EXAMINATION. 8 April 2005 (pm) Subject ST3 General Insurance Specialist Technical. Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE

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1 Faculty of Actuaries Institute of Actuaries EXAMINATION 8 April 2005 (pm) Subject ST3 General Insurance Specialist Technical Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 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. 4. Mark allocations are shown in brackets. 5. Attempt all 8 questions, beginning your answer to each question on a separate sheet. 6. Candidates should show calculations where this is appropriate. AT THE END OF THE EXAMINATION 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 the 2002 edition of the Formulae and Tables and your own electronic calculator. ST3 A2005 Faculty of Actuaries Institute of Actuaries

2 1 You are the actuary to a general insurance company which writes only employers liability insurance. List the data you require to carry out an assessment of the appropriateness of the risk premiums. [8] 2 You are the general insurance actuary for a small insurance company which writes only coach fleet and car fleet commercial motor insurances. Describe the differing claims characteristics of these two types of fleets. [7] 3 Explain the importance of relevant, accurate data for a general insurance company underwriting private motor insurance. [8] 4 You are the general insurance actuary to a company which writes only commercial property insurance. Describe the following characteristics of this class of business: (i) purpose and benefits [2] (ii) perils covered [1] (iii) exposure measure [1] (iv) claims [4] (v) rating factors [2] [Total 10] 5 You are the Chief Actuary working for a general insurance company that writes only commercial property business. The Board has indicated that it wishes to take over a similar company with whom your company is in direct competition, but has not yet made any formal approach. Outline the major actuarial investigations that you would undertake in order to assess the viability of this proposal. [10] ST3 A2005 2

3 6 You are an actuary working for a small, general insurance company that specialises only in long-tailed insurance risks in its local insurance market. The company has a moderate level of free assets. The Board, who require a risk averse investment strategy, has asked for a review of the investment guidelines given to the company s investment managers. It is assumed that there are no regulatory investment restrictions. (i) Outline the instructions that would be given to the investment managers in respect of the assets that they may or may not hold, including any relevant limits. [6] At a recent Board meeting, one of the members suggested that, given the long-tailed nature of the risks insured and the current low historic level of the stock market, the equity proportion of the investment portfolio should be increased to benefit from future stock market increases. (ii) Explain the advantages and disadvantages of his suggestion for the company. [6] Another Board member has suggested increasing the proportion invested in indexlinked Government bonds. (iii) Explain the advantages and disadvantages of this suggestion compared with that given to the previous Board member. [4] [Total 16] 7 A global relief agency provides humanitarian assistance to victims of natural disasters in poor countries around the world. It is looking into its sources of funding for large natural disasters and is thinking of buying a catastrophe insurance policy. The policy pays out a fixed sum of $100m if a large natural catastrophe leads to more than 500 deaths during the term of the policy. The premium for the policy is likely to exceed $10m per annum. (i) (ii) (iii) Discuss the advantages and disadvantages to the relief agency of purchasing such a policy. [5] Discuss the advantages and disadvantages to the Insurer of writing such a policy. [4] Two different insurance providers are competing to write this policy. Company A thinks that the number of such events has a Poisson distribution with Poisson parameter of 10%, while Company B estimates the Poisson parameter to be 8.33%. Company A requires a return on capital of 10% while Company B requires a return on capital of 15%. Both companies allocate capital to this contract using the same methodology. The amount of capital is set to ensure that the probability of ruin for this contract on a standalone basis is less than 10%. Using approximations where appropriate, calculate which of the two companies will have the higher premium. [9] [Total 18] ST3 A PLEASE TURN OVER

4 8 You have just been appointed as the actuary to a small general insurance company which writes two classes of business, A and B, throughout the territory. All business is written through insurance brokers. The only financial information you have been presented with is shown below. All figures are as at end Class A Gross written premium 1, Net written premium Net earned Premium Claims (all after reinsurance recoveries) Paid total to date Current case estimates IBNR/IBNER Total claims cost Expenses Commission Investment return Profit Class B Gross written premium 1,000 1,250 1,500 1,750 Net written premium 950 1,188 1,425 1,662 Net earned Premium 950 1,069 1,306 1,543 Claims (all after reinsurance recoveries) Paid total to date Current case estimates IBNR/IBNER Total claims cost 690 1, ,120 Expenses Commission Investment return Profit 40 (486) 23 5 (i) Comment on the financial characteristics (including financial trends) of each of the classes of business the company writes, using any appropriate financial ratios. [14] (ii) State, with reasons, which classes of business A and B are likely to be. [4] (iii) Describe the issues the company will face in the short term and any actions you would recommend. [5] [Total 23] END OF PAPER ST3 A2005 4

5 Faculty of Actuaries Institute of Actuaries EXAMINATION April 2005 Subject ST3 General Insurance Specialist Technical 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 28 June 2005 Faculty of Actuaries Institute of Actuaries

6 Subject ST3 (General Insurance Specialist Technical April 2005 Examiners Report 1 This question asked candidates to consider the risk premium. Those who spent time talking about expenses, commission etc did not gain marks for such comments. On the whole though this question was answered very well. Policy Data For each policy Dates on cover Dates of endorsements and change in cover All rating factor details: Trade / Industry / Occupation Turnover Number of employees Health and safety policies Source of business Materials handled Processes involved Location Payroll Exposure Cover / exclusions Limit of indemnity Past claims experience Size of deductible Details of risk premiums charged, may need to be a proxy Claims Data Date of occurrence Date claim reported Date of re-opening Dates and amounts of payments Estimates, if they exist, of amounts outstanding Rating factor details as they were at the time of the claim and/or Link to policy information Type of claim, i.e. injury or disease Type of peril Page 2

7 Subject ST3 (General Insurance Specialist Technical April 2005 Examiners Report Dates of settlement Other data Industry statistics to back up own data where it is sparse Changes in underwriting / claims handling / policy conditions Inflation statistics for wage inflation, court award inflation and care inflation Information about any legislative changes which will have impacted in past and any that may impact future experience 2 This question asked for the differing claims characteristics. Many candidates listed claims characteristics without identifying how they differed between the two types of business. Some candidates also described claims characteristics and then said that they would be similar. Neither of these approaches would have gained many marks if any. Coach fleet may take longer to settle small claims as the insured may be unwilling to take a coach out of service to rectify minor cosmetic damage. This will depend on how busy the company is. Lower theft claim frequency likely for coach fleet Overall claim frequency could be higher or lower depending upon circumstances, e.g. mileage travelled, area driven, area kept. If a coach fleet has a total loss this will be a large claim. Also if all coaches are stored together overnight there is potential for an aggregation of risk, e.g. fire. This is less likely to be a risk for a car fleet. Leads to a more skewed claims cost distribution. Average claims size of coach fleet third party property damage claims will be higher than for a car fleet. This will include some total losses in respect of third party vehicles. Hence settlement delays will be greater for coach fleets. For a coach fleet there is a potential accumulation of risk There will generally be fewer vehicles per fleet for coaches and hence more random claims experience. Page 3

8 Subject ST3 (General Insurance Specialist Technical April 2005 Examiners Report Likely to be more overseas exposure for coaches and hence possible notification delays and currency issues. Fewer small claims for coaches as generally higher excesses on the policies. May be different legislation impacting upon coach passenger claimants compared with car fleets. If a coach was full of passengers and had an accident could be many individuals hurt or killed which could lead to much larger claims than if a car had a similar accident. Dealing with such a coach claim would take a long time and be very expensive. Again if a coach hit another vehicle it could do more damage than a car and so bodily injury claims are more likely and likely to have a higher average cost. 3 There were many points that could be made in the solution to this question. Several candidates however concentrated on the issue of over / under charging and effect upon expenses. Hence they missed out on several of the other points. Marks for this question were generally very low. Policy, claims and expense data are essential for reserving to ensure sufficient funds are retained to pay future claims and to highlight any concerning trends This is also likely to be required for insurance Regulatory purposes, accounts or otherwise both to satisfy reserving requirements and to demonstrate that the company is run in a sound manner, e.g. with regards to investment strategy, capital use and planning. Similar data is also required for pricing to ensure that there is no adverse selection and to aim to maximise profits. More accurate / complete data enables better pursuit of these goals Relevant, accurate data is required both for assessing appropriate levels of reinsurance and to provide to reinsurers in order to maximise the chance of obtaining the desired cover for an appropriate premium. Such data is also required for persistency, portfolio movements and quote strike rate management information to assess the business you have on your books at any particular time. In a competitive market such as motor, improved data can give the edge in terms of more accurately pricing risks to win more profitable business and help avoid the less profitable categories. Without relevant accurate data, poor underwriting decisions become more likely Page 4

9 Subject ST3 (General Insurance Specialist Technical April 2005 Examiners Report Customers will not appreciate providing irrelevant information and will not want to take the time. So the company must restrict info requested to just the minimum to enable underwriting, in order to ensure volumes of business are optimised. Exclusions / Excesses must be recorded correctly to ensure that the correct policy cover information is applied in the event of a claim. This information underpins management decisions. Poor data may result in poor decisions being made Relevant, accurate information may help to prevent fraudulent behaviour 4 This question was generally well answered with some candidates scoring nearly full marks. Purpose is to indemnify the policyholder against loss or damage to their commercial property e.g. office, shop, factory. In addition there may be business interuption cover Benefit is the amount indemnified for loss or damage subject to limits or excess. Perils covered are fire principally but also including explosion, lightning, theft, storm and flood. In addition there may be business interuption. Exposure used is the sum insured year however there are two complications: Stock amounts may fluctuate considerably. Stock may be covered on a declaration basis, determined retrospectively with an adjustment premium. No standard way of allowing for inflation in the policy. Claims characteristics Claims arise from sudden and determinable events (except subsidence) Notification delays are short apart from subsidence Different inflation rates affect buildings, contents and business interuption sections Possible accumulations owing to location Generally low claim frequency compared with other property insurance Many claims likely to be impacted by reinsurance arrangements Good estimates of claims amounts can be made Page 5

10 Subject ST3 (General Insurance Specialist Technical April 2005 Examiners Report Settlement delays are generally short but can be increased if there is a need to verify the value of the stock held in a commercial property or the validity of a claim. Claims distribution is skewed as claims are fairly consistent in size with few total losses but more varied than domestic properties as the properties insured are less homogeneous. Exposed to moral hazard especially in an economic downturn. Claims may be reopened. Large claims will be subject to negotiation / arbitration about the amount of the claim Rating factors The main rating factors are monetary value, location, trade / business. Other rating factors which may be used are: EML Age of building Fire protection equipment Number of floors / floor area Surveyors report / score Construction type Excesses Indemnity period for business interuption Security / links to police station Claims history 5 Alternative approaches to this question gained marks regarding the detailed amount of information given as the examiners felt that the question did not make it clear when the actuarial investigations were due to take place. Marks were not given however for investigations of a non-actuarial nature. Even allowing for the alternative approaches most candidates mentioned only a few of the investigations that would be carried out. Many candidates concentrated on aspects of getting the data rather than investigations e.g. trends. Claims related: Frequency and Average Cost trends by Accident year, Development year and Payment year to highlight any potential new developments cost per unit exposure analysis large loss ratio Probably only have statutory accounts and returns available Page 6

11 Subject ST3 (General Insurance Specialist Technical April 2005 Examiners Report Need to investigate reserving trends in conjunction with the claims related trends e.g. UPR, (A)URR, OSCR, IBNR compare with previous years. Are there any noticeable trends? Also, investigate trends in claims handling costs and associated reserve. solvency levels and free reserves statutory solvency requirements / levels of coverage market share portfolio movements new business levels / premium volume premium rates charged if obtainable / industry premium levels the asset mix and any associated changes Funding of the takeover Alternative use of funds Restrictions on purchase anti-competitive laws. Other accounting ratio investigations important Loss/Claims ratio, Expense/Combined ratio, Commission rates, Investment returns, Profit margin, Return on capital employed, Share price / p.e. ratio reinsurance purchased, recoveries made, reinsurers security goodwill taxation and regulation policy conditions Check for any trends in the wording of audit statements weakening in the sign-off has there been any apparent Investigate recent or possible future legislation changes that may impact the business. Investigate similar trends in other potential companies Investigate the credit standing of the company Investigate the combined model office Investigate the synergies that the combined operation will have. Investigate the effect upon the benefit schemes of the two organisations. Investigate the impact upon data owing to different ICT and product structures. Investigate any savings in claims handling expenses Page 7

