Faculty of Actuaries
Institute of Actuaries
EXAMINATIONS
April 1999
Subject 403 — UK Fellowship General Insurance
Paper One
You must answer this subject only,
you may not attempt another subject in the 400 series.
Time allowed: Three hours
INSTRUCTIONS TO THE CANDIDATE
1.
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.
2.
You must not start writing your answers in the booklet until instructed to
do so by the supervisor.
3.
Write your surname in full, the initials of your other names and your
Candidate’s Number on the front of the answer booklet.
4.
Mark allocations are shown in brackets.
5.
Attempt all 6 questions, beginning your answer to each question on a
separate 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 available
Actuarial Tables and an electronic calculator.
403(1)—2
1
You are the actuary of a general insurance company, and have been asked to model the economic value of an insurance product using net present value techniques.(a) List the key assumptions in the modelling process. [3] (b) Describe the considerations involved in choosing values for these
assumptions. [9]
[Total 12]
2
(i) Outline the basis of taxation of a United Kingdom proprietary generalinsurance company. [4]
(ii) Describe the extent to which each reserve can be offset against tax. [4] [Total 8]
3
(i) Define the terms exposure measure, risk factor and rating factor. [4] (ii) State an appropriate exposure measure and list the risk factors andrating factors for each of the following classes of business: (a) Employers’ Liability
(b) Marine Hull [10]
[Total 14]
4
(i) Define the following terms: (a) excess of loss reinsurance(b) experience rating [3]
A reinsurer has been asked to quote for a 500,000 excess of 500,000, unindexed, each and every loss cover, on a portfolio of 1000 identical risks, all written with a sum insured of 2 million, for the 1999 underwriting year. The following information has been provided:
Accident Number Ground-up loss year of policies development factor
1996 700 1.3
1997 800 1.4
1998 900 1.5
Claims inflation has been at a level of 3% per year compound throughout this period and will continue to be at that level. Pure IBNR is negligible, but reported claims may be expected to increase in line with the appropriate ground-up loss development factor. The following is a list of the paid amounts plus outstanding reserve on all claims exceeding 250,000.
Accident year
1996 300,000 600,000 900,000
1997 400,000 700,000 800,000 500,000
1998 350,000 800,000 400,000 650,000
(ii) Calculate an experience rated pure loss cost for the layer, for the 1999
accident year. [5]
An alternative method has been suggested to determine the pure loss cost, based on the limited expected value (LEV) curve shown below. This curve shows, for example that if claim payments were limited to 25% of the sum insured then total loss costs would be 80% of the level they would otherwise be.
Percentage of sum insured 25 50 80 90 100
Percentage of total loss cost 80 90 95 98 100
The insurer is able to write to a 70% loss ratio, and charges 20,000 per risk. (iii) Calculate the pure loss cost under the new proposed method. [4] (iv) List the factors to take into consideration when deciding which method
to use. [3]
It has been decided to adopt a pure loss cost of 1.4 million. The company uses a concept known as “leverage ratio” in its capital allocation, which is defined as the ratio of premium to capital allocated. The following information is available.
Commission/brokerage 10%
Internal variable expense 5% Internal fixed expense 5,000
Leverage Ratio 2.0
Required Return on Capital 15% Investment income/tax ignore The reinsurer will write 50% of the layer.
(v) (a) Calculate the office premium that should be charged. (b) Calculate the return on capital the reinsurer may expect to
achieve if the contract is, in fact, placed for a premium of 2
million in total. [5]
403(1)—4
5
A large proprietary general insurance company writes household, creditor, domestic mortgage indemnity guarantee, motor and commercial business, and it currently has a solvency margin of 80% of annual premium.(i) Discuss the reasons why this insurer may want to purchase
reinsurance. [7]
(ii) Describe appropriate reinsurance arrangements for each class of
business. [10]
[Total 17]
6
The Insure Kwik Company is an insurance company whose only classes of business are private motor and household insurance, sold direct to the public. All quotation requests are handled by a telephone call centre that is part of the head office. The profit and loss account for the 1998 financial year is shown below, with all items in thousands of pounds.Total Motor Household
Premium earned 30,000 20,000 10,000 Investment income 3,000 Total income 33,000 Claims incurred 26,000 17,000 9,000 Management expenses 5,000 Gross profit 2,000 Taxation 500 Dividend 500 Retained profit 1,000
Investment income has been achieved at a rate of 7% per year on invested funds. The company does not use reinsurance.
The Board has considered the financial figures, and considers that the present return on capital is not satisfactory. The marketing department has
conducted research that has led to the following conclusions.
• The proportion of policies that renew rather than lapse is affected by the premium rates. Each change of 1% in premium rates is likely to be followed by a change in the proportion that renew, in the opposite direction, of 1½% in the case of motor policies and 2/3% in the case of household policies.
• The number of enquiries handled at the call centre is likely to change by 1% for every 1% change in the amount the company spends on advertising, the two changes being in the same direction.
• The conversion rate of enquiries into new policies is likely to change by 2½% for motor and 2% for household, for each 1% change in premium rates, the changes being in opposite directions.
(In the above, a 10% rise in a 50% renewal rate, for example, should be interpreted as raising it from 50% to 50% × 1.1 = 55%.)
The actuarial department has suggested that rating structures are now
optimal, in that an across-the-board premium rate change would not have any effect on the average amount of claims per policy. It also confirms that claim reserves are considered to be good estimates of ultimate payments.
The number of policies has remained constant for a number of years, and the movement statistics during 1998 were:
Motor Household Policies at start of year 60,000 40,000
Lapses at renewal 20,000 8,000
New policies 20,000 8,000
Policies at end of year 60,000 40,000
Endorsements 3,500 7,500
Number of claims 12,500 3,500
(The number of claims has been constant for a number of years. The number shown is the number of new claims received in the year.)
The company is organised in the following departments:
Management Includes functions such as accounting, general
management, actuarial, and marketing. It also includes supervisors in other departments.
Quotations The staff who receive telephone calls asking for quotations, and provide them through an on-line computer system. New business The handling of accepted quotations, producing policy
documents, and initiating collection of the first premium. Policy servicing Processing renewals, premium collection, endorsements. Claims Receiving, handling and paying claims.
The total expenses in 1998 were broken down as follows. (Thousands of pounds)
Premises costs 300
Staff costs 2,850
Depreciation 350
Call centre phone system running cost 700 Postage, stationery, other ‘phone 300
403(1)—6
Staff costs were broken down as follows.
