature and currency.

Premiums will be received in advance of claims, and these can be invested.Need to allow for the split between annual, and monthly premium business,and for the fact that some monies may be held by third parties.

Consider the effect of inflation on the liabilities. Can these be matched?

Matching considerations may run counter to solvency requirements - longterm assets have high volatility.

Marketability of assets - the insurer is small, and claims may fluctuate fromone month to the next.

Consider the free assets - you want to maximise the return, but in deciding onthe investment policy the insurer needs to consider the size in relation to:

• annual premium income• expected claims each year• absolute size of the liabilities at any time• SMSM

The effect of the reinsurance arrangements should be taken into account.The insurer will not want to stray too far from industry norms.

2 Actor,director or producer illness, accident or deathContract disputesWeather perils disrupting timetable of filmingFaulty filmDamage to negative during editing


Page 3

3 (i) Whatever claims have developed in relation to an origin year, thefuture development pattern will follow that experienced for otherorigin years.The past development for a given origin year does not necessarilyprovide a better clue to future claims than the more general loss ratio.

[2]

(ii) U/W Initial % not Expected Actual TotalYear Estimated reported Future Reported Estimated

Ultimate yet Reported Claims UltimateClaims Claims Claims

1995 700,000 10% 70,000 500,000 570,0001996 1,125,000 20% 225,000 500,000 725,0001997 1,600,000 50% 800,000 1,000,000 1,800,0001998 2,125,000 90% 1,912,500 400,000 2,312,500

The total estimated ultimate claims are 5,407,500

(iii) Reported claims are lower than original estimate by 142,500Is the original LR appropriate?Are the reported reserve estimates reliable?Is the development table accurate?Older years are below the initial expected losses, recent years above –has the initial expected loss ratio allowed fully for marketdevelopments?There is a big jump in loss ratio from 1996 to 1997. Is there anyparticular reason for this?

4• Investment portfolio evaluation, to assess the performance of investment

managers• Cash flow / asset-liability modelling to set investment policy• Allocation of income and capital between classes for pricing and

profitability measurement• Risk-based capital allocation to enable solvency evaluation or profitability• Calculation of return on capital to allow shareholders to assess

management performance.

5 (i)• To arrive at a risk premium per policy.• To select rating factors• To determine premiums using experience rating procedures• To demonstrate the estimated effect of changing the level of cover• To determine the effect of excess of loss reinsurance• To estimate the variability of claims experience• To estimate the impact on the reserves of industrial diseases• Financial planning• Workload management/staff planning


Page 4

• Statutory requirement to do so

(ii)• Specify the purpose of the investigation• Collect data• Group and modify data• Compare data with a suitable density function• Fit the data to the density function• Check that goodness of fit is acceptable• Fit different model if not

6 Valuation of the AssetsThe asset valuation bases, andmethod used for recognising capital gains will affect the stated surplus

Investments heldWeak security of investments undermines high asset valueUndue concentrations of investments do likewise.

Mix of businessDifferences between the mixes of business − such as short tail or longtail will distort comparison.Long tail classes require a larger solvency margin for same relative financial strength

Unusual eventsCatastrophes − a company with little catastrophe protection needs

more capitalHigh expenses from internal reorganisations

Third Party ExposureFinancial security of reinsurer affects quality of reinsurance levelsOr any other debtor, especially brokers, affects quality of assets

Presence of equalisation reserves, or other hidden types of capital.Differences in reinsurance arrangements.

7 Restrictions on the type of business an insurer may writeLimits on the premium rates that may be charged.A requirement to maintain a minimum level of solvency,measured in some prescribed manner.Restrictions on the typeor amount of assets that may be taken into account to demonstrate

solvencyA requirement to use prescribed bases for valuing assets/liabilitiesLegislation to protect policyholders should a general insurer failLicensing of agents to sell insuranceRequirements to provide informationControl of sales outletsApproval of staff and directorsRestrictions on volumes written


Page 5

8 Lack of previous experienceVariability of experienceChanging types of businessChanging risk characteristicsAntiselection by policyholdersChanging attitudes to claimingClimate effectsCatastrophesExchange rate movementsLatent claimsNew types of claimClaims inflationLegislative changesJudicial changesPoor managementPoor underwriting

9 (i) A catastrophe excess of loss policy normally allows the reinsured tomake only one claim on the policy. Most policies allow the cover to berestored after a claim, so that the reinsured still has protection. This iscalled reinstatement. Normally there will be a limit on the number oftimes the cover may be reinstated.

A reinstatement may be free, or a premium may be payable. If there isa premium, it will normally be a proportion of the original premium. Itwill be payable whether or not the whole of the cover has beenexhausted, and will be proportional to the amount of the claim to thelayer.

(ii) Original premium ÷ width of layer. (Does not include reinstatementpremium in calculation.)

(iii) The option with no reinstatements would have the higher rate on line.The low rate on line of the underlying risk suggests that the probabilityof two losses is very low. The expected value of a reinstatementpremium is greater than the expected value of a second loss, so theexpected net payments by the reinsured are lower under the secondoption.

10 (i) Class of businessSize of individual risksLikely accumulation of risksVolatility of claims experience - numbers and amountsSize of class relative to total written premiumsSize of free reservesPremiums written relative to size of free reservesAvailability of reinsuranceAvailability of coinsurance


Page 6

Need for technical assistanceManagement attitude to riskSecurity status of reinsurers

(ii) (a) Company A is directly responsible for 40% of $750,000 = $300,000under the coinsurance agreement.Company X takes 5% of $300,000 = $15,000 under the quota shareagreement.There are two possible approaches (or indeed anything betweenthe two). However, candidates need to recognise that there is aneed for an assumption, to state the assumption and then tofollow it through in the calculation.Assumption 1 Company A takes the full three lines of cover,ceding 75% to the surplus reinsurers. Therefore, its net claim is25% × ($300,000 − $15,000) = $71,250.Assumption 2 Company A keeps the maximum $50,000retention, so that its proportionate retention is $50,000 ÷ (95% ×40% × $500,000) = 1 ÷ 3.8. Therefore its net claim is ($300,000 −$15,000) ÷ 3.8 = $75,000.

(b) As company B is a coinsurer alongside A the insolvency does notaffect the amount to be paid by A.As company Y is a reinsurer of A the insolvency will affect therecoveries A can make. In the most extreme case, A will lose theamount it is owed by Y; in practice, there will almost certainly bea partial recovery from the liquidators of Y. The actual answerwill lie between the answer in (a) and a revised amount,assuming that there is no recovery at all from Y. The answer inthat case depends on the assumption made in (a) above.Assumption 1 In this case A will have to pay an extra 75% × 50%× ($300,000 − $15,000) = $106,875, so the total will be $178,125.Assumption 2 In this case, A will have to pay an extra 50% ×($300,000 − $15,000 − $75,000) = $105,000, for a total of $180,000.

(iii) Details of loss:Description of property, processes and materials usedDate and time of lossEstimated costCause of loss

Explanation why loss amount exceeded the EML


Page 7

11 (i) (a) UPRThe amount set aside from premiumswritten before the accounting dateto cover risks incurred after that date

(b) DACA deduction from unearned premiumas they become earnedfor acquisitionand commission costs

(c) URRThe reserve required to cover the claimsand expenseswhich are expected to emerge from an unexpired period of cover

(d) AURRThe reserve held in excess of the UPR to allow for anyexpectationthat the UPR will be insufficient to cover the costs ofoutstanding risks

(ii) AssumptionsClaims in accident year 1998 occurred on average at 1 July 1998The business resulting in AY 1998 claim was written on average on 1January 1998Period of cover is twelve monthsJune 1999 business was written on average in the middle of the monthClaim cost inflation period for June 1999 business is 17½ monthsClaim frequency inflation is 0%The mix/riskiness of business within products A and B is unchanged

Average written premium (AWP) of Product A is unchangedAWP of product B is increased by 1.062

− 1 = 12.36%

Loss ratio of Product A at June 1999 is 75 × 1.00517.5 = 81.84%Loss ratio of Product B is 105 × 1. 00517.5

÷ 1.062 = 101.97%

The GWP at June 1999 is £8 million for Product A and £2 million forProduct BCombined loss ratio = 81.84% × 0.8 + 101.97% × 0.2 = 85.90%


Page 8

(iii) AssumptionsRisk spread evenly throughout the year

Unexpired Loss ratio % Loss ratio % GWP GWP UltimateCover Jul for Product A for Product B A B Claim98 to Jun 99 £M £M Costin 24ths £M

Jul 98 1 75 × 1.005^ 6.5 105 × 1.005^ 6.5 5.0 5.0 0.387Aug 98 3 75 × 1.005^ 7.5 105 × 1.005^ 7.5 5.0 5.0 1.168Sep 98 5 75 × 1.005^ 8.5 105 × 1.005^ 8.5 5.0 5.0 1.956Oct 98 7 75 × 1.005^ 9.5 105 × 1.005^ 9.5 5.0 5.0 2.752Nov 98 9 75 × 1.005^ 10.5 105 × 1.005^ 10.5 5.0 5.0 3.556Dec 98 11 75 × 1.005^ 11.5 105 × 1.005^ 11.5 5.0 5.0 4.369Jan 99 13 75 × 1.005^ 12.5 105 ÷ 1.06 × 1.005^ 12.5 5.5 4.5 4.948Feb 99 15 75 × 1.005^ 13.5 105 ÷ 1.06 × 1.005^ 13.5 6.0 4.0 5.657Mar 99 17 75 × 1.005^ 14.5 105 ÷ 1.06 × 1.005^ 14.5 6.5 3.5 6.352Apr 99 19 75 × 1.005^ 15.5 105 ÷ 1.062 × 1.005^ 15.5 7.0 3.0 6.888May 99 21 75 × 1.005^ 16.5 105 ÷ 1.062 × 1.005^ 16.5 7.5 2.5 7.564Jun 99 23 75 × 1.005^ 17.5 105 ÷ 1.062 × 1.005^ 17.5 8.0 2.0 8.229

Total 53.827

Marks are given for:Correct formula for one month (say July 1998)

= [75% × 5.0 + 105% × 5.0] × 1.0056.5 × 1/24 = 0.387Combined GWP × Loss ratio for A + BClaims cost inflationUnexpired coverCorrect answer for July 1998Correct answer for August 1998 to December 1998Correct adjustment for January 1999 GWP

and loss ratioCorrect answer for January 1999 = 4.948Correct answer for February 1999 to March 1999Correct answer for April 1999 loss ratioCorrect answer for April 1999 = 6.888Correct answer for May 1999 to June 1999Correct overall unexpired claim cost = 53.827

(iv) UPR = 60.0less DAC of 15% × 60.0 = −9.0

equals 51.0

Unexpired claim cost 53.8less investment return of 10% × 53.8 = −5.4plus claim handling costs of 2½% of 53.8 = 1.3

equals 49.8

Surplus of 1.2Therefore no need for an AURR


Page 9

(v) Difference in expected ultimate loss ratiosDifference in GWP distribution throughout the twelve months ending30 June 1999The acquisition costs might be different due to:

different distribution channels, for exampleProduct A may be sold direct, Product B through brokers

Commission rates may therefore be differentValue of investment return depends upon claim paymentsProduct A may have a greater Comprehensive mix (more short tail)than Product B


EXAMINATIONS

September 1999












Faculty of Actuaries303—S99 Institute of Actuaries

303—2

1 A general insurance company is constructing an asset-liability model todetermine the likely future relationship between its assets and liabilities.

(i) State the particular factors that will need to be incorporated into themodel if it is to be used to assess future solvency. [4]

(ii) List, with brief reasons for their interest, the parties who may beinterested in the level of the solvency of the company. [3]

(iii) Discuss briefly whether it would be more effective to use adeterministic or a stochastic model. [3]

[Total 10]

2 State the reasons why a general insurer would analyse its claims data. [5]

3 You are the actuary to an insurance company that writes industrial propertybusiness with large deductibles. It is subject to large losses, which are usuallyreported quickly. Reserves are always set up in respect of these losses, butthese are often found to be excessive or inadequate. You are concerned aboutthe estimation of ultimate claims from this line of business, which has beencarried out using the chain ladder method and has often been unstable in thepast. It has been suggested that the use of Bornhuetter-Ferguson methodswould provide an element of stability in reserve estimates.

Discuss this suggestion. [5]

4 List the guidance notes published by the Institute and Faculty of Actuarieswhich relate to general insurance business, and state what each relates to. [6]

5 List the portfolio movements that are normally monitored by a generalinsurance company, and state the reasons for monitoring them. [5]


6 Company A is a medium-sized general insurance company, writing a variety ofproperty and liability risks. It expects a loss ratio of about 75% on itscommercial property portfolio, which accounts for about 60% of the company’stotal premium. At the end of the company’s past year it had capital of 28% ofthe premium written during the year. It has recently taken out a reinsurancetreaty, from which the following information has been extracted.

Name of reinsured: Company A

Subject business: All business written by the reinsured in the class“commercial property” with an inception date during1999.

Reinsurance premium: 41% of original premiums of the subject business, to bepaid on 31 December 1999.

Commission: A reinsurance commission of 9% of original premiumsof subject business shall be paid to the reinsured. Thisis part of the 41% reinsurance premium.

Limits: Losses shall be paid to the reinsured in excess of atotal loss equal to 70% of original premiums of subjectbusiness, up to a maximum total loss of 111% oforiginal premiums of subject business.

Termination: This treaty shall be terminated with effect 31December 2003, and all monies due as claims or profitshare shall be paid to the reinsured immediately.

Profit share: On termination of the contract a profit share shall bepayable to the reinsured. This shall be calculated as97½% of the profit. The profit shall be calculated as41% of the original premiums of the subject businessless any claim payments made to the reinsured underthis contract.

Discuss this reinsurance treaty. You should consider the nature of thecontract, the nature and amount of the protection and any other benefits itprovides, the reasons for taking it out, and how it might meet those criteria.

[10]

303—4

7 Give examples of errors which might be made in entering data into a computerclaims system, and suggest automatic proceedings which would reduce theprobability of them occurring. [5]

8 You are the pricing actuary for a reinsurance company. You are being asked toquote for a quota share reinsurance of the cedant’s book of liability business.The inception date of the policy is to be 1 January 2000. The broker hassupplied you with the following information.

• Between 1990 and 1997 premium increases kept pace with increases inlosses and the underwriting loss ratio was fairly stable at around 85%.

• Since 1997 the market has softened. Premium rates fell by 5% per annum in1998 and 1999 while losses increased at 10% per annum over the sameperiod. The company has cut back on its new writings as a result.

• Written premium in 1989 was 500.

The following statistics have also been provided, and you have made thecalculations shown.

Underwriting year: 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999Written premium: 500 600 700 800 900 1,000 1,100 1,200 600 300


Paid lossesData evaluated as at 31 December each yearLast diagonal as at 30 June 1999

AccidentYear 0 1 2 3 4 5 6 7 8 91990 26 48 65 89 208 257 298 319 339 3511991 28 43 76 93 229 280 331 353 3621992 40 66 72 104 279 336 384 4001993 18 68 88 139 313 382 4121994 25 80 110 150 368 3951995 32 63 137 168 2911996 31 71 152 1571997 27 104 1111998 51 541999 10

Year-on-year development

AccidentYear 0 – 1 1 – 2 2 – 3 3 – 4 4 – 5 5 – 6 6 – 7 7 – 8 8 – 9

1990 1.85 1.35 1.37 2.34 1.24 1.16 1.07 1.06 1.041991 1.54 1.77 1.22 2.46 1.22 1.18 1.07 1.031992 1.65 1.09 1.44 2.68 1.20 1.14 1.041993 3.78 1.29 1.58 2.25 1.22 1.081994 3.20 1.38 1.36 2.45 1.071995 1.97 2.17 1.23 1.731996 2.29 2.14 1.031997 3.85 1.071998 1.06

Average year-on-year development factors

All years:

2.15 1.49 1.29 2.27 1.18 1.14 1.06 1.04 1.04

All years excluding last diagonal:

2.39 1.59 1.36 2.43 1.22 1.16 1.07 1.06

Last three years:

2.10 1.68 1.19 2.13 1.16 1.13 1.06 1.04 1.04

Last three years excluding last diagonal:

2.64 1.86 1.36 2.44 1.22 1.16 1.07 1.06

303—6

Incurred lossesData evaluated as at 31 December each yearLast diagonal as at 30 June 1999

AccidentYear 0 1 2 3 4 5 6 7 8 91990 123 511 384 404 416 421 425 425 425 4251991 135 561 420 445 458 463 468 468 4681992 169 661 496 524 542 547 553 5531993 201 763 572 606 625 631 6341994 220 869 651 685 708 7121995 242 970 726 766 7791996 267 1,073 805 8241997 295 1,174 1,0261998 372 9301999 202

AccidentYear 0 – 1 1 – 2 2 – 3 3 – 4 4 – 5 5 – 6 6 – 7 7 – 8 8 – 9

1990 4.15 0.75 1.05 1.03 1.01 1.01 1.00 1.00 1.001991 4.16 0.75 1.06 1.03 1.01 1.01 1.00 1.001992 3.91 0.75 1.06 1.03 1.01 1.01 1.001993 3.80 0.75 1.06 1.03 1.01 1.001994 3.95 0.75 1.05 1.03 1.011995 4.01 0.75 1.06 1.021996 4.02 0.75 1.021997 3.98 0.871998 2.50

Average year-on-year development factors

All years:3.71 0.77 1.05 1.03 1.01 1.01 1.00 1.00 1.00

All years excluding last diagonal:

3.98 0.75 1.06 1.03 1.01 1.01 1.00 1.00

Last three years:

3.40 0.79 1.04 1.03 1.01 1.01 1.00 1.00 1.00

Last three years excluding last diagonal:

4.00 0.75 1.06 1.03 1.01 1.01 1.00 1.00

(i) Describe in detail how you would use the Paid and IncurredBornheutter-Ferguson methods to estimate ultimate losses for thisbusiness for each accident year. You should explain all choices andassumptions you would use. You are not required actually to calculatethe estimated ultimate losses [16]

(ii) Estimate the ratio of discounted ultimate claims to undiscountedultimate claims as at the start of an accident year. Use a 10% p.a.interest rate.

[5]


(iii) Assuming brokerage of 2½%, commission of 5%, premiums paid evenlythroughout the year and a required profit load of 10% of undiscountedpremiums calculate the required ceding commission for this treaty.State any assumptions made. [5]

[Total 26]

9 In a particular country, all insurance business is accounted for on a one-yearbasis, but may be accounted for on an accident year basis or an underwritingyear basis.

Company A and Company B operate in this country. Company A uses anaccident year basis and company B uses an underwriting year basis. Theirbalance sheets as at 31 December 1998 are given below. Both companies havehad stable levels of premium income for a number of years.

Company A — balance sheet as at 31 December 1998

Cash on hand 3,000 Unearned premium 4,000Other investments 11,000 less DACs 800

3,200Claim reserves 6,000Share capital 500Share premium account 1,500Retained profits 2,800

Total assets 14,000 Total liabilities 14,000

Company B — balance sheet as at 31 December 1998

Investments 14,000 Claim reserves 12,000Share capital 500Retained profits 1,500


(i) Discuss how these two bases would differ in the context of one-yearaccounting, and the consequences for the recognition of profits. [5]

Company A has agreed to acquire all the shares of Company B as at 31December 1998 for 2,500. At that date, Company B’s balance sheet will berestated in accordance with Company A’s, and the two companies will bemerged. In accordance with the laws of this country, any goodwill arising fromthe transaction will be written off immediately. Company A’s own loss ratio inunderwriting year 1998 is expected to be 60%. In the course of Company A’sdue diligence exercise, the following facts have emerged about Company B.

• The premium written in 1998 was 3,200.

303—8

• No premium will be received in respect of the 1998 underwriting year afterthe end of the year.

• The expected loss ratio on underwriting year 1998 was 88%. This is theconclusion of the due diligence exercise, rather than Company B’smanagement’s opinion.

• Average commission on underwriting year 1998 was 25%.

• Business is renewed predominantly on 1 January and 1 April, to the extentthat the average inception date of all policies was 1 April. (Which may beconsidered to be exactly 25% through the year.)

• All claim reserves need to be increased by 10% to conform to the standardsof Company A.

(ii) Prepare the balance sheet of Company B at 31 December 1998 on anaccident year basis to Company A’s reserving standards. [5]

(iii) Prepare the balance sheet of Company A at 31 December 1998 after thetakeover has been completed. [4]

(iv) Comment on the differences between Company A and Company B thatmay be inferred from the balance sheets and other information, and theeffect of the takeover on Company A’s financial position. You mayassume that all assets yield income of 7½% per year. [14]

[Total 28]


EXAMINATIONS

September 1999


EXAMINER’S REPORT

Introduction

The attached subject report has been written by the Principal Examiner with the aim ofhelping candidates. The examiners are mindful that a number of interpretations maybe drawn from the syllabus and Core Reading. The questions and comments are basedaround Core Reading as the interpretation of the syllabus to which the examiners areworking. They have however given credit for any alternative approach or interpretationwhich they consider to be reasonable.

The report does not attempt to offer a specimen solution for each question - that is, asolution that a well prepared candidate might have produced in the time allowed. Formost questions substantially more detail is given than would normally be necessary toobtain a clear pass. There can also be valid alternatives which would gain equal marks.

D S BrandChairman of the Board of Examiners

30 November 1999

� Faculty of Actuaries� Institute of Actuaries

Subject 303 (General Insurance) — September 1999 — Solutions

Page 2

Overall, this was a difficult exam, and it was to be expected that candidates would finddifficulty in some areas. However, the examiners were concerned in a number of areaswhere very few candidates appeared to have any understanding of the concepts beingexamined.

1 (i) The main problem with the answers to this question was that manycandidates failed to give any consideration to the question of modelsintended to demonstrate solvency, rather than modelling in general.Allow for any statutory requirements relating to the valuation of assetsand liabilities.A comparison may then be made of the actual level of solvency with thatacceptable to the statutory authorities,And any higher minima, such as those really acceptable to supervisors orto rating agencies.

Assumptions:Likelihood of catastrophes and accumulations.Vulnerability of capital to major shocks such as these.Effect of actual non-proportional reinsurance coverages on catastrophes.Spread of different risk groups within the portfolio.Insurer’s experience of writing different classes of business.Expected level of profitability, both underwriting profit and level ofinvestment income generated (model tail length of classes).

(ii) This section was generally well answered.Statutory authorities — to protect policyholders.Company management — duty to company / shareholders / policyholders.Rating agencies — provide accurate information.Brokers — to place business with solvent companies.Shareholders — to monitor their investments.Policyholders — to check the solvency of their insurers.Competitors — to try to discover competitively useful facts.Potential purchasers of the company — to assess its value.

(iii) This section was generally well answered.Might test variability using variations in assumptions with adeterministic model.Easier to test effects of particular scenarios using a deterministic model.Stochastic more complex, and harder to get right.Stochastic harder to parameterise.

Stochastic more effective in incorporating allowance for volatility is assetvaluesAnd uncertainty in claims experience.Stochastic may take into account correlations between and within assetsand liabilities.Stochastic allows construction of probability distribution for outcomes.


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2 Most candidates knew the main reasons and scored reasonably well.Estimating the cost of outstanding claimsto set reservesMonitoring the actual runoff of outstanding claimsagainst estimated amountsMonitoring the adequacy of reinsuranceComparing the relative profitability of various parts of the accountReviewing current premium ratesPricing new productsFinancial planningMonitoring the asset-liability position

3 Almost no candidates considered the paid and incurred approaches separately,despite the difference in the effect likely. Almost none realised that when theclaims incurred average 100% of ultimate in an early report then the weightattached to the initial expected losses is minimal, and that therefore the incurredBornhuetter-Ferguson method has almost no effect on the incurred chain ladderestimate, or that it is inappropriate to use the Bornhuetter-Ferguson approachwhen a reduction in incurred claims is anticipated. Some candidates suggestedgiving a credibility-inspired weight to the initial expected losses, which is asensible variation of the Burnhuetter-Ferguson. Some suggested that when claimsare reported quickly, as is normal in this class of business, it would be better toreply on case estimates. This is a sensible suggestion, but the problem in this caseis that case estimates have proved unreliable, and to use this approach we wouldneed to find some way to improve the quality of case estimates.

It is not stated whether the paid or incurred Bornhuetter-Ferguson (BF) methodis intended, and whether it is likely to replace a paid or incurred chain laddermethod. If paid methods are intended, then the BF is likely to be animprovement on the chain ladder, provided a sensible initial expected lossestimate is available, as its development will be more stable, and less affected byearly swings in paid amounts. However, these methods ignore the amount ofreserves set up in respect of reported claims. This is normally thought to be avaluable source of information, even though in this case it is noted that thereserves are often badly inaccurate.

If it is intended that incurred methods be used, the BF suffers from a veryserious weakness. This is that if reductions in incurred claims are more normalthan increases, the formula does not make sense, predicting a reduction which isa function of initial expected losses rather than the reported claims which aresubject to reduction. Also, even if there are only modest further increases inincurred claims to be expected, then the initial expected losses are given littleinfluence in the projected result, and therefore little opportunity to exercise astabilising influence. From the information available, it appears likely that oneof these will be the case.

It may be found useful to consider the results of Bornhuetter-Ferguson methodsin addition to the current methods the company uses.


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4 This question was surprisingly badly answered, as it is straight bookwork. Thismeant that while a reasonable number of candidates obtained full marks, othergained little or no credit. Some candidates evidently felt that it was outside thescope of the examination, as the specific application of the guidance notes is theUnited Kingdom, but the answer is a direct quotation from the core reading. Allmembers of the Institute and Faculty should be aware of the nature of professionalguidance, which can be obtained only by familiarity with the guidance notes. Ofmore importance, since the last amendment to the syllabus and core reading,GN14 has been withdrawn and GN12 amended significantly. Under the normalexamination rules, an answer would have been accepted as fully correct if itcorresponded either to the syllabus/core reading or to the correct situation at thetime of the examination.

GN12: An actuarial report on the reserves or financial soundness of aninsurance company or Lloyd’s syndicate.

GN14: Providing the actuarial reports on Lloyd’s run-off years of accountrequired under Lloyd’s byelaws.

GN18: Providing a Certificate of loss reserves to the International InsurersDepartment in respect of a UK insurance company authorised in theUnited States of America.

GN20: Providing a statement of actuarial opinion to the Council of Lloyd’s inrespect of solvency reserves under the Lloyd’s Valuation of LiabilitiesRules.

GN 32: The work of the Appropriate Actuary of a Friendly Society.GN 33: Providing statements of actuarial opinion to the International Insurers

Department and the New York Insurance Department in respect of therelevant US insurance or reinsurance business of a Lloyd’s syndicate.

5 This question was generally well answered.The movements which are normally monitored are:• New business• Lapses at renewal• Endorsements• Mid-term cancellations

By studying movements and their trends, an insurer can:• Measure the growth or contraction of the business and of its different parts.• Get an early indication of unusual losses or gains in business volume. These

may indicate if the insurer’s rates or conditions are out of line with themarket.

• Assess the effects of a new set of rates or a marketing campaign on thebusiness, and thus the sensitivity of the portfolio to market forces.

Movements will give an early indication of adverse or favourable changes. Thesemay indicate the need for a review of premiums or terms and conditions. Theymay also be used to help reconcile accounts data and in-force statistics.


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6 This question was generally answered very badly. Few candidates realised thatthe policy in question was financial reinsurance, and most of those who did failedto analyse the policy on its merits as a financial reinsurance considering theinsurer’s probable motives in effecting such cover. Many candidates analysed thecompany’s gross and net position, rather than looking at the effect on the companyof the reinsurance, which would have revealed the lack of risk transfer. Ofcandidates who did identify the lack of risk transfer, many identified it as a flawin the policy design, rather than a fundamental part of it. Past examinations havesuggested that candidates are familiar with the concept of financial reinsurance,but the response to this question suggests that they lack knowledge on how sucharrangements might be constructed. A good number of candidates did identifycorrectly that the policy would have a beneficial effect on the company’s solvencypurely in terms of the solvency margin:net premium ratio. Unfortunately, ifcandidates failed to recognise the nature of the policy, it was not generally possibleto award significant marks. The examiners gave favourable consideration tocandidates who had analysed the reinsurance as if it was a conventional stop lossproduct, and had got very low marks, but whose analysis of it as a stop lossproduct was sensible and detailed. However, such analysis would generallysuggest that there were a number of major inconsistencies in the product, whichmany candidates who took this approach spotted. Some candidates thought thatthis was a proportional reinsurance, apparently on the basis that the reinsurancepremium is expressed as a proportion of the subject premium. It should be notedthat almost all reinsurance premiums, whether of proportional reinsurance or not,are expressed in this way. The worst candidates simply listed the conventionalreasons for effecting reinsurance, or examined the policy in the light of what thecompany’s overall reinsurance strategy ought to be. Some candidates understoodthe commission clause to indicate that 41% premium was net of the 9%commission. This had not been intended, and would change the financial natureof the policy profoundly, however, its purpose was understood.

The policy transfers almost no risk. The company expects a loss ratio of 75%.Therefore, it is unlikely that a paid loss ratio of 70% will arise by 31 December2002, so no money is likely to be paid to the reinsured before 31 December 2003,when the treaty terminates. On the other hand, a profit share 97½% of anyclaim payments which might be made means that the total amount then paid toCompany A will vary very little as a result of the loss experience of the reinsuredbusiness. This type of reinsurance is known as financial reinsurance, or finiterisk reinsurance.

The total amount that Company A receives back is likely to be very close to 40%of the underlying premium, whatever the loss ratio may be.

Since it provides almost no protection against loss, Company A must have hadsome other motive in taking it out. The policy’s nature is close to what is knownas a time and distance policy, a form of financial reinsurance, or finite riskreinsurance. It may be viewed as placing money on deposit, or as a method ofimproving the Company’s apparent solvency position. As the company’s solvencyratio is only 28% of premiums, which would normally be considered low, thelatter is probably the company’s motive.

The yield on the funds placed is (40/32)¼ − 1 = 5.7% per year. This may or maynot be a reasonable yield, depending on the current yields for a four year deposit


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in the currency in which Company A’s business is written. The tax treatment ofa transaction such as this in Company A’s domicile, and the security rating of thereinsurer, are both matters that will affect whether or not it may be considered agood and appropriate investment of the company’s funds.

In taking out this reinsurance the company loses assets equivalent to 32% of thepremium for the class. However, it will be able to reduce reserves by 40% of thepremium in anticipation of reserve recoveries. This will release 8% of this class’spremium, and improve the solvency ratio. Since premiums have been ceded bythis transaction, measuring the ratio on net premium will give a greater rise.However, it does not change the company’s underlying position at all. If thecompany had had problems with its capital adequacy this transaction will notrelieve them in the way that a quota share cession, for example, would havedone. Because it is artificial, some jurisdictions prohibit the treatment of thistype of policy in this way, but presumably this is not the case in Company A'sjurisdiction, or it would not have taken out the treaty.

It is possible that Company A might be permitted to use discounted reserves inits balance sheet. This might achieve the same effect without the aid of artificialtransactions.

7 This question was reasonably well answered. Few candidates noted the pointabout currency, which may be a major concern to an insurer operating in anumber of countries, or in the London Market, or a marine, aviation or travelinsurer, to name just three examples. A number of candidates were concerned withdates of birth, rather than dates in general, which would not be a matter ofconcern to most insurers.

• Information could be entered onto the wrong claim record.

The claim and policy numbers should both be in series that mistakes are difficultto make — a single digit wrong or two numbers swapped will give an invalidnumber, and it should not be possible for a policy number also to be a claimnumber.

• Incorrect amounts may be entered, or correct amounts in the wrongcurrency.

There should be some check on amounts. Very large or small claims should bequeried if entered. This is especially important if working in a variety ofcurrencies. A query should be raised if an amount is entered in a differentcurrency from previous entries. A query should be raised if the claim is not inthe currency of the country of the address of the policyholder (this will not applyfor marine insurance, travel insurance and some other classes).