12 Subject ST3 (General Insurance Specialist Technical April 2005 Examiners Report Investigate the benefit of any diversification by location, different industries and different materials handled etc. 6 Part (i) of the question asked for relevant limits. Most candidates failed to give sufficient limits with many not giving any at all. Some candidates did give limits but selected very high proportion of equities which even for a GI company writing longtail business is not appropriate, especially if it is small. A lot of the answers were regarding general comments about investments for a GI company rather than the instructions given to the investment mangers. Parts (ii) and (iii) were generally well answered. (i) Content will include: guidelines for the split of assets, giving ranges for each major asset class this will most likely give maximum and minimum ranges indicate mean duration, mean maturity, maximum maturity permitted, etc. Cash (20% 30%) Fixed interest (50% 70%) Index linked (20% 40%) Equity (0% 20%) Indirect property (up to 10% of the 20% max for equity) No direct property investment Domestic currency only >80% of Fixed interest must be Govt guaranteed The remainder of Fixed interest must be AA or better Benchmark for investment return Limit equities to bluechip or equivalent Funds under management should be split broadly equal between at least two different investment managers For Cash no more than w% of funds under management with any one deposit holder. For other assets no more than x% of the insurers total assets should be invested in any one company in aggregate, etc. The insurer should not hold more than y% of any particular issue The insurer should not hold more than z% of any one company s total debt in aggregate (counter-party risk), etc. Page 8

13 Subject ST3 (General Insurance Specialist Technical April 2005 Examiners Report (ii) Advantages Returns may be higher, in which case the company would improve its overall investment performance Equity may be better matched for real, long term liabilities If currently low level of equities then to increase holding could be appropriate for diversification Disadvantages Returns may be lower, in which case the company would see worse investment performance Equity has a greater volatility of potential returns, which means there is an increase in risk Equities too long to match most liabilities Capital requirements are likely to be risk-based, which means equity treated as higher risk Equity is less liquid, which is disadvantageous in GI business where funds may be needed at short notice to cover unexpectedly high levels of claims Equity is less secure, so greater risk of default (iii) Advantages Inflation link offers some protection for real liabilities Highest level of security Long term should be a suitable match Lower volatility, so generally lower risk than equity Possible lower level of dealing expenses Page 9

14 Subject ST3 (General Insurance Specialist Technical April 2005 Examiners Report Disadvantages Appropriate term may not be available The inflation link may not be suitable (wrong inflation) Overall expected returns are lower Possibly less liquid / smaller volumes available 7 Most candidates managed to make a reasonable attempt at the first 2 parts of this question which involved a non standard product. Part (iii) proved very difficult for most candidates and hence overall the marks for this question were generally on the low side. The solution below to part (iii) was not the only one that would have been accepted by the examiners, in particular using different terms in the Taylor Series expansion would have given a different answer. (i) Advantages Guaranteed funding in the event of a large catastrophe enabling the agency to concentrate on relief efforts rather than fund raising. Certainty about the amount available for relief efforts. Enables better planning and budgeting as there is no need to build up contingency funds etc. Controls cash flow Disadvantages $10m dollars may be perceived to be a high annual cost for insurance and the relief agency does not have the funds. Contributions may not be as forthcoming if contributors realise that their money is being paid over to an insurance company. If event is near the end of the term of the policy may be difficulty in determining if the 500 deaths occur during the term of the policy. If there are no large catastrophes during the year, then the agency will lose the premium. The insurance provider is likely to add margins and profit loadings on the premiums and thus the premium for the policy is likely to be higher than the expected benefit to the agency. There may very few providers of such policies in the market i.e. Demand may outstrip supply and this may lead to the insurance provider overcharging for the policy. Page 10

15 Subject ST3 (General Insurance Specialist Technical April 2005 Examiners Report There may be delays in receiving the funds from the insurance provider as it may want evidence of the loss of life etc. The agency may be able to raise the required funds anyway from public sympathy for the victims of the disaster. Man made disasters such as civil war would not qualify for benefit under the policy. The relief agency will be working to prevent loss of life and so may in some situations not get the benefit under the policy due to its own success. In such situations, the relief agency may request some financial compensation. This may lead to disputes with the insurance provider. Need for a clear definition of what constitutes a natural disaster. Many of the events that the relief agency is concerned with may not result in great loss of life but may still be large catastrophes in terms of the numbers of people requiring assistance. Effects of inflation may reduce real level of cover Risk of insurer default. Number of deaths is not indicative of size of loss Payment is irrespective of number of deaths once it reaches 500. (ii) Advantages Fixed benefit payable on occurrence of an event leading to a valid claim. Short tailed Selling such a policy would bring in income from a new source and possibly open up the possibility of selling such policies to other relief agencies. There may be marketing advantages to being associated with the relief agency. The policy would bring catastrophe exposure to parts of the world that the provider is unlikely to be selling much insurance to. Therefore it would not aggregate much with its other catastrophe exposures (i.e. diversification). Pricing may be attractive as few companies in the market would be willing to write such policies. Page 11

16 Subject ST3 (General Insurance Specialist Technical April 2005 Examiners Report Disadvantages The definition of loss under the policy is somewhat subjective. There may be difficulties in establishing the loss of life from an event. This could lead to disputes with the relief agency. It may be difficult to price such a policy as good data may not exist on the frequency of such events (i.e. there is a greater risk that claims could exceed premiums than in other situations). The relief agency would have an incentive to exaggerate the loss of life from a particular disaster. Independent verification may be difficult to obtain. An event may occur in a part of the world where the relief agency does not operate. In such a situation, the insurer would end up paying out even through the relief agency does not spend that money providing any assistance to the victims. Difficult to reinsure at reasonable rate Volatile claims experience Liquidity issue in event of a claim Political downside if do not pay out. (iii) Loss cost for Company A = 100 * 0.1 = 10m Loss cost for Company B = 100 * = 8.33m Company A Premium = 10m + 10% * Capital Company B Premium = 8.33m + 15% * Capital Page 12

17 Subject ST3 (General Insurance Specialist Technical April 2005 Examiners Report The Capital is set such that exp ( Capital * R) is approximately equal to 0.1. where R is the root of M(R) cr = 0 M(R) 100 (1 + )R = 0. M(R) = exp(100r) = R R 2 using the Taylor Series expansion Therefore R is the root of R R R 100R 0. R = 0.02 where is the safety load Using the approximation probability of Ruin = exp( R * Capital) = 0.1 exp( 0.02 Capital) = 0.1 Capital = m / In the case of Company A, 2 = m / 100m = sqrt(1.1513) = = 10% * Capital / 10m So Premium = 10m * ( * = 20.73m In the case of Company B, = 15% * Capital / 8.33m 2 = m / 55.53m = sqrt(2.0731) = So Premium = 8.33m * (1 + = 8.33 * = 20.32m Hence company A will be more expensive. 8 Most of the candidates made a good attempt at this question, particularly part (i). The examiners were encouraged by this as this type of question has been poorly answered in the past. It demonstrated an understanding and interpretation of accounts. There was some confusion regarding at which point in time the figures related to, even though the question stated that all figures are as at end (i) Class A GWP is decreasing sharply NWP is decreasing even faster than GWP. This could be because the reinsurance premium is rising as a % GWP or that the company is buying more reinsurance as the size of the portfolio decreases. NEP = NWP so all the policies are written on the first day of the accounting period. Loss ratio is increasing over time. Page 13

18 Subject ST3 (General Insurance Specialist Technical April 2005 Examiners Report Small proportion of claims are paid a long tail class Lots of IBNR/IBNER which increases (as % of WP) as get closer to the future as would expect. Expenses are not falling as fast as premium. Could be due to claims handling costs as claims are long tail. Commission is stable at 15% of GWP, or increases from 20% to 25% as % of NEP Investment return is decreasing very slowly. Investment return is high as % of GWP Again consistent with a long tail class as substantial reserves will be held and these will be fairly stable. Profit has decreased in amount over time but as a percentage of GWP has increased over time. This is a result of the decrease of GWP with a stable reserve pot and higher proportion of investment return. Class B GWP is increasing sharply, in fact at the rate that it is falling in class A NWP is also increasing at the same rate as GWP. Percentage of GWP paid in reinsurance is constant at 5%. NEP for 2000 is the same as NWP. Could mean that same volumes were written in 1999 as in NEP for subsequent year suggests that the average policy is written mid way through the year i.e. that policies are written evenly over the year. Commission is again stable at 15% of GWP, or around 17% of NEP. Expenses start at 10% of GWP and increase slightly over time to 12% by Investment return is relatively stable at circa 3% of premium. Increasing slightly as a % GWP. Page 14

19 Subject ST3 (General Insurance Specialist Technical April 2005 Examiners Report Proportion of claims paid is far greater than class A i.e. this class is shorter tailed. IBNR/IBNER moves over time as expected. Looks like there is a large notified but not paid claim in loss ratio for this year deviates sharply from the average. Profitability has declined over time as % GWP, consistent with the rapid growth company has undertaken. Growth at this speed is often not possible without a decline in profit. (ii) Class A EL, PL anything else long tailed with reasons Class B any short tailed class, household due to large claim / weather / subsidence event in 2001 (iii) Issues Expenses are increasing over time. Need to investigate why this is happening and identify any opportunities to reduce expenses. Reinsurance costs on class A seem to be increasing. Need to investigate why and consider whether current reinsurance arrangements are the most appropriate. Profit for A as % of WP increasing in revenue accounts but underwriting profitability of business written is decreasing, cannot rely on the investment returns on long tailed class. Look at bringing class B back into profitability. Changes in mix of business within each class owing to rapid expansion / contraction. Investigate whether the reduction in volume in class A and increase in class B is intentional Investigate investment strategy. Investigate capital requirements Staff and systems, class A will need experienced staff to handle a class that is clearly decreasing over time. Staff may leave for another company once they see they have no long term future. Need plan to retain and reassure staff otherwise will lose ability to service business. Page 15

20 Faculty of Actuaries Institute of Actuaries EXAMINATION 9 September 2005 (pm) Subject ST3 General Insurance Specialist Technical Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 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. 4. Mark allocations are shown in brackets. 5. Attempt all 8 questions, beginning your answer to each question on a separate sheet. 6. Candidates should show calculations where this is appropriate. AT THE END OF THE EXAMINATION 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 the 2002 edition of the Formulae and Tables and your own electronic calculator. ST3 S2005 Faculty of Actuaries Institute of Actuaries

21 1 (i) Explain the difference between accident year accounts and funded accounts. [2] (ii) Give four examples when funded accounts could be appropriate. [2] [Total 4] 2 (i) Define the terms: (a) (b) suretyship moral hazard [2] (ii) Explain how a general insurance company writing suretyship business can minimise the risk of moral hazard in respect of the cover it provides. [4] [Total 6] 3 You are a consulting actuary who has been approached by a general insurance company, which writes more than one line of insurance business. (i) (ii) You have been asked to comment on the recent relative profitability of the different lines of business for this company. State, with reasons, the types of investigations that you will need to carry out in order to do so. [3] On completion of the above task, you are asked to comment on the company s reinsurance structure. List the types of investigations that you would carry out. [4] [Total 7] 4 A reinsurance company writes a book of catastrophe reinsurance contracts to an expected combined ratio of 60%. It estimates that its aggregate claims distribution is compound Poisson with and the claim size distribution is exponential with mean of $1m. (i) (ii) Calculate the minimum amount of capital it needs to ensure that its ultimate probability of ruin stays below 0.5%. [5] Ignoring investment income, calculate the return on capital that the reinsurer would generate if it held the amount of capital that you calculated in (i) above. [1] (iii) Suggest potential practical limitations of the above solution. [1] [Total 7] ST3 S2005 2