Management 500
Call centre (quotations) 800
New business 250
Policy servicing 700
Claims 600
Management has determined that the cost of running the call centre is proportional to the number of requests received for quotations. Premises costs and depreciation will not vary with any likely changes in business levels. Postage, stationery and other ‘phone costs may all be allocated to the three servicing departments, in proportion to staff costs on each of their
transactions. Advertising costs may be varied at the discretion of the Board. (i) You have conducted a time-and-motions study to assess the amount of time each transaction takes up, weighting them by the salary levels of the staff involved. The results are as follows:.
Motor Household
Processing a new proposal 4 3
Inviting a policy renewal 1 1
Processing a renewal 3 2
Processing an endorsement 6 8
Processing a claim 14 7
Allocate the staff costs of the new business, policy servicing and claims departments between the two lines of business, using functional costing
based on these weights. [5]
The Board has decided to increase premium rates by 10% for motor and 18% for household, in order to improve profitability, to take effect from 1 January 1999. However, recognising that this will depress the amount of business written, it has decided to increase advertising spending by £200,000 in the coming year. You should assume that expenses and claims are not affected by inflation.
(ii) Estimate the level of management expenses for the 1999 financial year,
justifying any assumptions you make. [12]
(iii) Estimate the profit and loss account for the 1999 financial year, stating
any further assumptions you make. [5]
(iv) Comment on your results. [7]
Faculty of Actuaries
Institute of Actuaries
EXAMINATIONS
April 1999
Subject 403 — UK Fellowship General Insurance
Paper One
Subject 403 (UK Fellowship General Insurance) — April, Paper 1 — Examiners’ Report
Page 2
1
(i) Future written premium income Future claimsFuture expenses Investment return Reinsurance
The economic environment Catastrophes
The insurance cycle
[1 mark for four; ½ mark each thereafter, maximum 3] (ii) Future written premium income
Monthly figures
split by source of business Consult sales managers Future claims
Claims split into development of notified claims and IBNR
new claims from unexpired business and future business
Future expenses
Commission is a % of written premium Staff cost is more difficult to predict
because they depend on projected business growth and staffing plan
and allocation to this product. Investment return
Depends on current investment policy and projected future investment policy. Reinsurance
Depends on existing arrangements including possible changes
and possible new arrangements The economic environment
Future inflation and interest rates increased moral hazard during economic recession Catastrophes
Difficult to make explicit allowance
Implicit allowance in future claims rates and loss ratios The insurance cycle
Take account of current position in the cycle and likely future movement
Subject 403 (UK Fellowship General Insurance) — April, Paper 1 — Examiners’ Report
2
Tax is payable at normal corporation tax rates on trading profit.Losses are carried forward to offset any profit in the following year.
Investment income and realised gains, but not unrealised gains, are included in the trading profit.
Differences relate to investment income, investment gains, overseas profit, technical reserves and depreciation
Level of reserves must be regarded as proper
Eligibility of certain reserves is often individually negotiated with the tax inspector
Inland Revenue can disallow a reserve if it feels that the insurer has been consistently over reserving in the past
Specific technical reserves:
Reported - allowed (case and statistical reserves) UPR - allowed as per company act accounts
AURR - allowed provided that it is justified statistically that the UPR is insufficient
IBNR - require statistical justification Claims handling expenses
- allowed for expenses which relate directly to claims reserves which are acceptable by the IR, and reserves for external claims expenses are allowable. Expenses relating indirectly to claims are not allowable
Equalisation reserves
- insurers are required to establish these reserves for certain classes of business. Statutory rules govern transfer to reserve (tax deductible) and transfers from the reserve (on which tax is payable)
Other catastrophe reserves are not allowable
3
(i) Exposure measure. Basic unit used by insurer to measure amount of risk.Usually over a given period eg vehicle year.
Risk Factor. A factor which is expected to influence the intensity of risk
Usually statistically backed
Rating Factor. A factor used to determine the premium rate charged. Measurable, verifiable, objective.
A risk factor or a proxy for a risk factor. (ii) Exposure Measure
EL: payroll (preferably) or man-hours-worked Marine hull: insured value
Subject 403 (UK Fellowship General Insurance) — April, Paper 1 — Examiners’ Report
Page 4
Risk factors
EL: Trade
Processes
Legal awards/judicial climate Safety and risk control standards Training standards
Management awareness/attitude Marine Hull: Miles travelled
Routes travelled Crew training/ability Management ability Vessel type
Vessel condition and maintenance Rating factors EL: Payroll Industry/occupation Location of workforce Materials handled Processes involved Deductible Past experience Marine Hull: Sum insured
Type vessel Flag of operation Classification society Deductible
Past experience
4
(i) (a) Excess of loss reinsurance:Cover for losses which exceed a defined amount up to an upper limit (usually)
Defined amount and upper limit may be indexed (stability clause)
Usually relates to individual losses but may be aggregate / catastrophe (b) Experience rating:
Premium for risk depends on claims in previous periods, or that period
Subject 403 (UK Fellowship General Insurance) — April, Paper 1 — Examiners’ Report (ii) Accident Loss Inflation Development Inflated Loss
year (000s) factor factor and to
claim developed layer
1996 300 1.09273 1.3 426,164 0 1996 600 1.09273 1.3 852,327 352,327 1996 900 1.09273 1.3 1,278,491 500,000 1997 400 1.0609 1.4 594,104 94,104 1997 700 1.0609 1.4 1,039,682 500,000 1997 800 1.0609 1.4 1,188,208 500,000 1997 500 1.0609 1.4 742,630 242,630 1998 350 1.03 1.5 540,750 40,750 1998 800 1.03 1.5 1,236,000 500,000 1998 400 1.03 1.5 618,000 118,000 1998 650 1.03 1.5 1,004,250 500,000
The total loss to to the layer is 3,347,811 (the sum of the last column). The experience-rated loss for the 1999 accident year = 3,347,811 × 1000
÷ (700 + 800 + 900) = 1,394,921
(iii) The attachment point is 500,000, which is 25% of the Sum Insured. LEV( 25%) = 80%
Limit + Attach is 1 million is 50% of the sum insured. LEV(50%) = 90%
Hence we are covering 90%-80% = 10% of losses. Therefore, the expected loss is:
% of loss we cover × loss ratio × premium per risk × number of risks
= 10% × 70% × 20,000 × 1,000 = 1,400,000
(iv) Method 1
- Credibility, number years, number claims - Is claims inflation appropriate?
- Are LDFs appropriate?
- Failure to capture individual variability in claim development Method 2
- Is the LEV curve appropriate for these risks? - Is the underlying LR reliable?