• A claim may be entered for an incorrect date.

The system should automatically check that the policy was on-risk on the daywhen the claim occurred. A query should be raised if there is a very long gapbetween the date of loss (or reporting to the insured) and reporting to theinsurer, or if the date of loss was later than the date reported.


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• Information may be entered against the wrong policy.

Other details, such as policyholder surname, deductible, and the fact that paid +estimated outstanding < sum insured, should be checked against the informationon the policy record.

• Information may be missed out.

A claim should not be accepted until all fields have been filled in, possibly withnull entries.

8 This question was answered moderately. The most important common fault wasnot considering whether or not tail factors were required. A number of candidatesnoted that the paid claims were not fully developed, but concluded that the methodcould not be used, or used it without incorporating a tail factor. One strangemisapprehension of many candidates appeared to be that paid claims shouldalways be associated with written premium and incurred claims with earnedpremium. This entirely depends on whether accident year or underwriting yearclaim cohorts have been used to compile the paid and incurred claims, and thenboth sets of data should be compared with the same premium.

(i) The first decision is which set of development factors to use to project thelosses. The last diagonal of data represents six months’ development,rather than a year’s, so it is not appropriate to use the sets of factorswhich include the last diagonal. Therefore one of those calculatedexcluding the last diagonal should be used. Some candidates noted thatthe last diagonal was significantly different from the previous developmentfactors, but failed to connect it with the half year’s experience. Somecandidates suggested adjusting the last diagonal of data to incorporatethis, some noting that it was a pity to have to throw away data. This is areasonable alternative approach, but, especially at early durations, theprecise amount to adjust by is problematic

Neither triangle of development factors appears to suggest that thedevelopment pattern is changing over time. The paid one is erratic, butthere is no evidence of systematic increase or decrease. If there were, itwould be appropriate to base our chosen factors on recent diagonals only,or to extrapolate the trend into the future. As it is, it seems best to usethe average development factor for all years excluding the last diagonal.In practice we might smooth the observed average factors. A significantnumber of candidates thought that the paid triangle was extremely volatile,some suggesting that it was so volatile that it was necessary to discard it.In fact the triangle would not be considered to be particularly volatile inpractice.

The question of whether or not a tail factor is needed ought to beaddressed. With incurred claims the answer is almost certainly not. Allnine observations of claims after development year six show nildevelopment, so development may be assumed to be complete at thatstage. With paid claims, development continues in the tail, and may beassumed to continue beyond the development horizon for which we have


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data. We would have to extrapolate the trend we observe in the tail. Inpractice we would do so, but also refer to benchmarks, discussions withthe broker, the direct writer and any other available source of informationin forming a judgement. A possible value would be (continuing on fromthe observed value of 1.06): 1.04 × 1.03 × 1.025 × 1.02 × 1.015 × 1.01 ×1.007 × 1.005 × 1.003 × 1.002 × 1.001 × 1.001 = 1.17. Most candidatesmade sensible comments on which set of averages to choose, and it wasquite acceptable to prefer the last three years if sensible arguments werestated. Few candidates mentioned the alternative sources of information.

The use of accident year implies the use of earned premium to estimateinitial expected losses. We should estimate this value using the averageof written premium in the accident year and in the prior year. However,we should check with the broker whether or not this is appropriate — theclass of business may have a particular “renewal season”.

A question arises as to whether or not it is appropriate to use the B-Fmethod to project incurred losses from development year 1, since thesegenerally fall substantially in development year 2. The reduction cannotbe a result of new claims being reported (as this would require them to benegative claims), but must be the taking down of reserves, which havealready been reported. Therefore, it is inappropriate to project thereduction on the basis of initial expected losses. It may also beinappropriate to use the method without amendment after developmentyear 0, for the same reason.

As part of the procedure, proportionate future development of claims mustbe estimated. This is done for each development year by taking theselected development factors for later development years, and the tailfactor if any, and multiplying them together. However, in this contextthey must be adjusted to mid-development year values. It may be enoughto do this by simple interpolation, but especially in the early stages, itmay be that development is slowing down and the second half of the yearshould have less of the factor than the first. It may also be the case thatcedants tend to report losses shortly before the end of the year, in whichcase the reverse may be the case. Particular care needs to be taken overthe value used for the 1999 accident year, which at the moment is atdevelopment year −½. There are standard interpolation methods thatmay be used, and the underlying situation should be discussed with thecedant or the broker. Most candidates demonstrated by the construction offuture development factors appropriately, but few pointed out the need formid-year interpolation, or the difficulties surrounding its estimation.


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A similar problem exists in relation to the 1–2 factor on the incurred,which is a substantial reduction. It may be that this actually happensover a longer period or a shorter one — for example a reserve review atthe end of each year of claims of a certain age, which tends to producereductions. The actual underlying half-year development factors could besimilar to either of these two examples:

0–½ ½–1 1–1½ 1½–2 2–2½ 2½–35 0.79 .85 .88 .9 1.18

or 2.5 1.59 1.25 .60 1.04 1.02

Whichever is chosen will have a profound effect on the results and shouldbe based on a knowledge of the underlying situation.

The process of calculation is as follows:

1. Estimate earned premium for each accident year.2. Calculate initial expected losses for each accident year, as the

product of the result in (1) and an initial expected loss ratio based onthe broker’s pricing information.

3. Take the chosen development factors, and estimate developmentfactors to ultimate from each development year, as the product oflater year-on-year factors, and any tail factor.

4. Interpolate the results in (3) in an appropriate way to get mid-yearfactors.

5. Estimate future development percentages as the complement of thereciprocal of the results in (4).

6. Estimate future development as the product of the results in (2) and(5).

7. Estimate ultimate losses as the sum of the results in (6) and thereported or paid claims.

(ii) The worst common mistakes were to use the incurred claims pattern and touse cumulative, rather than incremental, amounts. Some candidates useda particular year to do the calculations. This was acceptable.

- Use paid development pattern- Using the uninterpolated pattern, then assuming payment midway

through the period we should discount by ½ year, 1½ years, 2½years etc.

- Must spread out paid tail or assume tail is paid on average two tothree years after payment period before the tail. (Answer shows 3years.)

0–1 1–2 2–3 3–4 4–5 5–6 6–7 7–8 8–9 9–Ult

Incremental uninterpolated pattern:

4.2% 5.9% 6.0% 5.8% 31.3% 11.7% 10.4% 5.3% 4.8% 14.5%

0–1 1–2 2–3 3–4 4–5 5–6 6–7 7–8 8–9 9–10


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Discount: 0.953 0.867 0.788 0.716 0.651 0.592 0.538 0.489 0.445 0.350

Multiply and add back up: 0.608

(iii) Most candidates failed to attempt this question.

- Assume brokerage and commission are accrued at the same rate aspremium.

- Assume premium paid on average after six months, that is adiscount factor of 1.1−½ = 0.953.

- Ignore internal expenses (assume they are included in profitloadings).

- Equate present value of income and present value of outgo.Premium × 0.953 = Losses × 0.608 (or whatever was calculated inpart (ii) ) + profit + commission × 0.953 + brokerage × 0.953 + cedingcommission × 0.953.

- Assuming premium adequacy in 2000 is the same as in 1999 weexpect accident year 2000 loss ratio to be 114%.

- Required ceding commission is 100% – 114% × 0.608 / .953 − 10% /.953 − 2.5% − 5% = 9.28%.

9 (i) This question required candidates to think beyond the circumstancesoutlined in core reading, which treat underwriting year accounting purelyin terms of three-year accounting. It should have helped that there wereexample balance sheets later in the question. Many candidates didunderstand the central point of the question, which was the treatment ofthe exposure still to take place. Some students were confused by theconcepts of funded accounting and closed and open year — in a context ofone-year accounting each year would be closed at 31 December, so thatthere would be no open years. Others mentioned reinsurance to close,which is only ever relevant in the context of Lloyd’s syndicates.The underwriting year basis anticipates all losses from business alreadywritten, whether or not the exposure period has expired by the accountingdate. Therefore, there would be a need for a reserve in respect of anylosses that will occur after the balance date on any unexpired cover atthat date, which would not be needed under accident year accounting.Conversely, there will be no need for any reserve in respect of unearnedpremium, which does need to be set up under accident year accounting,not would there be any credit in respect of deferred acquisition costs.

The consequence of using the underwriting year basis rather than theaccident year basis is that any profit or loss which is expected on theunexpired period of cover will be anticipated in the accounts, with possiblefollow-on effects on the timing of tax and dividend payments. Under theaccident year basis, the recognition of profit is deferred until the coverperiod has expired; the recognition of losses may be similarly deferred,unless an additional amount for unexpired risks is set up as a reserve, inwhich case the timing of the losses will be the same.


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(ii) Most candidates correctly calculated the unearned premium and DACs.Some candidates simply increased claims reserves by 10%, withoutremoving the unexpired portion, and double counts reserves for theunexpired period of cover. Some candidates changed the reserve amounts,but instead of taking the difference. It would be nice to be able to do this inreal life. Some candidates tried to reckon whether or not an additionalamount for unexpired risk would be appropriate. This was a sensibleapproach, but as this part of the question is a step towards calculating amerged balance sheet, it is at that point that this needs to be considered.This was not clear from the question, and candidates who did this wouldnot have been penalised.

First, restate Company B’s balance sheet in accident year format, andadjust to Company A’s standards, which may or may not be realistic. Theunearned premium should be 3,200 × 25% = 800. DACs on this should be25%, or 200. Losses on the unearned premium should be 800 × 88% =704, but given that reserves need to be increased by 10%, The Company Bwill have reserved only 704 ÷ 1.1 = 640. Consequently, the reservesshould be (12,000 – 640) × 1.1 = 12,496. Therefore the accident yearbalance sheet is

Investments 14,000 Unearned premium 800Less DACs 200

600Claims reserves 12,496Share capital 500Retained profits 404


(iii) This part of the question was generally badly answered. Common mistakesincluded not taking out of the assets the purchase price that Company Ahas paid to the shareholders of Company B, or adding it to Company B’sassets in the apparent belief that the purchase price is received by the targetcompany itself, and adding B’s share capital on to A’s. Few candidatesseemed to understand the nature of a share premium account, and believedthat it would be affected by the transaction. Many candidates did notappreciate the comment that goodwill must be written off immediately.The implication of this is simply that the assets and liabilities of CompanyB can be taken into Company A’s balance sheet, any difference goingdirectly into retained profits. This simplifies, rather than complicates, thecalculations required.Company A’s commission ratio is 20% (to judge by the relationshipbetween DACs and unearned premium). Add on the loss ratio and we get80%. Therefore, there is a profit margin of at least 20% on unearnedpremium. This amounts to 800. A similar calculation on B gives a loss of13%, or 104. Overall, there seems to be no need for an additional amountfor unexpired risk, even if we were to take account of the expenses ofrunning off the business.


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Company A has paid 2,500 for Company B. Any goodwill is written off.Therefore, adding the companies’ balance sheets together, but deductingthe purchase price, we get:

Investments 25,500 Unearned premium 4,800Less DACs 1,000

3,800Reserves 18,496Share capital 500Share premium a/c 1,500Retained profits 1,204


The remaining cash of 500 could be shown separately from the rest of theinvestments.

(iv) This part was generally poorly answered. Candidates did not seem tounderstand many of the implications of simple balance sheets. Somecandidates suggested that Company A was poorly invested as so much of itsassets were in cash. However, this ignores the fact that cash would alwaysbe placed at overnight interest rates and would therefore yield investmentincome to Company A, and that a company on the verge of buying anotherfor cash needs to have a cash hoard available to fund the purchase. Therewere also some comments that revealed that candidates did not understandthe existence of the share premium account. Some candidates evidentlythought that it reflected the performance of Company A’s shares on thestock market. It actually indicates that Company A has at some timeissued shares for a consideration in excess of their face value.The ratio of reserves to annual premium suggests strongly that the twocompanies write different types of business. A’s is short tail, withreserves being only about fifteen months’ claims. Many candidates madethis point, although some looked at the ratio and simply concluded thatCompany B was better reserved than Company A, despite the fact that weknow that in the restated balance sheet, the two companies are reserved onthe same basis. (Assuming that the unearned premium is half the year’swritten premium.) B’s reserves, as they are now restated, amount to 47months’ claims. This suggests that A’s business is property or motor, andmay include domestic and smaller commercial business. B’s is more likelyto be industrial risks, with a large proportion of liability business.

The average tail of claim payment is much longer for Company B thanCompany A — roughly four years compared with nine months. A appearsto be rather more profitable than B. Taking account of investment incomealters this position — to some extent. A’s profit before managementexpenses per 100 of premium is 100 – 60 × 1.075−¾ – 20 = 23.17. B’s, onthe other hand, is 100 – 88 × 1.075−4 – 25 = 9.1. After managementexpenses this is likely to be only a modest profit at best. The merger willadd little to A’s profit, unless either there are synergetic expense savings,or else management action can be taken to improve B’s performance.

Before the merger, Company A’s solvency ratio was 4800/8000 = 60%,which would probably be considered healthy for a company writing


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generally low-risk, short-tail lines of business. On its own assessment, B’swas 2000/3200, or 62½%. Some candidates included only retained profit,or only share capital, in their solvency calculations. This suggests a lack ofunderstanding of the elements of a balance sheet. This was higher than A’sbut as it was involved in higher risk, longer tailed business, it wasprobably less satisfactorily capitalised. A number of candidates got thefirst half of this point, but failed to notice the second. On Company A’svaluation its solvency ratio was 992/3200, or 31%, which is a much lesssatisfactory position. This is an important point, which many candidatesfailed to notice. It is possible that Company B’s valuation of liabilities iscorrect, but if we know that the two companies valuation of liabilities areon different bases, then a comparison without adjustment is liable to bemisleading.

The combined solvency ratio is 3204/11200 = 28.6%. This would generallybe considered low for a company with a significant long tailed liabilitybook of business. It may raise concern in the market, and is a lot lowerthan Company A’s previous level, although Company A may well havebuilt up its cash hoard in anticipation of the takeover, so its previousposition may have been misleading. Many candidates realised thatCompany A’s solvency position had worsened as a result of the merger, butfew seemed to realise that that is an automatic consequence of a majoracquisition for cash.

The overall expected profit if operations continue as before, includinginvestment income on shareholders’ funds, is 11,200 – 2,400 + 0.075 ×25,500 – 7,616 = 3,096 before management expenses are deducted. Thiswill perhaps allow retained profits to be built up to boost the solvencymargin, but will place significant constraints on growth, and possibly onCompany A’s dividend prospects.

It is difficult to see what benefit the takeover has brought to theshareholders of Company A, unless it can bring about significantimprovements in the performance of what was Company B.


EXAMINATIONS

17 April 2000 (am)












Faculty of Actuaries303—A2000 Institute of Actuaries

303—2

1 Describe the consequences for a general insurance company of settinginappropriate levels of technical reserves. [5]

2 List the major areas of risk and uncertainty facing a general insurer. [3]

3 You are the chief actuary for a general insurance company that is currentlyassessing the possible takeover of another insurance company.

• The target insurer has a large worldwide property and liability portfolio ofbusiness.

• In the last year severe ice storms and typhoons occurred in North Americaand the Far East respectively, resulting in an unusually high level ofclaims for the insurer, and claims being made on its reinsurers.

• There have been a number of recent high-profile passive smoking claims onwhich the courts have found against the insurer with very large awards fordamages paid.

One of the many key ratios you are considering is the claim ratio. Discuss thefactors you would take into account in analysing this ratio. [5]

4 You are the chief actuary to a general insurance company. The company’smain lines of business are employers’ liability, marine, aviation and privatemotor insurance.

(i) Describe the features of the business that would influence the choice ofinvestments to be held in respect of these classes of business. [4]

(ii) Describe how the investment portfolio will affect the choice of discountrate used in calculating the technical reserves. [2]

[Total 6]

5 (i) Describe briefly the main stages in the life cycle of a claim. [2]

(ii) Explain how the periods between those stages might differ betweenclaims for home buildings insurance and employers’ liability insurance.

[2][Total 4]


6 You have been given the following summary information, extracted from theaccounts of a general insurance company. All figures are in € (millions).

Profit and loss account for the year ended 31 December 1999

Gross premium earned 500Adjustment for reinsurance 240

Net premium earned 260Gross claims incurred 720Adjustment for reinsurance 450

Net claims incurred 270Investment income 210Net commission paid 54Adjustment for deferred acquisition costs 2

Net commission earned 52Other expenses of management 60Gross profit 88Taxation on Profit 22

66

Balance sheet as at 31 December 1999

Technical provisions net of reinsuranceUnearned premium net of DACs 108Outstanding claims 475IBNR 1,517

Total 2,100Issued and paid-up shares 100Retained profits 400

2,600

Ordinary shares 1,500Land and buildings 200Fixed interest securities 800Broker balances 100

2,600

Discuss the nature of this company’s business and its financial condition,insofar as they can be determined from these accounts.

[10]

7 (i) List the reasons why a general insurance company models claims. [4]

(ii) Describe the main requirements of a financial model. [4]

(iii) List the items that would be included in a financial model that is to beused in framing investment policy for a general insurer. [6]

[Total 14]

303—4

8 You are the actuary of a small general insurance company that writes onlyhome buildings and contents insurance. Legislation has recently beenintroduced in the territory where your company writes business that allowslocal governments to serve notices on the owners of properties that have beencontaminated by pollution, requiring them to restore the land to anuncontaminated state. The Marketing Director has asked you to consideradding to the standard buildings insurance policy a new option to cover thepotential liability of the homeowner for the cost of cleaning up land arisingfrom the service of such a notice.

(i) Describe the particular risks to the company of writing business of thistype. [3]

(ii) Describe the exclusions that might be associated with the proposed newarea of cover and the problems that might be associated with theseexclusions. [3]

(iii) State with reasons the existing reinsurance arrangements you wouldexpect a company such as this to have in place before these newproposals were made. [3]

(iv) Explain how those reinsurance arrangements might need to be changedif the proposal is carried out. [3]

[Total 12]

9 In a particular country, there are three general insurance companies,Company A, Company B and Company C, writing a similar mix of property andliability insurance. Each company analyses its claims experience in a differentway. Company A analyses its experience by year of accident, Company B byyear of reporting and Company C by year of underwriting. Explain briefly theprinciples of each method, including the treatment of IBNR claims, anddiscuss each method’s advantages and disadvantages. [15]

10 A large industrial corporation has recently acquired a general insurancecompany that has traditionally written personal motor business. The newmanagement wishes to expand the business into homeowners insurance, smallcommercial lines insurance, larger commercial risks insurance and personalcomputer extended warranty insurance. The motor portfolio has traditionallybeen written through independent brokers. The insurance company operatesin a region that is susceptible to windstorm.

(i) List the various options that the insurer may have in distributing itsproducts. [3]

(ii) Describe briefly how the general insurance company’s choice ofdistribution channels may affect its business and the decisions it mustmake, under the following headings.

• Volume/market• Expenses/setup• Risk premium• Experience in particular products and distribution channels [10]

303—5

(iii) List the types of traditional reinsurance protection available to thecompany and indicate the suitability of each type of cover for theportfolio it intends to build. [6]

(iv) List the areas of cover that may be provided in the personal computerwarranty policy and the data from each that should be recorded inorder to enable future claims investigations. [7]

[Total 26]


EXAMINATIONS

April 2000


EXAMINERS’ REPORT

� Faculty of Actuaries

� Institute of Actuaries


Page 2

1 This question was largely bookwork and was reasonably well answered.

Inadequate levels of technical reserves can lead to.

� Inappropriate pricing decisions.

If they are overstated, this might:

� Worsen the apparent results, leading to a loss of confidence by shareholders,brokers and the stock market.

� Reduce the apparent solvency margin, causing possible problems with theregulators.

� Tie up assets that could be applied more usefully to other projects, or have aneffect on the investment policy for example in relation to matching liabilities.

If they are understated, this might:

� Lead to profits being prematurely distributed, leading to future problemsmeeting liabilities.

� Tax payments could be higher in the short term than would otherwise be thecase.

� Might set inappropriate reinsurance arrangements.

2 This bookwork question requiring a list was very well answered by most

candidates.

Premium riskClaims experienceExpensesCommissionInvestment incomeCatastrophesLatent claimsThe acquisition and renewal of businessPoor policy wordingsInflationJudicial decisionsLegislationInsurance CycleFailure of third partiesFraudManagement risk


Page 3

3 This question involved considering the factors influencing the claim ratio. Many

candidates failed to gain marks by giving general answers and not giving properconsideration to the specific points raised in the question.

The claims ratio is defined as Claims incurred/Premium earned.It is usually calculated net of reinsurance.Although will need to calculate gross to assess the performance of the targetcompany’s underwriters bearing in mind the recent catastrophes.Will need to look at overall ratio and separate ratios by class of business andterritory.Will probably wish to analyse in local currency to avoid the impact of exchangerate movements,but also in home currency terms.Will need to consider the strength of the reserving basis.Claims incurred incorporates estimates of outstanding claims, including IBNR.The former are likely to be high because of recent storms and the latter highbecause of the recent court decision.The trend in this ratio over the last five to ten years is likely to be severelydistorted because of the above.So it is useful also to look at this ratio with the effects of each removed, ifpossible.There may be prior year movements that will affect the ratio, especially on thetobacco claims.Comparison with other companies and hence form a benchmark.

4 Several candidates did not structure their answer around the business categories

mentioned in the question and produced a generic answer. In addition somecandidates showed a lack of knowledge of the coverage given under different typesof insurance. In particular their were several cases of confusion regardingaviation and travel insurance.

(i) Many employers liability claims are reported and settled quickly.However, some may take some time to determine / agree liability, some ofwhich may go to court and experience lengthy delays.Also the potential for latent claims is now considerable.Settlements are likely to be in real terms.

Marine and Aviation claims may be for damage and/or liability. Delays inreporting are not significant.However, settlement delays, especially for liability claims can often belengthy due to the number of parties involved.

Private motor claims are mostly reported and settled quickly.A few liability claims may take a few years to settle.Many claims are for repairs and will be affected by wage, inflation and thelevel of prices of motor vehicle parts.

Country of business and hence currency of liabilities.


Page 4

(ii) If used it is likely to reflect the total return on assets backing thetechnical reserves.

May use a different discount rate for different parts of the business.

Where mismatched a notional portfolio reflecting a more matched positionmay be used instead.

A lower discount rate than that calculated may be used to make a smallimplicit allowance for contingencies

There may be statutory rules about whether or not you discount, andwhat rate should be used.

No discounting of liabilities is likely

5 This question was generally well answered.

(i) Period (for some types of liability claim) for the condition to develop.

Occurrence of insured event.

Claim reported to the insurer.

Claim processed by the insurer.In some cases a period of time may be allowed for any medical conditionsto settle.

Claims accepted by insurer and any disagreements in respect of theamount to be paid are sorted out.

In some cases disputes may result in lengthy court proceedings

Partial payments and outstanding estimates.

Claim settled and file closed.

Claim reopened if conditions reappear

(ii) Some liability claims may have a long period of gestation, thereby leadingto long delays before the condition is reported,whereas property insurance claims encounter few reporting delays. Themain exception to this is probably subsidence.

May be lengthy delays in determining liability in employers liabilityclaims — long tailed.Usually delays are short in property claims


Page 5

6 This very good question regarding the interpretation of accounts was very poorly

answered by most candidates. Many candidates failed to calculate simple ratiosproerly and to recognise when their calculations were wrong, for example when theproportioned reinsured was greater than 100%. In addition, many candidatesfailed to reconcile their calculations with the information given by for examplestating that the company was losing money as the combined ratio was 147%,despite the P&L account showing a profit.

The company’s outwards reinsurance premium is 48% of its inwards premium.This would generally be considered to be a high proportion. It may indicate thatthe company writes high-risk business that needs a lot of protection, or possiblythat it obtains a lot of business from other companies with a reciprocalarrangement. It is not likely to need surplus relief, as it has a high level of freecapital.

The gross loss ratio is 144%, but the net is only 104%. This may indicate theclever use of a soft reinsurance market, or possibly one or two major lossesoccurred or came to notice during 1999 that meant that the reinsuranceprogramme was extensively used.

The adjustment for DAC is small, suggesting that premium levels were stable in1999.

Technical reserves are more than 8 years’ premium. Unless the company’sbusiness has reduced greatly, and we know that it has not in the past year atleast, this suggests that the company’s business is very long tail. This is how thecompany can be profitable: it generates enough investment income to offset theeffects of a loss ratio of 104%, commission of 20%, and expenses of managementof 23%, a combined ratio of 147%.

Capital is 500, about 200% of premium. This would normally be considered avery high ratio, but with such a long tail account, and the possibility of needingto strengthen reserves, it is probably merely prudent. There is no mention ofwhether or not reserves are discounted. If they are not, then the effectivesolvency position is even stronger than this.

The assets show a larger proportion of equity type assets than is usual for ageneral insurance company. This is probably related to the long tail nature ofthe account. Presumably this reflects a large portion of liabilities being to someextent linked to inflation.

The return on capital is 15%. This is healthy, but not extremely high, and wouldbe lower still if reserves were discounted.

Broker balances are 20% of net premium, suggesting an average credit term ofabout 2½ months.

The company’s assets yielded about 8% during 1999.


Page 6

7 This question was generally well answered.

(i) To arrive at a risk premium per policy.To select rating factors.To determine premiums using experience rating procedures.To demonstrate the estimated effect of changing the level of cover bychanging the level of deductibles or the effect of reinsurance.To estimate the likely variability of claims experience.To estimate the impact on reserves of latent claims/industrial diseases.Financial planning.To set the reserves.For asset / liability modelling.

(ii) The model must be valid, rigorous and adequately documented.The model chosen must reflect adequately the distribution of the classes ofthe business being modelled.The parameter values being used should be appropriate to the classes ofbusiness being modelled.The outputs from the model should be capable of independent verificationfor reasonableness and should be readily communicable to those to whomadvice will be given.The model must be robust to internal or external changes.Must be realistic and easy to use.

(iii) Actual investments held at start of projection

Amount of liabilities at start of projection split by currency

The expected payment profile and variability associated with payments

Nature of liabilities and how strongly correlated to price and wage inflation

An asset / economic model that produces projections of expected wage and price

inflation and their variability, expected investment returns by type and currency of

investment and variability of investment return by type of investment

The amount of business to be written in the future, split by currency and nature

Tax rate

Reinsurance

Any restrictions on investment policy, either statutory or management specific

Definitions of solvency and return to be used in assessing the benefits of any one

investment strategy

The amounts of any dividends paid

A rule or target

8 (i) A question about a non-standard coverage. Most candidates failed togenerate many valid points.

(ii) Again, poorly answered. Few people cosidered excluding death, bodilyinjury or illness, or even mentioned the policy limit and excess.

(iii) A standard question. Generally well answered.

(iv) Few people mentioned the need to re-negotiate the existing treaties, orthe possibility of setting-up stand-alone cover for the new risks.


Page 7

(i) There is little or no claims data available from any source.So the ability to accurately estimate claims costs likely to arise from thissource is very limited.

There is always uncertainty surrounding new legislation and how it willbe interpreted and operate in practice.

The legislation may change in the future in such a way that the effectsare retroactive.

As an option to the homeowner there is a risk of adverse selection.Those homeowners in high risk locations may be more likely to take upthe cover.

There is a risk of moral hazard,where the homeowner knows that the land is already contaminated at thetime the cover is taken out.

Large accumulations of risk may arise,where many homes in the same road or estate are covered.

(ii) Deliberate pollution caused by the homeowner. However this may bedifficult to prove.

Contamination which arises as a direct or indirect result of a homeownersactions. For example, interfering with a precautionary measure, such asa membrane, installed to prevent such contamination.However, difficult to prove — may be caused by a previous owner

Pre existing conditions

Exclude certain specified types of contamination

Death, bodily injury, disease, illness or injury to mental health.

Blight — loss in value of the home as a result of the contamination

Criminal penalties in any way related to the contamination.

Costs below the designated excess level for such claims and above thespecified policy limit.

(iii) Quota share treatyto increase the spread of risks, as the insurer is small.

Risk XOLfor very expensive homes.

Aggregate XOLto cover concentrations of risk by area or type of claim.

Cat XOL (or Stop Loss)


Page 8

to cover against the effects of a catastrophe and hence limit the risk ofinsolvency.

(iv) May desire a larger layer of cover on the Aggregate XOL policy, orincrease the limit on a risk XOL policy to cover the increasedconcentration of risk and potential for large claims.

Treaties may have to be renegotiatedif the current reinsurers do not wish to insure the new option.

Alternatively, separate treaties may be arranged solely for this particularoption.May use QS, Surplus, risk XOL or Aggregate XOL or a combinationthereof depending on what the reinsurers deem to be acceptable.

9 A bookwork question that was generally well answered.

Accident Year

� Claims are grouped by the time period during which they occurred.

� All claims in a cohort belong to the same period of exposure.

� They will all therefore be subject to the same risk environment.

� Even though they may have been written under different rating and policyconditions.

� IBNR claims will be included (eventually) in the time period in which theyoccurred,

� as will recoveries and re-opened claims.

Year of Reporting

� Claims are grouped by the time period in which they are reported to thecompany,

� irrespective of when they occurred.

� An apparent advantage is that no further claims will be added after the end ofthe time period.

� The method does not allow for the cost of IBNR and reopened claims.

� Claims will arise from different exposure periods

� which may have different volumes of business, cover applying and claimssettlement patterns.

� Hence any claims patterns derived may not represent the current position.

Underwriting Year

� Claims are assigned to the calendar year in which the policy was written

� Irrespective of whether the claim occurred in the first or second calendar yearof the policy.

� Therefore claims occurring on two consecutive calendar years will be assignedto the same claim year.

� The method follows the way in which funded accounts are divided

� and follows the total outcome of all policies written in each year.

� It takes up to two calendar years before all claims have occurred


Page 9

� and an additional period before all are reported.

� Each cohort of claims will have occurred over a wider risk period than anaccident year cohort.

� IBNR claims included (eventually)

10 (i) Bookwork. Well answered.

(ii) Poorly answered. Candidates did not consider that differentdistribution channels will attract different market segments, and hencehavedifferent risk premiums. Few mentioned the possibility of using market orreinsurer data to counter the stated lack of experience.

(iii) Bookwork. Generally well answered.

(iv) Few people seemed to know what benefits were likely to be provided.Most failed to mention labour or transportation/call-out costs. A numberseemed to think coverage would be given for electrocution, or for missingcomponents in the system.

(i) Possible distribution channels are:

� personal lines/small commercial lines brokers

� employed staff paid by salary and/or commission

� direct telephone

� direct mail

� direct internet

� affinity groups

� banks and other financial institutions

� specialist brokers for large commercial risks and inwards reinsurance

� personal computer retailers and manufacturers.

(ii) The implications are:

Volume/market

A move to direct marketing may alienate existing source for motorbusiness.

Different channels may give access to different segments of the market.

Different channels may have different profitability owing to competitiveposition.

Direct methods are suitable only for personal lines and small commercial.


Page 10

Expenses/set up

Direct operations would require significant investment in infrastructureand training.

Persistency of business will determine the spreading of new businesscosts.Rates may need to vary by channel to reflect differing expense structure.

If distributing through banks or other financial institutions — who doesall the processing and claims handling — net rate agreement.

Risk Premium

Market segment may vary by distribution channel; therefore rates mayneed to vary by distribution channel.

Lack of experience

The company appears to lack experience in both the new products andalso the distribution channel. Need to acquire this by using market dataand also possible assistance from reinsurers.

Even reinsurers may not have adequate experience for the PC extendedwarranty product.

(iii) Quota Share

These are new classes of business and distribution channels, so we maywant to share the experience with a suitable reinsurer for thehomeowners/motor/small commercial/PC extended warranty. Also therewill be overriding commission to assist new business strain.