22 5 You are an actuary working for a general insurance company that writes a wide variety of classes of insurance. You have been asked to attend a cross-functional group looking at how to improve the company s defence against fraudulent claims. As part of your preparation you have been asked to suggest ways in which fraudulent policyholder behaviour may be reduced. Outline the suggestions you would make. [14] 6 The government of a small developing country wants to encourage the development of the agricultural sector in its country. One of the measures it has taken is to establish a specialist insurance company to provide crop insurance to farmers in its country. The insurance company would charge an annual premium and provide compensation to farmers for crop failure resulting from drought, disease or pests during the policy year. The compensation provided will equal the sum insured less the proceeds from the sale of the crop. (i) List the rating factors that the insurance company might use to set premiums. [3] (ii) Describe the characteristics of claims that the insurer can expect to receive. [5] (iii) State the factors that will influence the level of capital that the insurer will need. [5] [Total 13] 7 You are an actuary working for a general insurance company that has been in business for three years, writing only motor insurance third party liability, in a country that does not allow claims equalisation or catastrophe reserves. (i) (ii) State the required technical reserves likely to appear in the management accounts and the matters you would consider in determining the reserving methods to calculate these reserves. [18] Discuss how you would overcome any particular issues or difficulties faced in applying the methods discussed in (i). [6] [Total 24] ST3 S PLEASE TURN OVER

23 8 You are a general insurance actuary working for an insurance company which writes only household business. (i) (ii) (iii) Describe, with examples, the adjustments that may be made to the base experience to obtain the burning cost premium. [10] Explain the adjustments that may be made to the burning cost premium to calculate the premium the customer is charged when initially taking out a policy. [10] Describe any further adjustments that may be made to the premium in (ii) to derive a renewal premium. [5] [Total 25] END OF PAPER ST3 S2005 4

24 Faculty of Actuaries Institute of Actuaries EXAMINATION September 2005 Subject ST3 General Insurance Specialist Technical 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 29 November 2005 Faculty of Actuaries Institute of Actuaries

25 Subject ST3 (General Insurance Specialist Technical) September 2005 Examiners Report 1 Most candidates had no problems with this question. (i) (ii) Accident year accounts consider all income earned and outgo incurred in a year and permit the release of profit at the end of the year. Funded accounts consider the business written in each year and do not permit the release of profits until the end of a subsequent year (usually the third year). Where underwriting year is fundamentally important Lloyd s market Reinsurance written on a policies incepting basis Significant delays in premium payment and claim settlement and in making recoveries Marine and aviation business Regulatory requirement 2 Credit for (i) part b was given to students who used the alternative definition of Making the insured event more likely to happen as a result of being insured, e.g. a household contents policyholder not taking as much care in checking that doors and windows are locked. Many candidates could not define suretyship and hence missed out on a few of the points in part (ii) or added points that were not relevant to this type of insurance. (i) (a) Insurance to provide a guarantee of performance or for the financial commitments of the insured. (b) 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 or by submitting a false claim. (ii) Good underwriting Suitable policy wording / exclusions Provisions of suitable cover including any limits and excesses Data sharing with other companies Analysis of claims information may highlight patterns Regular contact with insured to build confidence and understanding Page 2

26 Subject ST3 (General Insurance Specialist Technical) September 2005 Examiners Report Expert claims handling. Double trigger Obtain relevant info regarding financial status and obligations of the insured 3 Most candidates managed to make a reasonable attempt at this question. (i) Reserving analysis to check the expected ultimate liabilities for each line of business An analysis of the expenses and levies attributed to each line of business to check their allocation An analysis of cashflow for each line of business in order to work out the net present value of underwriting profits from each line of business. Determine the required level of capital to support the business Allocation of the required capital amongst the various lines of business Determine the return on capital for each line of business. Investment risk based on asset risk to assess default risk Investigation of bad debts on each class Investigation of reinsurance to assess cost effectiveness Investigate the effect of the insurance cycle for each class to see effect of likely profitability Investigate change in mix of business within each class to assess effect upon changing profitability Investigate the effect that the occurrence of large claims may have had on each line of business (ii) The amount of risk that can be retained safely having regard to the insurer s solvency position. The extent of likely exposure to accumulations of risk The need for catastrophe reinsurance and the appropriate upper and lower limits for such cover The extent for possible need for reinstatement covers Page 3

27 Subject ST3 (General Insurance Specialist Technical) September 2005 Examiners Report Competitiveness of reinsurance prices and availability of cover and technical assistance Check on strength and solvency of reinsurer. Competitors reinsurance structure Regulatory requirements Alternatives to reinsurance Cost and effectiveness of commuting existing covers Past reinsurance cost / benefit 4 This question generally resulted in either almost full marks or nil. Many candidates gaining only 1 or 2 marks with the initial definitions but not being able to carry out the calculation. (i) Probability of Ruin is approximately equal to Exp ( RU) where U = Capital required R = adjustment coefficient = α λ / c = α θ /(1 + θ) μ = $1m. α = 1 / μ = 1 θ = 1 / = R = 1 * /( ) = 0.4 Probability of Ruin = Exp ( 0.4 * U) < 0.5% 0.4 * U < ln (0.5%) 0.4 * U < U > I.e. the capital required is greater than $13.25m (ii) Return on Capital = 0.2 * / = 1.0% (iii) Model not appropriate Approximations used not correct or not appropriate Regulatory requirements may be different Ignores other business that may be written by the company Page 4

28 Subject ST3 (General Insurance Specialist Technical) September 2005 Examiners Report Future experience different from past 5 This question was on the whole better answered than the examiners had expected. The better candidates were able to show that they had considered many ways in which the fraudulent behaviour could be reduced. X-check policy cover dates against date of accident Look for multiple claims from the same claimant, surname, address, postcode, etc. Tighten underwriting criteria Check previous claims history of the policyholder at inception Introduce some form of experience rating Increase / introduce excesses Spot checks on claims of various sizes Set up confidential fraud line with possible incentives Write indemnity only policies Set up fraud department Attempt to identify any oddities about the claim, such as flood damage on a dry day Corroborate info provided by claimant with independent sources. E.g. witnesses Review previous claims history any repeat claims in internal data Consider data sharing with other companies E.g. highlight any double coverage Collaborate with police, media and other insurers to advertise penalties for fraud using specific example cases previously discovered Use of in-house / appointed repairers / loss adjusters Use of own home service sales force Settle claims by replacement items rather than cash settlement Ensure policy wording is as tight as can be with appropriate declarations of facts provided Send out claims handler to view claim incident where economically viable Page 5

29 Subject ST3 (General Insurance Specialist Technical) September 2005 Examiners Report Ensure claims handlers are well trained and receive regular refreshers Maintain good links / relations with relevant police and related authorities and share information Require original receipts to demonstrate value Require medical evidence from recognised professional Highlight penalties for fraud on policy wording Use of voice recognition techniques and recording of telephone calls for purposes of lie detection / claim verification 6 Again the examiners were pleased with the general standard of answers for this question with candidates demonstrating that they could apply their knowledge to a non standard GI product. (i) (ii) Type and mix of crops grown Geographic region in which the crops are grown Size of the farm Availability / method of irrigation Pest control techniques used Level of excess Claims history Sum insured. Most claims will be reported at the end of the growing season although some will be notified during the season. Most claims will be settled quickly, i.e. very soon after the growing season Claims size will be related to the size of farms in the country. Claim frequency likely to be low in most years There will be significant accumulations of claims from adverse weather conditions / pest epidemics. Accumulations might occur from the same geographic region or type of crop. If a period of drought / disease / pest extends over several years, then the insurer could face several years of high losses. Page 6

30 Subject ST3 (General Insurance Specialist Technical) September 2005 Examiners Report Potential for fraudulent claims if a farmer does not tend his crops properly and then claims under the insurance policy. Potential for moral hazard as farmer does not aim for highest sale price for crop as insurance will pay anyway Short tail, therefore relatively little impact from claims inflation. Quick reinsurance recoveries Potential for claim disputes regarding definition of drought / cause of crop failure. (iii) Likelihood of accumulations and catastrophes. Volatility of claims experience Level of uncertainty from poor data quality for pricing Liquidity risk Credit risk from reinsurers / policyholders / third parties The level of premiums charged in relation to expected claims (loading factor / risk margin) Desired level of ruin probability. Expected volume of business Level and variability of expenses Level and variability of investment income that the insurer is expected to generate Reinsurance structure and price. Regulatory requirements. There may be minimum capital requirements. Rating agencies. The insurer may wish to achieve a particular rating. Implicit or explicit guarantees from the government with regard to capital support in future. Required profitability Dividend policy 7 Credit was given in either part of the candidates answer for valid comments listed below in both parts (i) and (ii). Page 7

31 Subject ST3 (General Insurance Specialist Technical) September 2005 Examiners Report Although most candidates were able to list the required technical reserves, there was generally not enough discussion as to the matters to be considered in calculating such reserves. Most candidates did comment upon the fact that the company had only been in business for 3 years but did not go into enough detail as to how to deal with this. A few candidates failed to realise that third party liability insurance also covered third party liability to property damage and instead only considered third party liability to bodily injury claims. (i) All technical reserves to be stated on a gross and net basis Consideration of any regulatory issues Consideration of level of margin in reserves Consistency with existing methods Consider currency of reserves Unearned Premium Reserve 365ths method most accurate when risk is evenly spread Calculates unearned premium by multiplying office premium by ratio (365 # days since inception) / 365 But requires computer records, which should be available 24th / other similar methods less accurate Risk may not be evenly spread though need to investigate claims experience to date and probably industry data to devise a suitable earnings formula DAC UPR may be directly reduced for acquisition costs or a DAC can be created as an asset to offset the overstatement Additional Unexpired Risk Reserve Required where initial premium is considered insufficient to cover the estimated ultimate claims outgo Might assume not required, if confident in original pricing basis However, could compare with industry claims experience there may be recent trends apparent since business written Page 8

32 Subject ST3 (General Insurance Specialist Technical) September 2005 Examiners Report O/S Reported Claims Reserve / IBNER Case estimation likely to prove most fruitful as low frequency, high severity expected for this class and because the company is very young Separate allowance is required for IBNR Chain ladder techniques unlikely to be of any use for bodily injury as too little data available and not even close to being fully run-off Chain ladder could be considered for property damage but need to consider any changes in settlement procedures Bornhuetter-Ferguson method may be helpful though but must be confident in ultimate loss ratios Allowance for discounting If using an average cost per claim method then need to allow for changes in nil claims IBNR Could take a simple proportion of premium / o/s claims reserve however, not very robust as loss ratio may not be stable / affected by adverse claims experience Delay table method not viable as insufficient stats available Projection method likely to be of most use, but need an ultimate loss estimate perhaps there are industry stats available to help. Re-opened claims reserve if not included within O/S reported reserve Claims Expense Reserve With case estimation of o/s claims can include allowance for direct expenses Or can look at industry estimates to assess a proportional addition Indirect expenses will need to be based on prior estimates from business plan / model projections as the business is still very young Page 9

33 Subject ST3 (General Insurance Specialist Technical) September 2005 Examiners Report (ii) Split the data between bodily injury and property damage Try to use several different methods for estimating each reserve to ensure that the resulting reserves are sensible Approach reinsurers for technical assistance, as they are likely to have significantly more experience on which to base estimates. Actuarial consultants can provide similar assistance. More frequent reviews of claims and expense stats will ensure that most up-todate info can be fed into the process Future inflation may be different to past inflation in which case would need to allow explicitly for inflation in projections May have been trends in the past which need to be allowed for, e.g. in respect of legislative changes. All claim costs would be required to be put onto the same basis. There may have been a large individual or catastrophe claim in the three years. Would need to adjust the data for this by e.g. removing such an item from the base data and making a separate allowance at the end. Obtain any industry data 8 This was a bookwork question aimed at a particular class of business. Many candidates managed to only mention a few of the adjustments required and even fewer examples. Part (iii) of the question called for a comparison of a renewal premium with a new business premium at a point in time. Some candidates interpreted the question to mean how the renewal premium for an individual policyholder would be derived from the new business premium the policyholder was charged the previous year. The examiners considered this interpretation but did not consider it valid. (i) Unusually light / heavy experience. Claims experience fluctuates over time. An example in household is that some years suffer from storms more than others. If the experience of the base period does not appear typical the insurer must choose another base period, aggregate more years experience or apply an adjustment factor to the affected base year. Factor will be subjective. Large / exceptional claims. Have to decide whether to leave claims in, truncate them or remove them. This will depend on the extent to which Page 10