(v) Required return on capital 15%
Hence required return on premium = 15% ÷ leverage = 15% ÷ 2 = 7.5% Office premium = ( pure premium + fixed expense) ÷ ( 1 – commission and brokerage – var exp – profit load)
= (1,400,000 + 5,000/.5)/( 1 – 10% - 5% - 7.5%) = 1,819,000
Subject 403 (UK Fellowship General Insurance) — April, Paper 1 — Examiners’ Report
Page 6
Given the contract has a premium of 2 million:
Return on premium = 1 – loss ratio – commission and brokerage – var exp – fixed expense ratio
= 1 – 1.4/2 – 10% - 5% - 0.005/.5/2 = 14.5%
Hence, return on capital = return on premium × leverage = 14.5% × 2 = 29%
5
(i) Stabilise the technical result as some of the classes do have a volatile claim experience year on year.Limit the effect of catastrophes - in particular weather related claims on property business.
Limit the concentration of risk, for example: - flood or subsidence exposure
- overseas property if it is in an area prone to say hurricanes or earthquakes.
For this insurer gaining technical help wouldn’t be a reason to purchase insurance, but it would be a secondary benefit - particularly helpful in areas such as the rating of flood or subsidence risks, or if the insurer was looking to move into a new field such as health insurance.
If the class be large compared with the free reserves and other classes, the insurer may decide to set up some QS treaties.
By reducing the variance in claims payments, less risk capital is needed so more business can be written on a given capital base.
Reduce the risk arising from an individual class, for example: - too much DMI or Creditor which both have a link to the economy
- enable large risks to be accepted - e.g. commercial property The reinsurance may be perceived as good value.
(ii) In making a decision on what reinsurance to buy, consider: - the split of business - is there a need to spread the risk? - type of cover available in the market place
- the terms available in the market - the security status of the reinsurers
- the size of the free reserves - affects the level of retention - the availability of co-insurers
Household
Risks are mainly weather-related catastrophes e.g. storm and flood. There may be several layers of XL.
Some of the layers may not be 100% reinsured. Possibly aggregate XL if it can be obtained. Possibly risk XL on liability exposure. Commercial
Surplus based on the EML Risk XL
Subject 403 (UK Fellowship General Insurance) — April, Paper 1 — Examiners’ Report Motor
Layers of XL
Possibly quota share, but less likely Creditor
Risk is that there is an economic downturn and unemployment increases.
May choose to limit exposure via QS. Possibly will not have any reinsurance.
An option is to take out aggregate XL over a period of time - say 3 years. (difficult to obtain).
DMI
Risks are similar to Creditor - account is affected by a downtown in the economy, but in conjunction with falling house prices.
Again possibly QS to limit exposure.
6
(i) Costs must be allocated in proportion to the number of transactions, multiplied by their relative times.New business
Motor: £250,000 × 4 × 20000 = £192,308 4 × 20000 + 3 × 8000
Household: £250,000 − £192,308 = £57,692 Policy Servicing
Calculate total weights (in thousands):
Motor Household Inviting renewal 60 60 40 40 Process renewals 3(60 − 20) 120 2(40 − 8) 64 Endorsements 6 × 3.5 21 8 × 7.5 60 Total 201 164 Allocated cost: Motor: £700,000 × 201 ÷ (216 + 164) = £385,479 Household: £700,000 − £385,479 = £314,521
[This may be broken down as follows:
Motor Household
Inviting renewal £115,068 £76,712
Processing renewals £230,137 £122,740
Endorsements £40,274 £115,068
This information is not necessary for answering this part of the question, but it will be helpful in the next.]
Subject 403 (UK Fellowship General Insurance) — April, Paper 1 — Examiners’ Report Page 8 Claims Motor: £600,000 × 14 × 12,500 = £526,316 14 × 12,500 + 7 × 3,500 Household: £600,000 - £526,316 = £73,684 Total Motor £1,104,103 Household £445,897 Total £1,550,000
(ii) First estimate the number of movements, and the cost of processing those movements.
Renewals invited
There should be the same number as last year – the book is in
stationarity, and the premium rate rises will not affect policy numbers until the renewal is actually invited. Therefore they will cost the same as last year. That is £115,068 + £76,712 = £191,781. (Preserving decimal places in the underlying calculation.)
Renewals processed
This will be the same number as last year (as the same number were invited), reduced because of the premium rate rises. The reduction in motor is 15% and in household 12%. These will also be the changes in the cost.
Motor: £230,137 × 0.85 = £195,616 Household: £122,740 × 0.88 = £108,010
Total: £303,627
The actual numbers renewing will be (60,000 – 20,000) × 0.85 = 34,000 and (40,000 – 8,000) × 0.88 = 28,160, respectively.
Proposal Processing
There has been a 40% increase in advertising, and accordingly a 40% increase in quotations. However, the premium rate rises will have caused falls in the number that would otherwise have been accepted of 25% and 36%. The cost will be proportional, hence:
Motor: £192,308 × 1.4 × 0.75 = £201,923 Household: £57,682 × 1.4 × 0.64 = £51,692
Total: £253,615
Assume that the number of claims and endorsements are proportional to the average number of policies in force, measured by half the sum of the beginning and ending numbers. The ending numbers are:
Motor: 34,000 + 20,000 × 1.4 × 0.75 = 55,000 Household: 28,160 + 8,000 × 1.4 × 0.64 = 35,328
Subject 403 (UK Fellowship General Insurance) — April, Paper 1 — Examiners’ Report The average numbers therefore are 57,500 and 37,664 respectively. Endorsements Motor: 57,500 ÷ 60,000 × £40,273 = £38,595 Household: 37,664 ÷ 40,000 × £115,068 = £108,348 Total: £146,943 Claims Motor: 57,500 ÷ 60,000 × £526,316 = £504,386 Household: 37,664 ÷ 40,000 × £73,684 = £69,381 Total: £573,767
Note that this assumption is probably a poor one in respect of claims, as the actual claims handled include some from a number of years back, and only part of the total handling of this year’s claims. However, no information is given to enable a better one to be made.
Total processing costs are
£191,781 + £303,627 + £253,615 + £146,943 + £573,767 = £1,469,733 Increase this by 185/155 to allow for the postage, etc, cost, gives £1,754,197.
The advertising cost and the cost of staffing and running the call centre will all rise by 40%, giving (800 + 700 + 500) × 1.4 = £2.8 million. Other costs should not change, giving total expenses for 1999 of £1,754,197 + £2.8 million + £1,150,000 = £5,704,197.
(iii) We may expect earned premium to be half of last year’s, plus the same amount uprated for premium increases and reduced for the closing business in force.
Motor: 10,000 × (1 + 55 ÷ 60 × 1.1) = 20,083 Household: 5,000 × (1 + 35.328 ÷ 40 × 1.18) = 10,211
Total: 30,294
Assume that the investment income increases by 7% of 1998’s retained profit, to 3,070
Claims incurred should change in line with the average number of policies in force.