Surplus

Large commercial risks will be very variable in size, so a surplus treatymay be suitable. This will give the insurer the opportunity to write largerisks without taking on excessive risk on its own account.

Aggregate XL

The quota share will not protect the company against the accumulation ofclaims from a single source (e.g. subsidence) so aggregate XL may beneeded.

Risk XL

There will be exposure to large single losses, so risk XL may be required.


Page 11

CAT XL

The area is known to be susceptible to windstorms, and other catastrophicevents are always possible. This could be protected against by cat XL.

(iv) Policy benefits:

� Replacement of faulty parts

� Labour for replacement and repair

� Transport costs/callout charge

� Replacement of system if beyond repair

Factors:

� Manufacturer

� Manufacturer’s warranty period

� Manufacture date

� Components of system (VDU/CPU/printer)

� Model numbers

� Retailer

� Extended warranty period

� Cost of system (possibly broken down by component)

� Purchaser type — individual/business

� Cover provided

� Date of purchase

� Location

� Date of loss

� Claim amount by component


EXAMINATIONS

18 September 2000 (am)




1. You have 15 minutes at the start of the examination in which to read thequestions. You are strongly encouraged to use this time for reading onlybut notes may be made. You then have three hours to complete the paper.








� Faculty of Actuaries303—S2000 � Institute of Actuaries

303—2

1 (i) State the advantages and disadvantages of discounting technical reserves.[4]

(ii) Company A and Company B have always had exactly the same portfolio ofbusiness, each taking 50% of any risk on a coinsurance basis. In theirpublished accounts, company A sets reserves that are intended exactly topay for outstanding claims, discounted at the rate of interest the companyexpects to earn on its assets. Company B’s reserves always include a 20%margin for prudence above the amount it believes necessary to pay theseclaims, and it does not discount its reserves.

Discuss the differences between the accounts of Company A and CompanyB, as they would appear to an analyst who was not aware of thisinformation. [10]

[Total 14]

2 (i) Define experience rating. [1]

(ii) Describe how prospective and retrospective rating methods work. [4]

(iii) Explain how number-based and cost-based experience rating systems areused. [6]

[Total 11]

3 (i) List the main uses of policy and claims data in a general insurancecompany. [3]

(ii) List the main aspects of an insurer’s experience that should be analysed ifthe insurer is to maintain adequate control of its business. [2]

[Total 5]

4 A general insurance company that writes only motor business exclusivelythrough brokers has experienced a gradual but increasing reduction in its marketshare over the past five years. The company has decided to use the internet witha view to preventing further reduction and achieving 50% of its sales throughthis medium within the next five years. Discuss the possible effect this strategymay have in the following areas of the company’s business:

• The Cost Structure• Broker Arrangements• Calculation of Premiums• Business Mix and Volumes• Reinsurance Arrangements [10]


5 You are the actuary to a general insurance company writing product liabilityinsurance. The Chairman of the company has noticed that the Government hasrecently issued a new index linked government loan. This pays a nominalcoupon of 1.5% per year, and both the coupon and the capital value of the loanare indexed to the local consumer price index. It matures in 2016. TheChairman has suggested that this loan would be an appropriate investment forthe company. Explain, with reasons, whether or not the stock should bepurchased. [5]

6 A large reinsurance company has recently received a request from a smallinsurance company for technical assistance. The insurer, which has totalreserves of $60 million and currently writes $25 million of annual premiums, allof which is private household insurance, has decided to expand into commercialproperty insurance with a view to writing roughly the same volume of businessin that class in terms of premium income, thus doubling its total premiumincome. The reinsurance company has been asked to provide assistance insetting the premium rates to be charged, and to provide suitable reinsurancecover for this new class and for the company as a whole. As actuary to thereinsurance company you have available risk premiums for different types ofcommercial property that you can provide to the insurance company.

(i) Explain how the insurance company should formulate the total premiumto be charged for each risk. [5]

(ii) Describe:

(a) the reinsurance arrangements you would recommend, includingany limits or restrictions to the cover, and

(b) the information the reinsurance company would require from theinsurance company with regard to the risks it underwrites. [5]

(iii) Describe how the reinsurance company should price each part of thereinsurance policy. [6]

[Total 16]

303—4

7 You are the actuary of a major insurer that for the last ten years has beenwriting twelve year warranty business covering major damage caused bybuilding defects in new homes. The table below shows the policies issued andresulting claims outgo for a particular builder whose premium rates are underreview at his own request.

U/W No of Claims paid in year after writing (thousands)Year policies 0 1 2 3 4 5 6 7 8 9

1 20,000 7 15 20 30 40 95 160 195 220 2302 18,000 9 15 20 25 55 125 145 175 1703 12,000 10 20 20 40 85 135 150 1554 11,000 9 15 30 30 80 120 1155 10,000 8 25 40 50 70 906 8,000 10 30 35 45 557 13,000 10 20 25 258 15,000 9 15 159 25,000 6 10

10 26,000 4

(i) Describe the main claims features of this business that can be deducedfrom the above table. [3]

(ii) You are aware that a competitor insurance company has quoted for thisbusiness. You know that the rate the competitor quoted is lower than therate you are currently charging, but you are not sure precisely what thatrate is. Explain with reasons how you would calculate the new officepremium to be quoted, given that the necessary loadings for expenses,commission and reinsurance are already known. [9]

[Total 12]

8 A general insurance company wishes to review its premium rates. It hasmaintained a full database of the policy and claims data required to analyse theexperience for a particular risk group.

Discuss why it may be necessary to make adjustments to the base data before itcan be used in a rating exercise. [15]

303—5

9 You are the actuary to a small general insurance company that writes personalaccident business.

One type of policy has a term of five years. Policyholders may buy it in units,each of which costs €20, payable at the start of the term. Each unit pays amonthly income of €100, payable at each monthly anniversary of the policy fromthe policyholder’s accidental death until and including the end of the term. Inaddition, a lump sum of €1000 per unit is payable at the end of the term, if thepolicyholder has died as the result of an accident during the term of the policy.The policy is sold through agents, each of whom receives a commission of €5 perunit sold.

Describe in detail how you would set technical reserves for this policy. You mayassume that the business is profitable so that there is no need for an additionalamount for unexpired risks, and that the company does not discount its technicalreserves. You need not consider the effects of outwards reinsurance. [12]


EXAMINATIONS

September 2000


EXAMINERS’ REPORT


Subject 303 (General Insurance) — Examiners’ Report 2000 — Solutions

Page 2

Candidates are reminded that under the current examination system the answers have tobe provided in a hand written form and therefore the examiners can only take intoaccount solutions to the extent that they are legible.

The examiners are required to test the candidate’s knowledge of the subject and also to alimited extent, the ability of the candidate to apply the knowledge and principles inpractical situations. Most candidates do not succeed in obtaining a pass as a direct resultof not being able to demonstrate to the examiners that they are able to apply theknowledge and principles of the subject in a practical situation. At first glance it mayappear that examiners go out of their way to contrive situations and contracts that are sounusual that most candidates may never meet these situations in practice. However thesesituations are the ones where the well-prepared candidate can demonstrate that heunderstands the principles of the subject and is not just regurgitating bookwork

1 The bookwork component of this question was answered well by the majority ofcandidates, however very few candidates were able to apply the knowledge in aparticular situation. The number of marks for a given question does provide anindication of the number of points that are required for full marks, against thiscriteria the majority of candidates provided a superficial solution for part (ii).

(i) Advantages

Discounted reserves give a more realistic value of assets required to meetexpected liabilityMore useful for assessing solvencyMore useful for pricing and comparing profitability of classesReleases profit earlier (if no additional security margin is introduced)Reserves smaller, appears more solvent

Disadvantages

Removes margins which would help if experience is worse than expectedDifficult to derive payment pattern for some classesComplex and difficult to determine rateNeed to allow for amounts not invested (for short tail classes difficulties mayoutweigh any small benefit of discounting)Earlier release of profit also leads to earlier crystallisation of tax liability

(ii)

As Company A has set up lower reserves for the same premium income, it willappear to be more profitable on an inception-to-date basis. However, the positionin any particular year will depend on whether the companies are growing orshrinking. If they are growing then the reserves will increase, and Company B’swill increase by more than company A’s. As the companies will have the sameearned premium, but Company B will have a higher claims cost, it will appear tobe less profitable. Conversely, if the amount of business being written isreducing, Company B will appear to be more profitable.

Subject 303 (General Insurance) — September 2000 — Examiners’ Report

Page 3

Company B will have a higher amount of reserves for the same premium. Theanalysts may deduce that its business is longer tailed than that of Company A.However, with higher reserves higher investment income will be allocated to itstechnical account, which will make its insurance business appear more profitablethan Company A’s. In a year when premiums are rising this will offset, partiallyor totally, the premium effect; if premiums are falling, it will exacerbateCompany B’s apparent greater profitability.

One consequence of appearing to be more profitable, at least on an inception-to-date basis, is that Company A is likely to pay more tax on its profits thanCompany B, assuming that that is the taxation basis under which they operate.It may also have released more in dividends. If it has, and its retained profit isequal to Company B’s, the companies will appear to be of equal solvency strengthon the most widely used basis. However, in that case its assets will be lower thanCompany B’s and it will generate less investment income.

On the other hand, if it has maintained its total assets at the same level asCompany B, then, with a higher tax bill it must have released lower dividends toits shareholders despite its higher apparent profitability, since both companiesmust have paid out the same amount in total to achieve this. In that case,although its underlying strength is the same as Company B, it would appear tobe more solvent, as more of its assets would be accounted for as capital and lessas liabilities. The investment income of the two companies will be the same, butCompany A will appear to be generating more from the investment ofshareholders’ funds and Company B more from its insurance business.

Effect of tail of businessEffect on smoothness of profit

2 This question was answered well by the majority of candidates

(i) Experience rating is a system in which the premium for an individual riskdepends, at least in part, on the claims experience for that risk.

(ii) With prospective rating the premium at the renewal date depends on theexperience of the risk prior to that date.The insurer takes on all of the underwriting risk in the next policy period.With retrospective rating the premium for the current policy period isadjusted, based on the experience of that period of risk.A deposit premium is paid at the start of the period of cover.And will be followed by an adjustment premium or refund at the end ofthe period.

(iii) Number based systems:Systems based on claims frequency are normally used for small individualrisks with relatively low expected number of claims.This is because the variability of the claim cost in any one policy yearwould be too great to judge the relative severity of the underlying risk.The accumulation of a sufficiently credible experience would take toomany years.


Page 4

Cost based systems:These systems tend to be used for larger risks with numerous claims.In these cases, the aggregate cost of claims experienced in any one year isa more stable indicator or the relative level of that risk.The large number of claims makes a number-based system impractical.

3 This question was answered well by the majority of candidates

(i) AdministrationAccountingStatutory returnsInvestmentFinancial controlManagement information Risk managementReservingExperience statisticsPremium ratingProduct costingMarketingReinsurance

(ii) Claims data: frequency and average cost, by location and class of businessExposure dataPortfolio movementsExpensesPersistency and profitability by sourceInvestment performanceSolvencyReinsuranceRun-off experience

4 This question, though requiring some thought and application to the scenariogiven, was largely bookwork in nature. However, given this background, it wasanswered well by very few candidates. Candidates on the whole did not providesufficient breadth or depth in their answers.

Cost structure changes will include:

IT development costs — recruitment and equipment costs.

Overheads may fall as efficiency gains are achieved.

Advertising costs may increase in the short term to help achieve the desiredtarget level of business, though may fall in the longer term where less expensivemeans are available on the internet.

Cheaper claims handling may become possible where smaller claims are handledover the internet and by use of e-mail.

Brokers fees may fall overall as less business is put through them.


Page 5

However, the costs per policy may rise where less cost effective deals are struck(i.e. the costs fall less than the business going through the brokers). Effect onbroker relationship. Capital efficiency should improve as the balance ofpremiums with the brokers should fall. This will free up a portion of the insurersassets which were otherwise tied up. Shift to fixed expenses from variable.

The cost structure will change as more of the expenses (maintaining aninfrastructure) are fixed and less (commission) are variable.

Premiums calculation:

Another complete set of premium rates will be required.Different rating structureIt should be easier and more cost effective to update these periodically to takeaccount of new experience.

More frequent updates will become possible.

More sophisticated premium calculation system may be possible.More extensive policyholder information can possible be captured via thismedium by developing easy to use system.

Also greater flexibility in data collection enables potential new rating factors tobe collected and tested.Test the market with the ratesTake account of competitors rates

Business mix and volumes:

The mix of business will change as those purchasing insurance via the internetwill have different characteristics.Likely to be more sophisticated.Different geographical spreadPossibly increased proportion of policyholders in the 20–40 age range.Thus an increase in the concentration of risk is likely.

The projected volume of business is highly uncertain.A lot will hinge on advertisingthe design of the website andsocial trends towards the increasing use of the internet at home.

Renewal rates may increase due to the ease of renewal via this medium.This in turn may help to reduce costs per policy and thus premiums.With this sales medium likely to become more popular in the future, earlyentrance to this potential market may reap rewards in the longer term throughgenerating customer loyalty.

Reinsurance arrangements:


Page 6

Premiums may need to be negotiated where reinsurers perceive an increase inrisk — perhaps due to potential increased concentrations.

New aggregate excess levels may be desired due to the increased concentrations.

Any quota share arrangements may need to be renegotiated as the reinsurermay be less comfortable with the change in approach.There may be increased risk of fraud early on as the system developed will stillbe in its infancy.Technical help from reinsurer

5 This question, though not completely bookwork, was fairly straightforward,requiring a systematic approach to consideration of the liabilities andcorresponding appropriateness of the asset in question. As a result it wasanswered reasonably well. However, many candidates did not describe the natureof the liabilities for which the asset was being considered, and even whendescribed the description was often incomplete or inaccurate. This led tocandidates not con ncluding whether the asset was a “good” or “bad” match forthe liabilities in question.

Product liability covers faulty design, faulty manufacture, faulty packaging andincorrect instructions.Property damage / bodily injuryUsually on a claims incurred basis (rather than relating to year of sales).

There are some long reporting and settlement delays.Where time is taken to attribute physical conditions to the correct cause andwhere claims relate to rogue drugs causing settlements to continue for someyears.

Possible accumulation of claims.

The suggested asset purchase is appropriate by reference to the real nature ofsome of the liabilities caused by the delays.

However, the term of the asset is considerably longer than the likely term of theliabilities.And the volatility of the suggested asset (long term, low, index-linked coupon) isless suitable where the liabilities are uncertain rather than fixed in nature.

May be a suitable purchase for part of the free reserves.However, expected return on this asset is likely to be lower than that which canbe earned on equity.However, part of the free reserves must cover the SMSM, so may be suitable forpart as less volatile than equities.

Does this asset fit in with the portfolio currently held?

Other classes of businessPercentage of total businessCurrency


Page 7

Type of inflation linkMarketability in respect of accumulation of claimsRegulatory needsValue for money

On balance, argue whether or not worth bidding.

6 Given the bookwork nature of most of this question, it was for the most part poorlyanswered. Candidates, on the whole, failed to cover the full range of itemsrequiring consideration. In particular, many candidates failed to provideadequate explanation of the points in part (i) (as asked by the question).Particularly poorly answered were parts (ii)(b) and (iii).

(i) Office premium = risk premium + expenses + commission + reinsurance −investment returns + loading for profit and contingency

Risk premium = obtained from reinsurer.

Possibly adjust risk premium.

Calculate risk premium for home business from claims data.

Expenses = loading for variable and fixed expenses (i.e. per policy, per $premium, per claim and per $ claim)Must also allow for expense inflation over the period until all claimsarising are fully settled.Anticipated changes in office efficiency.Renewal / lapse rates to determine how many policies to average the costsover.

Commission — will depend on the proposed method of sale and averageanticipated future rate.

Reinsurance — may vary by risk — perhaps a variable and fixedcomponent — depends on the reinsurance arrangements set-up.

Investment return — will need to allow for current investment conditions,inflation, tax and late receipt of premiums.Unlikely to be significant as the business is relatively short-tailed.Profit and contingency loading should allow for desired return on capitaland risk reward, risk free rate of return, inflation, degree of uncertainty,market conditions and tax.

Variable expenses will automatically vary by size of risk through thedifferent premium paid and different expected claim amounts.

Fixed expenses — may wish to vary this loading by size of risk.

Commission likely to vary by size of risk to some degree.

Reinsurance – Quota share / Surplus will vary per premium:


Page 8

Risk XL premiums should be based on the characteristics of risk.Aggregate XL / Cat XL should vary by degree of risk and uncertainty.

Profit and contingency should vary by perceived degree of risk anduncertainty.

Risk free rate of return, inflation, degree of uncertainty, competitivenessand tax.

(ii) (a) Quota share with maximum size of riskOr surplus reinsurance treatyOr Risk XL working layer with maximum size of riskOr combination

There are likely to be limits to business volumes in the first fewyears.

Aggregate XL to cover against accumulations of risk.Cat XL to cover against widespread storm damage, etc.

Perhaps stop loss for commercial property or for whole business toprotect against insolvency.

May also include limits to the size of risks, number of each type ofrisk, volumes of risk by location.

(b) Owner, location, type of business.

Size (floor area), type of property, age of property, method ofconstruction, number of floors.

Security systems, fire prevention systems.

Policy number, value, premium, EML, SI, Period of cover.

Date incepted, underwriter’s name. Expiry date, if policy notannual.

Previous insurer, claims in last five years for whole companyinsured.

(iii) Proportional reinsurance arrangements simple − relevant proportion ofpremiums + commisions / loadings, etc.

In theory:

Risk and Aggregate XL covers will need to be modelled by frequency andaverage cost from ground up though the reinsurer will have to base thison data available from its existing book of similar reinsurances.Use different sets of assumptions to see how results may vary.


Page 9

Base on assumed business volume with adjustment clause for significantdeviations from expected.Premium will reflect expected claims outgo + contingency loading toreflect the expected variance in the results.

In practice:

The theoretical rate will need to be assessed.In practice though the rates charged will be largely dictated by marketconditions.However, in this case since the insurer has asked the reinsurer fortechnical assistance the market rates are of less relevance.

Cat XL — look at past experience on other similar Cat covers offered.Likely to reflect market rates more than actual experience.

7This question relating to a less common type of insurance was very poorlyanswered. Even though the table was headed “Claims paid in year…”, manycandidates proceeded to assume that the table related to cumulative costs.Practically all candidates showed little understanding of the term “long-tailed”,which was irrelevant in this question given that the earliest exposure periods werestill incomplete. Part (ii) was especially badly answered, with practically allcandidates suggesting that the usual chain-ladder methods could be applied tothis class of business.

(i)

It is a long-term policy and claims will be affected by inflation. At present, theearliest years are not fully run off.Costs are highly variable between calendar years, underwriting years andduration.Earlier years are more volatile than later ones in their development.Policy is long term in terms of claims, but we cannot tell whether or not it is long-tail.Most claims are long delayed from inception towards end of policy term.Relatively low cost per policy. Fixing houses is expensive, as claim frequency isalmost certainly very low.No obvious catastrophe.Significant step up from year 4 to year 5.

(ii)

Pure risk premium per unit exposure= expected claim amount per unit of exposure, or= (no. claims / no. pols) × (no. pols / exposure) × (total claim amount / no. claims)

Office premium p.u. = Risk premium p.u. + Expenses p.u. + Commission p.u. +Reinsurance prem p.u. + Profit p.u. + Contingency loading p.u. – investmentreturn


Page 10

What period are the rates to be applied for?What is the mid-point? Ok for short term agreementOr should they be indexed? Ok for long term agreement.

Need to allow for inflation from time point at which risk premium estimated tomid point of base period for future rate to be charged and claim payment date

To calculate risk premium need to analyse claims data.None of the insurance years in the current book of business are fully run-off oreven the risk period expiredTherefore need to find external sources of data if available,Otherwise need to estimate run-off pattern by some other means

Data in respect of other builders may also be helpful for identifying trends

Chain ladder methods useful as a cross-check,but fail to provide sensible answers because;

Triangle at later durations is highly uncertain,

The run-off pattern is not necessarily consistent over time,Due to variation of weather conditions, economic conditions – homeowners maydelay reporting claim if the policy has not yet expired, unless wishing to sell thehome and move on

Because the policy term is 12 years very little is known about the more recentinsurance years as most of the risk is as yet unexpired.The quality of risk is likely to vary over time for a number of reasons. E.g.minimum building standards, quality of workmanship, mix of business (changein proportion of types of home)

Need to analyse the data at least making allowance for differences betweenunderwriting year, development year and calendar year – Can use a multivariateanalysis,Model the data to estimate parameters for each of the three sets of variables,though information is limited with regard to most recent underwriting years.These can then be used for estimating the bottom half of the triangle

To what extent is the result from this builder credible? Should we rely on its ownresults or use industry-wide statistics?

This is a large builder (26,000 homes in one year). To what extent are therestatistics on the probability of such a builder going bankrupt.

Need to allow for any underlying calendar year trends believed to exist –apparent within the dataE.g. Social inflation and the effects of global warmingExpected changes in the quality of the building workAssume average run-off pattern, unless there are clear reasons for a change tooccur in the future.E.g. changes in the types of home constructed so that different types of claimwhich appear at different durations become more likely to arise


Page 11

Adjust for known catastrophe or rare claims within the data not expected tooccur regularlyAnd add a contingency loading in respect of these items

The analysis of total claims paid per unit exposure (home) is unlikely to be veryinformative on its own.Would help to analyse frequency per home and average cost per claim separatelyif possible to identify different trends therein

For example rising average costs may indicate rising inflation in rebuilding costsor a change in the types of claims seen

What profit margin should be allowedperhaps base it on the degree of perceived risk, allowing for the very long term ofthe policy.

How do the calculated rates compare with those quoted by the competitor,Or those previously charged.

Does the recent analysis in any way indicate that a lower premium can becharged

Should the business be priced as a loss leader with a view to maintaining marketshare or expanding

Contingency loading should allow for the risk of catastropheand the considerable random variation as demonstrated within the data shown

Due to the length of term of the policies written will need to allow for investmentreturns on net balance of premium remaining throughout the policy duration.

In calculation of the risk premium the assumed rate of return should be based ona matching portfolio of assets likely to be held as technical reserves.Also the rate should not be chosen independent to the inflation assumptionsused. There should be consistency between them – it is the difference betweenthe assumed investment return and inflation rate that is most important

8 This bookwork question provided the candidate with little guidance on the areasto be covered and therefore required a systematic approach to consideration all thepotential areas. Probably as a consequence this bookwork type question was notanswered well by the majority of candidates.

Unusually heavy or light experience:

• Claims experience tends to go in cycles• For some classes unusually heavy or light years may be experienced in

isolation• Especially if the risk is affected by climate• If experience is untypical then choose another base year• Or aggregate more years’ experience• Or apply an adjustment factor to the base year


Page 12

• Which would obviously be subjective• Although industry data may be available.

Large or exceptional claims:

• May be left in the data• Or truncated and spread• Or removed• Depending on the extent to which similar claims are likely to occur in the

future

Trends in claims experience

• If trends are detected in the base data, it is important to attach more weightto recent experience

• Allowance for inflation• Trends should also be investigated to see whether or not they are likely to

continue into the future• Or of they are the results of a one-off change in company or market practice.• If they are expected to continue then an assumption will be needed to allow

for them.• It may be necessary to adjust past data.

Changes in risk:

• Changes in risk can be difficult to deal with.• They may show up as trends and be dealt with as such.• Alternatively, major elements of the risk could be separated in the base data• And projected separately• And combined with an assumption about the future mix of risks.

Changes in cover:

• Changes in cover can be difficult to allow for.• Major changes are likely to involve the perils covered• Or the limits and excesses applied to each claim.• They may also arise from changes to underwriting• Or to claims settlement procedures.• If a peril is no longer to be insured• It may be possible to exclude these claims from the data.• If a new peril is to be insured• It may be necessary to use external data• Such as market statistics, consumer or manufacturer data, government

statistics.• Changes to limits or excesses are more complicated.• If there is a detailed database allowing all claims to be separately considered,

it may be possible to adjust each claim to the original gross amount• And project the gross data to the new rating period.• Otherwise it will be necessary to make more approximate adjustments• Based on any knowledge of the underlying claims cost distribution.• Either way the information will be incomplete


Page 13

• As many insureds will not notify claims below or near the excess points.• Future changes in the risk environment other than normal trends will need

to be identified.

Changes in reinsurance cost:

• It will be necessary to allow for changes in reinsurance cost.• Maybe necessary to incorporate IBNR• Margins in reserves (positive and negative)• Errors in data• Changes in claim definition including treatment of NIL cost claims

9 Candidates are expected to be able to apply the knowledge and principlesunderlying the subject in various situations. This question required the candidateto apply his knowledge of technical reserves in the context of a particular type ofcontract. In setting out the formula for calculating the Unearned PremiumReserve most candidates made the appropriate assumption that the incidence ofclaims is approximately uniform over the period of cover, however manycandidates failed to then allow for the reduction in the claim amount over theperiod of the contract, and merely stated that the usual formula could be used.Many candidates failed to observe that once a claim was made the claim amountpayable could be calculated exactly and therefore an exact method should be usedto calculate the outstanding claims reserve in preference to the usual triangulationbased methods used for other classes of business.

The technical reserves that might be required in respect of this product are:

• unearned premium reserve• outstanding claims reserve• IBNR• Claims expense reserve• Catastrophe reserve• No need for UPR for policies already claiming

Unearned premium reserves cannot be calculated in accordance with the usualformulae since the term is not one year and the risk is not constant throughoutthe term. If a policyholder should die accidentally in the first month of the policy,the total benefit would be €100 × 60 + €1000 = €7000, whereas if he should dieaccidentally during the last month it would be €1100. In general, if he dies inmonth n (n = 0,1,2, … 59), the benefit will be €100 × (60 – n) + €1000 = €7000 −€100n. The amount of premium earned each month should reflect this.

The probability of a person dying accidentally each month should not vary unlesssome extremes of age are included. If the most dangerous ages for young maleaccidental death are included then assuming a level probability will be slightlyconservative, and might be acceptable. If older ages are included someadjustment to this assumption may be needed.

The premium earned in each month should be proportional to the risk, or to70 − n. (n = 0, 1, 2, … 59)


Page 14

The sum of these weights is 60 × 70 − 60 × 59 / 2 = 4200 – 1770 = 2430After m complete months of the policy the proportion of the risk remaining willbe

59

n m

(70 n) 2430=

− ÷�

= ((60 – m) × 70 – (59 + m) / 2 × (60 − m)) / 2430

= (4200 – 70m – 1770 – 30m + 59m / 2 + m2 / 2) / 2430

= (2430 – 70.5m + m2 / 2) / 2430

= 1 – 47m / 1620 + m2 / 4860

Hence the unearned premium per unit of policy for a unit taken out exactly mmonths ago is €20 × (1 – 47m / 1620 + m2 / 4860). To hold this for a policy thathad a curtate elapsed duration of m months would be slightly conservative. Thecorrect value could be approximated by adding on half a month to get €20 × (1 –47m / 1620 + m2 / 4860 – (70 – m) / 4860). The exactly correct value for a policythat had had d days since its last monthly anniversary is, in a 30-day month, €20× (1 – 47m / 1620 + m2 / 4860 – (70 – m) / 2430 × d / 30).From this, 25% may be deducted to allow for deferred acquisition costs.

Setting reserves for outstanding claims should be relatively simple. We knowexactly how many monthly payments remain on each claim. If this is t, then foreach unit of the policy we should reserve €100t + €1000. We may need to addany unpaid payments between the date of death and the valuation date ifpayment has not yet started, for example if it is still not proved who is entitled toclaim the benefit. If a claim is in dispute, for example if it is not clear whether ornot a death was a result of an accident, then a proportion of a full reserve mightbe set up.

To estimate IBNR, the time taken to report claims should be investigated. Thevalue of an IBNR claim is straightforward, along the lines of outstanding claims.We should calculate the claim amounts of all policies if they had become claimsin each previous month, in the same way as outstanding claims, and get anaverage value across all policies for each individual month.

We may get the expected number from a delay table. This should be constructedfrom the record of past claims by month of occurrence and by number of monthsdelay until reporting. This may be used to give the proportion of claims beingreported by the nth calendar month end after the accident (n = 1, 2, 3, …). Letthis proportion be pn , let the number of claims reported in the nth month prior tothe valuation be Nn , and let the average amount of claim on policies in forceduring that month be Vn. Then the IBNR is equal to

n n n nn 1

(1 p ) N V / p∞

=

−�


Page 15

Claims expense reserve would most likely be a percentage of the claims cost orpremium.


EXAMINATIONS

2 April 2001 (am)

Subject 303 � General Insurance





3. Write your surname in full, the initials of your other names and yourCandidate�s Number on the front of the answer booklet.






� Faculty of Actuaries303�A2001 � Institute of Actuaries

303 A2001�2

1 State the reasons why a general insurance company may undertakeinvestigations with respect to its investments. [3]

2 You are the actuary for a general insurance company that writes householdbuildings and contents insurance. List distinct rating factors that are likely to beused to rate this business. [4]

3 (i) Define the term reinstatement premium. [2]

A $1m xs $1m excess of loss reinsurance treaty has the following terms and losshistory in the year it was written.

• up front premium of $200,000• 1 reinstatement at 120% additional premium

In chronological order the only losses (from ground up) to potentially impact thistreaty are:

1. $1.5m2. $5m3. $1.8m4. $1.5m

(ii) Calculate how much of each loss is recoverable. [2]

(iii) Calculate the reinstatement premiums generated by each loss. [2]

(iv) Calculate the rate on line of this contract. [2][Total 8]

4 (i) Define three year accounting. [1]

(ii) Explain, with examples, why three year accounting is used. [4]

(iii) At the beginning of year one, 100 premium is received and 5% commissionis paid. 10 is paid out in claims halfway through year one, 30 halfwaythrough year 2 and 20 halfway through year 3, and claims handlingexpenses are 50% of the claims paid.

Calculate the first declared profit for this tranche of business using thethree year accounting basis, given investment return of 4% per annum.

State any assumptions that you make. [5][Total 10]

303 A2001�3 PLEASE TURN OVER

5 Discuss the different approaches which could be used to protect policyholdersfollowing the insolvency of a general insurance company. [8]

6 Discuss briefly the validity of each of the following statements.

(a) When calculating loss ratios to maintain correspondence�

• � paid claims should be compared with written premium

• � accident year claims should be compared with earned premium

• � incurred claims should be compared with earned premium

• � underwriting year claims should be compared with writtenpremium

(b) Surplus Reinsurance is a form of non-proportional reinsurance.

(c) Deferred acquisition costs are shown as a liability on the balance sheet.

(d) The Basic Chain Ladder method assumes that the oldest year is fully run-off.

(e) The paid chain ladder method produces lower IBNR estimates than theincurred chain ladder estimate due to outstanding claims being includedin the latter. [9]

7 You are an actuary for a general insurance company which writes private motorinsurance.

Describe briefly the reasons why you may undertake an actuarial investigationof premium rates for this business. [6]

303 A2001�4

8 You are the actuary for a general insurance company and are about to perform apremium rating exercise for a class of personal lines business.

(i) List the claims data needed to perform the premium rating exercise. [4]

(ii) Explain briefly why the introduction of new premium rates is likely totake place some time after the period of the base claims. [3]

(iii) (a) Describe briefly the problems that may arise as a result ofintroducing a new premium rating basis some time after theperiod of the base data used in deriving the new premiums.