34 Subject ST3 (General Insurance Specialist Technical) September 2005 Examiners Report claims of this type are expected to occur in future. Examples in household would be a large public liability claim or a total loss of a large property. Trends in claims experience. Investigate any trends in base data to see if they are likely to occur in future. If so need to project the trend and include. If not likely to occur in future then exclude. Rate of increase of cost of building work is likely to be a trend in household business. Changes in risk over time can be very difficult to deal with. Could be dealt with as trends. Or may separate them out, project and combine with explicit assumptions about the future mix of these risks. This will also need to be done for different types of claims if the mix of claims is changing significantly. Example is that due to global warming the risk presented by weather is changing over time with wetter more flood prone winters. Changes in cover can also be difficult to allow for. If perils are no longer insured the insurer may be able to exclude from the base data all claims that wouldn t be covered in future. Example if subsidence stopped being covered then all claims of this type could be excluded from the analysis. However if a new peril is introduced then it is harder to make an adjustment. Here external data will need to be used such as market stats, government data or consumer stats. If the change is to the level of limits or excesses then it is more complicated. May be possible to allow for increases in these by looking at individual claims e.g. if household excess increases from $50 to $100 then add the old $50 excess onto amount insurer paid out and then adjust for the effect of the new excess before analysing the claims. If the detailed claims information is not available then an approximation will have to be made using the claims cost distribution. Many insureds will not inform the insurer of losses that occur below the excess point. Changes in the impact of reinsurance will need to be allowed for e.g. cat XL retention changes assuming the calculations are performed net of reinsurance. (ii) Once a burning cost premium has been calculated it will need to be projected forwards to give the future risk premium. This is a central risk estimate of the cost of future claims. Claims inflation needs to be allowed for from the mean payment date of claims in the base period and the mean payment date of claims arising during the exposure period of the new rating series. Ideally the insurer will be able to adjust claims values by a specific index for the loss type. Page 11

35 Subject ST3 (General Insurance Specialist Technical) September 2005 Examiners Report In order to get to a risk premium rate the projected claim cost must be divided by a corresponding projected value of the exposure. Again need to project at an appropriate rate of inflation. This could be very different to what is used for the claims. Commission is usually a percentage of premium and would be loaded in this way. If a different way of paying commission is used this should be reflected in the premiums. Expenses, divide into fixed and variable. Often load these separately. May also here load only the expenses incurred in writing a piece of new business. Also include tax, levies and any industry wide compensation schemes. Allow for smoothing across rating cells. Allow for new business and/or joint policy discounts. Allow for any regulatory issues which may affect what rates may be charged. Investment return should be allowed for by discounting expected claims payments and expenses to the date on which the premium is received. As household is not a long tail class this is less important. Allowance should be made for whether premiums are payable monthly or annually. Reinsurance costs should be allowed for. Usually loaded as a percentage. As household insurance as a minimum there would be catastrophe XoL cover. Contingencies should be allowed for. Often a percentage loading, this can be considered with the profit loading. Return on Capital / Profit Margin. Need to load a profit margin having regards to what is required to give a reasonable return on the capital needed to support the risks underwritten. Rate of return should correspond to the risk to which the capital is exposed. Competitive considerations may affect premiums. Insurer may decide to take a smaller return in order to sell more policies and therefore make a lower $ profit than otherwise. Need to consider where we are in the insurance cycle. Also look at competitors prices and assess likely volumes. Household insurance is not as price sensitive as motor insurance. Compare to previous rating series and assess effects of changing to new set. (iii) Renewals different as: Expenses could be different, costs less to renew a policy than write a new one. Could reflect in premium. Case by case underwriting could be applied at renewal if not possible at new business e.g. business acquired through the internet. Page 12

36 Subject ST3 (General Insurance Specialist Technical) September 2005 Examiners Report Commission paid could be different Competitive considerations, if policyholder is likely to renew then may increase premium to more than would charge a new customer. And vice versa. Business plan, may prefer to retain business at a lower margin, especially if seen as a good risk / will enhance risk profile. May be gradually moving to a new rating set so no direct correspondence between new business and renewal rates. May have a team who have premium flexibility in order to maximise retention of business, this will again make premiums different from new business ones. END OF EXAMINERS REPORT Page 13

37 Faculty of Actuaries Institute of Actuaries EXAMINATION 6 April 2006 (pm) Subject ST3 General Insurance Specialist Technical Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 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. 4. Mark allocations are shown in brackets. 5. Attempt all 6 questions, beginning your answer to each question on a separate sheet. 6. Candidates should show calculations where this is appropriate. AT THE END OF THE EXAMINATION 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 the 2002 edition of the Formulae and Tables and your own electronic calculator. ST3 A2006 Faculty of Actuaries Institute of Actuaries

38 1 You are the actuary for a small general insurance company with a low solvency margin. The insurer only writes commercial property and household risks which are located in a small country. (i) (ii) Explain the differing claims characteristics of these two classes of insurance. [3] Suggest, with reasons, the types of reinsurance that this company might purchase. [7] [Total 10] 2 You are the actuary for a general insurance company writing household buildings and contents insurance. (i) (ii) (iii) List the information you would seek to determine estimates of exposure for future flood damage. [3] Describe how the total exposure to a major flood loss could be assessed using the information in (i). [7] Discuss the degree of difficulty that you would expect to arise in obtaining the information. [3] [Total 13] 3 An insurance company specialises in writing commercial property insurance business. As part of the company s business planning, it prepares financial projections using a number of stress tests. One such stress test makes the following assumptions: (a) (b) A geographic region where the company writes 25% of its business is subjected to a strong earthquake and A rise in interest rates causes a 20% fall in the bond market. Describe the particular risks that the company would face under such a scenario. [15] ST3 A2006 2

39 4 You are an actuary working for a reinsurance company. You have been asked to help price a new quota share reinsurance contract protecting a short tail class of business. You have been given the following historical data from 2001 to 2005 underwriting years on the business that is subject to the quota share. Year Written Premium m Incurred Losses m Rate Change N/A % % % % Rate change figures indicate the percentage increase / decrease in premiums collected from an identical risk from one year to another. You also know that claims inflation has been running at 4% per annum over this period for this class of business and that premium rates in 2006 are expected to fall by 5%. (i) (ii) (iii) Calculate the loss ratio that can be expected for 2006 for this class based on all of the historical experience and the rate change and inflation assumptions given above, stating any assumptions you make. [9] State other information that you would require in order to determine if this quota share contract is expected to be profitable for [5] The ceding company has told you that it expects its loss ratio in 2006 to be 85%. Suggest reasons why the ceding company s expected loss ratio for this contract might be different from the value calculated in part (i). [5] [Total 19] ST3 A PLEASE TURN OVER

40 5 (i) Explain how you would obtain an indication of the strength of a general insurance company s claim reserves based on published information. [5] Company ABC is a general insurance company. The following information is available: Gross written premium (GWP) 2,000 2,500 3,000 3,250 2,000 Outstanding claims b/fwd Policy count at mid-year 30,000 32,000 35,000 All monetary amounts are $000s. Unearned premium reserve brought forward into each year is 10% of the GWP in the previous year. Claims paid in each year are 60% of the GWP in that year. Over the period 2002 to 2005 commission has been paid to intermediaries at 8% of the gross written premium. Expenses of writing and handling claims on the business are $5 per policy and 2% of claims paid in the year respectively. Reinsurance costs are 5% of gross written premium. Investment return is earned at a rate of 5%. Cost of capital and free reserves are to be ignored in calculating investment return. (ii) Using the above information, and stating any assumptions you make, calculate the pre tax profit ABC made in 2002, 2003 and [9] (iii) Comment on the results in (ii). [4] [Total 18] 6 You are the pricing actuary for a general insurance company that underwrites event insurance. You have been approached by a charity that is organising a fun run for up to 2,000 people and wishes to arrange suitable insurance cover. To maximise possible attendance the organisers will be accepting entries on the day. Your company is not authorised to write motor insurance. (i) (ii) (iii) Describe the types of insurance cover, excluding motor insurance, that the event organising company may wish to purchase. [8] List, with reasons, the information you might require from the event organiser in order to establish the risk premium for this event. [10] List, with reasons, the policy exclusions you would expect to see under each of the products described in part (i). [7] [Total 25] END OF PAPER ST3 A2006 4

41 Faculty of Actuaries Institute of Actuaries EXAMINATION April 2006 Subject ST3 General Insurance Specialist Technical 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 June 2006 Comments Individual comments are shown after each question. Faculty of Actuaries Institute of Actuaries

42 Subject ST3 (General Insurance Specialist Technical) April 2006 Examiners Report 1 (i) Commercial Property More scattered cost distribution than household due to singular nature of properties involved. Settlement can be delayed by the need to verify the value of stock / need to liaise with other insurers if only cover a part of the damaged property. Also business interruption cover will be longer tailed as need to see how long the business is out of action before the lost profits can be quantified. Claim frequency tends to be lower for Commercial Property/higher for Household Household Consistent in size and distribution with a small number of larger total losses. Settlement usually quick. A subsidence event may cause an uplift in the number of claims and average cost would also increase (more dramatic effect than would be for commercial property). Possibility of geographic concentration. (ii) Company is small with low solvency margin so protection of solvency position is a primary concern. All types of reinsurance will assist with protection of the solvency margin. Stop loss reinsurance could be purchased to protect solvency margin. Often it isn t available and certainly not at a reasonable price. With all types of reinsurance the value for money should be considered, i.e. the protection it brings, including security status of reinsurer compared to the cost. Commercial property is insured so some use of surplus reinsurance to allow to write a variety of risks of a variety of sizes. Also allows to fine tune exposure by ceding more of the risk in areas where already have some properties on risk. The small size of the insurer may indicate that quota share needs to be used to allow more risks to be written, giving a more balanced risk profile. Quota share reduces NWP compared to free reserves, helping the solvency position. Page 2

43 Subject ST3 (General Insurance Specialist Technical) April 2006 Examiners Report This may also encourage reciprocity, relevant as write Household and this may be regionally based e.g. Building Society. Only property insurance is written in a small country so cat XL will be required to protect against insolvency in the event of a catastrophe occurring. Assuming perils exist in this country (like flood and subsidence) that give rise to large claims for individual properties then risk XL will be needed. Also if there is potential for aggregations (from a defined peril or a geographic concentration) then aggregate XL will be needed to cover the portfolio. The need for both these types of reinsurance will be exacerbated as the company is small. Financial reinsurance to protect balance sheet/transfer risk to reinsurer Any regulatory requirements must be complied with including those that affect the choice of reinsurer / reinsurance programme. Comments on question 1: A bookwork question generally reasonably well answered. Only a few identified subsidence/bi settlement delay issues for Household/Commercial Property respectively. The best candidates identified all the reinsurance types and how each type of reinsurance helps protect the solvency position (which is a big issue for a small company). 2 (i) &(ii) All relevant standard rating factors for Household Insurance (sum insured, postcode, etc) Any flood excesses Height of property above mean sea level. Number of floors of house. For a flat which floor it is on. Distance and height above closest major river/lake. Height of sea defences/river defences. Quality of defences (earth/concrete etc.). Long term weather patterns/climate trends (e.g. predicted rainfall) Previous experience of flood claims Reinsurance coverage details Trends in sea level as a result of global warming. Total exposure to flood Note difference between coastal flooding from the sea and river flooding. Sea flooding due to increased volumes of water and salinity liable to be much more destructive than fresh water. Sea flooding will only affect properties fairly close to sea level River flooding affects properties on the flood plain of rivers. Page 3