Motor: 17,000 × 57,500 ÷ 60,000 = 16,292 Household: 9,000 × 37,664 ÷ 40,000 = 8,474
Total: 24,766
Assume that there is no change in the dividend policy, that
Subject 403 (UK Fellowship General Insurance) — April, Paper 1 — Examiners’ Report
Page 10
be a constant proportion of gross profits, and we have the following profit and loss account:
Premium earned 30,294 Investment income 3,070 Total income 33,364 Claims incurred 24,766 Management expenses 5,704 Gross profit 2,894 Taxation 724 Dividend 500 Retained profit 1,670
(iv) The premium rate rises have served their purpose in that the
company’s profits have increased by about 46%. Whether or not this is now a satisfactory position depends on the company’s criteria.
Assuming a 50% solvency margin, which would not be unusual for a company of this type, then the gross return on capital is about 19%, which would generally be considered satisfactory.
It is important to realise that this is a transitional year. The stationary position will be more favourable, with higher earned premium and lower claims, which by themselves will add about £1½ million to gross profits.
Much depends on whether or not the higher lapse rates will continue beyond 1999. It may be that they will not, as policies now on the book are those who did renew or start after the rate rises. It may also be that competitors will be in a similar position and raise premiums, which should improve the company’s competitive position. If so, then advertising can be scaled back. As the extra advertising and the associated increase in the activity of the call centre cost £800,000 in 1999, this could be a significant source of future profit.
Faculty of Actuaries
Institute of Actuaries
EXAMINATIONS
September 1999
Subject 403 — UK Fellowship General Insurance
Paper One
You must answer this subject only,
you may not attempt another subject in the 400 series.
Time allowed: Three hours
INSTRUCTIONS TO THE CANDIDATE
1.
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.
2.
You must not start writing your answers in the booklet until instructed to
do so by the supervisor.
3.
Write your surname in full, the initials of your other names and your
Candidate’s Number on the front of the answer booklet.
4.
Mark allocations are shown in brackets.
5.
Attempt all 7 questions, beginning your answer to each question on a
separate 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 available
Actuarial Tables and an electronic calculator.
403(1)—2
1
(i) List the factors that need to be taken into account when moving from the expected losses to the theoretical office premium for an insuranceor reinsurance policy. [3]
(ii) (a) Make and justify assumptions for such factors for a commercial property insurance policy issued by a direct writer.
(b) Using these assumptions, calculate the theoretical office premium when expected losses are £1 million. You may ignore the impact of insurance
premium tax. [7]
[Total 10]
2
List the advantages and disadvantages of assessing statutory solvency requirements using the following methods:(a) a statutory minimum solvency margin determined as a proportion of written premium or a proportion of claims incurred,
(b) a risk-based capital approach which takes into account the risk profile of the business written and under which the solvency margin is
calculated as a proportion of the volatility of past profits. [8]
3
You are an actuary assisting the underwriter of a reinsurance company to price a motor excess of loss policy for £1 million excess of £1 million. You have worked out that the expected losses to the layer will be £450,000 next year. The reinsurance manager of the ceding company explains that his reinsurance purchasing budget is limited and asks if he could amend the cover so that an annual aggregate deductible of £150,000 is included. (This means that the first £150,000 of losses which would otherwise be recoverable under the policy will not be paid by the reinsurer.)(i) State the additional information you require to evaluate the impact of
the annual aggregate deductible. [3]
(ii) Discuss how you would estimate the revised premium assuming you had all the required information. You may ignore brokerage,
commission, investment income and expenses. [3]
(iii) State with reasons the effect on the appropriate profit loading of the
change. [2]
[Total 8]
4
Describe the main provisions in the United Kingdom for protecting general insurance policyholders in the event of their insurer not being able to meet its5
(i) You are a consulting actuary who has been advising the claims manager of a general insurance company on the feasibility of introducingstatistical methods for valuing outstanding claims as an alternative to individual case estimation, which the company currently uses to assess reserves on its private motor and employers’ liability business.
Set out the key points you would make in a report to the claims
manager outlining the advantages and disadvantages of each method of assessing reserves, the general requirements for the use of statistical techniques, and the problems which might be encountered. [15] (ii) The company’s managing director is newly appointed and has a
non-insurance background. He is concerned to know which financial
aspects of the company’s business are influenced by the claims reserves, and has asked for your views. Draft a reply. [Including 4 for drafting, 8] [Total 23]
6
A general insurance company intends to launch a range of personal accident products. It is intended that these be sold through direct mailing to “affinity lists” — that is, the insurer will market them to the customers or members of other organisations.(i) Outline the cover commonly provided under personal accident
insurance sold to individuals. [9]
(ii) Discuss the arrangements that will need to be made governing the relationship between the insurer and the affinity groups when selling products in this way. You should consider particularly the financial
arrangements. [5]
(iii) Discuss the pricing of this insurance. [9]
[Total 23]
7
Discuss the suitability of ordinary shares as a medium for the investment of the assets of a United Kingdom general insurance company. [23]Faculty of Actuaries
Institute of Actuaries
EXAMINATIONS
September 1999
Subject 403 — UK Fellowship General Insurance
Paper One
EXAMINERS’ REPORT
Faculty of Actuaries Institute of Actuaries
Subject 403 (UK Fellowship General Insurance) — Sept.1999, Paper 1 — Examiners’ Report
1
(i) Investment Income: Speed that losses are paid out (notincurred)
Speed that premiums are received *
Speed that acquisition expenses/overheads are paid *
Acquisition Expenses: Advertising cost/Sales commission etc Contribution to overheads
Profit Loading
The two points marked * were not generally picked up; others were more commonly picked up.
(ii) Investment income:
Assume interest=6% per annum
Current rate on short-term gilts Earned for 9 months
Losses paid fairly quickly in short-term class Premium paid on average mid way through year
Premiums typically ¼ly in advance, but delay with brokers Assume acquisition expenses of around 6%
Typical for direct writers
Assume contribution to overheads of 5%
paid at the same rate that premiums are received Profit Loading 10% of undiscounted premiums
With 50% solvency margin, amount to RoE of about 20%
Premium = £1, , * ( ( * ( 000 000 1 6%) 1 6%) 1 6% 5%) 10% 912 1 2 + + − − − − − = £1,252,203
This part was moderately answered, with more successful candidates generally going into more detail. Some candidates lost marks by not constructing the formula
appropriately.
2
It should be noted that many of the things listed below are double-edged, and can be advantages or disadvantages. For example, the difficulties over the definition of volatility are the other side of being able to allow for theparticular aspects of it that are considered most important. The marks should be given if the candidate appears to understand the issue, rather than for getting the classification “right”, in accordance with the list below.