(b) Explain how these problems may be mitigated.[9]

(iv) State the non-claims related factors to be taken into account beforederiving the final premium to be charged to the customer. [6]

[Total 22]

9 You are the actuary for a medium sized general insurance company that writeshousehold insurance business. The cumulative paid and notified (paid plusoutstanding) claims for this class of business for the last five years ofunderwriting are shown below:

Paid Claims ($000) Notified Claims ($000)

UnderwritingYear

0 1 2 3 4 UnderwritingYear

0 1 2 3 4

1996 10 20 30 40 50 1996 40 80 78 77 771997 9 21 32 41 1997 40 86 80 771998 10 23 35 1998 41 77 871999 10 27 1999 46 792000 11 2000 46

AssumedDevelopment

Pattern

18% 41% 61% 80% 100% AssumedDevelopment

Pattern

53% 102% 103% 100% 100%

(i) Discuss the reasonableness of the above assumed development patterns ofpaid and notified claims. [8]

(ii) Discuss how the ultimate claim cost estimated by the Basic Chain Laddermethod would be affected if during 2000 there had been a majorhurricane that had caused the paid losses in underwriting year 2000 to be50 instead of 11 and the notified losses to be 100 instead of 46. [6]

(iii) Discuss how the accuracy of the ultimate claim cost estimated by theBasic Chain Ladder method in part (ii) could be improved. [3]

303 A2001�5

(iv) Calculate, in respect of the 2000 underwriting year, the discount factor tobe applied to the undiscounted outstanding claims reserve to give thediscounted reserve as at 31/12/2000. Assume a 10% interest rate and thatthe assumed development patterns given in the question are correct.

State any further assumptions you make. [6]

(v) Discuss the effect on the technical reserves the company may hold if theinformation given was for Accident Year instead of Underwriting Yearbut all the numbers within the triangles were unchanged and you werepreparing Accident Year accounts instead of Underwriting Year accounts.(You are not required to explicitly calculate any reserves.)

State what additional information you would need to be able to quantifythis. [7]

[Total 30]


EXAMINATIONS

April 2001


EXAMINERS� REPORT


Subject 303 (General Insurance) � April 2001 � Examiners� Report

Page 2

1 There were many points that the candidate could make in response to thisquestion, as a consequence most candidates scored well.

Evaluation of the existing portfolio

• ALM to assist in setting investment policy• Allocating investment income between classes of business• Allocating capital between classes of business• Allocating risk based capital• Determining the return on capital• Determine discount rate to apply to liabilities• Determine the return made on the investments compared to appropriate

benchmarks• To evaluate the performance of the investment managers• Statutory assessment• Determine level of non-investible assets• Check liquidity• Check security• Put value on assets• Check matching by currency / term / nature

2 This question tested the candidates understanding of rating factors in relation tohousehold product. Many candidates missed the obvious factors of sum insuredand number of bedrooms. Some candidates showed their lack of understanding ofrating factors by including risk factors which could not be used as rating factorsi.e. difficult to measure or verify. The better candidates managed to list enoughfactors to score reasonably well though.

Sum insuredNumber of rooms / bedroomsLocation / postcodeExcessBusiness useOwner occupied or rentedType of propertyType and standard of constructionAge of buildingAge of policyholderLocks / alarm / neighbourhood watch � security discountsClaims history / NCDOccupied day / nightHeating methodOccupationSexPeriods property is vacantHigh value items


Page 3

3 The answer given below is the one the examiners had expected the candidates tocome up with. It was however clear to the examiners that the course material mustindicate an alternative way in which such contracts work. As a consequence, theexaminers gave full credit for the alternative approach providing the candidatewas consistent in parts (ii) and (iii). Most candidates scored very high on thisquestion.

(i) The premium payable for the restoration of full cover following a claim.For higher levels of XOL reinsurance a claim my lead to the amount ofcover for the remaining period of insurance to be reduced or terminatedunless a further premium is paid for reinstatement. Such a premium mayalso be required for lower layers of cover if there is a limited number offree reinstatements.

(ii) $0.5m, $1.0m, $0.5m, $0m(iii) $0.12m, $0.12m, $0m, $0m(iv) 20% as the reinstatement premium is not included

4 This question was answered very well by the majority of candidates(i)

• This is the usual form of funded accounting• underwriting profits are first recognised at the end of the third

accounting year from the start of the underwriting year.(ii)

• Used because underwriting year is of fundamental importance e.g. at Lloyd�s (determines who is on risk)

• e.g. for reinsurance contracts that operate on a policies incepting basis• because for some classes considerably more information is available

after three years compared with after only the first year regardingpremium payment, claims settlement and making reinsurancerecoveries

• e.g. marine and aviation insurance and non-proportional reinsurance

(iii) Assumptions

• no other expenses• claims expenses incurred at same time as claims paid• no further claims incurred• valid assumption about taxation

Year 1 Year 2 Year 3

Brought forward 0 83.5 40.95Premium 100 0 0Commission 5 0 0Expenses 5 15 10Claims 10 30 20Investment return 3.5 2.45 1.05Carried forward 83.5 40.95 12.00

i.e. profit at the end of the third year is 12.00


Page 4

5 Most candidates did not score very well on this question. Candidates showed alack of wider thinking other than the basic understanding of the Policyholders�Protection Board

In the event of insolvency there will be two broad categories of policyholderliability outstanding, outstanding claims not yet settled and unexpired periods ofrisk

Appoint insolvency practitioners, with any excess outstanding liabilities to bemet by the Government from taxes.This offers the maximum protection.But is unfair as the cost is met by all taxpayers

Meet outstanding liabilities via levies on the insurance industry.As above, but unfair on those policyholders who are more astute and companieswhich are better run.

Require deposits to be held in an insolvency fund which can then be used in theevent of insolvency.As above, but to a lesser degree since the insolvent insurer will have contributedat least in part to the outstanding liability.Could apply the above systems to just private policyholders, or those whopurchased compulsory insurance on the basis that corporate policyholders aremore able to assess the likelihood of future insolvency and take steps to avoid orwithstand the effects.Could apply the above systems to just specific types of insurance or outstandingliability which are deemed of greater importance.E.g outstanding claims, rather than unexpired riskOr liability claims rather than property damage

Apply the above approaches to only outstanding claims.Insureds lose out to the extent of cover not then providedMay not be able to get such advantageous rates on new coverMay need to cover a specified period after failure as insureds would otherwisewithout realising be without insurance coverCould give refunds in respect of unexpired periods of riskBy covering all remaining periods of risk, ensures little or no risk periods of non-insurance

Additional marks were given to those candidates who mentioned ways ofreducing the risk of insolvency in the first place. Marks were also awarded foradditional valid points such as requesting capital from parent (if one exists) orfinding a purchaser for the company.


Page 5

6 This question proved to be one of the main questions which showed thosecandidates who understood some basic principles of general insurance and coulddemonstrate to the examiners their understanding. Some candidates thoughtthat everything must be false in such questions and therefore proceeded to argueagainst all such statements, whilst others limited their answer to each part byone word statement of true or false.

(a) Only if the paid claims are underwriting year paid claims.

True. As claims incidence reflects exposure.

Only if the incurred claims are accident year incurred claims.

True. As claims incidence reflects exposure.

(b) False. It is a form of proportional reinsurance where the cedant is free tochoose(within limits) the proportion of each risk ceded.

(c) False. They appear as an asset � held to reflect the spreading ofacquisition costs over the exposure period.

(d) False. The method assumes that past development pattern is stable butnothing else.

(e) False. Both methods estimate the same thing, the ultimate claim. IBNRis simply the ultimate claim less a known figure, the incurred claim. If allthe assumptions behind the two methods are valid they should producevery similar answers. The paid development method is as likely toproduce higher IBNR estimates as it is lower ones.

7 Many candidates could not demonstrate to the examiners sufficient reasons forcarrying out such an exercise, although most mentioned the more commonreasons.

To ascertain the overall profitability of the current premium ratesTo ascertain the overall profitability of proposed new premium ratesTo analyse segment level profitability of the current premium ratesTo analyse segment level profitability of proposed new premium ratesPerformance of current premium rates not in line with expectationsComparison of current rates with competitorsReview the suitability of current rating structure in light of the current riskenvironment, allowing for changes in the political areas, legislation, traffic, newtechnology etc.Assess effect of lapse ratesAssess new potential rating factorsAssess impact of cover changes, new perils in, old perils out, excess etc.Assess extent of X-subsidiesAssess change in cost of reinsuranceAssess need for APURChange marketing strategy


Page 6

8 This was a fairly straightforward bookwork question which the examiners thoughtthe well prepared candidate would score highly on without too much difficulty.However, it proved that many candidates failed to score sufficient marks on thisquestion owing to lack of bookwork detail and the skills needed to answerpart (iii b).

(i)• Date claim occurred• Date claim notified• Dates of payments• Amounts of payments• Date(s) of settlement• Date(s) of reopened• Estimates of the outstanding amounts• Rating factor details (at the time the claim occurred)• Cause of claim• Type of peril• Claim number

(ii)• The length of time that can elapse before sufficient claims have been

notified on which to base a rating exercise• Delays in processing and analysing the claims experience• The time taken in assessing and receiving agreement that the

premium rates can be changed• The administrative time taken to implement a rate change• Time taken to receive approval from a regulatory body (necessary in

some countries)

(iii) (a) Experience in the intermediate period may turn out to be differentto that expected because

• Claims trends not as expected• Claims inflation not as expected• Commission rates have changed• Expense levels have changed• Volume assumptions have proved inaccurate• Competition and market has changed• Investment returns have changed• Changes in legislation and court awards• Cover changes in product• Changes in risk levels

(b) scenario test the profitability so the range of possible outcomes isunderstooduse the most up to date data that is available and developedenough, use different periods for different perilsconsider competitors likely reaction to any rating changes that arein the pipeline (i.e. where the decision has been taken but the ratesare not in the market)


Page 7

analyse the results of previous rating changes to try and assess thelikely changes in volumes

(iv)• Expenses � fixed

� variable• Loading � per policy

� proportional to premium� per claim� proportional to claims

• Commission if applicable• Investment return both income and capital growth• Reinsurance costs i.e. the net cost to the insurer of buying

reinsurance• Profit margin required by the company• Discounts available e.g. loyalty discounts• Payment method (admin fee for monthly payers)• Competitive analysis• Required growth of business volumes by number of policies and

premium and hence standing in the market in respect of market share

9 The examiners were very disappointed in the majority of answers given to thisquestion. There did not appear to be a time problem for the exam as a whole andin fact a significant number of candidates attempted question 9 earlier thanothers. In recent examinations for 303 there has been a trend of candidates notbeing able to demonstrate their interpretation of a set of data. The class ofbusiness in the question was one that most candidates should be fairly familiarwith, but many candidates failed to mention more than a couple of the obviouspoints and most did not demonstrate their understanding of this particularsituation. Part (ii) was not very well answered in that there was very littlediscussion given in most candidates answers � most candidates merely made acouple of calculations. Despite the question not referring to pricing the business atall, several candidates indicated curtating the effect of the hurricane andspreading the cost over all years which is not an approach used in reserving..Although part (iv) was a straightforward discounting question many candidatesmanaged to make it more complicated by not reading the question carefully andnoting the instructions given. In addition many candidates attempted to calculatethe discount based on the notified triangle as well as the paid. The examiners weregenerally pleased though with the answers given by those candidates whomanaged to get as far as the last part in showing their understanding of thedifferent bases of accounting year definitions.

(i)• The notified pattern shows slight redundancy after 24 months.• This is not untypical for this type of business that is typically reported

quickly with fairly accurate case reserves being posted soon afternotification. The main exception to this would be in the case ofsubsidence claims on buildings policies.


Page 8

• As this is an underwriting year triangle we would expect around 50%of the exposure and hence 50% of all losses to have been reported bymonth 12.

• The paid pattern seems unusually slow for such a normally shorttailed class of business. Actual pattern will depend upon the mix ofcontents and buildings.

• It appears to be developing linearly which is unusual. • The paid pattern is clearly not fully run-off after 60 months. The

notified pattern probably is and it shows that the paid claims are onlyabout 50/77=65% paid at this stage.

• The selected paid pattern looks wrong because it is not fully run-offand should therefore be queried.

• The paid and notified data both seem very stable. There is no evidenceof unusual losses in the data that could distort the developmentpatterns. The paid claims would be expected to lag behind the notifieddata.

• The selected patterns are consistent with the data (apart from the lackof a paid tail).

(ii)• The true ultimate claims should be increased by the cost attributable

to the hurricane.• Whether the ultimate claims calculated using an unadjusted chain

ladder method accurately reflects this depends on the relativereporting and payment patterns of hurricane compared to non-hurricane losses.

• If hurricane related losses are reported faster than non-hurricanelosses then the unadjusted notified chain ladder estimate willoverstate the overall claims and vice-versa.

• Similarly, if hurricane related losses are paid faster than non-hurricane losses then the unadjusted paid chain ladder estimate willoverstate the overall claims and vice-versa.

• The relative reporting speeds of hurricane and non-hurricane losseswill be influence by when during the year the hurricane happened. Ifthe hurricane happened early in the year it is likely to be morereported than non-hurricane losses.

• If most policies are 12 months in duration then there will be somehurricane related losses in the 1999 underwriting year.

• The ratio of hurricane paid/notified losses is (50−11)/(100−46)=72.2%.This is much higher than the non-hurricane ratio of around 25%. Thiswould imply that Hurricane related losses are shorter tailed thanaverage and/or that the hurricane took place towards the beginning ofthe year.

(iii)• The simplest way to improve the accuracy would be to remove all the

hurricane related losses and project those separately.• We are still left the problem of how to accurately project the hurricane

loss but at least is does not distort the non-hurricane triangle.


Page 9

• If the hurricane occurred in the early part of the year we could assumeall loss notification have now been received and assume zero (or evenslightly negative) hurricane related claims.

• If the hurricane happened towards the end of the year we could use anexposure based approach (i.e. look at all the properties insured by X inthe path of the hurricane and estimate the likely frequency andseverity of future claims.

(iv)• Assume claim payments made mid-year (or any reasonable

assumption).• Assume ultimate claims are selected based on selected payment

pattern (or adjust calculations accordingly).• Use incremental paid pattern �� 18%, 23%, 20%, 19%, 20%.• Discount to end of 31/12/2000 for the 2000 underwriting year

i.e. pattern is 12 months old already.• Formula is

23% *1.1^ 0.5 20% *1.1^ 1.5 19% *1.1^ 2.5 20% *1.1^ 3.5(100% 18%)

− + − + − + −−

• Answer is 0.84

(v)• For accident year accounts we need a UPR reserve in addition to the

outstanding claims reserves.• Depending on the profitability of the book we may also require a URR

in addition to the UPR. • You may be allowed to discount before deciding whether a URR is

required • As data in triangles in unaltered the numerical value of the IBNR

calculated will be identical. • The difference is that for the underwriting year triangle the IBNR will

be represent future losses in respect of all business written up to31/12/2000 and not just the amount earned up to 31/12/2000.The overall level of reserves will be lower for the company with theunderwriting year data by the amount of the UPR (plus any URR ifapplicable).

• Additional data required:− Premium volume with inception and expiry dates to enable

UPR to be calculated− Knowledge of the underlying business to decide if even

incidence of risk or not− Information required to estimate (discounted) loss ratio for

recent years to see if URR required


EXAMINATIONS







3. Write your surname in full, the initials of your other names and yourCandidate�s Number on the front of the answer booklet.






� Faculty of Actuaries303�S2001 � Institute of Actuaries

303 S2001�2

1 A general insurance company is considering writing property damage insurancecover.

State the main types of property likely to be insured. [3]

2 Describe briefly the areas of risk and uncertainty for a general insurancecompany writing a small heterogeneous book of business. [10]

3 A general insurance company is wishing to review its reinsurance arrangements.State the factors that may influence its decision. [7]

4 Explain briefly what is meant by:

(a) discovery period(b) facultative reinsurance(c) IBNER(d) moral hazard [6]

5 (i) Explain what is meant by EML. [2]

(ii) Write down the maximum EML that can be insured, and not go beyondthe maximum reinsurance cover, if the only reinsurance the company hasavailable is a surplus treaty with N lines of cover and a maximumretention of R. [1]

(iii) An insurer (C) takes on a risk with EML of $10m. C has a risk excess ofloss contract $5m xs $1m with reinsurer A which applies before a surplustreaty with reinsurer B. The surplus treaty provides a maximumretention of $3m and 4 lines with the minimum always being ceded.Determine how much A, B and C each pay if a claim for $9m occurs. [4]

[Total 7]

6 (i) Describe two distinct methods used to account for general insurancebusiness. [3]

(ii) Describe the four accounting concepts which are widely used in preparingthe financial accounts of a general insurance company. [5]

[Total 8]

303 S2001�3

7 (i) State the prime objective regarding the investment of assets of a generalinsurance company. [2]

(ii) List the factors which influence a general insurance company�sinvestment policy. [3]

(iii) Describe briefly the ways a supervisory authority could influence theinvestment policy of a general insurer. [4]

[Total 9]

8 You are the actuary for a general insurance company that writes only ten-yearnew home warranty business, in a country where all homes must be built to a setof minimum standards. The warranty is purchased by the builder beforeconstruction commences, on behalf of the purchaser for a single up-frontpremium � the purchaser of the home then becomes the policyholder on legalcompletion. The policy covers new homes from the date first occupied againstthe cost of major damage resulting from building defects where the cost ofrepairs exceeds $2,000 (at 1/4/2001 prices � linked to the house re-building costindex), and the builder is no longer in business. New IT systems are beingdeveloped for all parts of the business. As part of the design process you havebeen asked to specify your data requirements.

State the items of data you are likely to require for reserving and pricingpurposes. [12]

9 You are the actuary for a general insurance company which was established fiveyears ago. Since then it has written only third party motor insurance.

(i) Describe, with reasons, the extent to which the basic chain ladder methodmay be relied upon for assessing the required level of outstanding claimsreserves. [10]

(ii) Describe the additional steps you might take to assess the required levelof reserves. [3]

[Total 13]

10 You are the actuary for a general insurance company writing only commerciallines business. You have recently been asked by one of the underwriters toassist with a request from the owner of a small Christmas tree farm forinsurance cover against all major insurable risks in respect of that business.

(i) Describe the main insurance products the farm is likely to need and theassociated perils covered by each product. [8]

(ii) List the rating factors you would use in premium rating each part of thecover in (i). [7]

(iii) Describe the main characteristics of claims likely to arise under eachelement of cover. [10]

[Total 25]


EXAMINATIONS

September 2001


EXAMINERS� REPORT

Introduction


The report does not attempt to offer a specimen solution for each question - that is, asolution that a well prepared candidate might have produced in the time allowed. Formost questions substantially more detail is given than would normally be necessary toobtain a clear pass. There can also be valid alternatives which would gain equal marks.

K FormanChairman of the Board of Examiners20 November 2001


Subject 303 (General Insurance) � September 2001 � Examiners� Report

Page 2

1 Most candidates scored full marks on this question although some failed to mentionanything more than Buildings Insurance.

Residential buildingsMoveable property / contents / possessionsCommercial buildingsLand vehiclesMarine craftCropAircraft

2 There were many items that could have been covered in this question which waslargely bookwork. Candidates who clearly knew their bookwork scored very highmarks. There was a good range of marks on this question which demonstrated thatsome candidates could not recall or did not understand the wide range of areas ofrisk and uncertainty in general and how in particular such a book of business wouldbe affected.

Premium rating structure does not accurately reflect the cost of the insured risks.This may result in adverse selection.The overall level of office premiums may be too lowAllowance for expenses is too low due to business volumes lower than expectedBusiness volumes / profit may be volatile due to competition.Poor policy wording may result in additional unanticipated claimsThe insurer will have to take appropriate measures to avoid moral hazard.The insured risk profile may not be even over the policy durationClaims costs or frequency may be greater than expected � adverse fluctuations.Claims costs or frequency distributions may be different from those expected.There may be concentrations of risk, for example for fleet business where more thanone driver from the same fleet is travelling to the same destinationGeographical spread of risks should be considered, to avoid unnecessaryaccumulations of riskPossible under reserving by the insurer poses a serious risk of insolvency.Incorrect recording of data poses considerable risk as accurate data is crucial for thecorrect assessment of premiums and reserves.Higher inflation than anticipated represents a minor risk �if liability cover is included then most of the liability is short-tailed, though there maybe some longer tailed third-party liability / injury elements which have greater impact.Poor performing, illiquid or mismatching investments pose considerable risk.Where the market is competitive, underwriting margins will be tight and investmentreturns a more significant element.If investments are not sufficiently liquid then there is risk of exposure to randomfluctuations in the level of claimsRisk of investment defaultCatastrophes represent a considerable area of uncertainty.Inappropriate or insufficient reinsurance levels of reinsuranceThird party defaultExposure to risk from political and legal changes / precedents


Page 3

3 Although this was a fairly straightforward bookwork question many candidates failedto mention more than a few distinct points. Very few candidates scored more than halfmarks on this question.

Classes of business writtenChange in company strategyReduce volatility of claims experience / smooth profitsSize of free reservesTotal premium writtenGeographic area covered (e.g. flood is only a risk in some places)Accumulations of risk, too much in one geographic areaAccumulations of risk, too much of one class of businessAccumulations of risk, risks where claims can occur in more than one class ofbusinessAccumulations of risk, inwards reinsurance (but may not even know what you arereinsuring)Availability of reinsurance / capacityValue for money of reinsurance � return commissionSecurity status of available reinsurersAny regulations on the amount and types of reinsurance that must be purchasedExisting relationship with broker / reinsuranceRisk aversity of management

4 Most candidates could define the four terms. The main one causing difficulty wasIBNER. Clearly candidates were guessing in some cases what it meant and in othersclearly had no idea such as stating that it stood for Incurred But Not Ever Reported.

(a) A time limit, usually defined in the policy wording or through legislativeprecedent, placed on the period within which claims must be reported.Generally applies to classes of business where a long delay may occur fromorigin of claim to awareness of condition giving rise to a claim and subsequentreporting � e.g. employer�s liability.

(b) A form of reinsurance covering a single risk, commonly used for very largerisks or portions of risk written by a single insurer, that are shared amongseveral reinsurers. More time consuming than a Treaty.

(c) A reserve reflecting expected changes (increases and decreases) in estimatesfor reported claims.

(d) The risk that an insured may attempt to take an unfair advantage of the insurer,for example by suppressing information relevant to the assessment of risk orby submitting a false claim.


Page 4

5 This question provided a wide range of answers. Although an unusual reinsurancearrangement, not only did candidates not understand the order in which the twocontracts worked but many had difficulty in understanding that for the surplus treatythat the minimum was always ceded. Some demonstrated that they did not understandthe significance of the EML. A few candidates thought that the EML was the largestclaim that could arise.

(i) EML is the expected or estimated maximum loss

The largest loss expected to arise from a single event in respect of an insuredproperty which may well be less than its market or replacement value.

Used as an exposure measure in rating certain classes, including reinsurance.

(ii) (1+N) * R

(iii) $10m EML is split as followsA:B:C 5:2:3

Claim is $9m, A will pay $5m, B will pay 2/5 of (9�5)= $1.6m, C will pay$2.4m

An alternative answer of 5:0.75:3.25, was accepted if explained as it wasapparent that from the tuition material that candidates could have interpretedthis question in that way although the examiners consider the first solution tobe more valid.

6 Very few candidates had problems with this straightforward bookwork question.

(i) One year accounts, which consider all income earned and outgo incurred in ayear and permit the release of any profits at the end of the yearFunded accounts, which consider the business written in each year (andincome and outgo pertaining to that business) and do not permit the release ofprofits until the end of a subsequent year (usually the third year)

(ii) Going concern, that the business will continue to operate for the foreseeablefutureAccruals, revenue and costs are recognised as they are earned and incurred notas they are received and paidConsistency, like items are treated in a similar manner within each period andfrom one accounting period to the nextPrudence, revenue and profits are not anticipated and provisions are made forall known liabilities.


Page 5

7 Most candidates gained good marks on this question. The main area where marks waslost was in part (iii) in describing ways a supervisory authority could influence theinvestment policy.

(i) Maximise returnsubject to meeting all contractual obligations andrecognising the uncertainty involved

(ii) Term of liabilitiesNature of liabilitiesAmount of liabilitiesCurrency of liabilitiesAbsolute size of free reservesSize of free reserves relative to written premiumSize of non-investible fundsCulture / risk aversenessRegulatory requirementsMoral / marketing aimsAsset deemed over / under pricedExpected returnInvestment manager�s adviceAvailability of assetsLiquidity / marketabilityTaxExpenses

(iii) Restriction on which asset types are admissible for establishing solvency andmeeting a minimum level of solvencyRestriction in amount for which each asset is admissibleCustodianship of assetsPrevent some assets being heldPrescribe that other assets must be held and amount thereofRequire mis matching reserves to be held if certain assets are heldRequirement of investment manager being experienced / take professionaladviceSpecify asset valuation methodology for statutory purposes

8 There were many items of data which could have been mentioned for this class ofbusiness. Scores were generally low because candidates could not extend the normaldata items needed to the particular product in the question. Nearly all candidatescould list the basic items but only the better candidates could state many itemsrelating to the data required about the builders.


Page 6

Policy Data:Cover / Identifiers

Policy numberPolicy statusAddress Geographical location (postcode, etc.)House purchase price / sum insuredHouse-rebuilding cost index at purchaseFees paid / premiumEndorsements / ExclusionsPolicy LimitsSite numberCommissionSource of businessExcess

Dates

Date policy purchasedDate home startedDates of various stages of constructionDate home completedDate first occupiedDate of legal completionAssociated dates on which information is recordedTerm of policy / end date

Technical / Risk information

General risk information

Site sizeHouse type (detached, terraced, flat, etc.)Construction type (brick & block, timber frame, etc.)Number of floorsNumber of bedrooms / size of propertyFloor space areaSite managerSpecial featuresBuildings standards in forceInspection certificate


Page 7

Construction information

Ground conditions / treatmentTrees / subsoilFoundations typeGround floor typeWall typeWindow / door typesRoof typeBasement?

Builder data

Builder current trading statusTrade associationDate commenced tradingDate ceased tradingReason for ceasing to trade (bankruptcy, retired, etc.)Builder size (number of homes completed in last n years)TurnoverProfitBuilder IdentifierAny subcontracting informationOther accounts informationCredit RatingCompany DirectorsHow long has the builder been in businessPremium rating category / measuresPast claims history

Claims Data:

Identifiers

Claim number (link to policy)Name of current ownerClaim statusClaim accepted as valid?Claim investigated or cash settledRemedial works contractor identifier

Dates

Date damage first noticedDate reported


Page 8

Date investigatedDate accepted as validDate initial damage case estimate madeDates of paymentsDates closedDates reopened

Technical / Damage information

Type of damage / defect (code)Damage / defect descriptionLocation of damageCausation of damage

Financial information

Initial estimate of repair costCurrent estimated cost of repairs / outstanding amountsPaid so farType of cost � repairs / alternative accommodation / technical investigationRecoveries made from third parties

Other data

Competitors premiumsInvestment returns � for discount rateRelevant inflation indices: RPI, NAE, House re-buildingSalaries of staff employed to handle claimsLegal and professional costsEquipment costs (computers, stationary, etc.)Economic cycleBuilding cycleProfit loadingsContingency loadingReinsurance arrangementsEarning pattern of premiums


Page 9

9 Many candidates failed to demonstrate to the examiners the reasons why the BasicChain Ladder method was not the best to adopt in this case. Some candidates failed todistinguish between the damage and injury type claims. In part (ii) almost allcandidates mentioned Bornhuetter- Ferguson and other methods but failed to expandon further additional steps.

(i)

Outstanding Claims Reserves = Outstanding Reported Claims + IBNR + OutstandingClaims Handling Expenses + Reopened Claims ReservesShould always use more than one method to establish technical reserves.BCL often more useful as just a broad brush check on other methods.BCL method is very simple and has numerous implicit assumption.Effect of large claims in dataClaims triangle unlikely to be fully run-off, so BCL cannot be used on the existingdata to estimate the tail-end liabilities.BCL assumes a stable run-off pattern from year to year. This is unlikely to be thecase with TP cover which has low claim frequency and a skewed cost distribution.Earlier years less credible as growing account from nothingMight be reasonable for more frequent damage claims which are reported and settledquickly for relatively small amounts.However, particularly poor for injury claims which can often take considerably longerto settle and are less frequent.Future inflation is implicitly assumed to follow that experienced in the past data,which is quite likely not to be the case.Internal factors such as changes to the claims handling process may have occurred toinvalidate the �same pattern as the past� assumption.As too can External factors, such as changes in the legal process.Changes may also have occurred to the underlying risk due to things like;Increased traffic conditions, changes to court award levels, changes to the risk profiledue to competition or rate changes.The most recent years are very uncertain, especially in respect of the injury claimliabilities, due to the longer delays.

Extent of reliability for IBNR will depend on basis of data.Paid claims triangle � little is known of latest year.Incurred claims triangle � greater information for latest year.

Extent of usefulness for estimating claims handling expense reserves will depend onthe extent to which the claims data includes or excludes associated claims handlingcosts

(ii)

External data and curve fitting might be available in order to assess the likely extentof the �tail�May use additional methods of assessment, including amongst others;Inflation adjusted chain ladder


Page 10

Bornhuetter-FergussonAverage Cost per claim methodsAnalysing the various delays in the lifecycle of a claim may provide insight into howthe �tail� may lookMay approach reinsurers for technical assistanceMay adjust the data for known internal and external factorsAsk the underwriters or other expertsOther reserves such as UPR, APUR etc.

10 This question tested the candidates ability to determine which types of insuranceproducts would be required for such a commercial enterprise. Most candidatesmanaged to mention most of the products but some demonstrated that they did notunderstand the difference between perils, risk factors and rating factors. Somecandidates clearly ran out of time and failed to complete part (iii)

(i) Employers Liability:This insurance indemnifies the insured against legal liability to compensate anemployee or their estate for bodily injury, disease or death suffered, owing tonegligence of the employer, in the course of employment.Perils are largely grouped as;Accidents caused by negligence of the employer or by other employeesExposure to harmful substancesExposure to harmful working conditions

Public Liability:The insured is indemnified against the legal liability for the death or bodilyinjury to a third party or for damage to property belonging to a third party,other than those liabilities covered by other liability insurance.Perils will include compensation for injury from falling objects, pollution, etc.

Motor Fleet Third Party Liability:Third Party Liability indemnifies the owner of a motor vehicle againstcompensation payable to third parties for personal injury or damage to theirproperty.

Motor Property DamageIndemnifies insured against loss or damage arising to their vehicle fromspecified perils such as theft, subject to any limits or excesses.

Commercial Property Damage:As per motor property damage..For Commercial Fire perils include mainly fire, but can also includeExplosion, lightning, theft, storm, flood and vandalism

Pecuniary Loss:Protects the insured against bad debts or other failure of third parties or effectsof recession, as specified in the policy


Page 11

Fidelity Guarantee:Covers the insured against financial losses caused by dishonest actions by itsemployees, including loss of money or goods owned by the insured or forwhich the insured is responsible, and reasonable fees incurred in establishingthe size of the loss.

Business Interruption:Indemnifies the insured against losses made as a result of not being able toconduct businessPerils will include items such as fire at insured�s property, and fire atneighbouring properties.

Product LiabilityIndemnifies insured against legal liability for death or injury to third party, ordamage to property belonging to a third party arising from product fault. Perilsinclude faulty design, packaging, misleading instructions etc.

Group Medical and Personal Accident InsuranceIndemnifies the insured against some or all sorts of the costs for medicaltreatment and fixed amounts for loss of limbs etc.