44 Subject ST3 (General Insurance Specialist Technical) April 2006 Examiners Report Estimation for flooding Obtain history of max water levels over say last 50 years Project maximum likely water levels in future Identify all properties which lie at or below this level Obtain history of max sea levels over say last fifty years. Project maximum likely sea level. Identify all properties which lie at or below this level. Use postcode/full address to determine location. By use of ordnance survey maps, or other contour map identify which postcodes are at risk. Noting that not all of a postcode may be at risk make qualitative judgement as to proportion of properties at risk within each postcode. Noting that even a major flood will generally not result in each affected property being a total loss use either historical data or judgement to estimate average loss as proportions of sum insured. Add together the sum insured for all exposed properties adjusted by the two factors calculated above. Any government directives For alternative well reasoned approach to estimating flood exposure. (iii) From Proposal Form Easy to obtain standard rating factors from proposal form Height and distance are not easily derived from postcode. Height above sea level difficult. most homeowners probably do not know exactly so Number of floors should be simple. Floor of flat no difficulty. Distance and height above nearest river do not know exactly so difficult. again most homeowners probably With all questions on proposal form there may be a moral hazard if proposer aware that flood exposed property may attract higher premium. Page 4

45 Subject ST3 (General Insurance Specialist Technical) April 2006 Examiners Report Other sources Comments on question 2: Height of sea defences can easily survey a particular part of the coastal defences. Quality of defences the coastline may be long so would be costly. Global warming a lot has been written on this. Global warming/weather patterns, lots of info already available Previous claims experience, possible industry and own experience Future sea levels timing unclear. Broker or policy holder resistance to changing information required. For this question in particular points in answer to (i), (ii) and possibly (iii) were given if answered in any section. Answers to this question were generally poor. Only a few candidates suggested practical and realistic methods of determining total exposure to a major flood loss or considered the different types of major flood risk (sea, river, lake) and the different risk consequences of each. Some candidates discussed burst pipes which isn't a major flood loss. In part (i) better candidates thought through a variety of sources of information, but most just listed the detailed policy and claim information that would be available on a home policy. For part (ii) often candidates just explained how to do a rating exercise with no reference to flood. Some candidates seemed to think one company would have enough historic claims data to rate solely on their past experience hence demonstrating that they didn't understand the peril and frequency with which it occurs. Part (iii) was poorly answered with many candidates not going into sufficient detail about the degree of difficulty in getting each piece of information. 3 Risks relating to level of claims reserves The company will have a lot of uncertainty about the level of reserves to set aside to pay the claims from the earthquake. The gross losses that it will have will depend upon: The amount of damage caused by the earthquake. The amount of exposure (in terms of insured properties and their sums insured) that the company has in the affected region. Coverage provided by the insurance policies that the company writes (property damage, business interruption etc.). The company may find itself in dispute with some of its policy holders if the policy wording is ambiguous. Claims inflation following the earthquake may be higher than the company anticipated when pricing the policies. (due to shortage of building materials and labour). Page 5

46 Subject ST3 (General Insurance Specialist Technical) April 2006 Examiners Report The company will have to incur increased claims handling costs e.g. loss adjusters fees, etc. Moral hazard from policyholders inflating claims and unscrupulous builders encouraging this. Lack of control by authorities: looting/arson; increasing losses. Timing uncertainty: delays due to scale of event. Political/altruistic pressure to pay claims up front. Risks relating to reinsurance Appropriateness of reinsurance protection e.g. Whether the company has purchased catastrophe reinsurance. Adequacy of cover. Is there any danger that the reinsurance cover is exhausted? Possible increased cost of reinsurance in subsequent years. Need to buy additional reinsurance for the current year (if any is indeed exhausted). Availability of reinsurance following the earthquake. Solvency of reinsurers. Multiple exposures for reinsurer from other insurers. Need for bad debt provisions on potential reinsurance recoveries. Possible disputes with reinsurers. Risks relating to investments If the company holds bonds as part of its assets, then it will suffer a fall in the market value of its investments. The company may have to sell those assets at a depressed price to pay its claims from the earthquake. The company may have to change its investment strategy in line with its lower solvency level. The company may have to increase contributions into its staff pension scheme if the scheme has suffered losses due to the bond market fall and this fall is not offset by an increase in expected future investment income. Page 6

47 Subject ST3 (General Insurance Specialist Technical) April 2006 Examiners Report Risks relating to new business There will be uncertainty about the premium levels that the company will be able to charge after the earthquake. The company would be expecting premiums to rise but they may not rise as much as expected. Also the company may not have enough capital to write the level of premium that it wants for future periods. Business risks Contributions to pension fund increase/salary rises impacting contributions. The company may be downgraded by the rating agencies if it suffers a significant loss. This would affect its ability to write business in the future. Company insolvency Regulatory intervention The company may not be able to meet its regulatory solvency requirements and be subjected to regulatory intervention. The company may have to raise capital at a depressed share price (share issue) or higher interest rates (debt issue). The company may have to pay into an industry compensation fund if other insurers become insolvent. The company s own operations may be affected by the earthquake e.g. damage to offices, power outages, disruption to communications etc. The increased level of claims after the earthquake may lead to increased frequency of operational losses e.g. mistakes in paying claims, fraud, etc. The company s key business partners (e.g. brokers) may be affected by the earthquake and could lead to loss of business or defaults amongst the company s debtors. Brokers and policyholders may choose not to renew cover with this insurer due to its weaker financial strength. The company may have to post collateral to back its obligations to policyholders (e.g. Letters of credit or other security arrangements) Comments on question 3: Candidates who scored well tended to focus on different types of risk, not just claims, reserving, reinsurance and investment issues, but also considering operational and other third party risks. Many candidates tended to focus on one aspect such as claims or solvency and overdevelop this at the expense of other aspects. Page 7

48 Subject ST3 (General Insurance Specialist Technical) April 2006 Examiners Report 4 (i) Underwriting Year Inflation index premium index Inflated losses on level premium loss ratio = =(1-0.05) % =1.04^ =0.95*(1+0) % =1.04^ =0.95*(1+0.05) % =1.04^ =1.00*(1+0.10) % =1.04^ =1.10* % Weighted average loss ratio: 97.2% Simple average loss ratio: 96.5% Assuming 4% future inflation Assuming similar policy conditions/coverages Assuming incurred losses include IBNR/IBNER Assuming no change in business mix % (ii) More information about rate changes for 2006 Projected volumes of business in 2006 (Written Premium) Information on large or unusual exposures Information of large loss experience. Any IBNR, particularly for Commissions including profit commissions, brokerage, overrider etc. Loads for internal expenses both fixed and variable. Taxes and any other levies. Any costs of retrocession. Investment income. For this we need to know payout pattern and premium receipt pattern as well as investment yields on suitable assets. Relevant comments on changes in any of above. (iii) The past 5 years may be too short a time frame to capture the extremes of the loss experience. For example, if this portfolio of business has had unusually heavy claims experience in the last 5 years, then the average loss ratio over a longer time period may be lower. There will be differences of opinion from the buyer s and seller s perspectives. Page 8

49 Subject ST3 (General Insurance Specialist Technical) April 2006 Examiners Report Errors in data supplied or errors in calculation Oversimplification or differences in calculation/method used Claims expenses/reinsurance coverage changes of direct insurer. Difference in definition of premiums and claims (i.e. gross/net of commission) There may be difference in opinion of: Coverage provided in 2006 vs historic years. Type of claims incurred. Claim inflation. Legislation or regulation that affects claims. Propensity to claim. This means that the future experience may be very different from the past. The company may be planning to target a particular segment of the portfolio and hence increase its exposure to that part. There may be changes in underlying economic conditions / crime rates that affect the claims experience. Comments on question 4: Candidates responses were mixed. Some candidates did not produce a loss ratio as asked in the question. A number of candidates did not read the question that the data was by underwriting year and decided to convert premiums to accident year using certain assumptions. Some candidates did not use all the information given (e.g. only using 2005 data to estimate 2006). Several candidates inflated premiums in the same way as claims rather than the correct method of adjusting for rate changes. Very few candidates actually provided any appropriate assumptions thereby losing out on marks. Parts (ii) and (iii) were reasonably well answered, with the best candidates giving a range of possible different reasons why the figures differed in part (iii). 5 (i) Compare results against competitors writing similar business Examine individual accounting items gross and net of reinsurance. Examine ratios, within and across years. Less information will be available as only looking at published information. Credit rating. Prior year reserve adjustments Level of discounting if disclosed or used Evidence of additional contingency reserves Page 9

50 Subject ST3 (General Insurance Specialist Technical) April 2006 Examiners Report Ratios to be considered are: Notified claims reserves to premium income IBNR claims reserves to premium income Claims expenses reserves to outstanding claims reserves outstanding claims reserve to claims paid (ii) Accounts GWP UPR b/f UPR c/f Earned Premium Claims paid Claims reserve c/f Claims reserve b/f Claims incurred Commission Expenses $5 per policy Expenses 2% claims pd Expenses total Reinsurance Investment return Insurance return Assumptions No AURR is required. Assume no DAC allowed for or alternatively used correctly in calculation No reinsurance recoveries are made or they are included in the figures given. Using the number of policies at 30/6 is a fair approximation to number on risk over the year. Investment return 5% of average of total reserves for each year. (iii) Claims ratio is stable at 76/77%. Average written premium per policy increased from 2002 to 2003 and then stayed the same 2003 to Page 10

51 Subject ST3 (General Insurance Specialist Technical) April 2006 Examiners Report Average claims per policy are increasing at similar rate as loss ratio is stable Expenses as % of premium decreasing slightly over time. Will always be fairly constant per policy as most of expense is per policy Insurance return (i.e. profit) is increasing in absolute terms also as % GEP and GWP. Average premium has increased but investment return increased more than proportionately due to increasing reserves. Relevant comment about strengthening of reserves Relevant calculations to support strengthing of reserves comment. Comments on question 5: Part (i) was generally not well answered. A number of candidates thought that it was important to have strong free reserves or free assets when the question clearly stated "claims reserves". Only a few candidates suggested comparing different ratios between companies. Part (ii) was generally reasonably well answered except for investment income where, in a large number of cases investment return was calculated on outstanding claims only (technical reserves do include UPR, many candidates did not seem to know this!) and for a good number of candidates on Profit which is just wrong! Again, very few candidates stated any assumptions they were making. Part (iii) was poorly answered with very few candidates scoring well: many candidates did not comment on the level of reserve strengthening taking place nor any trends in the data year on year. 6 (i) Public liability for claims made by members of the public for damage, claimants costs and expenses in respect of accidental bodily injury or property damage. Employers liability for claims made by temporary staff, helpers and volunteers. Negligence on the part of company (comment made under either EL or PL cover) Property damage all risks, covering loss or damage to insured property at the event, including transit to and from the event. Cost of hiring replacement items for the event. Accidental loss or destruction to money whilst in transit or in storage at any authorised residence. Page 11

52 Subject ST3 (General Insurance Specialist Technical) April 2006 Examiners Report Cancellation insurance Covering cancellation, abandonment or postponement of the event due to reasons beyond the control of the organiser. Non-appearance cover Covering the cancellation, abandonment or postponement of the event due to the non-appearance of specified persons due to reasons beyond their control or the organisers. Theft by employees/fidelity guarantee Terrorism cover Covering the cancellation, abandonment or postponement of the event due to, or damage / injury caused by, terrorist activities (ii) Sum Insured/ limits of indemnity for each aspect of cover. Date of proposed event. Duration of proposed event. Length/Terrain of course Location of proposed event. Estimated number of participants. Estimated number of onlookers. Has the event been held before. If so, what differences are there this year. Past claims (or incidence) experience as this may affect the likelihood of accidents. Will there be trained marshals / police providing road supervision as this will affect the exposure to risk of accidents for participants. Numbers of helpers and volunteers as this will affect the exposure to potential injury of employee and also affects the exposure to risk of accidents for participants. Details of any equipment that will be required in order to determine the potential costs involved in the event of damage and additional hire costs. Page 12