(a) Advantages
Takes into account each company’s individual experience Simple to administer
Easy to verify Disadvantages
Penalises companies that hold adequate reserves Or charge adequate premiums.
Subject 403 (UK Fellowship General Insurance) — Sept.1999, Paper 1 — Examiners’ Report
Page 3 Does not distinguish between companies with similar levels of but different mixes of business
Including direct companies compared with pure reinsurers (b) Advantages
Recognises the volatility inherent in the business Penalises companies that are poorly reserved Or have inadequate premium rates.
May take asset risk into account
And other types of risk – credit risk for example Disadvantages
Practical difficulties of deciding: Definition of profit
Definition of volatility
Should it depend on company or industry experience? Period over which to measure volatility
How to allow for reinsurance and reinsurer security
Whether or not same proportion should be applied to the volatility of all companies.
This question was generally well answered.
3
(i) We need an idea of the variability of the result. This was the only part of the question that most candidates answered. Few gave valid examples or explanations. For example, do we believe it will be between £400,000 and £500,000 with absolute certainty, of is there a 45% probability of a complete loss, with no other result possible? The former will reduce expected losses by £150,000 a year, the latter by only £67,500. We need to express the losses as a random variable with mean £450,000.(ii) The impact on the expected loss amount is the difference between the expected loss of the random variable and the expected loss of the random variable capped at the amount of the aggregate deductible. In statistical notation the expected losses after the annual aggregate deductible = E[Losses] – E[Losses;AAD]. E[Losses;AAD] <=AAD with equality only when the standard deviation of the distribution is zero. This part of the question was not generally answered in detail, and few candidates gained many marks.
(iii) The amount of money that could be lost as downside risk is the same before and after the aggregate deductible, but will be higher as a proportion of premium, so the percentage loading for profit should be higher.
Overall, this question was not well answered. Candidates failed to go into sufficient detail.
Subject 403 (UK Fellowship General Insurance) — Sept.1999, Paper 1 — Examiners’ Report
4
For individuals insured under a policy written by an insurance companyauthorised to underwrite business in the United Kingdom, protection is provided under the Policyholders Protection Act and administered by the Policyholders Protection Board. The Board will pay 100% of a valid claim under a compulsory type of insurance (such as motor third party liability), or 90% under other classes, less what the insurance company is able to pay. This is financed by a levy of up to 1% per year on the written premiums of all insurers authorised to write business in the United Kingdom. Protection is limited to private people, not companies.
If a Name at Lloyd’s defaults on his obligations, policyholders may be
reimbursed from the Central Fund. This is financed by an annual levy on the authorised premium limit of each Name. The levy is set at such a level that it will be expected to be sufficient to cope with any defaults that may occur in the coming year.
This question was generally well answered, although many candidates did not supply enough points of detail to get as many marks as they might have done.
5
Overall, this question was moderately well answered. Most candidates gained areasonable number of marks, but many omitted important points of detail. The area covered below under Statistical Estimation was especially sparsely covered. Part (ii) was generally adequately answered, although the four marks available for drafting showed wide variations, with the quality of work varying widely.
(i) The following points should be made: Case Estimation
Advantages
Allows for facts and circumstances of each claim.
Can allow for variability arising from small portfolios, large claims, random variation.]
Provides early indication of trends in the experience Past history is not required.
Disadvantages
May be insufficient data when received to make accurate estimate of claim.
Does not allow for IBNR, reopened claims or late development Administration costs may be high
Requires consistency from claims handlers.
Sensitivity testing is not possible as some assumptions such as future inflation may be implicit.
Statistical Methods Advantages
Subject 403 (UK Fellowship General Insurance) — Sept.1999, Paper 1 — Examiners’ Report
Page 5 Can use explicit assumptions
Methods may disclose trends in numbers and amount of claims Methods may be easier to understand and explain
Disadvantages
Past experience may not be repeated in the future, because of Changes in policy terms and conditions
Changes in portfolio mix
Changes in reporting and settlement patterns Changes in law or court awards
Industrial action / other delays affecting settlement speed Changes in taxation
Changes in market environment – e.g. end of knock for knock Changes in size of account
Distortion because of large claims, nil claims, part payments Need to estimate tail factor
May need to advise reinsurers of large claims outstanding. General conditions for statistical estimation to work: Large number of outstanding claims in these classes
Pattern of settlement numbers and amounts reasonably stable Data has been collected for a number of years (five at least) No major changes in portfolio mix
No large claims which cannot be identified and treated separately Element of uncertainty in claim estimation
e.g. private motor injury where liability amount may not be settled for years
The possibility of hybrid systems – statistical estimation for all claims not more than two years old, or not assessed as being large, and case assessment for these – should be mentioned.
(ii) Premium rates
The underwriting profit
Deferment or acceleration of tax on profits The amount of dividends declared from profits
The visible solvency margin and hence the amount of free assets. Reinsurance renewal negotiations
6
This question was poorly answered. Few candidates gained more than 1 or two marks on either part (i) or part (ii). There seemed to be little knowledge in depth of how policies of this nature are designed, although it is a standard type of policy.(i) Cover is normally of fixed amounts. That is, when an insured event occurs, a set level of benefit specified in the policy is paid, rather than an indemnity amount. Cover may be for lump sum benefits, usually paid only in the event of permanent injury or death, or regular income payments. Often policies are offered in multiples of a fixed sum assured – say £50,000.
Subject 403 (UK Fellowship General Insurance) — Sept.1999, Paper 1 — Examiners’ Report There are two main outcomes in respect of which claims are paid: death and personal injury. A policy may cover either, but more normally both. The injury must be suffered in an accidental event – the normal policy wording is that it must arise from violent, visible and external means. A policy which provides benefits on death or injury will normally limit the total benefit which may be payable. For example, if a claim is paid in respect of a serious injury, which then leads to death, the death benefit will normally be reduced by the amount already paid.
Cover for injury is normally on what is known as a “continental” scale. This is, that the full benefit will be paid out on the most serious
injuries, such as paraplegia, the loss of by amputation or the complete loss of use of at least two limbs, or complete blindness. Lesser injuries will give rise to smaller payments, and there may be a detailed list ending with a small payment in the event of the loss, for example, of a single toe. Normally only the worst single injury to a particular insured person from one accident will trigger payment, but if there were two separate injuries in different parts of the body both might be payable, so long as the total claim was within the policy maximum.
It is usual for a full sum insured to be payable upon death, but this is not necessarily the case if the main intent of the policy is to provide for care or rehabilitation for an injured person. On the other hand,
providing a lower sum insured may cause difficulties if somebody dies after becoming seriously injured. One exception is with children, in respect of whom death benefits are usually limited to the cost of a funeral, while the costs of care and rehabilitation are likely to be just as great as for adults.