Crop insurance:Indemnifies the incurred against losses made to the crop

� disease� fire� storm� drought

(ii) Employers and Public Liability:Payroll / number of employeesType of businessClaims experienceLocation of workforceEquipment used / Processes involvedMaterials handledHealth & Safety measures / proceduresTrainingTurnoverDeductible

Motor Fleet:Use of vehicleAge of vehicleNumber of vehicles


Page 12

Value of vehiclesType of coverExcessOccupation of driversSex of driverAge of driverType of vehicleLocation of vehicle overnightWeight / capacityArea of use (local / national)Maintenance proceduresLevel of useClaims experience

Commercial PropertySize of farm / number of buildings / sum insuredUse of buildingsConstruction designLocationValue of stockAge / condition of buildings / machineryExcessClaims experience / training providedFire precautionsSecurity measures

Pecuniary Loss, Fidelity Guarantee, Business Interruption:Type of businessTurnover / earnings / sum insured / profits / projected salesValue of work in progressMaterials handledEquipment UsedIndemnity period (3-5 years)Years trading to datePrevious bankruptciesFinancial Controls / Security(Cash kept on site)

Product LiabilitySize of treesAssociated componentsPackagingChemicals used in farming processLocation of sales (country)

Medical / Personal AccidentAgeSexCover


Page 13

Number of people coveredRegionMedical historySum insured for PAActivities in workplace

Crop Insurance:LocationPast claimsVariety of treeUse of pesticidesSum insured / crop valueSecurity measuresExclusionsTree densityFire prevention measures

(iii) Employer�s Liability:Many claims likely to be reported and settled quickly. However, some may becomplicated due to origination over long periods of time.So long reporting delays (due to appearance and notification)And long settlement delays (due to determination and agreement of extent ofliability and settlement of conditions).E.g. Asbestosis, or here perhaps long-term effects of use of chainsaw.Therefore long-tailed.Claim frequency quite low, but seasonal effects.Average cost of claim distribution quite skewed.Potential for quite large individual claims and accumulations of risk arisingfrom the same cause.

Public Liability:Similar to Employers� liability, though reporting delays unlikely to be longMotor Liability Claims:Greater frequency than Employers� and public liability claims.Cost distribution not dissimilarReporting and settlement quicker, though not as fast as property damageclaims.Accumulation of risk not quite so great � class action case shouldn�t arise.

Motor and Commercial Property:Claim event sudden and easily determinable, so few reporting and settlementdelays.However, some settlement delays can occur on larger claims to verify value ofstocks, etc.Frequency is greater than liability claims.Average cost distribution is less skewed.


Page 14

Accumulations are generally possible where there is a risk of fire on aparticular business park site. Though this is unlikely to be the case unlessthere are neighbouring farms also covered

Pecuniary Loss & Fidelity Guarantee:Generally few reporting and settlement delays � short-tailed.Frequency and cost of claims usually low.

Business Interruption:Generally few reporting and settlement delays � short-tailed.Frequency and cost of claims usually low.Though settlement delays may be longer than for Pecuniary Loss owing togreater need for verification.

Product LiabilityGenerally few reporting delaysMay be long settlement delays in determining liabilityLow claim frequencyVery skewed cost distribution

Medical / Personal AccidentGenerally few reporting and settlement delays � short tailedSometimes subject to disputeClaims often quite small in size

Crop Insurance:Short tailed, except for claims arising from diseaseCatastrophicFrequency effectsLow frequencyHigh average cost


EXAMINATIONS

17 April 2002 (am)




1. Enter all the candidate and examination details as requested on the front of your answerbooklet.

2. You have 15 minutes at the start of the examination in which to read the questions.You are strongly encouraged to use this time for reading only, but notes may be made.You then have three hours to complete the paper.

3. You must not start writing your answers in the booklet until instructed to do so by thesupervisor.


5. Attempt all 7 questions, beginning your answer to each question on a separate sheet.


Hand in BOTH your answer booklet, with any additional sheets firmly attached, and thisquestion paper.

In addition to this paper you should have available Actuarial Tables andyour own electronic calculator.


303 A2002�2

1 Describe the areas of risk and uncertainty in respect of expenses and investments for ageneral insurance company writing only a small volume of business. [9]

2 (i) (a) Describe the benefits provided by Employers� Liability insurance.

(b) Describe briefly, with examples, the distinct groups of insured perilsfor such business. [5]

(ii) List the main rating factors that are used to set premium rates for EmployersLiability insurance. [2]

[Total 7]

3 (i) You are the actuary for a recently formed but rapidly growing generalinsurance company writing only motor insurance business. The assets of thecompany consist solely of index-linked government securities and cash.

Discuss the appropriateness of the investments currently held. [7]

(ii) Describe briefly the controls that a supervisory authority might impose on theassets of a general insurance company. [4]

[Total 11]

4 (i) List the uses of a statistical claims model. [3]

(ii) Explain the difference between deterministic and stochastic modelling. [3]

(iii) Discuss the factors that would influence your choice between a deterministicand a stochastic model. [4]

[Total 10]

5 A general insurance company writes only motor insurance business. Five years ago itreplaced one of its existing rating factors with a new one, with a view to improving itsunderwriting result and overall profitability. Pre-tax profits since then, however, havefallen steadily each year. The Board of the company is of the (currently unfounded)opinion that these poor results are due to the replacement of the rating factor madefive years earlier. As Chief Actuary, you have been asked to investigate the cause ofthe recent reduction in profits.

Describe briefly the main actuarial investigations you would carry out to do this andtheir respective purposes. [12]


6 A large industrial company is seeking to expand its operations on a global scale. Thecompany wishes to ensure that it has appropriate insurance arrangements toadequately manage the risks involved in the existing business, and make anyappropriate changes in respect of the expansion.

You are the Chief Actuary for a large multi-national general insurance company thatprovides most forms of insurance cover, with the exception of fixed benefits relatedinsurance. Your company already insures some of the above company�s risks andthose of some other industrial companies with global operations.

You have been asked to assist the company with the insurance aspects of their existingbusiness and possible expansion of business.

(i) Describe in general terms how you would determine which risks are insurable.[2]

(ii) Describe briefly the various types of insurance product that might beappropriate in helping to manage the industrial company�s risks. [6]

(iii) Describe briefly the factors that you would consider in assessing the extent towhich your company can insure the industrial company�s various insurablerisks. [6]

(iv) Describe in detail the various reinsurance arrangements that your companywill need to have in place, assuming that your company decides to provideinsurance coverage for the industrial company for all the insurance products in(ii). [6]

(v) What factors do you expect your lead reinsurer to consider in deciding to whatextent they will accept the placement of the active risks. [5]

[Total 25]

303 A2002�4

7 (i) State why insurance reserves may be calculated for a general insurancecompany. [4]

You are the actuary for a general insurance company that writes only MIG (MortgageIndemnity Guarantee) business for a number of small regional building societies.MIG covers mortgage lenders for the difference between the amount owed by aborrower who has defaulted on their mortgage and the resale value of the repossessedhouse. The amount owed by the borrower consists of the outstanding mortgage,interest payment in arrears and any costs incurred in selling the house. MIG cover istaken out at the same time as a mortgage and covers the lender for a specified period,usually the term of the mortgage. A claim occurs when a repossessed property is sold.

(ii) Discuss the characteristics of this business that affect which reserves might beneeded and describe the methods that may be used to estimate such reservesfor MIG. You should indicate which method(s) are likely to be used for eachof the reserves. [18]

(iii) Discuss the relative sizes of the reserves that are likely to be estimated forMIG. [4]

[Total 26]


REPORT OF THE BOARD OF EXAMINERS ONTHE EXAMINATIONS HELD IN

April 2002


Introduction


The report does not attempt to offer a specimen solution for each question � that is, asolution that a well prepared candidate might have produced in the time allowed. Formost questions substantially more detail is given than would normally be necessary toobtain a clear pass. There can also be valid alternatives which would gain equal marks.

K FormanChairman of the Board of Examiners

25 June 2002



Page 2

1 On the whole, this question was poorly answered by many candidates. Althoughsubstantially bookwork, this question required candidates to pull together a broadrange of points. Some candidates focused too much on one of either Expenses orInvestment, rather than covering both in detail. The examiners were additionallylooking for some application of the details given in the question i.e. referring to thesmall company; some candidates did this well.

Expenses

Commission is normally expressed as a percentage of the premium paid and soOnly possible uncertainty is if different types of intermediaries are paid differentlevels of commission. In this case a change in the mix of the source of business could result in actualcommission payable being different to that projected even though business volumesare in line with expectations.

Change in staff and accommodation costs as the business increases/decreases. This could be particularly relevant for a small company as the decision about when tochange premises etc. can significantly increase costs.

Changes in legal and professional costs. No control, affected by supply and demand

Changes in the rates of inflation that affect expenses, e.g. medical costs, salaries

Using an expense allocation that is not appropriate leading to anti-selection

Volumes of business different to expected and hence different contribution to fixedexpenses

Mix of risks different to expected

More relevant for small company as fixed expenses higher proportion of total

Claims expenses higher than expected

Business risks which affect expenses

Investments

Premiums take credit for expected investment performance of investments held tomeet liabilities in respect of the business. There is uncertainty regarding the performance of these assets income and gains.

� Market conditions worsen� Proportion of investible assets less than expected� Claims paid faster than expected � or any other mismatching comment� Forced to realise assets at an unfavourable time� Limited diversification of investments for small company� Investment expense higher than expected


Page 3

� Poor investment management� Tax� Default risk� Investment legislation

2 This was a bookwork question for which a well prepared student could scoremaximum marks.

For part (i)(a), the examiners were surprised by the number of candidates who couldnot describe Employers Liability benefits, which is contained within core reading.Some candidates mistook �rating factors� for perils in part (i)(b). Part (ii) wasreasonably well answered.

(i) (a) Benefits

Employers Liability insurance indemnifies the insured against legalliability to compensate an employee or their estatefor bodily injury, disease or death sufferedowing to the negligence of the employerin the course of employment.

(b) Perils

accidents caused by the negligence of the employer or other employees

e.g. safety guardsexposure to harmful substancese.g. chemicals, coal dust, asbestosexposure to harmful working conditionse.g. loud noises, repetitive strain, stress.

(ii) Rating factors

Payroll, no of employeesType of industry or occupationPrevious claims experienceLocation of the workforceThe materials handledThe processes involvedTurnoverSize of deductibleLevel of staff training / score risk assessmentProvision of first aid facilities


Page 4

3 This question was generally well answered.In part (i), some candidates described motor business as short tail and did not discussthe suitability of the investments in terms of matching bodily injury claims. Theweaker candidates talked about the need for liquidity whereas the stronger candidatesrecognised that premium income would be sufficient to pay most claims in the shortterm owing to the growing account of the business. Part (ii) was well answered.

(i) Would want to maximise return subject to meeting liabilities as they fall due

Rapidly growing => size of free reserves relative to written premium andstatutory solvency may be under pressure

Different matching considerations for vehicle damage and bodily injury

Balance of these liabilities depends on type of policies written (e.g.comprehensive vs third party liability)

Vehicle damage claims reported and settled quickly

Bodily injury claims longer tail

Cash is liquid

�.and has stable capital value (good for solvency)�. but does not provide inflation protection for either the property damageclaims or the bodily injury claims

Index linked government securities provide some inflation protection

�..but inflation affecting bodily injury claims in particular will notnecessarily correspond with the type of inflation underlying the index

Can get ILGS with different terms

�so can try to match tail of liabilities

ILGS capital values can be volatile and may not be suitable if solvency underpressure

However marketability of assets not an issue as can pay claims out ofpremiums currently being received but may depend upon currency of assetsand liability

Risk of default with both cash and ILGS is low

Value for money: would expect other asset classes to produce higher returnsover the longer term e.g. equities

So would consider using other asset classes for matching the free reserves


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However other assets may not be appropriate if there is then a currencymismatch

Different taxation rules for different assets may affect decision

May depend upon any statutory solvency test

May be compulsory type of investment

(ii) Restriction on the amount and type of certain types of assets that can be takeninto account when assessing solvency

Custodianship of assets

Prevention from holding certain assets

Prescription to hold certain assets

Requirements to hold mismatching reserves

Specify asset valuation methodology

Requirement of investment manager to be experienced/take professionaladvice

Forced disclosure of investment policy

Specification of minimum solvency margin

4 The examiners were pleased by the standard of the answers to this question.Candidates seemed to apply their knowledge well in answering part (iii).

(i) Calculate a risk premium per policy Select rating factors Determine premiums using experience rating procedures Estimate the effect of changing the level of cover by changing the levels ofdeductibles Demonstrate the effect of reinsurance Estimate the likely variability of claims experience Examine effect of actual versus expected claims experienceEstimate the possible effect of industrial diseases on the reservesProduce reserve estimates A check against case estimatesAssess the degree of solvency Allocate capital to different classes or categories of business Financial planning Workload management / staff planning Assess profitability of different classes As part of Asset Liability Model to set investment policy


Page 6

(ii) Each of the parameters in a deterministic model have fixed values The model produces results in the form of a point estimatePossible to sensitivity test the results of a deterministic model by running themodel with different parameters values Some of the parameters in a stochastic model (e.g. number of claims or claimamounts) are allowed to vary and have their own distribution functionA stochastic model must be run many times using a random sample from thedistribution functions The model produces results in the form of a probability distribution

(iii) Time and manpower available: stochastic models are more complex and time-consuming

The nature of the parameters within the model�.�e.g. stochastic models are more effective in allowing for volatility in assetvalues The availability of data: there may not be sufficient data to permit the fittingof distribution functions with any level of certainty The need to be able to explain the model and communicate findings e.g. tothose with less modelling experience; stochastic models can be more difficultto explain Purpose of the investigation Deterministic automatically done to get stochasticCurrent proceduresMore informative: any additional information obtained by using a stochasticmodel may not be useful e.g. reserving: requiring only a best estimate reserve for the accounts�or a reserve that is likely to be adequate in 95% of possible outcomes

5 The answers to this question were on average disappointing. Many candidates wroteout a lot of bookwork without relating their answer to the details given in thequestion.

Some candidates assumed that the Board of the company was correct in itsassumption about the cause of the poor profitability. These candidates thereforefocused on the impact of the change in rating factor without considering otherdrivers. Some candidates assumed the Board was incorrect and did not discuss theimpact of the change in rating factor at all. Those candidates who considered arange of factors scored highest.

Need to investigate the following:Underwriting profitability- to check if poor results are due to quality of underwriting- look at underwriting procedures and guidelines and adherence to themClaims analyses. E.g. multiple regression, etc. using both the old and new factor.- to investigate the effect of the change in rating factorThe effects of competition on persistency e.g. lapse rate investigationto see if the change in approach 5 years ago mirrored those made by competitors orhas there been anti-selection.


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Has the insurance cycle affected the resultsCompare with market experience in respect of ULRCompare premiums required with premiums charged for deliberate underchargingHas there been an increase in competitive pressures, through either more players orlower premiums (soft market)Underwriting performance on homogeneous cohorts of business- to check for any adverse selectionInvestment performance against peer groups, benchmarks and past performance- to check if in line with targets / expectationsEffects of any internal changesE.g. Change in sales medium, commission rates, changes to internal processing,changes to claims handling, etc.- To ensure various expenses are in line with expectations.Effects of any external changes on profitability.E.g. Tax, legislation, solvency requirements, road traffic factors, etc.- To identify if poor results due to unexpected high claimsGeneral claims trends.E.g. Unusually large claims, high frequency, catastrophe events, etc.- To see if due to natural random variationEffectiveness of reinsurance arrangements- to see if due to inappropriate coverthird party / reinsurance bad debtMix of business- to investigate whether poor performance is due to poor coverage of overhead andother fixed expenses. Different cohorts will have different contribution ratesCoverage and policy wording- to see if any changes in premium were in line with the resulting changes in claimsexperience.Adequacy of reserving / changes to reserving practices- The level of reserves may have been set at increasingly prudent levels.Any changes in methodology of reservingAny strengthening of prior years reserves

6 Part (i) was well answered.

Despite a similar question in the September 2001 paper, some candidates struggled todescribe the common insurance products. Most candidates wrongly assumed thatbecause fixed benefit products were not currently offered by the insurance company,they would not be appropriate for the industrial company. Several candidatesconfused the names of different products (e.g. pecuniary loss and fidelity guarantee).

In part (iii), some candidates wrote at some length about rating factors rather thandiscussing more general factors that would influence the extent to which the companycan insure the risks.

Those candidates who applied the details in the question, rather than describing everytype of reinsurance contract indiscriminately, scored better on part (iv).


Page 8

The stronger candidates were able to distinguish between the considerations of theinsurance company in (iii) and those of the reinsurance company in (v).

(i) The company must have an insurable interest in the risk being considered.The risk must be of a financial and reasonably quantifiable nature.Also, ideally the risks should be independent of each otherShould be an ultimate limitShould minimise moral hazardAnd the probability of incidence should be relatively small

(ii) Employers liability- Indemnifies the insured against legal liability to compensate an employee ortheir estate for bodily injury, disease or death suffered, owing to negligence ofthe insured, in the course of employment.

Public liability- Indemnifies the insured against legal liability for the death of or bodily injuryto a third party or for damage to property belonging to a third party, other thanwhere covered by other liability insurances.Fleet motor 3rd party liability- Indemnifies the insured against compensation payable to third parties forpersonal injury or damage to their properties.Product liability- Indemnifies the insured against legal liability for the death of or bodily injuryto a third party or for damage to property belonging to a third party, thatresults from a product fault.Property (General)- Indemnifies the insured against value of loss or damage to the property or itscontents, subject to any limits or excesses.Commercial Property- resulting from pre-specified perils � E.g. Fire, storm, lightning, flood, theft,explosion, etc.Fleet motor property- resulting from accidental or malicious damage, fire, theft, etc.Marine & Aviation property (if oil industry then own tankers etc.) and GoodsInTransit- resulting from fire, explosion, jettison, piracy, etc.Professional Indemnity- if professionals in the company are negligent in the provision of their

servicesDirectors and Officers- for protection against company being sued for acts D&O performedFixed Benefits- for medical benefits / sickness schemePecuniary Loss- Protects the insured against bad debts or failures of a third partyFidelity Guarantee- covers the insured against financial losses caused by dishonest actions by itsemployees


Page 9

Business Interruption- indemnifies the insured against losses made as a result of not being able to

conduct business

Other valid types e.g. Project Insurance in case project to expand costs morethan expected

(iii) The extent to which risks are already covered for this companyThe extent to which similar risks are covered in respect of other companies.Relationship with insured and past profitabilityLikely profitability of additional businessHow will the cover be structured? Will the company be looking for a multi-year contract?Any other potential concentrations of riskby class of business- geographicallyCurrent level of free reserves. What scope is there for new business.Reinsurance / co-insurance arrangements in place- Do these risks fall within existing treaties- If not, how easy will it be to arrange additional cover, facultative oradditional treatiesAny legislative requirements / restrictionsThe Board�s attitude to riskThe potential for long-term involvement/desire to maintain existinginvolvementCurrent classes of business authorisedWillingness to extend classes authorised to writeBusiness strategyStaff expertise in areas of potential insurable risksCompetition � clearly this would bring in a considerable volume of business /premium incomeWhat data is available to assess the risks to be insured

Large company, so quota share treaties unlikely to be usedSurplus may be needed for large commercial property risks if insurer does notwrite much of this businessNeed to determine retention and number of lines for each riskHowever, likely to use the full range of non-proportional reinsurance productsavailable.XOL policies cover the insured for losses arising above a pre-specified lowerlimit up to a pre-specified upper limitRisk XOL relates to single risksAggregate (clash) relates to accumulations on multiple risks, due to a singleevent, or from a single cause through timeCat XOL relates to losses arising within a pre-determined time span from pre-specified eventsStop Loss relates to cohorts or portfolios of risksThese policies will often have a Stability Clause (particularly for liabilitybusiness) � i.e. indexed limits


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Risk XOL is likely to be arranged to cover risks such as marine & aviationproperty damage.

Aggregate XOL may be arranged and include several layers;- for each class of business separately- aggregated over several-classes- aggregated by insuredPlace business with different insurers to spread risk of reinsurer defaultCat XOL may be arranged to cover against specific pre-defined events, suchas Hurricane, Earthquake, etc. Stop Loss may be arranged, though for a large multi-national it may not beavailable

(v) If the risks fall under existing treaties then they will be automatically covered.

However, if not�The current relationship they have built up with your company Their confidence in the ability of the multi-national�s underwriters toaccurately assess the risksConfidence in insurer to deal with claims in acceptable mannerInfluence of business written by insurerAvailability of reinsurance for business it acceptsAvailability of profit sharing arrangementsThe quality of data providedThe cover already provided in respect of:- the insured in question from all cedants- other risks with your company- each class of business for all cedants- within the company�s geographical regions of operationAvailable capacityClaims experience in respect of each of the classes� risksWhether it is authorised to cover all of the classes required

7 This question was a reasonably good indicator of those who understood the subject ofclaims reserving and could apply their bookwork knowledge to a non standard classof business.

Part (i) was mostly well answered. A few candidates discussed why different types ofclaims reserve were required rather than why reserves would be calculated.There were a number of errors in part (ii):

� The most common error arose from candidates using a different definition ofa claim occurring to that clearly given in the question. This often revealed alack of understanding of an IBNR claim.

� Consequently, some candidates talked about the potentially long delaysbetween a mortgage default and the sale of the property and incorrectlyconcluded that IBNR reserves would need to be large.


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� Many candidates incorrectly described MIG as long tail. Whilst theexposure period is very long (theoretically up to the term of the mortgage)the reporting and settlement delays are short compared with many otherclasses of business.

� Candidates generally discussed a number of methods but did not make anappropriate selection for each type of reserve.

� Weak candidates suggested using the 365ths or 24ths method for the UPR.� Very weak candidates suggested using case estimates for UPR or IBNR!

Part (iii) was reasonably well answered.

(i) Reasons reserves are calculated include:� Determine the liabilities for the insurer�s published accounts� Determine the liabilities for the accounts for the supervision of

solvency� Determine the liabilities for the internal management accounts� Estimate the cost of claims in recent periods to get a base for

estimating future premiums required for a given level of profit� Value the company for sale/purchase� Value the company for setting the terms of a merger� Value the company for setting performance related pay for directors� To calculate tax liabilities� To determine investment strategy� Determine liabilities for any profit sharing arrangement

(ii) MIG is characterised by uncertainty and as such presents challenges forreserving.

The features of MIG are that:� Exposure period is up to 25 years. � However most insurers consider the exposure nil after 10 years as risk

is not uniform throughout term of cover and generally reduces overtime with rising house prices.

� Average claims amounts are surprisingly consistent over time for aparticular lender but mar vary by lender owing to different lending andrepossession practices.

� Hence the loan acceptance terms of the building societies are animportant factor and the reserving should be done at this level as wellas top down to check that performance is comparable to what would beexpected given the underwriting standards.

� Most of the variability of claims experience is based on the number ofclaims.

� In particular circumstances, e.g. growing unemployment, increasingmortgage rates and falling house prices, catastrophes can occur over along period.

� As such any UPR may not be enough to cover future claims onbusiness already written


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The likely reserves for this class of business are:Unearned Premium ReserveAdditional Provision for Unexpired RisksOutstanding Claims reserveClaims expense reserveIBNRIBNERMaybe Statutory Claims Equalisation ReserveCatastrophe reserveCase Estimates and various triangulation methods can be used to estimate suchreserves both by accident and underwriting year. Do average costs and numbers of claims separately.Split data by lender, region, type of mortgage, loan to value ratioUPRUse underwriting triangles of earlier years claims experience � inflationadjusted chain ladder to see pattern of claims and earned premiumaccordingly. Patterns may change from one underwiting year to another owing to changesin economic conditions.

Outstanding Claims ReservesClaims are normally settled very quickly and hence likely that only a few willbe outstanding. Hence the most likely approach is case estimates

Claims ExpensesLikely to be a percentage loading of any claims costs.

IBNRInformation may be available from lenders as to which properties have beensold but not yet notified to the insurer and thus likely to lead to claims. Inwhich case a count of number of claims can be taken and an assumed averagecost adopted based on recent experience. Alternatively calculate as apercentage of outstanding claims or use delay table method

IBNERAs stated, average costs are fairly consistent and as such the need for anIBNER is unlikely. In fact a negative IBNER may arise if mortgagees arepursued and recoveries for bad debts are made

Statutory CERRules for calculation likely to be set by Regulatory authority e.g. a percentageof premium is transferred to CER providing loss ratio is below a certainamount otherwise a transfer from CER

Catastrophe reserveCompany may set up a catastrophe reserve which may be in line with itspremium rating basis such that for years when no catastrophe occurs whateverthe loading in the premiums for catastrophes is transferred to the reserve.


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Re-opened Claims ReserveLikely to be zero (or in fact negative) so no method required

APURFor business written to date need to assess if UPR is sufficient to meet cost ofclaims and expenses for the unexpired period of risk. Need to project likely number of claims and average costs. Could use the B-Fmethod as this takes the belief about the claims development for each year andmodifies it only slightly unless there are large deviations in the future from theprojections.Easy to allow for some years having different development patterns to others.

Alternatively, if available, could model claims arising from arrears cases in thepast and based on current arrears cases project future claims resulting frombusiness already written.

(iii) Unearned Premium ReserveThis is likely to be the largest reserve given that a claim only occurs once thehouse has been sold, and exposure can last for up to say 25 years.

Additional Provision for Unexpired RisksThe size of this reserve depends on whether business written in the past hasbeen written at adequate rates.In particular the stage of the economic cycle when business was written andnow will have a big impact upon the size of this reserveIf past rates have been inadequate then the APUR could be the largest reserve.

Outstanding Claims reserve/Claims expense reserveWill be small as the time between a claim occurring and paying it will besmall.

IBNR/IBNERIBNR will comprise of houses that have been sold but the insurer notinformed. Very small. IBNER will be smaller than IBNR and most probablynil.

CER/Cat reserveBoth likely to be small compared to the UPR. Although the Cat reserve maybe large if built up over many years because when things go bad they go badin a big way.


EXAMINATIONS













� Faculty of Actuaries303�S2002 � Institute of Actuaries

303 S2002�2

1 Explain why it is important to understand the nature of any flaws, inconsistencies,errors and omissions within a set of data that is to be used for a review of pricing of ageneral insurance policy. [3]

2 (i) Explain what is meant by moral hazard. [2]

(ii) Describe the various moral hazards associated with household buildings andcontents insurance. [7]

[Total 9]

3 Describe briefly the factors that should be taken into account when determining theallowance that should be made for future investment return when pricing a generalinsurance product. [9]

4 A general insurance company writes only Public Liability business.

(i) (a) Describe the characteristics of the liabilities that you would expect forthis class of business.

(b) Suggest, with reasons, suitable assets that could be used to match theseliabilities. [6]

(ii) State the factors that will influence whether the company decides to matchliabilities and assets. [3]

[Total 9]

5 (i) Explain what is meant by the terms case estimation and statistical estimation.[3]

(ii) Compare and contrast these two methods of estimation. [6]

A general insurance company writes a large book of household buildings insurancebusiness. It is considering switching from a case estimated approach to a statisticalapproach for assessing the cost of outstanding claims.

(iii) Explain, giving reasons, which of the two methods in (i) is likely to be themost appropriate for this book of business. [3]

[Total 12]

303 S2002�3 PLEASE TURN OVER

6 You are the Actuary to a general insurance company which started transactinghousehold buildings and contents insurance on 1 January 1998. All business written ina year is based on the same premium rating basis. All reinsurance is on a quota sharebasis. The only accounting information available to you is:

Year 1998 1999 2000 2001

Net Written Premium* 25 50 100 200Net Earned Premium* 10 35 70 140Net Loss Ratio* 150% 130% 100% 75%

* the loss ratio is calculated on an occurrence basis and premiums are net ofreinsurance ceded

(i) Calculate the gross loss ratio for each of the four underwriting years, statingany assumptions that you make. [7]

(ii) Explain why the figures in (i) are unlikely to occur in practice. [4]

(iii) Discuss the effects that such rapid premium growth may have on an insurer�sbalance sheet and future business plans. [5]

[Total 16]

303 S2002�4

7 You are the Actuary for a medium sized general insurance company that writes mainlycommercial property business. Much of the property insured is in the North Easternarea of the country in which it operates.

The company has the following two reinsurance treaties, one with Company A, theother with B and C, which have been in place since 1 January 1997:

A 4 line surplus treaty with maximum retention of 500,000B 200,000 xs 500,000 individual risk excess of lossC 300,000 xs 700,000 individual risk excess of loss

The treaties operate in the order above. A stability clause provides for the indexationof the limits for the treaty with Company C only. This index started at a value of 100on 1 January 1997. To date six claims have arisen from risks written in 1997(amounts shown in 000s).

ClaimNumber

ExpectedMaximum Loss

Total Paid Index

1 1,000 500 1022 2,300 3,500 1043 1,600 300 1014 2,800 1,600 1055 1,200 800 1086 1,500 4,000 101

(i) Describe briefly the main features of surplus reinsurance. [4]

(ii) Discuss briefly the features of an individual risk that your company shouldconsider when deciding how much of that risk it should cede to company A.

[3]

(iii) For risks written in 1997, the company retained the maximum proportionallowable under the terms of the surplus reinsurance treaty.

Calculate the amounts payable by your company and by each of companies A,B and C in respect of claim 2, stating any assumptions you make. [4]

(iv) Comment on problems that the insurer may face with the existing reinsuranceprogramme for the above six claims, suggesting alternative reinsurancearrangements that would address these problems for future business. [6]

[Total 17]

8 You are the Actuary for a small general insurance company writing only personal linesmotor insurance business.

(i) Discuss the areas of risk and uncertainty inherent in the claims experience ofthis insurer. [18]

(ii) Describe the business risks to which this insurer may be exposed. [7][Total 25]


EXAMINATIONS

September 2002


EXAMINERS� REPORT

Introduction



K FormanChairman of the Board of Examiners

26 November 2002



Page 2

1 Many candidates mentioned points relating to only if the premiums were too high ortoo low and did not go into the greater detail which the examiners were looking for.As a result of this most candidates did not score many marks onthis question.

(i) Need to know the potential variability in the results produced from analysingthe data.

Different data problems will affect the results in different ways and to avarying extent. Understanding the nature of the problems will help indetermining what allowance must be made.

This will help to ensure that premiums are set at an appropriate level to ensuredesired profitability is achieved. If the premiums are set too high then likelyloss in business. If the premiums are set too low then could get selectedagainst.

At the high level, this will help to ensure the right decisions are made.

Helps in determining the cause of the data problems which can in turn help todecide what actions to take to prevent such problems arising again in thefuture.

Helps in finding improvements to the data capture methods.

2 The answer given below in part (i) below relates to the Core reading definition. Theexaminers accepted also an alternative definition which they thought was alsoappropriate � policyholder acts in a way that makes the insured event more likely justbecause they have insurance. In this case marks were given in part (ii) where thecandidate gave reasonable and relevant examples. Some candidates did not read thequestion carefully and gave examples not relating to household buildings andcontents business.

(i) The risk that an insured may attempt to take unfair advantage of the insurer,for example by suppressing information relevant to the assessment of risk orby submitting a false claim.

(ii) The homeowner may under-declare the rebuilding cost of the home atproposal.

This may simply be through failing to provide accurate information atpurchase.

Or may be due to failing to advise the insurer where modifications have takenplace.

E.g. Extentions, loft conversions, etc.


Page 3

With regard to contents insurance, the homeowner may deliberately under-declare the value of their contents at proposal

Or may fail to revise the figure through time where affected by inflation

The insured may fail to notify of changes to personal circumstances relevantfor assessing the risk.

E.g. The home may now be empty during the day

The homeowner may now work at home.Or may have provided misleading information regarding the security measuresat the property.

The homeowner may submit a false claim

Or inflate valid claim, perhaps including items that were never there or werenot damaged

The homeowner may have failed to disclose risk related information on theproposal form

E.g. Past claims, etc.

Fraud, arson and deliberate damage

Household security, e.g leaving window open when gone out

3 Most candidates made a reasonable attempt at this question but only the bettercandidates managed to get enough points to earn well in excess of half marks. Somecandidates concentrated upon the choice of assets and thus failed to mention many ofthe points which the examiners were looking for.

Mix of assets held to back the required level of reserves (including free reserves)- This will be important in order to assess the likely future returns, investibility ofassets (including premium payment pattern), risk of default.

Expected level of investment return- when the expected rate of return is low, this component is less important.