53 Subject ST3 (General Insurance Specialist Technical) April 2006 Examiners Report Expected costs, budget, expenses and net profit from the event in order to estimate the potential impact of cancellation and the potential impact in respect of loss / destruction of cash. Details of celebrities/officials due to attend the event (for non-appearance cover). Levels of excess per cover Dangerous peripheral activities on day of event (e.g. firework display/fun fair). (iii) Any excess applicable under each element of cover. Deliberate/criminal acts of negligence. Public and Employers liability: Participant liability as participants will be responsible for their own conduct (and related insurance). Road Traffic Act motor liability Damage to property in the custody or control of the insured. Property damage all risks, covering: Theft / losses from unattended vehicles Exclusion of losses not reported to police authorities Loss / damage due to Terrorism Theft where there is no sign of forcible or violent entry. Damage due to nuclear, biological or chemical risks. Cancellation insurance Anything within the control of the organiser. Anything arising from breach of contract. Due to lack of or inadequate attendance. Non-appearance cover Page 13

54 Subject ST3 (General Insurance Specialist Technical) April 2006 Examiners Report Any loss within the control of the organiser or participant. Any pre-existing medical conditions. Terrorism cover may be excluded. Comments on question 6: Many candidates adopted a scattergun approach listing all the types of insurance they could think of. Better answers showed more discrimination and showed they had thought about the question. Also poorer answers seemed to think that insurers would collect individual information on all participants, which may be nice but not practical nor economic. The best candidates were those that identified most of the relevant covers that needed to be considered. A number of candidates mistakenly decided that PL would cover fun run participants as well when, in reality, this would be an exclusion. A few candidates also commented on insurance coverage of the charity's own premises when the question was about event insurance. Part (ii) was answered reasonably well by most candidates. Part (iii) was not answered well with only a few candidates having a grasp of what exclusions would be made on any of the covers taken out. END OF EXAMINERS REPORT Page 14

55 Faculty of Actuaries Institute of Actuaries EXAMINATION 14 September 2006 (pm) Subject ST3 General Insurance Specialist Technical Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 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. 4. Mark allocations are shown in brackets. 5. Attempt all 8 questions, beginning your answer to each question on a separate sheet. 6. Candidates should show calculations where this is appropriate. AT THE END OF THE EXAMINATION 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 the 2002 edition of the Formulae and Tables and your own electronic calculator. ST3 S2006 Faculty of Actuaries Institute of Actuaries

56 1 Describe ways in which an insurance regulator can influence the investment policy of a general insurance company. [3] 2 Define the following terms and explain why they are used in an insurance contract (a) (b) (c) Risk attaching basis First loss Discovery period [6] 3 (i) Define the term Average (as used specifically in non-marine general insurance). [1] (ii) (iii) Explain, with an example, why it may be used in non-marine general insurance. [2] Suggest alternative approaches available to a general insurance company in situations where the term Average might apply. [3] [Total 6] 4 State the criteria that are desirable for a risk to be insurable, explaining why these criteria are desirable. [8] 5 (i) Explain the general principle of experience rating systems and comment on the benefits and drawbacks of such systems to both the insurer and the insured. [6] A bus company operates nationwide, with both local bus services and inter-city coaches. It has for some time self-insured its vehicles. The company has an established department which deals with all claims made on the bus company. The company is now seeking a quotation from an insurance company to cover the liability arising from all its fleet risks, both from its passengers and from third parties. (ii) Describe the statistics and other information that the insurance company would ideally like to have from the bus company in order to assess the likely future cost of insuring the fleet. [10] [Total 16] ST3 S2006 2

57 6 You are an actuarial entrepreneur in the process of setting up a new general insurance company to underwrite motor insurance only direct through the internet. You are midway through developing your IT requirements. The aspect you are currently considering relates to the data you propose to collect and hold. (i) (ii) Outline the data-related issues that you will need to consider in establishing your IT requirements. [10] Explain the problems that may occur as a result of using inaccurate data for determining the initial premium rates that you intend to charge. [6] [Total 16] 7 You are the reserving actuary for a small general insurance company. You are considering the claims reserve estimate produced by your team for household buildings and contents insurance, which has been calculated using purely statistical methods and paid data only. (i) Describe the main issues that may result in adjustments to the data being required in order to ensure maximum reliability of your final estimate. [10] When you compare your final adjusted statistical estimate for the claims reserve with the sum of the case estimates from your loss adjusters you find that there is a significant difference between the two totals. (ii) Explain why this may have occurred and how you might investigate the reasons for the difference. [10] [Total 20] ST3 S PLEASE TURN OVER

58 8 A general insurance company underwrites two classes of business, personal motor and commercial property. In personal motor business it expects to write 50m of premium with expected claims of 30m and expenses of 15m. In commercial property, it also expects to write 50m of premium with expected claims of 20m and expenses of 10m. The company has carried out an investigation to assess the aggregate claims distribution from the two classes. (i) Describe the steps that the company may have taken in this investigation. [5] The company concludes that claims in personal motor have a standard deviation of 10m and claims in commercial property have a standard deviation of 30m. The company also concludes that both the aggregate claim distributions can be modelled using lognormal distributions. The company also makes the assumption that claims from the two classes are statistically independent and that the total aggregate claim distribution (i.e. the sum of claims from both classes) can be approximated by another lognormal distribution. (ii) (iii) Calculate the mean and standard deviation of the total or aggregate claim distribution for the company. [2] Calculate the mean and standard deviations of the underlying normal distributions for each of the classes as well as the total claim distribution. [5] The company wants to ensure that it has sufficient capital to pay its claims even if they reached the 99.5 th percentile of the claim distribution. (iv) Calculate the 99.5 th percentile for claims in each class as well as the total. [5] (v) (vi) Discuss the reasons why the assumption of independence between the two classes of business may not be appropriate. [5] Calculate a reasonable range of minimum amounts of capital, based on different correlation assumptions, that the company needs in order to satisfy this 99.5% solvency level. Ignore taxes and investment income. [3] [Total 25] END OF PAPER ST3 S2006 4

59 Faculty of Actuaries Institute of Actuaries EXAMINATION September 2006 Subject ST3 General Insurance Specialist Technical 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 Stocker Chairman of the Board of Examiners November 2006 Comments Individual comments are shown after each question. Faculty of Actuaries Institute of Actuaries

60 Subject ST3 (General Insurance Specialist Technical) September 2006 Examiners Report 1 Restriction on the types or amounts of assets that can be taken into account when assessing solvency. Prevent the company from holding certain assets. Prescription to hold certain assets. Custodianship of assets Requirement to hold mis-matching reserves. Prescribing asset valuation basis for assessing solvency. Risk-based capital requirements varying by asset class Tax incentives/disincentives Requirement to hold assets in domestic currency. Comments on question 1: A bookwork question generally reasonably well answered. 2 (a) Risk attaching basis: A basis under which reinsurance is provided for claims arising from policies commencing during the period to which the reinsurance relates. The insurer knows there is coverage for the whole policy period when written. Alternatives are losses occurring or claims made. (b) First loss: A form of insurance cover in which the sum insured is less than the full value of the insured property, so that the policyholder has to bear any loss in excess of the sum insured. It is appropriate in circumstances where the policyholder considers that a loss in excess of the sum insured is extremely unlikely or the item is effectively priceless. Commonly used in fire business/commercial property. This approach is used to establish a more relevant figure for the sum insured on which to base the policy coverage. (c) Discovery period: A time limit, usually defined in the policy wording (e.g. in the sunset clause) or through legislative precedent, placed on the period within which claims must be reported. This term is used in policy wording to provide certainty regarding the length of time the (re)insurer is exposed to the risk of receiving claims i.e. it limits the (re)insurers exposure. It generally applies to classes of business where several years may elapse between the occurrence of the event or the awareness of the condition that may give rise to a claim and the reporting of the claim to the insurer. e.g. employer s liability or professional indemnity. Comments on question 2: Many candidates failed to define some or all of these terms. This was somewhat surprising as the answers for this question come directly from the glossary of terms in the core reading. Candidates should learn the meaning of the key terms in general insurance before attempting to sit the exam. Page 2

61 Subject ST3 (General Insurance Specialist Technical) September 2006 Examiners Report 3 (i) Average: This relates to the practice of scaling down the amount of a claim by applying the ratio of the actual sum insured to the amount deemed to have been the appropriate sum insured. (ii) Usually used in household buildings/contents insurance. For household buildings/contents insurance, the sum insured can only be obtained accurately by expert valuation which is expensive. By allowing the insured to select his own sum insured means that the cost of property valuation is not required which saves the insured money: to the insured s benefit. To the insurer s benefit, in the event of a claim, if the house is over-insured the insurer will not pay more than the actual claim, if under-insured the insurer pays the appropriate percentage. Ensures that the policyholder only gets the cover they have paid for. Discourages under-insurance. (iii) The insurer may: pay out in full pay out in full, but deduct an amount for the additional premium that would have been due if correctly insured pay out in full, but deduct an amount for the additional premiums that would have been due over several past years if correctly insured negotiate an alternative settlement decline to pay out at all/void policy improve underwriting involvement to ensure correct SI/introduce escalation clause use different exposure/rating factors to eliminate the potential for this to occur provide better upfront education of policyholders with regard to (under)insurance issues Comments on question 3: Most candidates understood the meaning of the term average, and could think of one or two alternatives approaches available to a general insurance company. The better candidates were able to generate a range of alternative approaches. In part (ii) few candidates attempted to answer the specific question on why average might be used. Page 3

62 Subject ST3 (General Insurance Specialist Technical) September 2006 Examiners Report 4 For a risk to be insurable: The policyholder must have an interest in the risk being insured. This distinguishes between a wager and insurance. The risk must be of a financial and reasonably quantifiable nature. Financial as claims settlement will be financial. This means the insurer can determine how much to pay out in the event of a claim and how much risk they are accepting. Individual risk events should be independent of each other. This is so that there is a spread of risk. The incidence and/or magnitude of the insured event must be uncertain. There should be a relatively low probability of the event occurring. Events that are certain to happen cannot be insured as payout is certain, need to be able to spread risk. There should be a large number of potentially similar risks which can be pooled in order to reduce the variance and hence achieve more certainty. There should be an ultimate limit on the liability undertaken by the insurer. This is so the insurer knows what they are liable to pay out in claims. Moral hazards should be eliminated as far as possible. These are difficult to quantify, result in selection against the insurer and lead to unfairness in treatment between one policyholder and another. There should be sufficient existing data/information to enable insurer to estimate extent of risk and likelihood of occurrence. This is so that the insurer can come up with a price. Comments on question 4: Bookwork: well answered by most candidates. 5 (i) Experience rating systems are systems by which the premium for an individual risk takes into account the claims experience of that individual risk. Some systems relate to numbers of claims, e.g. NCD schemes, Some systems relate to amounts as usually used for fleet rating purposes Some systems are retrospective. Some systems are prospective. Benefits: Small claims may be discouraged (benefits Insurer). Gives the policyholder an incentive to be cautious and take precautions to avoid claims (benefits Insurer and Insured). Page 4

63 Subject ST3 (General Insurance Specialist Technical) September 2006 Examiners Report Rewards good claims experience and penalises bad claims experience (benefits Insurer and Insured). Insurer must experience rate if this is standard market practice to avoid being selected against. Premium charged should be more representative of the risk of the policyholder having a claim (more so by amount rather than by number) (benefits Insurer and Insured). May encourage customer loyalty. Insured could be bad risk and be lucky (benefits Insured). Reduces administration for experience rating by amount (benefits Insurer and Insured). Can increase insurance companies control of underwriting for large risks (benefits Insurer). Drawbacks: Operates against the insurance principle of spreading costs (drawback Insured). Can make policyholders feel aggrieved if after many years claim free driving they have a claim and are penalised for it, e.g. in NCD systems (drawback Insurer and Insured). Can make policyholders feel aggrieved if they lose discount through a claim that was not their fault. Penalty for having a claim may be a large increase in premium, e.g. loss of NCD (drawback Insured). Increased administrative costs for rating by individual claims (drawback Insurer). Limited ability to distinguish between high and low risks if on average one claim is made by a policyholder once every five years (drawback Insurer). Does not achieve objective of rewarding better risks as the reward is given for not making a claim and not for being accident free (drawback Insured for NCD systems). Page 5