Regular income payments may be made while the insured is completely disabled (usually to the extent of being unable to work) until he
recovers, or possibly, if only permanent disability is covered, from the date that the disability was agreed as permanent, until, say, the insured’s 60th birthday. Sometimes it will be stipulated that no payments will be made before, say, two years after the accident, to allow the condition to stabilise.
Another possibility is that income payments will be made on a daily basis as long as the insured is in hospital as the result of an accident. The availability of reinsurance may be an important factor in
determining precisely what benefits may be offered.
(ii) Almost all candidates answered the points that have been underlined, but very few got any others . The arrangements will need to be
negotiated separately with each affinity group. Some will view it as a major income-producing exercise, others as a service to members. The level of commission, and therefore the gross premium, will vary
Subject 403 (UK Fellowship General Insurance) — Sept.1999, Paper 1 — Examiners’ Report
Page 7 There are two basic arrangements that could be made. The first is that the insurer would pay the affinity group for the use of its mailing list. The second is that the affinity group would receive a commission on each policy sold. A hybrid is also possible, in which some up-front payment is made and some commission, although at lower levels than if they were the sole way the affinity group were paid. Which is chosen will depend to some extent on the affinity group’s attitude to risk. It would be normal for the insurance company to pay the costs of the mailing, if a dedicated mailing were used. If the marketing material for the insurance is to be included in one of the affinity group’s regular mailing to its members then the insurer may be expected to pay a contribution to the mailing costs, plus the production cost of the marketing material for the insurance.
The affinity group may carry out some of the necessary policy administration. This will affect the financial arrangements in each case.
It is normal for an agreement to be made preventing the insurer from soliciting any more business from customers it has gained through the affinity group mailing, without the group’s permission.
(iii) This was rather better answered than the other parts of this question. Most candidates got around half of the points available. It will be
difficult to estimate loss costs from the insurer’s own records, even if it does already underwrite business of this type, because of the very low claim frequency. In this case, external sources of data may be more helpful. Assistance should be relatively easily obtainable from reinsurers, or government accident statistics. Loadings or discounts may be required in respect of the occasional affinity group which
presents high risks –a skiing club, for example, but a sensible guess may be sufficient in these cases. The price at which business may be
reinsured will to a significant extent govern the price that can be charged.
The difficulty comes in pricing for expenses. The collection of
premiums may be a variable factor between different affinity groups. At one extreme, the insurer may be responsible for initiating and collecting direct debits; at the other end of the scale the affinity group may collect all premiums with its membership fees and pass them to the insurer with a bordereau. The former could be costly to the insurer and the latter very cheap – the actual costs for each project should be costed in in each case.
The costs of mailing will need to be recovered. To estimate the loading required, we will need to consider the following three items:
• The cost of the mailing (including any up-front payment for the right to mail to the list);
Subject 403 (UK Fellowship General Insurance) — Sept.1999, Paper 1 — Examiners’ Report • The expected lapse rate of policies in force.
These items will need to be estimated from the insurer’s experience of such schemes. From the second we can estimate the number of policies expected to be written; divided into the first it gives the sum to be recovered from each policy. At this point we must add the cost of fulfilling the policy and setting it up, including any free gifts offered as part of the promotion. The third item may be used to work out the number of months or years the policy is expected to be in force, which may be used to derive the annual or monthly loading per policy. The lapse rate is likely to be affected, inter alia, by the way the premium is collected. A high visibility collection method, such as monthly by credit card, may make the insured think about cancelling each month. A low visibility method, such as the affinity group collecting it along with normal payments, may lead to a lower
cancellation rate. An annual collection gives a much higher premium to be paid, which may lead to low renewal rates, but leaves the policies that do renew in force for a whole year. This is something that must be considered afresh for every mailing.
When these elements are added together, loadings for profit and the agreed commission should be added. The resulting gross premium should then be reviewed – if very high or very low, the penetration assumptions may need to be revisited. However, the product is probably not very sensitive to the insurance cycle.
A typical formula for a monthly gross premium might be: £C £P £M
(1 p c)
+ +
− −
Where: £C is the expected monthly claim cost £P is the expected monthly processing cost
£M is the required monthly contribution to marketing cost p if the proportionate contribution to profit and overheads c is the agreed commission rate.
7
This question was moderately well answered. The areas that were generally known and understood are the need for matching in various ways, and the unsuitability of equities for most insurance liabilities on this criterion, the possibility of a degree of matching of longer tailed liability claims through equities, and the statutory solvency and admissibility implications. It was quite common for candidates to point out the liquidity drawbacks of equities.The objective of an insurance company’s asset selection strategy should be to maximise its investment return, subject to the overriding requirement to meet its obligations to policyholders and being able to maintain the required
Subject 403 (UK Fellowship General Insurance) — Sept.1999, Paper 1 — Examiners’ Report
Page 9 In general, over the long term, ordinary shares have tended to give a higher investment return than most other forms of investment available to general insurance companies. However, the value of shares often fluctuates sharply from day to day, and it may be difficult to sell significant quantities of shares at short notice without affecting the market. This would be especially true if the insurance company concerned were a large prominent one.
This gives rise to two particular problems for an insurance company wishing to place significant amounts of its funds in ordinary shares. Firstly, if the value of shares falls significantly, current valuation regulations, which require insurers to value their assets at market value, will mean that the company must reflect the fall in value in its assets in its statutory returns. In an extreme case, this could lead the company to become technically insolvent, even if it were satisfied that the income-producing potential of the assets was undiminished, and that the expected income remained enough to fund the liabilities. This might be countered to some extent by discounting liabilities to reflect the higher yield implicit in the assets’ lower price, but the ability to do this is constrained by regulations, and to introduce discounting at a time of market stringency might be seen as a sign of weakness by brokers and
regulators. Also, since the term of liabilities tends to be shorter than the term of ordinary shares, the solution could only be partial in any case. These points are important, but very few candidates commented on them.
The second problem is that if a company has a large proportion of its assets in equity shares, it may find it difficult should it become necessary to realise large sums of cash, for example to fund claims following a catastrophe. This would not be the case if the company’s assets were held in short term deposits or gilts, for which there is a large, highly liquid, market.
The usual investment principles that allow an insurer to be able to meet its liabilities are that assets should be matched to liabilities by term, nature and currency. In general, equity shares, which have no redemption date, are not well matched to insurance liabilities. These generally have a mean term of only a few years, even on long-tail classes, with reducing amounts being expected to be paid in successive future periods. In short-tail classes the average term of the liabilities may be only a few months. Only a small
proportion of claims, such as those arising from asbestos and pollution losses, have terms which are measured in decades rather than years, and may more appropriately be matched by equities. Significantly, these are the types of claim for which the discounting of reserves is likely to be most acceptable to the market.