Term of policy / Exposure profile- more relevant where policy term > 1 year and significant portion of exposure is laterin the policy term

Length of tail of the business being underwritten- long-tailed means more relevant

The capital allocated to back this particular part of the business


Page 4

- how is the capital allocation determined- just technical reserves, with free reserves elsewhere, or does it include a portion ofthe free reserves

Extent to which assets held are mismatched to the liabilities- mismatching increases the level of risk so a downward adjustment to the assumedreturn may be appropriate.

The degree of uncertainty in the expected level and timing of claim payments- increased certainty means less of a reduction for mismatching

Any legislative factors that affect the extent to which such allowance can be made.

Consistency with other assumptions, especially inflation

Investment expenses.

Tax treatment of investment returns- any allowance should be made net of tax

4The examiners were expecting the candidates to discuss liabilities as detailed below.The examiners considered the cases where candidates had interpreted the meaning ofliabilities as UPR etc. Marks were awarded for sensible remarks in these cases.Most candidates did not find this question difficult and hence scored reasonably well.The main reason for candidates not gaining marks on this question was owing to notmentioning the difference between property and bodily injury type liabilities.

(i) (a) Liabilities

� Property part is short to medium term� Linked to price inflation� Less variable amounts than bodily injury part� Generally smaller amounts than bodily injury part� Bodily injury part has more variable term than property, some very long

term� Delays occurrence-notification and notification-settled� Earnings linked� Court award inflation� Prone to court award accumulation� Occasionally very large bodily injury claim� Susceptible to moral hazard (e.g. slip/ trip)

(b) Assets

� Consider property and bodily injury separately


Page 5

� Property is short tailed so, same currency, short-dated governmentsecurities, other fixed interest, cash

� Bodily injury is longer-tailed, real, for which equities may offer the bestmatch.

� However, will need to match short term claims in the same way asproperty unless there is enough cashflow to pay out of premiums.

(ii) decide to match / not by:

� size of company� absolute size of free reserves� size of free reserves cf GWP� size of free reserves cf ultimate liabilities in a year� size of free reserves cf absolute liabilities at a point in time� existence of any required statutory minimum� reinsurance arrangements� liquidity of free reserves� attitude to risk of the company� statutory regulations e.g. admissability� availability� expected return on assets� value for money� desire to diversify / security considerations� extent of positive cashflow

5 Most candidates answered this question well. The main reason that most marks werenot gained was owing to the lack of comment in part (iii) for the possible need ofsome case estimating for e.g. subsidence claims.

(i) These terms relate to the determination of reserves for outstanding claims.

Case estimation � each outstanding claim is individually assessed to arrive atan estimate of the total payments to be made.

Statistical estimation � outstanding claims are assessed �en masse� inrelatively homogeneous cohorts, based on historical trends and patterns,adjusting for known or anticipated future changes.

(ii) Case estimation is:- labour / time intensive- Relies on skilled staff- subjective- suitable where claims are low frequency / high severity- suitable where the book of business is small- suitable if the company is relatively young, as there may be insufficienthistory for statistical estimation, especially for long tailed business


Page 6

- are suitable where there are significant volumes of qualitative informationrelevant for setting an accurate reserve, which require skilled interpretation byan expert.- this method can use all the available data including estimated inflation- more likely to spot errors on individual claims- it is difficult to ensure consistency through time and between assessors- Separate estimates for IBNR are needed- different statistical estimate methods allow for IBNR in different ways- The reverse may be true for statistical estimation- Statistical estimation may give inaccurate results if the past experiencecontains unusual features unlikely to be repeated e.g. catastrophes and largeclaims.

(iii) Book of business is large, which means that case estimation may beimpractical and costly.

Household buildings insurance is not high frequency in the same way ascontents insurance, so statistical estimation may not be very reliable.

However, for a large book of business, the volume of claims may still providea sufficiently sound basis for statistical estimation.Average Cost distribution is quite skewed. So for the lower frequency / highseverity claims statistical estimation will almost certainly be less accurate.Given the information above, statistical estimation for the majority of claims islikely to provide the most accurate estimate.

However, for the low frequency / high severity claims (e.g. subsidence), somecase estimation may be retainedDepends upon how long the company has been in operation.

6 The solution to part (i) is the approach that the examiners hoped most candidateswould use. In fact very few candidates used this approach or any other approachwhich the examiners considered reasonable with a reasonable set ofassumptions. Most candidates failed to recognise that of the business written in eachyear that 40% was earned in that year and that 60% was earned in the following yearthus making their assumptions invalid. Of those candidates who attempted this part ofthe question many stated that the gross and net loss ratios were the same andthus merely repeated the information in the question, although a few candidatesrealised that this must be wrong for 7 marks! The main problem appeared to be ableto distinguish between the occurrence year and underwriting year concepts.

Even though some candidates failed in producing a reasonable solution to part (i)they did go on to produce a reasonable answer to part (ii) for which there are manyreasons why the results in part (i) are unlikely in practice.

Part (iii) was answered well by the better candidates but some were put off by the firsttwo parts even though the third part could easily be answered without attempting theother two parts.


Page 7

(i) Assumptions

� All policies are earned over a one year period� The terms of the quota share have remained constant over the period

1.1.98 to 31.12.2001� As the company began trading 1.1.98 all premium earned in 1998 was

written in 1998� All business written in a year has same loss ratio

Calculation

Note NIA is net incurred claims on accident year basis, and NIU is netincurred claims on underwriting year basis.

Note that premium is earned 2/5 in the year it is written and 3/5 in the nextyearFor 1998 NIA are 10 � 1.5 = 15, and NIU are 25 � 1.5 = 37.5. Hence net lossratio on an underwriting year basis for 1998 is 150%.

For 1999 NIA are 35 � 1.3 = 45.5, as 37.5 � 15 = 22.5 of these claims were onbusiness written in 1998, then 23 claims occurring in 1999 on 20 earnedpremium, i.e. claim ratio of 115%. Hence net loss ratio on an underwritingyear basis for 1999 is 115% and thus NIU are 50 � 1.15 = 57.5.

Similarly for 2000 NIA = 70, 57.5 � 23 = 34.5 in respect of business written in1999, thus 35.5 for business written in 2000 on 40 premium, hence claim ratioof 88.75%.

For 2001, NIA = 105, 88.75 � 35.5 = 53.25 i.r.o. 2000 and 51.75 i.r.o. 2001 on80 premium, i.e. claim ratio of 64.69 and NIU of 129.375.

1998 1999 2000 2001NIA 15 45.5 70 105NIU 37.5 57.5 88.75 129.375NWLR 150% 115% 88.75% 64.69%

As QS reinsurance is assumed to remain constant the GWLR = NWLR

NotesNWP = net written premiumNEP = net earned premiumNWLR = net written loss ratio

(ii)� Rapidly decreasing loss ratio and year on year growth are unlikely to

happen at the same time� Household insurance is a commodity market and so usually sells on price� So to build a book quickly you have to be cheaper than the competition


Page 8

� Override or ceding commissions may mean that net ULR does not equalgross ULR

� Unrealistic that change premiums only once a year� Percentage reinsured likely to change over the years� Household profits tend to fluctuate with the occurrence/non-occurrence of

weather events� Any other comments about specific assumptions in the question not being

realised in practice

So a smooth(ish) increase in profits is unlikely

(iii) Effects are:

� Fast growth only available by writing business at premiums less than themarket (unprofitably?) or having a unique customer proposition.

� Reserve for claims / premiums would increase especially if rate areunprofitable

� New business strain could be considerable� Any imposed SMSM would mean capital considerations could restrict the

future rate of growth. If near the SMSM brokers may stop placingbusiness, even policyholder may hear that the company is �not safe�

� Unless there is enough capital to comfortably support growth then planswill need to be scaled back

� May change investment strategy� May change reinsurance strategy� May increase staff accommodation, IT systems etc.

7 Most candidates had few problems with most of this question. Parts (i)and (ii) weregenerally well answered. Several candidates could not perform the calculationrequired in part (iii). In particular, although the question stated that the �companyretained the maximum proportion� some candidates assumed that the maximum wasceded i.e. all lines were being used. This error has occurred in the past which wouldindicate that candidates do not read the question carefully or do not understandSurplus Reinsurance. Part (iv) caused the most problems though with somecandidates assuming that all the 6 claims applied to the same risk even though thequestion stated that the EML was different in each case. There were generally veryfew comments regarding the problems faced by the insurer in respect of this givenarrangement even though detailed information was available from the question.

(i) Proportional

� So claims shared in same proportion as premiums� Treaty� Proportion retained by direct writer may vary from risk to risk � Usually decided by direct writer � Subject to limits in treaty (numbers of lines / EML)� Which may be based on sum insured or EML


Page 9

� Enables insurer to write larger risks/ fine tune its exposure� Premium paid to reinsurer will be reduced for commission (return and

over-riding)� Administration more complicated than for quota share

(ii)� Size of risk; bigger the risk, more company will cede to A� Uncertainty of risk, frequency and severity� Concentration of risk for this one policy � Extent to which it fits in with existing portfolio � ��.potential for accumulations through similar location of risks � ��.& by type of property � prior facultative cover� Own experience of this risk

(iii)� EML of 2,300. Retain maximum of 500 => cede 1,800 to A i.e. 1,800/500

= 3.6 lines. Okay as <4. � Therefore A pays 3,500 x 3.6/4.6 = 2,739. � Net of surplus, company has claim of 761 � Of which 200 paid by B � Lower limit for treaty C becomes 700 x 104/100 = 728 � Therefore C pays 761 � 728 = 33 � And your company pays the first 500 and the gap between B and C i.e. 28

so a total of 528 � Check total payments equal 3500 and sensible comment if not � Assuming none of the companies default� There is only one payment made and that is 3500 at the time index is 104

(iv)� Where EML exceeds (4+1) � £500,000, as it does for risk 4 above, terms

of treaty with A are not met � In such situations, could arrange for facultative cover (either XL or

proportional) � Going forward, may wish to increase maximum number of lines in treaty

with A or buy more lines elsewhere � Need to consider whether XL excess points provide sufficient cover. � Risk 6 has blown through the top of the programme � C being indexed but B not being indexed creates a gap in the programme � This could be a problem when inflation is high and should be eliminated � Greater use of proportional reinsurance could be used to spread risk of

accumulations � Eg reciprocity to avoid geographical concentrations � E.g. aggregate excess of loss, catastrophe excess of loss� Reinsurers complaining about estimation of EML� Risk of reinsurance default � use more reinsurers� No problem with some of the claims


Page 10

8 Some candidates answered this question first rather than rushing their solution at theend. There was a wide range in marks on this question with the better candidatesscoring over three quarters of the marks available for what was largely a bookworktype question.

(i) The uncertainty arises as the outcome of business already written and thepremiums to charge in future periods.

Claims

Motor insurance claims are subject to wide variability. Especially as a small insurer there is uncertainty as to whether changes inclaims costs year on year are due to changes in the underlying risk or merelyrandom variation.Variability will exist in terms of frequency, amounts, incidence and cost ofhandling claims

Claims Delays

Delays from occurrence to notification result in uncertainty regarding thenumber and cost of IBNR claims. Delays from reporting to settlement result in uncertainty regarding the ultimatecost of claims. This uncertainty is greatest for the largest, bodily injury, claims especially ifthey involve legal proceedings.

Changes in cover

If cover is added / deleted from the motor policies there probably won�t besufficient data to make a reliable estimate of the impact of the change.

Characteristics of policyholders

If the company is aiming to attract different risks to those it has historicallyheld the claims experience may differ from the past. It is difficult to determine how the claims will change. There may be opportunities for anti-selection if the premium rates do notcorrectly reflect the risk. Unless there is superior accuracy in assessing the premiums which are lessthan the market norm (to ensure they are set at a profitable level) then throughadverse selection any inadequacy will result in severe loss making.Moral HazardUsage changes (e.g. fuel shortage)

Attitude to claims

Experience from the USA suggest that policyholder are starting to claim forevents they would not have done so previously. i.e. increasingly litigious society.


Page 11

Crime / fraud rate

As this increases AD and theft claims may increase. The timing of increasing crime rate is uncertain. This will be correlated to other economic indicators.

Judicial decisions

This is often referred to as �court award� inflation. New precedents will be setinvolving which types of claims are eligible for compensation and how muchthe settlements for them are.

Occasionally new level of awards are set for existing types of claims. This will immediately increase the average amount at which all future claimsare settled. Sometimes these decisions will be retrospective meaning that the uplift appliesto all outstanding claims as well as future ones.

Legislation

Fiscal, changes in tax, cost of cars, cost of repairsChange in cover, i.e. removing the upper limit on compensation or introducinga requirement, e.g. to pay hospital charges.Change in law, e.g. restricting the factors that can be used in underwriting, notusing driver age

Accumulation of risk

Could be exposed by business acquisition e.g. under 30�s or as a smallcompany geographically exposed by writing a lot of business near the headoffice, this could lead to an aggregation of claims from a weather event in thearea.

Catastrophe

A flood or hurricane could lead to many claims.

Currency risks

Paying claims in other territories exposes the company to the risks offluctuating currencies and currency mismatching if they do not hold reservesin other currencies.Reinsurance

This is subject to uncertainty as:

� Inadequately appreciate the scale of the risks and purchase inadequatereinsurance

� Doubts about the value for money and availability of reinsurance


Page 12

� For Cat whether the retention, reinstatement premium, upper limits etc. areOK

� Ability to make a recovery, solvency position of reinsurers

Policy wording

Must be precise so the only claims paid are those that the company intended toprovide cover for. Also with regard to reinsurance contracts so that the company can recoverwhat it expects to.

Inflation

Uncertainty about future inflation especially for bodily injury claims willaffect the actual profit made and hence the assessment of premium required toprovide cover in future periods.

(ii) Failure of third parties for example

� Non payment from brokers� Staff dishonesty� Default by supplier

Timing, premiums late, recoveries late, claims early

Competition

� Products are inferior� Prices uncompetitive, high expenses, inadequate analysis� Fall behind in technology, less business� Prices too cheap, unsatisfactory financial performance� Business affected by changes is legislation which other have allowed for� If lose business costs rise as fixed expenses have to be recoupedData may be inaccurate / incomplete

Insurance cycle

As the insurer only writes motor business there is no opportunity to crosssubsidise with classes at different stages of the cycle.As profits increase insurers enter the market, buy market share with lowpremiums, market premiums decrease until losses are made. Insurers leave themarket, prices increase and the market edges back into profitability.As only write one class at the bottom of the cycle will either lose business(puts pressure on fixed expenses) or lower premiums and decrease thesolvency position.

Other business risks include expenses, investment and managementincompetence


EXAMINATIONS

1 April 2003 (am)













303 A2003�2

1 A general insurance company writes only commercial property business. It writes 2policies, both of which have a sum insured of £3,000,000. Policy A has an excess of£500,000 and policy B has a deductible of £500,000. Each of these policiesexperiences a claim for £4,000,000.

(i) Explain the terms �deductible� and �excess� highlighting the primarydifference between them. [4]

(ii) Calculate the amount of the £4,000,000 loss borne by the insured and theinsurer for policies A and B. [2]

[Total 6]

2 You have been asked to determine the expected cost and variance of claims arisingfrom a homogeneous portfolio of insured risks by building a model.

(i) State the type of model likely to be used, giving reasons. [2]

(ii) Outline the steps you would take in developing the solution. [5] [Total 7]

3 You are the actuary for a medium-sized general insurance company writing personalmotor business. The existing reinsurance programme has for the last 5 years consistedof a small amount of quota share reinsurance and individual excess of loss cover of£10,000,000 xs £500,000. The Finance Director has suggested removing the excessof loss cover entirely.

Explain how such a course of action would be expected to influence thecharacteristics of the net liabilities and therefore the assets held by the company. [6]

4 (i) A global industrial company wishes to have a large commercial risk insured.List the potential providers of this cover, outlining their key features. [4]

(ii) State, with examples, the main ways in which an insurance company mayacquire business. [3]

[Total 7]


5 A small general insurance company (A) writing only property business cedes a quotashare reinsurance arrangement to a reinsurance company (B). The treaty cedes 40% ofthe protected portfolio. A pays 25% commission to acquire the business and hasinternal expenses of 7.5%. A expects to write £10m of business at a loss ratio of 65%.B bears the ceded proportion of A�s acquisition costs and expenses. B�s ownexpenses are 2% of gross premium received by B and B pays the broker 2.5% for thebusiness.

(i) Calculate B�s expected profit on this treaty, stating any assumptions that youmake. [4]

(ii) As a pricing actuary for B you have been shown this treaty by an underwriter.Describe what changes to the treaty you might suggest to the underwriterbefore the terms are agreed. [4]

[Total 8]

6 (i) Describe the different ways expenses could be categorised for a generalinsurance company when undertaking an expense analysis for pricingpurposes. [4]

(ii) Explain how the results of such an expense analysis would be included inpremium rates and why this is important. [5]

[Total 9]

7 (i) State a formula for calculating ultimate claims using the Bornhuetter-Ferguson (�BF�) method of reserving. [1]

(ii) Explain why the paid BF ultimate is generally similar to the paid chain ladderultimate for older accident years. [2]

(iii) Discuss the advantages and disadvantages of the following approaches forderiving an estimated loss ratio for use within the paid BF method:

(a) Use market loss ratios derived from industry benchmark information.

(b) Set the estimated loss ratio for year (x + 1) to the final selected ultimateloss ratio for year x.

(c) Use the ultimate loss ratios implied by the paid chain ladder method. [5]

[Total 8]

303 A2003�4

8 (i) List 12 main rating factors which may be used in pricing personal motorinsurance. [3]

(ii) (a) State four risk factors that are not normally used in pricing this type ofbusiness, describing the link between these factors and the ratingfactors that are used.

(b) Explain why the rating factors are used in preference to thecorresponding risk factors. [5]

The marketing department of a general insurance company which does not currentlywrite motor insurance business has proposed issuing a special annual policy to lowmileage drivers for private use only. Only the policyholder is insured and at the startof the policy year he pays a policy administration charge. During that year he thenpays for the insurance cover as needed on a daily basis by giving 24 hours notice andhaving the appropriate cost deducted from his bank account. You have been asked toidentify the differences between this policy compared to a standard annual policy.

(iii) Describe the advantages and disadvantages for the policyholder and theinsurance company. [7]

(iv) Describe the issues you would face initially in rating such a policy. [3]

(v) (a) State four data items that are likely to be collected by the insurer whichwould not normally be collected for a standard annual policy.

(b) Explain why these are likely to be required.[4]

[Total 22]

9 You are the actuary for a small general insurance company that writes only personallines motor business. A major motor manufacturer has approached your companywith an unusual offer. The manufacturer wishes to sell all its new cars with insuranceincluded in the purchase price i.e. their cars will have �free� insurance for a period of3 years. Their proposal is that your company underwrites and administers the motorinsurance and the manufacturer will pay a one off fixed premium per car sold for the3 years �free� insurance. This will not vary by any of the usual rating factors e.g. cargroup, age of driver or past claims experience.

(i) Describe the specific risks associated with the motor manufacturer�s proposalfrom the insurer�s point of view. [13]

(ii) Outline possible ways of mitigating the risks in part (i). [14][Total 27]


EXAMINATIONS

April 2003


EXAMINERS� REPORT

Introduction



Mrs J CurtisChairman of the Board of Examiners

17 June 2003



Page 2

The examiners were pleased with a slightly higher standard of solutions given by candidatesin this exam compared with recent diets. Comments on individual questions are givenbelow.

The examiners would like to remind candidates of the importance of reading the front coverof the answer booklet and complying with the instructions. The examiners were pleasedwith a significant overall improvement in handwriting. Examiners marking scripts areunder severe time pressure in marking all scripts by the deadlines given. Goodhandwriting helps. An additional factor which seems to be creeping into somecandidates scripts is the failure to indicate the question number of the question that isbeing answered, or in some cases indicate the wrong question number. Clearly examinerstake this into account when marking but such additional identification of which question isbeing answered does delay the marking process.

The examiners would also like to remind candidates not to write their solutions in pencil,only use the right hand side of the page and do not return scrap paper with theanswer booklet.

1 Most candidates were able to describe the terms deductible and excess, but only thebetter candidates highlighted the differences. Being able to apply the definitions to aparticular case seemed to cause a lot of confusion. In particular some candidatesmanaged to get the calculations the wrong way around even though they got thedefinitions correct. The examiners would like to emphasise to candidates thatapplication of knowledge is as important as the knowledge itself.

(i) Deductible is the amount deducted from a claim which would otherwise havebeen payable, i.e. it is borne by the policyholder. An excess is the sum that theinsured bears before any liability falls on the insurer. The primary difference isthat the deductible eats into the sum insured whereas the excess sits below thesum insured. Hence on a policy with a deductible the maximum the insurerwill be liable to pay is the sum insured less the deductible.

(ii) Insurer InsuredPolicy A £3,000,000 £1,000,000Policy B £2,500,000 £1,500,000

2 This question was generally very well answered, with many candidates scoring morethan 5 marks out of a maximum of 7.

(i) A model with distributions is required as the mean and variance are required.Stochastic is the most likely.

(ii) Clarify purpose of investigation / specify the objectiveCollect dataModify dataNot necessary to group data as homogeneousChoose a suitable frequency and severity density functions(correlations should not be an issue as one homogenous portfolio)


Page 3

Specify / estimate parameterscheck goodness of fit of distributionsAllowance for change in new business volumesconstruct modelrun model multiple times and collect each outcomesensitivity test the modelsummarise the results � mean, variance and distribution of outcomes

3 The examiners were disappointed with many of the answers to this question whichresulted in most candidates scoring less than half marks. Many candidates mentionedthe change in the net liabilities but did not go on to comment about the effect upon theassets held.

Need to meet liabilities as they fall due so tend to match assets to liabilities by nature,term, amount, currency Changing reinsurance programme may impact the profile of the net liabilities andtherefore the assets that would match them �.although the company may not be following a closely matched policy, particularlyif free reserves are large Removing the excess of loss cover will cause the impact of large losses on net claimsto increase Large claims tend to be bodily injury claims Therefore average term of net liabilities may increase if remove XL cover�. �and payments for the bodily claims tend to be longer tailed e.g. court casesSo more inflation protection may be required�.�.bodily injury claims inflation may be higher than damage claims inflation So might wish to move to longer term assets that give good inflation protection e.g.equities Greater variation in retained claims costRemoval of reinsurance may increase required statutory solvency so less investmentfreedomHowever with more exposure to random large loss movements, may need to chooseassets that are liquid


Page 4

4 Most candidates scored reasonably well on this bookwork question.

(i) Companies

Public or private insurance� limited liability, capital, distribute profits bydividends.

Captives � usually wholy owned Co. used by the owner to manage its risks.Larger reinsurance contracts are then placed by the captive.

Self retention groups/Mutuals eg P&I clubs � Companies owned by theparticipants � not for profit groups whose aim is to give value for money totheir members.

Government � as insurer of last resort / high uncertainty

Lloyd�s syndicates � capital provided by individual or corporate names toone year ventures who underwrite on their behalf. Unlimited liability forindividual names, limited liability for corporates. All change here!

(ii) Intermediaries � brokers, banksRetail linked to other sales � travel insurance, extended warranty, mortgagepayment protection Purchase another insurerIf captive, direct from parentEmployed sales staffMass marketing � mailshots, newspaper TV and Radio ads. Direct to customer internet, telesales

5 Although the solution given in part (I) was the one the examiners were looking foralternative solutions with a slightly different interpretation of the information given inthe question were accepted. The main problem encountered by candidates was thecorrect understanding of who pays what commission and expenses in such anarrangement.

(i) Premium 40% 4,000,000 (40% of £10m)� Claims 65% 2,600,000 (65% of £4m)� Commission 25% 1,000,000� Ins Exp 7.50% 300,000� Brokerage 2.50% 100,000� Own expenses 2% 80,000

Profit �2% (80,000)

Assume no investment income or other sensible alowance. Expense allocation is accurateLoss ratio will be as expected.Sales targets are met


Page 5

No taxNo other prior reinsuranceNo profit commission terms

(ii) 2% deficit. Realistically insurers expenses, brokerage, own expenses toosmall to recoup deficit

suggest reducing commission to A. Insurer may have fixed commission then difficult. Insurer may have variable commissions with scope for reduction

Suggest sliding scale commission, or lower initial commissions with a profitcommission.

Suggest Insurer writes to a lower loss ratio� insist on tighter wordings or min rate rises.� difficult to guarantee, rate rises may lead to anti selection

6 Candidates showed that they generally understand the issue of expenses relating togeneral insurance business. The examiners were looking for the distinctions betweenfixed/ variable and direct / indirect. Many candidates also wrote at length regardingclaims expenses, investment expenses etc and credit was given for this approach.

(i) Split fixed/variable. Fixed expenses are those that do not vary with business volumes e.g. CEOsbasic salary. Variable expenses are those that vary directly according to the level ofinsurance business that is being handled at that time and may be linked to thenumber of policies or claims or the amount of premiums or claims.Split direct/indirect. Direct expenses can be identified directly as belonging to a particular class ofbusiness. Indirect expenses are those that do not have a direct relationship to any oneclass of businessAll variable expenses are direct but fixed expenses can be direct or indirect.Split according to functionalitye.g. investment, acquisition, renewal etc.

(ii) How useAllocate as you wish the premium rates to be split, so for personal business will split at least by product and possibly by coverLink to business written or to claims..Separate fixed and variableApportion indirect expenses across classesSeparate new business and renewal in theory if not practiceWhy to get accurate costs / to cover expense costs overallto get accurate rates understand the level of cross subsidy in the rates


Page 6

e.g. renewals subsidise new business if there aren�t different premium rates foreach with the expenses splitunderstand the cost of writing business even if its not sold at the theoreticallycorrect rate

7 Credit was given in part (I) where candidates used a credibility formula or incurredBF approach. Even though the question asked for a formula for �Ultimate claims�,some candidates failed to give a formula and in several cases omitted to include thecurrent paid in their solution. Part (iii) turned out to be a good question to separatethose candidates who knew the topic and those who understood it.

(i) Let PBF=ultimate from paid Bornhuetter-Ferguson methodcdf = selected factor to ultimateEULR = expected ultimate loss ratioPrem = ultimate earned premium

Then PBF = current paid + EULR * Prem * (1�1/cdf)

(ii)� The older the accident year, generally the more developed an account is

and hence the smaller the cdf.

� For small cdfs, 1/cdf is large and therefore (1�1/cdf) is small. ThereforeBF ultimate become close to current paid. Meanwhile paid chain ladderbecomes closer to paid

(iii) (a) + Provides independent estimates+ May reflect market rate changes and inflation effects as well astrends in claims frequency and average cost+ less need of own data which may be lacking or not credible� Mix of business likely to be different for every company� Need to check treatment of premiums is consistent (i.e. gross or netof commission)� Need to check consistency of reinsurance cover- Market info not available- Market info out of date

(b) + Gives some credit to the account�s own experience with its uniqueportfolio of risks+ Can be sure that premiums and claims are calculated on the samebasis+ simple to apply� May want to adjust for inflation and premium rate changes� Year x may be an untypical year (e.g. exceptional large loss)� Dependant on own estimate of previous year� May be unreliable on long tail business


Page 7

(c) � Expected loss ratio would not be independent from claims on thatyear�.� If use paid chain ladder loss ratio as expected loss ratio, PBFbecomes equal to paid chain ladder.

+ Could possibly use for reported BF projections

8 With so many rating factors to choose from which the examiners accepted as possiblemain factors as those factors adopted by insurers do vary, most candidates scored fullmarks on part (I). The examiners would like candidates to note that the question askedfor 12 and therefore were not expecting candidates to produce a list of more than 12.Part (iii) onwards of this question sorted out the better candidates from those not sowell prepared in demonstrating their understanding. The poorer candidates gaveanswers which were not much more than repeating the details in the question.

(i) ExcessCovervehicle useVehicle ageStated milesdriver addressdriver occupationclaims record / NCDyears since passed testgender of main drivermarital statusadditional driversage of main driverdriving restricted to named driversmake & model of vehiclenot in use location � garagedparked on or off streetsecurity featuresmodificationsconvictions / endorsements to licence

(ii) (a) traffic density where car driven To kept locationdriver ability To claims record/age/sex/occupationtheft risk To driver address/not in use location/make & modelactual mileage To stated mileage

(b) Rating factors must be capable of being objectively measurable. In thecases above the risk factors can not be rating factors as they are notobjectively measurable and hence alternative rating factors are used.

(iii) ph adsonly pay for cover as neededpotentially lower annual cost


Page 8

good if drive infrequent long distances

ph disadsmay not want to or be able to give 24 hour�s notice / inconvenientillegally driving without insurance cover if forget to arrangemay not include theft / fire damage when not insuredno other drivers alloweddaily cover may seem expensiveabove a certain number of days the cost of cover will go above that of astandard policymay lose NCD within year of insurance

ins co adspotential to penetrate niche marketcould make affinity group dealgain additional rating data re low mileage driverspossibility of applying rate changes during the policy year.

ins co disadsadditional costs of administration � high if use call centrehigh startup costs if use e technology like email or text message and lowerongoing cost.computer system may not be able to hold all data requiredpossible disputes over cover if crash occurs when not coveredcover runs midnight to midnight? Or a more specific 24 hrs, if so need torecord time and date of covermore fraudulent claims / increased moral hazardtendency to increase mileage on days insured

(iv) none of own data therefore need to buy in data or run a pilotno data on the number of days low mileage drivers use their carsso daily rate is not known with certaintypeople identifying themselves as low mileage drivers may be high/mediummileage drivers so current data may not be reliable.The expenses and administration costs will not be known with certainty

(v) collect individual dates of cover to collect true exposure periodif �phone data collection then could ask about planned driving times &locations and collect additional data e.g. mileagebank details for deducting the daily charges � could be different from detailsfirst used, or previously used.Passwords etc to verify caller ID � more important than annual policy asmore frequently used.


Page 9

9 This question proved to be the most difficult for most candidates. The best solutionsnumbered the specific risks in part (I) and referred to each in turn in part (ii).Many candidates considered that product liability would be a major risk which wouldmore likely be only of a 2nd order risk. In part (ii) many candidates wrote at lengthabout reinsurance and the different types. Hence they did not pick up on the manydifferent ways of mitigating the risks.Time did not seem to be a problem for the majority of candidates.

(i) Anti-selection by:agepast driving experiencelocationvehicle typesCatastrophe riskPropensity to claim increases as will not worry about next year premiumIncrease in moral hazardDelay in receipt of premiumsPotential for business to be loss making, as small could threaten solvency.Contact lasts for 3 years so could be tied into loss making rates, also the needto predict inflation for 3 years.Car sales are seasonal�operational problems as small company doing theadmin.If volumes are small will not cover start up costsCurrency risk as manufacturer may sell in many countriesDifficulty in obtaining appropriate reinsurance cover.Solvency capital considerations as small company and this is a major motormanufacturer, it will substantially increase new business.Difficulty in setting the fixed price � long discussion as don�t know the mixof business are pricing for.Small insurance company will not have much useful historic data especially ofwriting brand new cars from this manufacturer.Billing mechanism will need the facility for verification so both parties agreehow many cars have been soldRisk that the manufacturer goes bankrupt and the insurance company does notget paid although the cover is given.Again there is the risk that the insurer itself becomes insolvent.UPR variable over the 3 years as the risk varies over the termIf the cover is only for the original purchaser this will exacerbate thevariability of UPR/earnings.Need to consider the investment strategy in respect of investing receipts forlonger than for an annual policy and risks associated with expected returns andsecurityIntroduction of, or increases in rate of, tax or levies imposed by thegovernment based on earned premiums.