64 Subject ST3 (General Insurance Specialist Technical) September 2006 Examiners Report (ii) The statistics the insurance company would ideally require to analyse initially should be sub-divided by: regional area and by intercity services separately data over the past ten years would be ideal with data further sub divided by type of bus Particular consideration for the following is required in respect of each exposure period: The number of miles travelled. Number of passengers per year. Number of vehicle years. Similar information (expected mileage, vehicles, number of passengers etc) is required for the future policy period. Claims Data Historical claims information is required. A one to one link is required between statistics on exposure and statistics on numbers of claims. Strict definition of year of claim required, by date of accident or notification. The following statistics are required: Data are required at individual claim level Type Paid Outstanding Historical claim development data required: Dates of reporting / settlement Changes in case estimates over time Additional information required is: The method of claim recording. The method of claim handling Age of bus fleet. Speed of renewal of bus fleet. Experience of drivers increasing or decreasing. Information on drivers (previous driving experience, endorsements, convictions). Turnover of staff. One person operated buses or driver plus conductor. Changes in bus routes over the past year/planned changes for the future Additional safety features in buses, if any, incorporated over the past years. Terms of insurance required, limits, excesses, etc Additional information used to assess: Any adverse/beneficial trends that are likely to develop in the future that will tend to increase/decrease the number of claims and/or the cost of claims Page 6

65 Subject ST3 (General Insurance Specialist Technical) September 2006 Examiners Report Reasons for any change in the experience over the past few years that can be detected in the statistics. Comments on question 5: Weaker candidates produced generic lists of statistics that could be used in pricing a motor risk. These lists generally failed to consider the particular features of the risk in question, for example, that the bus company has been self insuring for some time. As a result, some candidates listed statistics that were irrelevant to the particular risk, or missed out useful statistics. In addition to tailoring their answers to the risk described in the question, the best candidates clearly structured their answers. For example, strong answers separately described claims and exposure statistics, and the need for correspondence between the two. 6 (i) How much data needs to balance what s essential to avoid discouraging potential policyholders and cover likely future data requirements. IT issues how much storage capacity will be required System structure should be flexible enough to permit future changes Need to design secure, logical and efficient IT systems to provide reassurance to potential policyholders and encouraging new business. Aim to have advanced internal cross-checks to ensure majority of potential inaccurate info is corrected at source. Aim to ensure info is entered in a consistent manner to ensure the info captured can be analysed meaningfully. Need to design exception reports to investigate potential oddities. How will the data be captured and/or verified. e.g. Proof of possession, Claims History, access to car registration database, proof of entitlement to NCD. What information will other users require e.g. reinsurers, regulators, auditors. and the uses to which the data will be put e.g. reserving, rating, marketing, etc. Need to ensure backup arrangements exist and disaster plans. Aim to ensure designed for ease of data retrieval after input to ensure ease of reporting and analysis. Data security issues. Data Protection Act issues. Payment security issues. Page 7

66 Subject ST3 (General Insurance Specialist Technical) September 2006 Examiners Report (ii) May charge incorrect premium rates which may result in larger than planned volumes at loss making rates / worse than expected or smaller than planned volumes leading to insufficient coverage of fixed / start-up costs Or have incorrect rating structure resulting in adverse selection. May result in early solvency pressure at a time when capital is most scarce. May result in loss of regulator confidence leading to subsequent business restrictions / closure. May result in loss of market confidence with longer-term business retention implications. Inappropriate reinsurance purchased. May result in loss of reinsurer confidence. Comments on question 6: Candidates that scored poorly on part (i) often failed to read the question carefully enough, and as a result produced lists of rating factors for motor insurance. Also candidates often did not generate the breadth of points, getting bogged down in the detail of just one area. In part (ii), most candidates correctly identified that use of inaccurate data could lead to incorrect premium rates. Better candidates went on to identify the consequences of mis-pricing with regard to capital, regulation, reinsurance and market confidence. 7 (i) To avoid distortions in any statistical analysis it is important to ensure that all information is converted to a consistent basis for consideration. Changes in cover these will affect the relative exposure levels between different cohorts and hence the likely claims trends. Inflation differences in both past and future levels may affect the analyses if not stable through time. External changes affecting exposure. e.g. legislative or building regulation changes may affect both the likelihood and severity of claims. Change in geographic spread or premium rates may affect the mix of business. Large one-off claims where these may distort the analysis. Page 8

67 Subject ST3 (General Insurance Specialist Technical) September 2006 Examiners Report Significant / Catastrophe event. e.g. Weather related / Subsidence where these may distort the analysis. There are also many issues that may affect the claims runoff and distort any trend. e.g. reporting delays due to internal or external issues or mass sickness or postal strikes. Handling / settlement delays. Internal system changes. Seasonality / Regional bias. Changes in claim settlement procedures. Split data into homogenous groups, by class or claim type. Data cleaning/removal of errors. Reinsurance if net paid data is being projected. Consistent treatment of claims handling expenses. Tail factor. (ii) Different basis of reserving, e.g. loss adjusters may have under/over reserved, actuary may have included margins. Loss adjusters may each have different views on costing and inflation issues both of these can be investigated by means of an audit / review process with particular focus on the largest case estimates. Loss adjusters have more information upon which to base their estimates. Comparison of the largest differences can be investigated at cell level to see if there are any particular isolated large discrepancies. Statistical estimates may include loss adjustment expenses example of investigation for loss adjustment expenses Statistical estimates may include IBNR/unexpired risk provision example of investigation for IBNR/unexpired risk provisions Statistical estimates may include reinsurance recoveries Statistical estimates may have been discounted There may be errors in either or both statistical and case estimates which can be investigated by rigorous review of both sets of estimates. IBNR may be negative due to computer generation of too many case estimates for small claims, which later become redundant on the system. Case estimates may be out-of-date which may be highlighted through investigating the dates on which the case estimates were established. Page 9

68 Subject ST3 (General Insurance Specialist Technical) September 2006 Examiners Report There may be currency errors which may be highlighted through exception reporting. Statistical adjustments are approximated across groups of claims rather than assessed at individual claim level. To investigate any inaccuracies arising from this, statistical estimates can be calculated on several different bases using several different methods to ensure internal consistency / identify any flaws ensure the estimates are robust and not affect significantly by rogue cells to help understand any oddities in the results. Statistical estimates may be more accurate if, for example, they were based on incurred claims rather than paid claims, or premiums were used. Investigate the accuracy of data used in the statistical analyses. There may have been changes in loss adjustment procedures. Investigate whether loss adjusters look at all claims or whether case outstandings on small claims are set using a formulaic approach. Check reliability of formula based approach. Comments on question 7: Part (i) was reasonably well answered with many candidates identifying a range of issues that could require adjustment. Many candidates found part (ii) more difficult than part (i) even though this is a question that has been asked a number of times in the past. Stronger candidates appreciated that both statistical methods and case estimates are based on judgemental assumptions, and considered the possibility of different views being taken on these assumptions. Some candidates did not describe the investigations at all and therefore scored poorly. Generating a breadth of reasons for the difference was again a problem for many candidates. 8 (i) Collect claims data over an appropriate historical time period. The time period chosen should be long enough to have credible data and it should be recent. Subdivide the data into homogenous groupings (e.g. by peril or exposure period) taking care to ensure credibility within the cells. Adjust data to allow for: Claims inflation over the historical period to now. Changes in exposure over the period. Changes in policy conditions, limits and deductibles. Changes in legal / regulatory conditions. Page 10

69 Subject ST3 (General Insurance Specialist Technical) September 2006 Examiners Report Projection to ultimate. It may be advisable to allow for large/catastrophe losses separately Fit a range of probability distributions to the data within each grouping. Find separate loss distributions for frequency and severity of loss within the homogenous groupings. Use of binomial, Poisson, negative binomial for frequency, whole numbers or normal or translated gamma for severity. Select appropriate parameters for the fitted distributions. Combine the loss distributions for separate perils by closed form or simulation methods to obtain an overall aggregate claim distribution. The company might also have fitted a distribution (e.g. Lognormal, Pareto, Weibull) to the aggregate claims directly. Test goodness of fit. (ii) μ =μ +μ = = 50m A+ B A B A+ B A B σ =σ +σ = = = 1000 Standard Deviation of A + B = 1000 (iii) Mean of a lognormal distribution = 2 2 2μ+σ And variance = e ( e 1) σ = 31.62m e μ+ σ Std Deviation = e 2 2 μ+ 1 2σ e σ 1 Std Deviation = Mean. 2 e σ 1 Std Deviation / Mean = 2 e σ 1 = Coefficient of variation = CV => σ= 2 loge ( CV + 1) and μ = log e (Mean) 0.5σ 2 where μ and σ are the mean and standard deviation of the underlying normal distribution. Page 11

70 Subject ST3 (General Insurance Specialist Technical) September 2006 Examiners Report Class A B Total Mean = m Stdev = s CV = s/m ( CV 2 ) σ= loge μ = log e (Mean) - 0.5σ If working in, mean of A is 17.16, mean of B is and mean of total is (iv) 99.5 th percentile for a standard normal distribution is at So the 99.5 th percentile is given by μ σ Class A B Total ( CV 2 ) σ= loge μ = LN(Mean) 0.5σ th percentile th Percentile claim Alternative answers were allowed based on alternative number of decimal places used for the 99.5 th percentile of a standard normal distribution (v) Claims experience between the two classes is likely to be correlated due to: Both classes are likely to be affected by underlying economic conditions. For example, at time of low economic growth there tend to be more fraudulent claims, and theft claims. Events such as windstorms, earthquakes, flooding tend to cause losses in both classes of business. Both classes would be subject to bigger losses in inflationary environments. Legal changes may affect claims severity and frequency in both classes e.g. changes in court procedures, statute of limitations, and other legislation could affect both classes. Similar claim handling procedures. Higher crime rates would lead to more theft claims from both classes. Page 12

71 Subject ST3 (General Insurance Specialist Technical) September 2006 Examiners Report (vi) If we assume independence between the two classes of business, then loss given that losses are at 99.5 th percentile = = If we assume that the two classes are 100% correlated, then the loss given losses at 99.5 th percentile = = Negative correlation is not likely. Adjust for premium received (100) Adjust for expenses (25) Therefore capital required is between m and m. Comments on question 8: Part (i) was generally well answered with better answers discussing the aggregate distribution, poorer answers trotting out the standard bookwork. Part (ii) was simple but not universally well answered. Parts (iii) and (iv) were not difficult but many struggled or did not attempt. Part (v) was often poorly answered even though completely independent of the calculations. A few candidates actually suggested that the results of the calculations in previous parts of the question, which were based on assuming independence, indicated that the classes were not independent without spotting the flaw in this logic. Part (vi) was only answered reasonably by a small minority. Many candidates who correctly identified the method required for the question went on to lose marks due to calculation errors suggesting that they had not left sufficient time to check their answers. END OF EXAMINERS REPORT Page 13

72 Faculty of Actuaries Institute of Actuaries EXAMINATION 16 April 2007 (pm) Subject ST3 General Insurance Specialist Technical Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 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. 4. Mark allocations are shown in brackets. 5. Attempt all 6 questions, beginning your answer to each question on a separate sheet. 6. Candidates should show calculations where this is appropriate. AT THE END OF THE EXAMINATION 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 the 2002 edition of the Formulae and Tables and your own electronic calculator. ST3 A2007 Faculty of Actuaries Institute of Actuaries

73 1 You are an actuary working for a general insurance company with a small book offering professional indemnity cover to solicitors through brokers. Your CEO has noted that a competitor has recently been successful in growing its book by selling professional indemnity policies direct to small firms of solicitors. He suggests that you could increase your book with a major campaign marketing professional indemnity cover direct to other professions. (i) Outline the risks to the company of pursuing such a marketing campaign. [7] (ii) Suggest how the risks identified in (i) could be mitigated. [5] [Total 12] 2 A small general insurance company specialises in motor insurance. (i) (ii) Outline the principles that you would consider in deciding in which assets the company should invest. [9] Explain how these principles differ from those of a large general insurance company specialising in employers liability. [3] [Total 12] 3 You are the actuary of a large general insurance company. You have been asked to price a cross-class deal for a customer. The policy will cover the customer s motor fleet and public liability requirements. Another general insurance company has written the public liability cover in the past. The proposed structure for the policy is as follows: Motor: the general insurance company will provide unlimited cover for any individual loss. Public liability: the limit of indemnity on any one individual loss is 250m. The customer retains a deductible of 0.5m on each and every loss for the complete programme subject to an annual aggregate deductible of 15m. (i) Outline the concerns you would have with this proposed structure. [3] The customer has provided you with a large database of their individual claims data, as well as relevant exposure measures, for the past 10 years. (ii) Explain how you would calculate a risk premium for this product using the information on this database. [10] [Total 13] ST3 A2007 2