Matching by nature means comparing whether assets and liabilities are
defined in nominal terms, or affected by inflation after the balance date. Short tail claims may be affected by inflation, but with only a short period to
payment the level of uncertainty involved is unlikely to be significant, and will not justify investment in equities. Long-tail classes are usually liability or casualty insurance, and are greatly affected by inflation. In addition, they are often affected by what is sometimes known as “judicial” inflation, which is very hard to predict. Since dividends on equity shares are paid out of profit, which is derived from doing business in current money, they may be expected to rise
Subject 403 (UK Fellowship General Insurance) — Sept.1999, Paper 1 — Examiners’ Report with inflation, and to form a reasonable hedge against it. Therefore it may be sensible to hold equities against some of the longer-dated liabilities in these classes. The hedge is not perfect – few companies will have profits that are linked to judicial inflation – but it is better than most other asset types can offer. On the other hand, an unexpected burst of inflation will probably give rise to an increase in interest rates, which may lead to a rise in the yield from equities, giving rise to a fall in prices. This would exacerbate the problems of valuation at current market values, and of liquidity in the case of a sudden need for cash.
The question of matching by currency is a complex one. An equity share will be denominated, and its dividends paid, in a particular currency, but the underlying exposure will be to the currencies in which the company issuing the share does its business. A multinational company’s shares represent an investment in a number of currencies, which may or may not be a good match with the insurance company’s liabilities. This is a question that would require a detailed review. Most candidates got the simple point at the start of this paragraph, but almost none pursued the greater complexities.
There is also a danger of correlation between a company’s insurance risks and its investments. For example, a major eartquake in a large city might cause a large fall in local stockmarkets and a significant fall in worldwide ones, just at a time when assets needed to be sold to pay claims. Very few candidates commented on this.
A further problem exists in that a single company’s equity may be taken into account for the purpose of asset values in the statutory returns only up to 2½% of the insurer’s general business amount. This means that holdings have to be spread quite widely in order all to be admissible, and there is always a possibility that if the value of shares of which an insurer owns a large amount appreciate substantially then the company will be restricted in the amount of the appreciation in its shares it can take into account in the valuation. This point was generally well understood.
In summary, equity shares may give a better return than most of a company’s other likely asset choices, but a large holding may be a poor match for its liabilities and endanger its solvency and its ability to meet liabilities. A large solvency margin does give the company a cushion for this problem and allow it to make some investment in equities. However, shares are unlikely to form a large proportion of a general insurer’s investment portfolio for these reasons. The average for the largest United Kingdom insurers is about 15% to 20% of total assets, and is significantly less than their level of free assets, so that even a substantial fall in the value of these assets would not lead to technical
Faculty of Actuaries
Institute of Actuaries
EXAMINATIONS
April 1999
Subject 403 — UK Fellowship General Insurance
Paper Two
You must answer this subject only,
you may not attempt another subject in the 400 series.
Time allowed: Three hours
INSTRUCTIONS TO THE CANDIDATE
1.
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.
2.
You must not start writing your answers in the booklet until instructed to
do so by the supervisor.
3.
Write your surname in full, the initials of your other names and your
Candidate’s Number on the front of the answer booklet.
4.
Mark allocations are shown in brackets.
5.
Attempt all three questions, beginning your answer to each question on a
separate 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 available
Actuarial Tables and an electronic calculator.
Faculty of Actuaries
1
You are an actuary working for a general insurer with a large household account which currently uses only location as a rating factor on both buildings and contents. You have been asked to carry out a rating exercise for thisbusiness. Explain how you would go about this with particular reference to the following:
• collection and checking of data
• adjustments you would make to the data • the modelling approaches available
• calculation of the theoretical office premium • appropriate rating factors, and
• establishing the market premium [50]
2
You are the actuary of a United Kingdom general insurance company which writes many classes of insurance business through a broker network. A new director has recently joined the Board of Directors. Before his appointment, the director had little experience of the general insurance market, but did have some accounting experience. You have been asked to explain certain aspects of general insurance business.Draft a report to the director explaining the concept of accumulations of risk, illustrating your answer by reference to the following three classes of business written by the company:
(a) Mortgage Indemnity Guarantee (b) Domestic Household
(c) Employers’ Liability [15]
[Includes 2 for drafting]
3
It is January 2001, and you are the actuary in charge of reserving for an insurance company that writes commercial insurance of all types, originating mainly in the United Kingdom and the United States of America. Business is written directly rather than as reinsurance, and, when coinsured, the company has normally acted as the lead underwriter.During 2000, the company received a large number of claims arising out of the widespread failure of computer systems which occurred at the start of the year. The claims that have been received generally fall into one of the following categories.
Companies that have found themselves unable to operate because of the failure of their computer systems have claimed the costs of rectifying the systems under their fire policies (which are all-risk covers).
These companies have often also claimed compensation under the business interruption section of their fire policies for loss of profit and other expenses.
403(2)—3
Companies that have been unable to fulfil their obligations to customers have claimed the cost of compensating them under their general liability policies. Companies that sold products that failed at the start of 2000 have claimed the cost of replacement, modification, or compensation for consequential loss, including compensation for personal injury, under their products liability policies.
Companies whose equipment has failed, injuring employees as a result, have claimed the costs of compensating them from their employers’ liability policies.
Companies whose systems have failed have sued their external software suppliers, who have notified claims on their professional indemnity policies. Companies whose systems have failed have received suits against directors and officers from aggrieved shareholders, and these have been notified as claims on their Directors and Officers cover.
Companies which have suffered because of the failure of systems at their customers or suppliers have received suits against directors and officers from aggrieved shareholders, alleging that their oversight of these problems was inadequate, and these have been notified as claims on their Directors and Officers cover.
(i) Discuss the possible defences that the Company may have against these claims, irrespective of any specific exclusions. [17] Almost all policies renewed with commencement dates in 1999 had a specific clause included preventing any claims from causes associated with this problem. This was continued with renewals during 2000. Any claim on a policy with this exclusion has been rejected. A number of the claimants concerned have commenced lawsuits against the Company alleging that this exclusion is invalid. You anticipate that more will be launched if any of these is successful. Your legal advice is that the exclusion will probably be deemed to be valid in the United Kingdom, but that the position is far less clear in the United States. The Claims Department has left all these claims open, but has set a nil reserve.