(ii) Ensure the motor manufacturer pays up front to mitigate the risk of the motormanufacturer defaulting after cover has been provided. Individually rate the business retrospectively when customer and vehicleinformation is available (make assumptions for information gaps), run ratherlike a fleet so collect deposit premium based on estimated car sales and


Page 10

customer mix and then an adjustment premium at the end of the month/quarterbased on actual numbers and mix.Huge caution in the rates, probably means not cost effective for themanufacturer. Possibility of profit share but this would mean the manufacturer effectivelycarried a significant proportion of the underwriting risk.See manufacturers customer profile, e.g. mix by age, by postcode to assess thepeople who buy their cars.Say no to protect the company solvency. As the company is small this may bethe only response available.Ensure the insurer has the right to frequent rate changes so the mix can beanalysed and changes implemented quickly. Need to consider the expenseimplications of this frequent analysis and whether the resulting price will beattractive/ acceptable to the motor manufacturer.Consider the offers that competitors are likely to put forward, if any others areprepared to take this business.100% reinsure the business, cost? Will it be possible?Write as admin only with the manufacturer keeping the risk perhaps via acaptive reinsurer.Look at experience of similar schemes, if there are any currently operating inthe market.If the scheme is already operating, get the current claims information andadjust in the usual way adding margins as appropriate.Use consulting actuariesHave a short term notice in the contractual agreement to get outHave a clause in the agreement that if taxes / levies are increased then theseare paid by the manufacturer to the insurer


EXAMINATIONS













� Faculty of Actuaries303—S2003 � Institute of Actuaries

303 S2003—2

1 (i) Define the following terms:

(a) long-tailed business(b) latent claims

[2]

(ii) Outline the difference between these two terms. [1][Total 3]

2 You are the senior actuarial student at a large general insurance company writingmortgage indemnity guarantee business. You have been asked to undertake a reviewof the current premium rates for this business.

Outline the factors you would take into account in determining an appropriateallowance for future investment return when pricing this product. [6]

3 Your company has been underwriting commercial property insurance for severalyears.

(i) List the various delays that can occur in relation to the claims your companyreceives in respect of this product. [2]

(ii) You have observed a recent unanticipated trend of increasing delays at variousstages in the life cycle of a claim. Explain the possible causes of this and thelikely effect upon the ultimate claims cost. [3]

[Total 5]

4 (i) List the 4 main types of insurance cover provided by general insuranceproducts. [1]

A shipping company buys an annual hull property damage policy. The policy requiresthat a description of the claim is first notified to the insurer at the time of the incidentor when the ship reaches a major port.

If the damage is minor the ship continues with its scheduled voyages until aconvenient time when a full inspection can take place. At this point a more detailedassessment of the damage is made, the insurer is notified and the repair is planned. Ifthe damage is minor, the ship may continue its voyages until the repair is finallycarried out and the costs are finalised. If the damage is major then the ship is takenout of service immediately and if repair is possible it is carried out as soon as possible.

(ii) Describe the specific claim characteristics of this class of business. [8] [Total 9]

303 S2003—3 PLEASE TURN OVER

5 You are the actuary for a medium-sized general insurance company writing onlypersonal motor business. Your Finance Director has asked you to develop a modelthat can be used to test the impact on profitability and solvency of changing thecompany’s reinsurance cover. The existing reinsurance programme has for the last 5years consisted of a small amount of quota share reinsurance and individual excess ofloss cover of $10,000,000 xs $500,000.

(i) Discuss the factors that should be considered when deciding upon anappropriate reinsurance programme for this company. [8]

(ii) Describe how you would construct your model. [10][Total 18]

6 A general insurance company writes only personal lines motor business via brokers.

(i) Describe the perils covered by personal motor insurance. [2]

(ii) List the data required to investigate the appropriateness of the current riskpremium relativities. [9]

(iii) (a) Define burning cost premium.

(b) Describe how this may be adjusted, and state all the other informationthat will be needed, in order to calculate the final office premium. [7]

(iv) The proposed final office premiums are significantly different from thosecurrently charged. Explain the risks of implementing the new rating structure.

[7]

(v) Discuss methods which may be used to mitigate the risks identified in (iv). [7] [Total 32]

303 S2003—4

7 You are a consulting actuary for a large general insurance company that writescommercial insurance for large multinational companies. You have been asked bythe company to review the methodology and assumptions used by the company’sreserving team for the motor fleet business as at 31 December 2002.

The company’s reserving team has analysed “non-large” and “large” claimsseparately. A claim is described as large if it has exceeded $500,000 at some point inits history. The non-large claims have been projected using both paid and notifiedclaim chain ladder methods at a net of reinsurance level. The selected non-largereserve figures have been based on an average of the results of the two chain laddermethods. Reserves for large claims have been set to be 110% of the total large claimcase estimates, net of reinsurance, as at 31 December 2002.

The extract below shows historical development factors for the non-large paid andnotified claims triangles as at 31 December 2002, together with the company’sselected development patterns.

"Non-large" Net Paid — development factors for cumulative amounts

Accident Development yearYear 0–1 1–2 2–3 3–4 4–5 5–6 6–7 7–81994 5.076 1.673 1.357 1.286 1.189 1.161 0.997 1.0311995 4.408 1.775 1.495 1.294 1.176 1.065 1.0571996 5.396 1.768 1.456 1.416 1.082 1.1101997 5.201 1.694 1.411 1.217 1.2231998 5.409 1.621 1.430 1.3691999 5.354 1.772 1.4262000 5.899 1.6892001 5.238

Selected paid idf 5.500 1.700 1.430 1.300 1.180 1.100 1.040 1.020 1.000Selected paid cdf 23.933 4.351 2.560 1.790 1.377 1.167 1.061 1.020 1.000

"Non-large" Net Notified — development factors for cumulative amounts

Accident Development yearYear 0–1 1–2 2–3 3–4 4–5 5–6 6–7 7–81994 1.139 1.009 1.085 1.031 0.937 0.992 1.001 0.9981995 1.169 1.010 1.089 1.004 0.980 0.992 0.9991996 1.357 1.076 1.116 0.979 0.990 1.0081997 1.471 1.053 1.083 1.066 0.9911998 1.418 1.015 1.023 0.9911999 1.309 0.973 1.0452000 1.132 1.0222001 1.318

Selected notified idf 1.300 1.025 1.070 1.010 0.995 1.000 1.000 1.000 1.000Selected notified cdf 1.433 1.102 1.075 1.005 0.995 1.000 1.000 1.000 1.000

idf = incremental development factorcdf = cumulative development factor

303 S2003—5

(i) Suggest possible reasons why there are claims development factors less than1.000 within the above triangles. [9]

(ii) (a) Comment on the suitability of the company’s methodology andassumptions used to establish undiscounted reserves for its motor fleetaccount.

(b) Suggest alternative approaches. [9]

As part of your work for the company, you have also been asked to assist with thecompany’s discounting adjustments. The company’s accounting policy is to use adiscount rate of 5% per annum.

(iii) Using the company’s chain ladder selections and stating any assumptionsmade:

(a) Derive a payment pattern to apply to the 2000 accident year.

(b) Estimate a discount factor to convert the company’s undiscountedreserves to discounted reserves for the same accident year.

(c) Derive the discounted mean term to settlement for this accident year.[7]

(iv) List the factors you would consider in selecting a discount rate for reservingpurposes. [2]

[Total 27]


EXAMINATIONS

September 2003


EXAMINERS’ REPORT

Introduction The attached subject report has been written by the Principal Examiner with the aim of helping candidates. The examiners are mindful that a number of interpretations may be drawn from the syllabus and Core Reading. The questions and comments are based around Core Reading as the interpretation of the syllabus to which the examiners are working. They have however given credit for any alternative approach or interpretation which they consider to be reasonable. The report does not attempt to offer a specimen solution for each question — that is, a solution that a well prepared candidate might have produced in the time allowed. For most questions substantially more detail is given than would normally be necessary to obtain a clear pass. There can also be valid alternatives which would gain equal marks. J Curtis Chairman of the Board of Examiners 25 November 2003 © Faculty of Actuaries © Institute of Actuaries


Page 3

1 This question was generally well answered. Each of the two terms examined in this question can be found in the Core Reading glossary. The distinction between long-tailed (long delays from occurrence to notification/settlement) and long term (long exposure period i.e. long period of cover) is important but is not always appreciated by students. Most candidates seemed unaware that latent claims could be short-tailed.

(i) (a) Types of insurance in which a substantial weight of claims take several

years to be notified and/or settled…. ….from the date of exposure and/or occurrence. (b) Claims resulting from perils or causes of which the insurer is unaware

at the time of writing a policy…. ….and for which the potential for claims to be made many years later

has not been appreciated. (ii) Long-tailed relates to known / anticipated features of claims at the time of

writing whereas latent claims are by definition not anticipated at time of writing.

Latent claims can be short-tailed. 2 The question focuses on outlining considerations when allowing for investment

returns in pricing mortgage indemnity guarantee business. It does not require a discussion about which assets would be suitable, although many candidates took this approach. Points in relation to an appropriate choice of assets are only relevant in this question to the extent that assets actually held are mismatched to liabilities. Those candidates who discussed the nature of the liabilities and applied their bookwork points scored better. Need to consider likely return on assets backing technical reserves: • consider past investment returns on those assets • and investibility of those assets, including premium payment pattern of lender.

Technical reserves

• Term of policy is the term of the mortgage, so premium may be received 25 years or so before claim is paid.

• Most of the risk though is in the early years of the mortgage term, and premium is usually earned within the first 10 years, although even in those 10 years the risk is not uniform.and premium earning patterns are not constant.

• Delay between claims occurrence and settlement is relatively short so more concerned with assets backing unearned premium reserve (“UPR”).

• The UPR is very large…. • …and allowance for investment return is very significant.

Need also to allow for investment returns on assets backing capital: • These will be particularly significant…. • ….as MIG has relatively large capital allocation due to uncertainty of writing this

business.


Page 4

Allow for mismatching of assets and liabilities: • This is particularly important…. • .…as will be very difficult to determine future economic/property cycles and

hence claims costs. • Examples of mismatch are due to currency and legislative/solvency changes. • Downwards adjustment to investment return assumption may be high. Other points to consider • Consistency with other assumptions eg inflation. • Regulatory / statutory restrictions on pricing methods/assumptions. • Investment return should be net of expenses. • Investment return should be net of tax. • Take into account likely future tax changes given long term nature of MIG.

3 Candidates scored reasonably well on this largely bookwork question, though there were many more points available than required for full marks. Candidates did not

demonstrate a full understanding in part (ii) on how delays might impact the ultimate claims cost.

(i) Identification of damage / loss, manifestation

Reporting of damage / loss Delays in processing claim Assessment of extent of damage / loss Monitoring / delays due to business interruption Verification / agreement on extent Processing payment / settlement delay Recovery of reinsurance Recovery of salvage

Closing of claim file Reopening / resettlement

(ii) Possible causes: • Change of brokers. • Change of claims handlers — affects efficiency levels and delays. • Change in types of claim — as different types of claim will have different

features affecting handling time. • Change in mix of business or cover eg increased excesses so change in

size of claim. • Surveyors assessing the cost of claims take longer to assess. • External factors such as postal strikes, legislation, judiciary, economic. • Internal factors eg staff shortage, system breakdown.

Likely effect on ultimate claims cost: • Claims may be turned down if reporting delay period extends dramatically

(depends on policy wording) so reducing overall cost. • Delays to repairs will result in increases in average settlements due to

inflation so increasing overall ultimate cost.


Page 5

• Changes in delay will affect amount of investment return achieved, which will affect discounted value of ultimate claims cost.

Although not required to gain full marks, some credit was given for the following additional points:

• If reinsurers default (infinite delay) then the net ultimate cost will incr ease.

• Claims handling costs may increase if more time is spent dealing with claims.

4 For part (i), the majority of candidates know the four insurance cover types, which

appear in the Core Reading. However, candidates’ performance on part (ii) were disappointing given the importance in general insurance of understanding the characteristics of different claim types. Most noticeable was the lack of breadth and detail in candidates’ answers, with many candidates confining themselves mainly to a discussion of the delays in settlement and notification. It should have been clear to candidates producing short solutions that they were too brief to score the full 8 marks on offer.

(i) Liability

Property Damage Financial Loss Fixed Benefits

(ii) Claims origination: • sudden cause of loss • cause easily determinable Claims notification: • usually notified quickly • biggest claims notified very quickly • although minor knocks may be delayed Claims settlement / payment: • settled over time as repair scheduled • small claims can take a long time to settle • most claims settled within 3 years…. • ….longer than most property damage type claims • ….but still relatively short-tailed • settlement delays due to disputed liability

Claims amount: • repairs will be subject to claims inflation • reported amount can rise when inspection reveals more damage • actual settlement cost can be quite different from estimate • policy excess may result in nil claims • salvage recoveries will lead to reductions in paid claims


Page 6

• currency fluctuations may cause amounts to differ from expectations • damage exacerbated by continuation of journey • moral hazard due to false claims • lack of independence of claims assessor Potential for accumulations / catastrophes • geographic concentration and exposure to storm, harbour fire Claims distribution • low frequency (in ship years) • occasional total loss (actual/constructive) • skewed claims distribution

5 Well prepared candidates scored well on part (i),which was essentially bookwork. Some candidates appeared to ignore the details given in the question (eg one class, motor, medium-sized company) and lost marks for application. It was clear from scripts that some students were confused about how risk XL and aggregate XL contracts operate. In part (ii) the quality of candidates’ answers was variable. The stronger candidates were able to build upon the Core Reading’s list of steps required to build a model and thought about the specific requirements in this situation. (i) Stability of profits…. ….More excess of loss protection (i.e. lower excess point) may result in more stable results

....stability of profits will affect ability to pay stable dividends (which shareholders may prefer) ….particularly relevant as company writes only one class Nature of inwards claims with respect to frequency and amount…. ….several small claims but a few individual large losses on bodily injury claims Consider management/shareholder attitude to risk Size of free reserves: to what extent can the free reserves withstand adverse large loss experience? A couple of large bodily injury claims could cause problems. Company strategy: is the company expecting to expand its business? How much of a strain will this place on the free reserves? • Potential for accumulations… • ….is there too much exposure in one geographical area?

….individual excess of loss will not address this ….may decide need more quota share in order to write a wider range of risks

but maintain similar levels of net exposure, or aggregate XL Statutory solvency: how will changing the reinsurance protection impact the

statutory solvency position? Technical assistance: does the company benefit from technical help from

existing reinsurers? How will a change in the reinsurance programme affect this arrangement? Relationship with existing reinsurers

Regulatory requirements to hold reinsurance


Page 7

Market reputation: how will investors, analysts, brokers, customers react to any significant change in reinsurance programme?

Security status: reinsurers with better security may charge more for the cover Availability of reinsurance Value for money Availability of reinsurance (ii) Type of model/high level points:

• Prefer to use a stochastic model but could use deterministic with lots of sensitivity testing.

• Construct a model that projects cashflows over a 5 to 10 year period. • Projections need to be realistic so assumptions must be on best estimate

basis. • Include new business

Define objectives: • By varying the retention level, determine the effect of the excess of loss

reinsurance on profitability and statutory solvency. • Need to define profitability and solvency eg statutory definition?

Projections need to be realistic so assumptions must be on best estimate basis.

Collect claims data: • Determine future gross claims expected therefore need gross and

reinsurance data separately. • Use individual claims data. • Collect and use individual claims data for last 5– 10 years, gross of

reinsurance, grouping by risk categories Group data by risk categories eg bodily injury vs property damage Makes adjustments for: • Claims inflation • Cover provided • Deductibles • External factors • Changes to claims handling or settlement • IBNR by standard methods such as chain ladder or average cost per claim Choose variables to be modelled stochastically • Fit separate claims frequency and amount distributions • So can calculate individual recovery amounts • Check goodness of fit (can apply this to frequency/amount distributions

and/or combined distributions) • Derive a combined claims distribution function… • …by simulating separate claims frequency and amount distributions.

Also model: • Gross premiums


Page 8

• Reinsurance premiums – investigate likely reinsurance market premiums for XL cover at various excess points

• Reinsurance recoveries - compare these reinsurance premiums against modelled recoveries expected to be paid at different lower excess limits

• Compare these reinsurance premiums against modelled recoveries expected to be paid at different lower excess limits.

• Expense cashflows • Investment cashflows

Specify correlation between variables • e.g. allow investment strategy to react to claims experience and level of

free reserves

For each lower excess limit, run large number e.g. 1000 (say) simulations, projecting the cashflows of the model over the period.

Construct model so as to produce output relating to solvency and profitability. 6 Part (i) was straightforward with the perils listed in Core Reading. Candidates’

knowledge of the bookwork in part (ii) was disappointing, with many candidates failing to provide sufficient items. Partial credit was given to solutions that mentioned “rating factors” without listing them, although the number of marks available should have prompted more detail. A surprising number of candidates did not provide a clear definition of burning cost premium, although most were able to talk about adjustments to it. Noticeably, many candidates omitted to mention that the burning cost premium would need to be adjusted for IBNR claims. Most candidates appeared uncomfortable in dealing with the non-standard questions in part (iv) and (v) and did not generate sufficient ideas.

(i) Perils covered:

accidental damage to the insured vehicle malicious damage to the insured vehicle

fire of insured vehicle theft of insured vehicle

If the policy includes motor third party liability then the insured is indemnified against compensation payable to a third party for personal injury or damage to their property.

Although not part of Core Reading, credit was given for the following point:

Breakdown where roadside assistance included as part of cover

(ii) Policy data as it was at the date the claim occurred:

• policy number • start date • end date • endorsement date • policy term


Page 9

• type of cover • date of birth / age of drivers • gender of drivers • additional drivers • licence type • years held licence • risk address / postcode • broker code • details of previous accidents and convictions • claims history • security devices / safety devices • profession • marital status • transmission type • smoker / non-smoker (proxy for lifestyle) • vehicle group rating or other classification • make of car • model of car • engine size • fuel type • body type • modifications to vehicle • annual mileage • policy limits • excess compulsory and voluntary • use of vehicle e.g. private / business • where vehicle kept overnight • age of vehicle • value of vehicle • NCD • payment method • where insured to drive • policy number / link to claims data

Claims data: • claim number / link to policy data • accident date • notification date • claim amounts paid • dates claims amounts paid • claim recoveries made • dates recoveries made • estimated outstanding • dates the estimates were made • type of claim, TPBI, theft etc • claim description code e.g. collision with stationary vehicle • claims expenses e.g. loss adjusters fees, NHS charges


Page 10

• claim event number, to link claims from the same event for reinsurance recoveries

• settled indicator, settled, outstanding, re-opened • driver at time of accident • currency

Current rating structure

Changes in policy conditions Results of portfolio movement analysis Risk premium relativities implied by relativities of competitors' office premiums Reinsurers’ opinions Underwriters’ opinions Changes in legislation on allowable rating factors Future inflation assumption

(iii) (a) The actual cost of claims incurred during a past period as an annual rate per unit of exposure

(b) Include allowance for IBNR Adjust for unusually heavy/light experience, build in an average

amount of bodily injury claims Allow for trends in claims, e.g. greater recovery of health costs from

insurers by the government Adjust for legislative / judicial changes Allow for changes in risk and cover Allow for change in mix of business eg new/renewal Allow for estimated future claims inflation Different expense / commission assumptions:

• Underwriting expenses • Claims handling expenses split fixed variable • By new business and renewals • Allow for expense inflation

Allow for any discounts given

Commission if payable Profit loading Contingency margins Tax Reinsurance cost allocated to a policy Levies Investment return Competitive issues, insurance cycle (iv) New rates are higher:

Customers complain, expense impact in dealing with this. Customers don’t renew, expenses impact with the operation of fixed expenses.


Page 11

New business drops, fixed expenses not spread. Bad PR which further reduces new business and retention rates. New rates are lower: Lots of new business, financial impact of new business strain, can’t get enough staff, premises etc to cope with the influx of new business. Existing customers feel that they have been overcharged in the past and move their business elsewhere. Brokers are unhappy with the resultant reduced commission.

Competitors do not react as expected. New rates are differently structured. Cost of implementation may exceed expectations. Reinsurers not happy with the new rates. Risk of anti-selection if the rates are different to those offered by competitors in the market. May write volumes of business where little previous experience and rates uncetain.

(v) Easiest method is not to implement the new rating structure. Could then move

the old one to look like the new one but gradually. Renewal Manage price offered to existing customers, for example no premium increases or decreases by more than 10%. May mean that prices on renewal will be different to those for new business. Run the renewals as a closed book retaining the current pricing structure and use the new rates for new business only. Again this will mean that the rates will be different for new business and renewals which could lead to customer complaints. Give the customers an incentive to renew to soften the blow of price increases e.g. free mobile phone / road map / holiday vouchers.

Rather than reduce premiums significantly, offer loyalty discounts. New Business Test the prices for a short period, measure the effect on volumes, conversion rates and decide whether to fully implement. Move gradually to the new prices. Communicate to brokers, customers and staff the expected changes as a result of the implementation. Check if the levels of increase /decrease seen will be different to those being applied by competitors. Offer brokers profit commission.

Offer brokers volume commission. Increase advertising / marketing campaign. Spread distribution channels (not just broker). Arrange more reinsurance / get technical assistance.

If all prices have increased then another option is to reduce the cover instead of increasing the prices. The effectiveness of this depends on what is already included in the cover that can be removed without making the product stand


Page 12

out in the market.


Page 13

7 Some candidates gave very strong answers in parts (i) and (ii) but in general the examiners were disappointed with the lack of understanding that was shown in many scripts. The examiners gave credit for alternative solutions in part (iii) where the question had not specified the as at date for the discount factor. Although 31 December 2002 was the most logical choice, calculations as at 31 December 2000 were also accepted. The ability to produce payment patterns has been examined a few times in recent years and yet candidates seemed to be very poorly prepared for these calculations. Part (iv) was bookwork and well answered.

(i) Paid triangles:

Factors less than one may appear in the paid triangles when the incremental net paid for a particular accident year and development year is negative. This in turn may occur for the following reasons:

• Data error — some of the underlying records may have been recorded incorrectly or the triangle may have been constructed incorrectly.

• Extraction of large claims — only if the history of a large claim isn’t extracted fully from the “non-large” triangle.

• Currency — if the underlying currencies have not been converted at current exchange rates, some of the movements in the triangle may be due to currency fluctuations.

• Third party recoveries — the insurance company may have been able to recover monies from another insurer or via salvage from the insured.

• Reinsurance lag — there may be a time delay between payment of a gross claim and a subsequent reinsurance recovery.

• Policyholder repayment of amounts subsequently decided not covered eg due to fraud.

• There may be some premium adjustments due to experience rating, and it is possible, although unlikely, that these may included incorrectly within affect the paid triangle.

Incurred triangles:

Factors less than one may appear in the incurred triangles when the incremental net incurred for a particular accident year and development year is negative.

This is more common than with paid developments. This in turn may occur for any of the above reasons plus the following:

• Large claim settled at less than case reserve, outweighing positive incurred claim movement on other claims.

• Case reserving strength changes so that there is a one-off decrease in case reserves, and this outweighs paid movements in that year.

• Generally conservative case reserving philosophy so that negative incurred but not enough reported (“IBNER”) claims development outweighs paid claims.

(ii) Comments on methodology and assumptions • Selected factors look reasonable…. • ….except no paid tail factor and paid development unlikely to stop dead.


Page 14

• Incurred pattern reflects run-off savings => case reserving is prudent. • Using paid and incurred information — good to use both but paid factors

to ultimate very high on latest accident years so paid chain ladder less reliable.

• Would expect more weight to incurred methods on later accident years as incurred has more information and factors to ultimate are lower.

• Large losses have been treated separately - good if distort factors in triangle ie if large claims develop faster or slower than non-large.

• Large losses in danger of being over/under projected if remain in triangle. • Large losses likely to be complex bodily injury claims therefore probably

longer-tailed on average than non-large claims. • If remove large losses from triangle won't project emergence of new large

losses. • Is $500,000 an appropriate level? Large loss definition of $500,000 is

being used on all accident/devt years. Inflation means that company will effectively be removing more losses from the non-large triangle on the 2002 row than the 1995 row.

• Large losses will be bodily injury claims — case estimates use skill of claims assessors but may not be consistent from year to year

• Company has included an additional 10% of large loss case reserves. Is this amount appropriate. This may be held to bolster case reserves if believed to be insufficient or it may be held as an allowance for new large losses to emerge.

• Suggest use Bornhuetter-Ferguson or expected loss ratio method on 2002 accident year as a minimum

Suggested alternative approaches • Establish paid tail…obtain further historical data, benchmark or do curve

fitting / fit tail by eye. • Apply more weight to incurred methods on later accident years. • Use Bornhuetter-Ferguson or expected loss ratio methods on the 2002

accident year where the factor to ultimate is high. • Should project gross then allow for reinsurance separately to avoid

distortions due to changes in reinsurance programme. • Project by country to avoid currency distortions. • Split into homogeneous groups (eg BI vs PD, Large fleets vs small fleets). • Test 10% allowance for large IBNER/IBNR by looking at historical claims

developments for individual large claims or compile triangle of large claims.

• Adjust large claim definition by year to allow for inflation. • Perform ACPC or inflation-adjusted ACPC for large &/or non-large losses.

(iii) (a) Use paid pattern

[some candidates incorrectly used the incurred pattern or the average of the paid and incurred]

Assume no tail factor required or make suitable adjustment


Page 15

Development year 0 1 2 3 4 5 6 7 8 Use paid cdf (=ult/pd) 23.933 4.351 2.560 1.790 1.377 1.167 1.061 1.020 1.000 Calculate 1/cdf (=pd/ult) Cum % developed 4.18% 22.98% 39.07% 55.87% 72.63% 85.70% 94.27% 98.04% 100.00% Subtract adjacent %’s Incr % developed 4.18% 18.80% 16.09% 16.80% 16.76% 13.07% 8.57% 3.77% 1.96% For 2000 accident year* 27.57% 27.51% 21.45% 14.06% 6.19% 3.22%

27.57% in the above row = (100/(100 − 4.18−18.8−16.09))*16.8%

[As at 31 December 2002, the 2000 accident year has reached the end of development year 2. Need to normalise pattern so that percentages add up to 100% and can therefore apply pattern to reserves.]

(b) Assume that payments occur on average mid-way through the year Calculate xtv(t −½) for each future time period where v = (1 + 0.05)(−1)

and xt = % payable in year t: Development year 0 1 2 3 4 5 6 7 8

t 1 2 3 4 5 6 xt 27.57% 27.51% 21.45% 14.06% 6.19% 3.22%

v(t −½) 0.9759 0.9294 0.8852 0.8430 0.8029 0.7646 xtv(t −½) 0.26905 0.25564 0.18991 0.11857 0.04969 0.02461

Discount factor = Discounted reserves / Undiscounted reserves = Sum of xtv(t −½) / Sum of xt

= 0.90746

(c) Discounted mean term defined by: Discount factor = (1 + i)(−DMT) Take logs of both sides: Log(0.907458) = −DMT*log(1.05) => DMT = 1.99 years

[Also possible to use accurate formula: Sum{(t-1/2)xtv(t-1/2)}/Sum{xtv(t-/2)} but this would be more time consuming. Answer in that case would be 1.99 years]

(iv) Legislation/supervisory regulations Investment return earned on assets covering technical reserves…. ….allowing for non-investible assets (e.g. broker/reinsurer balances) Purpose of reserving / degree of prudence required

Extent to which assets are mismatched to liabilities / uncertainty Rate used previously for consistency


Page 16

Allowance for tax Allowance for investments expenses.


EXAMINATIONS

26 April 2004 (am)

Subject 303 General Insurance



1. Enter all the candidate and examination details as requested on the front of your answer booklet.

2. You have 15 minutes at the start of the examination in which to read the questions. You are strongly encouraged to use this time for reading only, but notes may be made. You then have three hours to complete the paper.

3. You must not start writing your answers in the booklet until instructed to do so by the supervisor.




Hand in BOTH your answer booklet, with any additional sheets firmly attached, and this question paper.

In addition to this paper you should have available Actuarial Tables and your own electronic calculator.

Faculty of Actuaries 303 A2004 Institute of Actuaries

303 A2004 2

1 State the reasons why a general insurance company might calculate IBNR reserves separately from other claims reserves. [2]

2 A general insurance company that writes commercial property insurance business wants to purchase excess of loss reinsurance protection in order to reduce the overall variability of its claims experience. You have been asked to recommend an appropriate reinsurance structure (limit, deductible, number of reinstatements etc). You decide to build a model of the likely claims experience and reinsurance recoveries.

(i) State the functionality that you would require of this model. [3]

(ii) State the other factors that the insurance company needs to consider before deciding to purchase the reinsurance. [5]

[Total 8]

3 You are the actuary for a general insurance company that writes motor fleet business. One of the options available to the insured is for it to take a voluntary aggregate deductible on its policy.

(i) (a) Define what is meant by a deductible. (b) Define what is meant by an aggregate deductible.

[2]

A particular insured currently pays £100,000 a year for insurance cover with no deductibles of any kind, and would like to consider the impact on its premium of adopting a £10,000 annual aggregate deductible. It has been suggested that each £1 of aggregate deductible should reduce the premium by £1.

(ii) Discuss, with reasons, whether the suggestion is correct, or whether the true reduction would be higher or lower than this (assuming that any loadings to the risk premium remain unchanged in monetary terms). [6]

[Total 8]

4 (a) State the ways in which a general insurance company can increase its gross written premium.

(b) State the constraints that it faces in doing so. [10]

5 (i) State what is meant by a soft market and explain how it occurs and persists. [4]

(ii) Describe the risks to a general insurance company of under-estimating the softness of a market. [6]

[Total 10]

303 A2004 3 PLEASE TURN OVER

6 A reinsurance company wants to introduce a new type of aggregate excess of loss treaty covering subsidence claims on household insurance business. The treaty will cover all subsidence claims notified, during a calendar year, to an insurer. The treaty will be subject to an aggregate deductible and an aggregate limit.

(i) State the characteristics of subsidence claims likely to be experienced by the insurer. [5]

(ii) State the advantages and disadvantages to the reinsurer of the proposal. [6]

(iii) (a) List the information that the reinsurance company would request from the insurer if it were trying to price this treaty.

(b) List the information likely to be required from other than the insurer in order to price this treaty.

[8] [Total 19]

7 You have been provided with the following financial information in respect of a general insurance company.

1999

2000

2001

2002

2003

Total

Gross Earned Premium 66

71

187

165

220

709

Reinsurance Earned Premium 12

19

103

72

76

282

Net Earned Premium 54

52

84

93

144

427

Gross Claims Incurred 29

51

210

249

148

687

Reinsurance Claims Recoverable 1

31

155

138

14

339

Net Claims Incurred 28

20

55

111

134

348

Net (of reinsurance) Commission 10

11

32

29

35

117

Net Assets 53

32

91

112

121

409

Management Expenses 5

4

12

14

11

46

(i) (a) Define the terms gross loss ratio, net loss ratio, expense ratio, combined ratio and solvency ratio.

(b) Calculate these ratios for each of the five years of data. [7]

(ii) Describe the changes in the company finances from year to year in the following areas calculating any additional statistics which support your analysis.

(a) The efficiency of the management at controlling expenses. (b) Growth. (c) Reinsurance purchasing. (d) Underwriting profitability. [10]

(iii) Suggest where the management focus should be in the coming year. [2] [Total 19]

303 A2004 4

8 You are advising a consortium of insurance professionals who wish to set up a new reinsurance company. The business plan is to write international liability reinsurance on a non-proportional basis. It is intended to reinsure professional indemnity covers and employers liability covers. The company will be able to accept business from any territory.

You have been asked to assist in deriving appropriate rating structures for the company to meet its targets. The financial backers require a return on capital of 40% per annum on average. The company wants to write £100m of premium income for each of the two types of cover.

You have already calculated risk premiums for the two different lines of business.

(i) List the adjustments that should be made to the risk premium to generate the office premium. [2]

(ii) Describe the ideal requirements of an actuarial model. [4]

The company wishes to use a stochastic actuarial model to allocate capital between the two lines of business such that the probability of ruin is the same for each line of business.