(ii) Discuss your approach to setting reserves as at 31 December 2000 for
claims arising from this problem. [18]
Faculty of Actuaries
Institute of Actuaries
EXAMINATIONS
April 1999
Subject 403 — UK Fellowship General Insurance
Paper Two
Subject 403 (UK Fellowship General Insurance) — April 1999, Paper 2 — Examiners’ Report
Page 2
1
This was a fairly straightforwardquestion regarding a premium rating exercise for a well known line of business. The question had been worded to direct the candidate into making points on particular aspects of the rating exercise.On the whole this question was answered better than the other two. However, some candidates produced far too much information and so ran out of time for the remaining questions. Most candidates scored good marks on the basic points as listed in the core reading. However, some candidates went little beyond the basic points and hence their solutions did not focus on the particular problem being set. Most candidates failed to mention the modelling approaches available other than referring to additive and mulyiplicative models.
Internal data
Split data between buildings and contents policies
Compile data over past, say, 5 years (consider a trade-off between how out-of-date the data is, and whether or not it is fully run off).
Claims and exposure data must have a link between them so that they can be matched together.
Claims data should include amounts and dates of payments, identify the peril and include any unpaid reported claims.
Make sure that the exposure identifies any changes in cover or risk details over the period.
It is generally fairly common to use accident year as the definition of year -although this experience will have policies written in more than one rating series, the claims experience is better developed than that of an underwriting year.
Decide on your measure of exposure - normally sum insured or number of bedrooms.
Establish whether or not the claims data includes claims handling expenses (both internal and external).
Data checks / exploratory initial analysis
Large claims – take account of the peril. A large claim on one peril could be an average-sized claim on another peril.
Reconcile claims and exposure data with another source of data such as management accounts.
Is the claims experience unusually light or heavy in respect of any particular year? Did you expect the data to show this or are there claims missing from the data set?
Carry out spot checks on the data at individual policy level – are the claims and exposure data correct?
Ensure that new business and lapses in a year contribute the correct amount of exposure to the calendar year.
Do you have good data for all the potential risk factors you want to investigate?
Coding of the data - is the coding of data for potential risk / rating factors reasonable? Are these fields well-populated?
Subject 403 (UK Fellowship General Insurance) — April 1999, Paper 2 — Examiners’ Report External data
Consider the possibility of augmenting the internal data with external data . For example, if data by peril is sparse, market data will give useful support to the insurer’s own data.
Reinsurers or external data providers may be able to provide other data to help in the assessment of the risk. For example: crime statistics; flood assessment systems.
Competitors’ rates will be needed for comparison, to assess the likely volume of sales. In this regard, it is necessary to compare the terms of the cover offered, the level of risks underwritten, and whether differences in structure explain differences in loadings for expenses and profit. Also consider the time period of this data.
ABI data to assess trends in, for example. fire and theft claims. Adjusting the base data
The base data may need to be adjusted to allow for: - changes in risk or cover
- trends in experience
- the large claims you have identified Allowance needs to made for any IBNR claims.
You may also want to adjust for unusually heavy or light experience or, alternatively, you can make an adjustment to the calculated risk premium after the base data has been modelled.
Consider trends in the claims experience.
Consider any inadequencies in the adopted estimates. Adjusting the base risk premium
Allow for expected inflation in claims from the base period to the period over which the policies will be in force.
Allow for changes in the expected average sum insured, or other way exposure is measured.
Also allow for any expected changes in cover or policy terms and conditions. You may make the adjustment here for trends in claims experience - consider frequency and severity separately.
Subject 403 (UK Fellowship General Insurance) — April 1999, Paper 2 — Examiners’ Report
Page 4
Modelling the experience
Construct separate models for buildings and contents.
Consider whether certain perils should be investigated separately. There are three broad approaches available:
- model claim frequency and average claim amount separately, using a stochastic approach for each
- model claim frequency stochastically and apply the expected claim amounts which have been obtained deterministically - model aggregate claim amounts deterministically
Additive / multiplicative modelling will be investigated.
Suitable probability distributions might be Poisson for frequency and lognormal or Pareto for claim amounts.
Parameters required by the distributions are estimated, and statistical methods are used to test their goodness of fit.
The stochastic models would be run a number of times to show the distribution of the modelled results. These will then form the basis of the risk premiums A generalised linear model can be used to investigate the potential rating factors.
When looking at possible rating factors, the current market factors should be considered together with other factors which it is felt could be used in practice in the market place. The number of factors which can be investigated is very dependent on the amount and reliability of the base data.
Possible rating factors which could be investigated are : policyholder age
property type property age
presence of NHW / alarms / locks location
However, some factors which are important for buildings may be unimportant for contents, and vice versa.
Calculating the theoretical office premium Make adjustments to allow for:
- expenses & commission,
- investment return (i.e. income and capital growth where
relevant) ( allowing for how the business is sold and whether it is paid on an annual or a monthly premium),
- profit, and
- cost of reinsurance (this should cover the net cost of purchasing reinsurance).
Subject 403 (UK Fellowship General Insurance) — April 1999, Paper 2 — Examiners’ Report This can be done by either:
- a fixed percentage to the risk premium rate, or
- a more detailed adjustment allowing for fixed and variable
expenses which allow for the size and nature of the business. The fixed expenses could be allowed for by margins in the premium calculations.
Initial expenses are generally incorporated into the overall level of expenses based on the assumed level of new business and its expected duration.
If discounts are given for certain groups of policyholders then you need to ensure that the policy expense loadings are still met. This can be achieved either by increasing the fixed loading in the formula to allow for the average level of discount, or by charging a separate policy fee to cover fixed expenses with no discount applying to the fee. Generally the policy fee approach is not taken in practice as it seems unacceptably high to policyholders compared with the cost of the risk.
Consider minimum premium - cost of some risks may be very small and you want to charge a little bit extra to at least cover a small contribution to fixed expenses. This can be done by applying a minimum sum insured (also helps to prevent under-insurance by policyholders).
Consider whether there are any other rating factors which you want to be taken forward into the rates, but for which you don’t currently have data on the factors. If they are to provide a discount then an adjustment would be required to the base rate if the discount is to be funding neutral.
Alowance for Insurance Premium Tax to be made.
Consider any loading to be applied if policyholders choose to pay by instalments.
Finally, having calculated a theoretical premium for each risk, a market competitiveness analysis should be done, and premiums are likely to need to be adjusted.
2
Most candidates failed to score sufficient marks as a result of not illustrating in detail the concept of accumulation of risk with reference to the three classes of business given. Instead many candidates wrote too much on issues which were not being asked about in thequestion.
This report explains the concept of accumulations of risk within the general insurance market.
An accumulation of risk is the possibility of an occurrence of many claims arising from one event or a series of connected events. The events which are likely to give rise to an accumulation vary by classes of insurance written and can be best illustrated by the following examples.