(iii) Describe the steps involved in using a stochastic model to derive this common probability of ruin. [5]

(iv) State the advantages and disadvantages of a stochastic model over a deterministic model in this situation. [4]

Using a stochastic model, you determine that professional indemnity reinsurance is a more volatile class of business, and requires 50% more capital to support every £1 of premium underwritten than employers liability reinsurance. The business plan shows that the profit available (after allowing for investment returns) on employers liability reinsurance is 12% of the premiums written, and it is intended that all lines of business produce the same return on capital.

(v) Calculate the total capital required for the business based on the business plan if the financial backers target is to be achieved. [4]

(vi) Describe the other factors that the consortium should consider before deciding upon a suitable amount of capital for this new company. [5]

[Total 24]

END OF PAPER


EXAMINATIONS

April 2004


EXAMINERS REPORT


Subject 303 (General Insurance) April 2004

Examiners Report

Page 2

1 This question was generally well answered with many candidates scoring the majority of the marks

The calculation method used for other claims reserves may not produce a result including IBNR The combined reported and non-reported claims in the reserve analysis process does not enable a true assessment of the cost of claims. Feedback into pricing enabling the true assessment of the cost of claims. Feedback into the business control cycle. To assist in asset / liability matching Statutory reporting requirements may insist on the separate quantification and reporting of IBNR claims reserves. To allow accurate comparison of the profitability of different lines of business.

2 This question was well answered by most candidates.

(i) The model must be capable producing claim distributions both gross and net of a specified reinsurance structure. Enable the user to test various reinsurance structures. Must accurately describe the insurer s CPI book, present and prospective. The model should run quickly and reliably with communicable answers, encompasing key deterministic variables.

(ii) Cost and availability of the various reinsurance structures vs their likely benefit. Security Status of the available reinsurers. Size of free reserves. Opportunities to find co-insurers. Any constraints placed by regulators and rating agencies. Impact on solvency requirements from regulators or rating agencies. Company s attitude to risk. Return on capital constraints. How does the chosen reinsurance structure compare with competitors. Size of book versus rest of business. Long term relationship with insurers. Alternatives to XOL reinsurance Extent of in-house experience in this line. Services available from reinsurers.

3 Most candidates could define what was meant by a deductible, however many candidates struggled with the second part. Several candidates did not state whether the suggestion was correct or not but talked around the possible reasons. Many candidates mentioned fixed expenses in their solutions and sensible comments were awarded marks accordingly.

(i) A deductible is the amount which, in accordance with the terms of the policy, is deducted from the claim amount that would otherwise have been payable and will therefore be borne by the policyholder.


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The aggregate deductible applies across all claims in total. It is the total amount of all claims borne by the policyholder before the insurance company becomes liable.

(ii) This is incorrect. If true, in an extreme example £100,000 deductible implies £0 premium, without removing all risk The mean of the aggregate distribution is the risk premium One pound of deductible reduces the premium by the expected value of claims less than or equal to that pound Assuming probability of claims exceeding the deductible is not 1 The reduction in risk premium would be less than the deductible

4 There were many possible points to make in this question, but some of the answers given by candidates did not demonstrate to the examiners their understanding, especially when it came to stating the constraints. Most candidates nevertheless managed to score reasonable marks on this question.

Charge higher premiums for the same exposure.

Take on more exposure: By reducing premiums where elasticity of demand is greater than 1 By expand into new classes of business (including inwards reinsurance and coinsurance) By expanding into new areas of risk within existing classes By writing larger risks within existing classes By development in new countries By acquire another Insurance company

Expand into new distribution channels e.g. Direct marketing, internet Increase advertising / marketing / customer services Incentives for customers e.g. alarm clock or pen Increase sales force Increase commission levels offered to agents / brokers Increase capital in order to obtain a higher credit rating which is more attractive to potential clients.

Constrains:

Level of free reserves. If it grows too much it may not have enough capital to support its business. Competition from other insurers and self retention if it tries to increase its premiums too much. There may be regulatory constraints on:

premiums that it can charge. authorisation to write lines of business / countries distribution channels that can be used minimum solvency ratio

It may not have the expertise to write new classes of business It may not have the staff / infrastructure to expand quickly.


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Acquisition of another company may be too costly. Expanding into new distribution channels may alienate existing distribution channels. Brokers may resist reduced premium as this implies reduced brokerage Company s reputation may inhibit growth

Cashflow New salesforce may be costly / difficult to recruit and train

5 Whilst the examiners had expected the solution as given in part (ii), it was clear to the examiners in their post exam meeting that the term under-estimating could have been interpreted as meaning either that premiums were higher or lower than the market. Hence marks were also awarded for the alternative explanation

The main problem encountered seemed to be that candidates did not know the difference between a soft market and a hard market.

(i) It is caused by over-supply of insurance capacity in certain products. Soft market is a term describing that part of the insurance cycle when business is least profitable. i.e. inadequate premiums being paid for the amount of risk assumed.

Its longevity and depth result from the true effects of claims inflation, broadening wordings cover and increases in exposure being under-estimated at the time of writing business.

Persists because premium increases lag behind claims notifications

(ii) Risks

Write a larger volume of unprofitable business than planned leading to Over statement of profits and under statement of reserves

managers not aware of true financial condition

leading to bad business decisions. Risk of writing larger volumes of business than planned and not being able to service it. There is a risk that the true profitability of business written is not known for some time and the company writes business at less profitable rates than it expects. Leading to a significant weakening of the financial condition of the company.

When the extent of this position is realised reserves must be increased (sometimes dramatically) leading to a reduced solvency position, requiring additional capital support and/or other remedial action. This reduced solvency may directly impact the quantity of profitable new business that the company can write and in the extreme may lead to the insolvency of the company.


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6 Many candidates did not demonstrate sufficient knowledge to perform very well in this question. This was the most difficult question on the paper and certainly sorted out those that could think around GI issues and those who struggled. In the majority of cases there were just insufficient valid points made.

(i) The frequency and average cost can be related to the economy (Housing market) i.e. there is a strong dependency on property selling as many subsidence claims arise following surveys for buyers. Such claims are also related to several other events, e.g. the weather (unusually dry spells), closeness of trees, pipes and soil conditions.

Long notification and settlement delays. Low frequency and high severity Can have high levels of reopened claims. Claim size distribution can be highly skewed. There can be significant accumulations of claim occurrences and notifications during particular periods. Claim costs subject to inflation. Date of occurrence is usually uncertain This may lead to disputes about coverage especially when there have been changes in the insurance company providing the cover. Need for individual loss assessment by a claims adjuster Active claim management can significantly reduce the cost of a claim.

(ii) Reinsurer Advantages: New product type and hence it may attract significant new business. Possible diversification away from its other products. May be highly profitable if there is very little competition. May enable it to attract more traditional business from its cedants. (Cross selling). Aggregate limit and deductible cap liability. Claims notified wording removes problem of late notification Such a product would be very attractive to insurers as it would enable them to price their own policies with more certainty

Reinsurer Disadvantages: Lack of data to price this business and possibly requirement for more capital. Risk of anti selection. If there are long lags between adverse weather and subsidence claim notifications, Insurers may be able to select against the reinsurer. Risk of anti selection. Exhaustion of aggregate deductible removes insurers financial incentive to monitor claims. How do you deal with reopened claims? They could just as easily be opened as new claims. Long settlement delays mean that the ultimate losses from the policy will not be known for a long time. If mispriced initially, then this could be very costly. Claim inflation is likely to be significant due to long settlement delays.


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Claim experience is potentially linked to the economic / housing cycle. This can be very difficult to price for.

(iii) (a) Data on past years experience. Notifications and ultimate losses by calendar year. Listing of all subsidence claims showing details of:

Notification date. Payments (dates and amounts) Changes in outstanding case estimates (dates and amounts) Additional details on the claims e.g. geographical area, likely cause etc.

In force policy counts, premiums and sum insured by geographic region. In order to check exposure to high risk areas. Expected policy count, premiums and sum insured for the exposure period by geographical region. Clarification from the insurer on how it handles reopened claims. Information about changes in excess levels and any changes planned for the future. Insurer s policy conditions Insurer s underwriting philosophy Expertise in handling claims

(b) Industry data on claim notifications and claim costs. Externally available models Own claims experience of subsidence Judicial findings and market practice Economic data on Housing Market. Building cost Index as a proxy for claim cost inflation. Climate and weather data e.g. Rainfall data, Soil moisture and composition data etc. Applicable Tax rates Expense loadings (including brokerage, commission and management expenses). Required Profit loadings Investment yields Cost of capital Contingencies Retrocession costs (if applicable) Competitors prices (if available)

7 This question was generally well answered, however there were some points on which candidates demonstrated that they did not understand accounts for a general insurance company and important statistics.

In the calculation of the solvency ratio in part (i) candidates were expected to make a reasonable assumption on how to obtain written premium from the data. Whilst not particularly accurate the assumption of net written being the same as net earned was accepted as in the solution below.


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(i) Gross Loss Ratio = The ratio of the cost of claims to premiums, both gross of reinsurance. Net Loss Ratio = The ratio of the cost of claims to premiums, both net of reinsurance. Can be on an earned basis or a written basis. Expense Ratio = The ratio of management expenses plus commission to premium Combined Ratio = The sum of the loss ratio (claim ratio) and the expense ratio

Solvency Ratio = The free reserves divided by the net (of reinsurance) written premiums.

1999

2000

2001

2002

2003

Total

Gross Loss Ratio 43.9%

71.8%

112.3%

150.9%

67.3%

96.9%

Net Loss Ratio 51.9%

38.5%

65.5%

119.4%

93.1%

81.5%

Expense Ratio 27.8%

28.8%

52.4%

46.2%

31.9%

38.2%

Combined Ratio 79.6%

67.3%

117.9%

165.6%

125.0%

119.7%

Solvency Ratio 98.1%

61.5%

108.3%

120.4%

84.0%

95.8%

(ii) (a)

Management Expense Ratio 9.3%

7.7%

14.3%

15.1%

7.6%

Expense Ratio as calculated above

27.8%

28.8%

52.4%

46.2%

31.9%

Management expenses rise dramatically as the company expands in 2001 and 2002, almost doubling from the 2000 expense level. Management expenses are brought under control in 2003 Similarly Expense Ratio increases dramatically in 2001.

(b) Growth

GEP Growth 7.6%

163.4%

11.8%

33.3%

NEP Growth 3.7%

61.5%

10.7%

54.8%

Growth in Gross premiums of 163% in 2001 is dramatic, similarly the 33% growth in 2003 is large. Large changes like this may be a result of acquiring another company.

Net Premium change is less volatile than the gross premium change The large increase into 2001 follows the increase in gross premiums. The large increase in 2003 is due to reduced reinsurance purchasing as a percentage of gross income

(c) Reinsurance purchasing


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Ceded Premium change 18.2%

26.8%

55.1%

43.6%

34.5%

RI Cost = RI Prem

RI Recoveries

11

(12)

(52)

(66)

62

Ri Loss Ratio 8%

163%

150%

192%

18%

Reinsurance loss ratio, and hence recoveries were low when the company was small. Ceded premiums have increased significantly with the growth in gross premiums Reinsurance spending has been good over the period with recoveries exceeding premiums.

(d) Underwriting profitability

Net UW Profit 11

17

(15)

(61)

(36)

Net profitability in the last three years has been negative Although negative, the underwriting profit has improved in 2003.

(iii) Comment: After a period of rapid growth it would be sensible for the company to consolidate. Expenses have been reduced dramatically in the last year and these need to be kept low reducing them if possible. Reinsurance purchasing has reduced probably as prices have risen due to the high level of recoveries in the middle years. A cost benefit analysis of reinsurance spending should be performed. Effort needs to put into gross and net underwriting profits.

8 Many candidates scored very high marks on this question. Most of the solution was straightforward bookwork. Several candidates did however seem to struggle with the calculation part (v).

(i) Expected investment return credited Commission Fixed expenses Other variable expenses Cost of retrocession Profit Adjustment for competition Contingencies Tax Cost of capital


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(ii)

the model being used should be valid, complete and adequately documented

the model chosen should reflect adequately the risk profile of the classes of business being modelled

the parameter values used should be accurate for the classes of business being modelled

the outputs from the model and the degree of uncertainty surrounding them should be capable of independent verification for reasonableness

The model, however, must not be overly complex so that either

The results become difficult to interpret and communicate

The model becomes too long or expensive to run.

(iii)

Definition of ruin

collect data

group and modify data

choose a suitable density function for each of the variables to be modelled stochastically

specify correlations between variables

estimate the required parameters for the chosen density function(s)

check the goodness of fit is/are acceptable and attempt a fit with different density function(s) if it is not

construct a model based on the chosen density function(s)

run the model many times, each time using a random sample from the chosen density function(s)

count the number of scenarios in which each of the lines of business produces ruin for the company

produce a summary of the results that shows the distribution of the modelled results after many simulations have been run

perform sensitivity tests on results

Calculate the capital allocation that equalises the ruin probability for each class

(iv) Advantages Captures interdependency of variables and general volatility better Capital required for infrequent events need concept of probability Provides additional output to management e.g. reinsurance purchasing Best practice/competition Deterministic model cannot do probability of ruin

Disadvantages More complex and time consuming Danger of spurious accuracy

(v) Capital for EL = y


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Capital for PI = 3y/2 Total capital = 5y/2 Required return on capital = 40% Required profit = 40% 5y/2 = y Profit for EL = £12m Same return on capital means profit for PI = £12m*3/2 = £18m Total profit = £30m Therefore, y = £30m Total capital = £75m

(vi) There may be a regulatory minimum level of solvency which this may not reach Need to consider how this compares to competitors, and the implication on market confidence Opportunity cost of capital may be better utilised elsewhere No track record, therefore The credit rating of the company will depend on the capital available

a lower credit rating will reduce the ability of the company to sell the reinsurance

The availability of capital may impact on the company s ability to raise any more Market may not be able to sustain sufficient premium to produce desired returns on a higher capital base Quality of people affects ability to raise capital

END OF EXAMINERS REPORT


EXAMINATIONS





1. Enter all the candidate and examination details as requested on the front of your answer booklet.

2. You have 15 minutes at the start of the examination in which to read the questions. You are strongly encouraged to use this time for reading only, but notes may be made. You then have three hours to complete the paper.

3. You must not start writing your answers in the booklet until instructed to do so by the supervisor.




Hand in BOTH your answer booklet, with any additional sheets firmly attached, and this question paper.

In addition to this paper you should have available Actuarial Tables and your own electronic calculator.

Faculty of Actuaries 303 S2004 Institute of Actuaries

303 S2004 2

1 (i) List the types of generic policy and claims data that would be required for a premium rating exercise. [5]

(ii) Give examples of the specific rating factors that should be considered when pricing:

(a) personal medical expenses (b) employers liability insurance

[4] [Total 9]

2 A general insurance company expects to write business at a loss ratio of 70% and incurs expenses of 10% commission and 10% other management expenses. It pays taxes of 30% of profits. It also pays out 10% of its post tax profits to shareholders in the form of a dividend. The insurance regulator requires it to demonstrate a minimum solvency ratio of 50% at the end of the year. Its current solvency ratio is 50%.

(i) Calculate the maximum growth rate that it can sustain without recourse to additional capital, stating any assumptions that you make. [4]

(ii) Suggest ways in which this insurer might be able to grow more quickly than the rate calculated in part (i). [5]

[Total 9]

3 State the advantages and disadvantages to a large multinational company of setting up a captive insurer. [6]

303 S2004 3 PLEASE TURN OVER

4 A general insurance company writes a wide range of general insurance products. The reserve estimates for each homogenous portfolio are calculated using the Bornheutter-Fergusson method. Company procedures dictate that the initial estimate of the ultimate loss ratio is not changed once selected.

You are an actuary responsible for setting the reserve estimates for a stable portfolio of short tailed business. You are reviewing the historical data for a fully developed year. In this year $100m of premiums were written in a soft market. The portfolio is reserved using the Bornheutter-Fergusson method based on reported claims, and at the time of writing the expected cost of claims was under estimated. The initially selected estimate of the ultimate loss ratio was 100% and the difference between the initial and actual ultimate loss ratio is 20%.

The expected run off pattern for this portfolio is given below.

End of year 1 2 3 Paid claims 30% 90% 100% Reported claims 50% 105% 100%

(i) Explain why reported claims at the end of year 2 might exceed the ultimate claims. [4]

(ii) Calculate the impact that the difference between the initial and actual ultimate loss ratio has on the declared profits of the company at the end of each of the three years, stating any assumptions you make. [4]

(iii) State the advantages and disadvantages to the company of its policy of not changing the initial estimate of the Bornheutter-Fergusson ultimate loss ratio.

[4] [Total 12]

5 (i) List the third parties whose financial failure could have an impact upon a general insurance company, giving in each case an example of the financial effect upon the insurer. [6]

(ii) Describe the measures that an insurance regulator might impose in order to reduce the risk of third party failure to the insurers that it regulates.

[4] [Total 10]

303 S2004 4

6 A general insurance company specialises in writing commercial property insurance business.

(i) List the rating factors that it is likely to use in order to determine appropriate premium rates. [3]

(ii) List the risks that the insurance company faces in relation to claims experience from this class of business. [4]

(iii) Give examples of the measures that the insurance company could put in place to control / reduce the variability of its claim experience. [7]

[Total 14]

7 The government of a small developing nation wants to encourage exports from that country. One of the measures that it has taken is to set up an export credit insurer. An exporter can buy credit insurance from the insurer for each consignment of goods that it exports. If the customer in the foreign country fails to pay for the goods, then the insurer indemnifies the exporter.

(i) Describe the characteristics of the claims that the export credit insurer is likely to receive. [5]

(ii) List the policy data items that the export credit insurer will need to capture when setting up a policy onto its system. [2]

(iii) Suggest appropriate ways to group claim development statistics for this insurer when carrying out a reserving exercise to set outstanding claim reserves. [2]

(iv) Describe how the unearned premium reserve would be calculated for this insurer. [2]

(v) Suggest with reasons, suitable reinsurance structures for the export credit insurer. [4]

[Total 15]

303 S2004 5

8 You are the actuary for a large general insurance company selling household buildings and contents insurance, through a broker network. The company has been writing this business for 12 years. In common with its competitors in the market, the company uses only geographical location and sum insured as rating factors.

The finance director of your company is considering the implications of introducing some form of experience rating in order to set the company apart from the rest of the market, and has asked for your assistance in analysing the impact of such a move.

(i) Describe the different types of experience rating that could be considered, and their consequences to the insurer. [4]

(ii) Compare the relative merits of the different options in this circumstance, and make a recommendation between the alternatives. [7]

(iii) Discuss the impact that the introduction of experience rating may have on the insurance company and its policyholders. [9]

It has been decided to introduce the experience rating from 1 January 2005.

(iv) Describe the portfolio movement analyses that could be put in place to monitor the impact of this introduction. [5]

[Total 25]

END OF PAPER


EXAMINATIONS

September 2004


EXAMINERS REPORT

Introduction

The attached subject report has been written by the Principal Examiner with the aim of helping candidates. The questions and comments are based around Core Reading as the interpretation of the syllabus to which the examiners are working. They have however given credit for any alternative approach or interpretation which they consider to be reasonable.

M Flaherty Chairman of the Board of Examiners

7 December 2004


Subject 303 (General Insurance) September 2004

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1 This question was answered well by most candidates.

(i) Policy data

Start and end dates of cover and dates of changes in cover

all rating factor details

all exposure measure details including limits, excesses etc.

source of business

details of premiums charged, unless they can be calculated by reference to the details on rating factors and exposure

premiums net of commission etc.

Claims data

date of claim event

date reported

date settled

date reopened

dates and amounts of payments (including recoveries & expenses)

case estimates, if they exist, of amounts outstanding (and date)

other types of estimates (e.g. factor estimates)

rating factor details i.e. link between claims and policy details

type of claim

details of payee

type of peril

(ii) Personal medical expenses

current age of policyholder

smoker/non-smoker

type of cover (hospital group)

extent of cover (excess, limits)

the extent of the family group covered

occupation

NCD as a proxy to medical history

post-code (address) as indicator of likely regional hospital costs

gender

Employers liability

payroll OR number of employees

type of industry or occupation

exposure and claims experience

location of the workforce

the materials handled

health and safety standards etc.

the processes involved

turnover

size of deductible


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2 The numerical solution in part (i) is the answer which the examiners had expected to be given. However credit was also given where candidates had assumed an Accident Year accounting basis.

(i) Let growth in business = k Premium in previous year = P Premium next year = P * (1 + k) Post tax profit = P * (1 + k) * (1 0.7 0.1 0.1) * 0.7 * 0.9 = P * (1 + k) * 0.063 Solvency margin required = P * (1 + k) * 0.5 Profit generate = additional solvency margin P * (1 + k) * 0.063 = P * (1 + k) * 0.5

P * 0.5 Solving for k gives 14.4%

Assuming no investment return Commission, management expenses and profit distribution continues at same rate Loss ratio is as assumed Calculation is done annually No reinsurance

(ii) Grow more quickly by:

Charging higher premiums for the same exposure Reducing cover for the same premiums Stricter claims control. Improved UW / risk selection Reducing expenses and policy acquisition costs. Reduce premiums with increase loss ratio more than offset by the reduction in per policy expenses Reducing the dividend that it pays out / not pay out a dividend at all. Raising additional capital. Buy additional quota share reinsurance. A suitably structured financial reinsurance deal Change investment strategy to increase investment return. Incorporate in a tax haven. Incorporate in a country with lighter insurance regulation.

3 Most candidates were able to make a reasonable attempt at this question, but there was a wide variety of answers with the better candidates scoring almost full marks.

Advantages

Tax efficient May be legislative or regulatory advantages Fill gaps in insurance cover available in the market Focus efforts on risk management Manage overall Insurance spend of the company


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Improved financial planning due to more predictable insurance premiums, especially the effects of the insurance cycle Access reinsurance capacity directly. Retain the expected profit that might otherwise be ceded to its insurers

Disadvantages

Administrative expense of setting up the captive Capital cost required to set up the captive The captive may need to get regulatory approval from all the countries that the multinational operates in order to accept risk from all its operating subsidiaries. Insurers may be able to provide assistance with risk mitigation / claims control. The captive may not have the same expertise in all the different countries that the company operates. By setting up the captive, the multinational is retaining risk. Setting up the captive may divert management focus from its core activities. Compliance with insurance regulatory requirements

4 Many candidates used the paid claims information in part (ii) whereas the question stated that the reserving is based on reported claims, hence a number of marks were lost. Also in part (ii) some candidates derived the figures of ultimate claims and did not go onto say what effect this had on the declared profits.

(i) Claims made which end up as nil claims E.g. Claims are made which fall outside the coverage of the policies Claim assessments cautious which leads to an overstatement of outstanding reserves Reported claims do not allow for salvage or subrogation which reduce the ultimate claims

(ii) Premiums 100 Initial estimate lr 100% Actual LR 120%

End of year 1 2 3 Paid 30% 90% 100% Reported 50% 105% 100%

Dev ratio 2.100 0.952 1 Cum f 2.000 0.952 1 = 1 1/cum f 0.5 0.05 0 Reported claims 60 126 120 Claim reserve 50 (5) 0 Est Ult Claims 110 121 120 Actual ultimate claims 120 120 120 Overstatement of Profit 10


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End year 1 profit calculated 10 too big Year 2 ultimate claims estimate deteriorates by 11, ultimate claims overstated by 1 Year 3 zero difference

Assumptions: Written premiums all become earned. Claims runoff according to the expected pattern.

(iii) + Simple method avoids any subsequent investigation + For a short tailed line the errors generated will be relatively small and short lived.

Does not allow for corrections once a different view of the likely ultimate claims is known

May not satisfy accounting standards which require best estimate reserves may give managers a false sense of security as to the true profitability of a

portfolio either too high or too low For long tailed lines the errors generated will potentially be large and long

lasting - Pay more tax than necessary as profit overstated

The errors may overstate the true solvency position of the insurer, leading it to take actions that may jeopardise the real solvency. In other cases the reserves may be too prudent and so reserves that are too high are held potentially restricting opportunities available.

The company may price using these reserve estimates, leading to incorrect premiums being charged.

5 Several candidates gave examples of third parties who not in fact third parties e.g. policyholders and staff. Apart from that most candidates answered this question reasonably well.

(i) Failure of a reinsurer could mean that it does not get reinsurance recoveries that it is due. It may also have to purchase additional coverage.

Failure of an intermediary / Broker would mean that it may not get some premiums owed to it.

Failure of a supplier of goods or services. The insurer would have to spend additional money securing those goods or service.

Failure of a Financial Organisation / Bond issuer in which the Insurer has assets. The insurer could lose those assets.

Failure of another insurer may mean that this insurer is asked to make payments into a compensation fund. However the company could benefit from a gain in extra business.


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(ii) Limit the amount of reinsurance that Insurance companies can place with a single Reinsurer.

Limit the amount of reinsurance that Insurance companies can take into account with a single Reinsurer when determining solvency.

Impose or increase a Statutory Minimum Solvency Margin

Limit the amount of assets the insurer can invest in a single company / bond issuer.

Require the licensing of intermediaries / brokers.

Require insurers to hold a bad debt reserve

Require insurers to hold certain asset classes or restrict asset classes

Require reinsurers to deposit assets / collateral to back their obligations to Insurers.

Require that reinsurers and other financial organisations have sufficient credit rating and are supervised more stringently.

6 In answering this question some candidates failed to realise that commercial property business is usually made up of buildings, contents and business interruption. In part (iii) the answers were generally very short and many candidates did not mention anything other than reinsurance.

(i) Sum insured Type of business (including hazardous chemicals) Location of premises Estimated maximum loss Age of building Safety equipment, including fire protection equipment Construction type Excess Risks covered Past claims experience Risk management procedures

(ii) Variability in claim frequency at any one time and from one period to another Variability in claim severity at any one time and from one period to another Individual large claim Notification delays Settlement delays Moral Hazard. Fraudulent Claims. Anti-selection. Crime Rates (theft and arson claims)


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Economic conditions, affecting attitude to claiming Judicial decisions Changes in legislation Accumulations of risk Catastrophes Currency risks Reinsurer security Reinsurance mismatch Policy wording Inflation Latent Claims Increases in claims expenses

(iii) Excess of Loss protection and Catastrophe XOL for large single events Surplus reinsurance for ceding out larger risks. Stop Loss / Aggregate XL reinsurance. Exclusions (Terrorism / NCB) Limits on size of risks that can be accepted. Reduce exposure to certain industries / types of businesses that exhibit greater variability of claim experience (e.g. Oil industry or large multinationals) Track and control aggregates by geographic region. Diversify by region, industry, type of business. Match liabilities and assets by currency in order to reduce currency risk Restrict the territories / currencies that it writes business in to reduce currency risk. Place reinsurance with financially strong reinsurers (AAA rated) Spread the reinsurance placement amongst several reinsurers. Employ specialist wordings staff to reduce risk from ambiguous policy wording. Impose excess / deductibles Impose catastrophe / event limits or other sub-limits Stricter claims underwriting to prevent fraudulent claims Review rating structure and rates more frequently to reduce anti-selection Diversify into other areas of insurance

7 The examiners were pleased with the general level of answers given to this question. The main area of difficulty was in considering what was actually insured. Several candidates included Goods In Transit within their answer. Examiners have also noticed recently that question asking for suitable reinsurance structures tend to get the standard answer of all types of insurance and not answers to the specific question.

(i) Claims will generally be short tailed as typical trade credits are 3 6 months. Claims will be in a number of currencies Individual claims will generally be small and limited to the value of the export consignment. There will be nil claims as late payments are made to the exporter resulting in the outstanding claim amount being reduced to zero


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There will be claim recoveries because some original invoices will be paid after the insurer has paid the exporter s claim There is likely to be accumulations of claims if a large number of exporters supply the same customer. Accumulations are also likely if a large number of foreign companies experience financial difficulty due to economic conditions within those countries. There is potential for fraudulent claims if the exporter and the customer are colluding.

(ii) Unique policy identifier Name & Address of policyholder Premium for the policy. Policy excess or deductible Value to consignment Currency of payment. Name & Address of customer Country of customer Business type of customer (Retail / Manufacturing / Services etc) Terms of trade for paying the invoice e.g. 30 days Date policy issued Date of despatch Date when Invoice is payable.

(iii) Split by Country Split by Currency. Group claims by the month in which the invoice is payable.

(iv) The Premium would all be earned on the date the invoice is payable as that is when all the exposure is.

Therefore UPR should simply be all the premiums on policies where the invoice date falls after the accounting date netted down for commission and other initial expenses.

(v) Aggregate XL reinsurance to protect against accumulations from failure of a single customer / multiple failures in foreign countries.

Stop loss reinsurance (if available) to protect poor experience across the book of business.

Risk excess of loss to protect against individual large claims

Quota Share reinsurance to lay off some of this risk and enable it to write a diverse portfolio.

Financial reinsurance to smooth results over economic cycles.


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8 Some candidates got the definitions the wrong way around, which meant that in part (ii) the points made were the wrong way around. However if candidates were consistently wrong then credit was given in part (ii) as appropriate. In addition credit was given if points were made in answer to one part of the question but fell into a different part in the examiners solution.

The question asked for a recommendation in part (ii) but some candidates failed to produce a recommendation and therefore no marks could be awarded. Any well reasoned recommendation would have scored marks.

(i) Experience rating can be prospective or retrospective, numbers or amounts based. With prospective rating, the premium at the renewal date depends to some extent on the experience of the risk prior to that renewal. The insurer takes on all the underwriting risk in such an arrangement. With retrospective rating, the premium for the current policy period is adjusted, based on the experience of that period of risk. A deposit premium, paid at the inception of the policy, will usually be followed by an adjustment premium, or refund, at the end of the period The insurer takes on less of the underwriting risk. Numbers based systems depend upon the number of claims made. Amounts based systems depend upon the total amount of claims made.

(ii) Prospective vs retrospective Broker network with many customers (personal lines) means prospective may be easier to apply Retrospective less risky to insurer Retrospective more difficult to apply as there is uncertainty as to the amount of some claims (e.g. subsidence) Prospective means quotes change at the time of underwriting more likely to have desired impact Prospective requires more data up-front 12 years should be okay Retrospective deals better with new customers Prospective therefore rewards loyalty Numbers vs Amounts If claims frequency is small then neither is ideal Numbers based more likely to discourage costly small claims Numbers more appropriate when claims size is very variable Amounts could be capped to make this more usable

Points for picking (my money is on prospective numbers (NCD))

(iii) Potential large movements in individual premiums at point of renewal Customers may not like the volatility introduced by such a system May cause an exodus of policyholders; good and bad In general, poorer risks see an increase in premiums Leave and go to cheaper competitors Company doesn t lose money on poor risks that leave


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Better risks see a reduction in premiums more likely to stay, even at high premiums relative to actual risk cost Likely to attract better risks from other insurers too Increased likelihood of attracting better risks if system can be applied to new customers too Important to get rates correct, or may be selected against Need to monitor profile of any new business closely Rapid growth from new business could cause new business strain

impacting on insurer s solvency Rapid growth from new business could cause poor service to customers resulting in loss of business and ability to write business in future Take care to ensure underwriting and claims systems are capable of capturing necessary information Costs of changing UW and claims systems capability Education of brokers is required Business may be more complex to administrate may lead to restructured commission Difficult to apply for new business as may need to rely on honesty of policyholder especially as no other insurer uses such a system

(iv) new business analyse the proportion of new quotes taken up, and/or the volume of business growth lapses or renewal analyse the proportion of policies renewed each calendar year endorsements analyse the rate at which policies are changed during the year mid-term cancellations analyse the rate at which policies are cancelled during the year conversion rate analyse the proportion of quotes taken up

All of the above need to be analysed by rating factor to monitor the changing nature of the portfolio.

Compare actual with expected

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