74 4 A motor underwriter has approached you for assistance with a new business premium quote on a fleet of 100 heavy goods vehicles commencing 1 January She has supplied you with the following unprojected historical claims data from the existing insurer as at 31 October Incurred Claim amounts in 000 s Accident Year Own Damage Incurred Costs Third Party Damage Incurred Costs Third Party Personal Injury Incurred Costs Earned Vehicle Years The following additional information is available: The prospective insured has always renewed the policy on 1 January each year. Damage inflation has been 4% p.a. for many years. Personal Injury inflation has been 7% p.a. in each of the calendar years 2003 to 2005, then 9% p.a. from calendar year Incurred Claims as a percentage of Annual Ultimate Projected Claims are estimated from internal data to be: As at development month Own Damage 70% 95% 105% 102% 100% Third Party 45% 80% 95% 100% 100% Damage Third Party Injury 30% 55% 75% 85% 95% Commission is 15%. Expenses are 100 per policy, 10 per vehicle and 7% of claims costs. Insurance Premium Tax can be ignored. Profit and contingency loading is 5% of the overall gross written premium. (i) Estimate the annual premium to charge the prospective client, using the data provided, stating any assumptions you make. [11] You have predicted that the average annual premium charged per vehicle during January 2008 on your company s existing account of 25,000 heavy goods vehicles will be 3,750. You decide to recalculate the premium using a credibility approach. ST3 A PLEASE TURN OVER

75 (ii) Recalculate the annual premium assuming you use a credibility factor for the fleet s own experience as: Z = minimum (1, 1 - σ/μ) where σ = the standard deviation of the yearly projected burning cost per vehicle observed from the five year data μ = the average of the yearly projected burning cost per vehicle observed from the five year data [4] (iii) Explain why the premium charged in practice may not equal the premiums calculated in parts (i) or (ii). [5] [Total 20] 5 You are the actuary of a large general insurance company that only sells insurance to large international companies. The underwriters are considering entering the smaller end of the commercial market through the creation of a new product that covers the insurance needs of construction and engineering tradesmen who are either sole traders, partnerships or limited companies with up to five employees. (i) (ii) (iii) Describe the distribution channels through which this new product could be sold. [8] Compare the marketing methods in part (i) to those which would be used for the insurer s existing business. [2] Describe the types of commercial insurance that these tradesmen may wish to purchase. [10] [Total 20] ST3 A2007 4

76 6 You have been provided with the following financial information for general insurance companies X, Y and Z for the accounting year All amounts shown are in $millions. Company X Y Z Gross Written Premium 50 2, Additional Unexpired Risk Reserve c/f Gross Outstanding Claims Reserve b/f Gross Claims Paid Gross Outstanding Claims Reserve c/f Non Acquisition Expenses Investment Income Current Assets at 31/12/ Current Liabilities at 31/12/ Investments at year end 125 3,500 1,000 Share capital at 31/12/ Acquisition Costs as a % of Gross Written Premium 30% 15% 20% (i) (ii) Construct the balance sheet for each of the three companies as at 31 December 2006, stating any assumptions made. [5] Derive underwriting, solvency and return on capital employed ratios for all three companies, stating any assumptions made. Taxation should be ignored. [9] (iii) Comment on the results in part (ii). [4] (iv) Define five other insurance related ratios that could be derived from the data to compare the performance of the three companies and state each of their objectives. [5] [Total 23] END OF PAPER ST3 A2007 5

77 Faculty of Actuaries Institute of Actuaries EXAMINATION April 2007 Subject ST3 General Insurance Specialist Technical 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 A Stocker Chairman of the Board of Examiners June 2007 Comments Individual comments are shown after each question. Faculty of Actuaries Institute of Actuaries

78 Subject ST3 (General Insurance Specialist Technical) April 2007 Examiners Report 1 (i) (ii) Biggest danger is charging insufficient premium this is a new distribution channel exacerbated by lack of data since only have a small existing book which might not cover the relevant professions Lack of expertise in the professions CEO may be interested in May be difficult to attract staff (e.g. underwriters) with enough experience of PI Inappropriate rating structure that could lead to anti-selection Could annoy brokers of existing PI book could lose this business Risk of loss of broker value (e.g. collating detailed underwriting and risk information from clients, administering policies and claims) Significant set up costs for direct operation might not be recouped if insufficient volume of business This could be more likely as this is a new channel, and other professions may prefer to place the cover through a broker The set up costs/ongoing expenses may be much higher than anticipated especially if we do not have experience in selling direct There is a danger that a competitor reacts e.g. by a similar campaign leading to lower volumes than anticipated Exposure to large losses Greater exposure to accumulation event as write more business and more professions, but may be more than offset by diversification benefit Reinsurance risk insufficient or unavailable coverage Regulation risk e.g. channel authorisation May sell bigger volume than expected leading to too much risk/increased capital requirement Reduced persistency (e.g. lower retention) Operational risk of setting the whole arrangement up Problem of lack of data might be mitigated by using reinsurer data if using reinsurance Industry data might also be useful if available Reinsurers could also provide expert advice in this field on rating and underwriting Alternatively recruit more experienced staff Reinsurers provide assistance in mitigating the risk of large single losses and accumulations (e.g. through per risk xl cover and cat cover) Use financial reinsurance or raise more capital to support balance sheet Difficult to mitigate the risk of annoying brokers. It may help to sound them out beforehand or allow them to sell the new product as well Difficult to predict competitor action but company should monitor competitors pricing levels Danger of low volume mitigated by market survey Full costing with experts on similar projects would help to assist in correctly estimating expenses (or similar sensible comments on controlling expenses) Page 2

79 Subject ST3 (General Insurance Specialist Technical) April 2007 Examiners Report Regular monitoring should ensure that volume controlled and addressed by regular rating action Check with regulators that this class and marketing method are allowable Research reinsurance market to ensure sufficient coverage available Check that relevant IT systems, human resource and facilities are capable of coping with new operation Carrying out pilots with friendly brokers will help identify issues early Comments on question 1: Part (i) was generally well answered by most candidates. For part (ii) not all candidates ensured that all of the points raised in part (i) were subsequently addressed. Candidates who identified the financial, operational and reputation risks scored particularly well in this question. 2 (i) Try to maximise investment return subject to meeting liabilities with chosen level of certainty Match assets and liabilities by term amount nature currency Motor property damage claims are mainly short tailed, so need liquid assets need to hold cash on deposit, very short dated assets such as short dated government securities to match liability outgo Motor third party claims are longer tailed and costs are influenced by inflation need to hold some longer dated real assets (index linked securities if available or low risk equities) Consider regulatory requirements : restrictions on assets that can be held prescription to hold assets custodianship of assets mismatching allowed Since company is small, need to have extra consideration of the level of uncertainty in reserves, so more secure, liquid assets required A small company might consider collective investment vehicles (e.g. unit trusts, investment company shares) Investment likely to be in assets of small unit size (e.g. no direct property investment Level of investment expenses of each asset type Tax efficiency of each asset type Availability of certain asset types Benchmarking against competition Availability of additional capital (e.g. parent company, shareholders) Diversification of assets held (within and between asset types) Page 3

80 Subject ST3 (General Insurance Specialist Technical) April 2007 Examiners Report Size of the free reserves (in excess of solvency requirements) As the company is small, the company is less likely to be able to accept the risk of investing in higher risk/reward investments (e.g. property) Expected growth plans and resultant needs to invest in the business Shareholders and management s attitude to risk (ii) Since company is large, assuming larger free assets, potential scope for more aggressive investment strategy. Employers liability claims are generally longer tailed and costs are influenced by inflation Greater need to hold longer dated assets providing real returns since better match by term for liabilities Equities and properties are an appropriate match Index-linked bonds (if available) for security and inflation hedge Potential investment in specialist areas such as large unit size, ventures, brokers, derivatives Likely to handle investments in-house through specialist team of managers giving greater control over investment choice Comments on question 2: Most candidates scored well on this bookwork question. A few candidates suggested investments in part (i) that were unlikely for a small company (e.g. direct property). 3 (i) (ii) Once the 15m aggregate is exhausted and/or as there is no aggregate limit on public liability, there is the potential for a single bad year Unlimited coverage for motor potential for large single loss Large limit for public liability potential for large single loss Do we have the required reinsurance coverage to protect the insurer against these? Need to clarify if the excesses/limits cover legal and other expenses Model the motor and public liability accounts separately Group claims by property damage and bodily injury per cover Need to model the frequency and severity separately in order to apply deductible Use client s data as start point (since large dataset) Pick a base period Use from the ground up data Adjust for IBNR and IBNER Adjust the claims for inflation Adjust for change in exposure Adjust for trends in data Adjust for changes in underwriting and claims handling procedures Page 4

81 Subject ST3 (General Insurance Specialist Technical) April 2007 Examiners Report Adjust for any changes in terms and conditions over period considered Compare outcome with any internal portfolio/external benchmark data - especially for large loss assumptions - consider credibility weighting to portfolio/benchmark Consider any relationship between claims received under motor and public liability covers to determine any correlation in experience Unlikely to be strong so probably model as independent. Could use deterministic modelling approach to determine parameter estimates for frequency and severity for each cover Determine the mean values for both parameters Alternatively could model the outcome of the individual accounts using stochastic modelling approach Carry out several thousand simulations and apply the product rules to the outcome The average outcome to the insurer in the simulations will give the expected loss cost to the insurer This would also provide the range of possible claims experience scenarios which could assist in determining suitable reinsurance arrangements Comments on question 3: This question was poorly answered by most candidates. Some candidates were of the mistaken opinion that unlimited liability for motor is abnormal. Many candidates suggested use of Generalised Linear Modelling techniques involving the use of rating factors when this was clearly inappropriate for a policy for which all losses are large losses. Furthermore, many candidates decided to cut and spread large losses when the purpose of the cover was to protect the insured against large losses. This requires an analysis of the claims size distribution to determine the impact of the deductible and aggregate deductible on the expected claim frequency and severity. Very few candidates explored benchmarking claims experience against internal/external claims data nor the use of deterministic and stochastic methods in pricing this policy, thus missing out on a significant number of the available marks. Page 5

82 Subject ST3 (General Insurance Specialist Technical) April 2007 Examiners Report 4 (i) Assumptions Assume claims inflation in 2008 = claims inflation in 2007 Development factors are on the same basis as claims stats Projected Claims Costs (before claim inflation allowance) Year Damage Costs Third Party Personal Injury Costs = = = = = Amounts in 000 Claim inflation adjustments to 2008 Year Damage Costs Third Party Personal Injury Costs = = = = = = = = Projected Claims Costs (after claim inflation allowance) Amounts in 000 Year Damage Costs Third Party Personal Injury Costs Total Burning Cost per vehicle = ( ) 1000 / ( ) = 2,178 Page 6

83 Subject ST3 (General Insurance Specialist Technical) April 2007 Examiners Report Gross Premium to charge client = (number of vehicles in 2007 burning cost per vehicle claims costs + policy expenses + vehicle expenses) / (1 commission rate profit and contingency loadings) = ( ) / ) = 292,683 Also identifying and allowing for any legitimate trends in the data, e.g. improvement in PI peril Alternative acceptable approaches scored equivalent marks (ii) Yearly burning cost observations 2003: 175,872/80 = 2, : 201,106/88 = 2, : 174,499/90 = 1, : 222,903/92 = 2, : 201,429/98 = 2,055 μ = ( )/5 = 2,180 σ = Square root of {(5 ( ) ( ) 2 )/(5 4)} = 190 Therefore Z = min (1, 1 190/2180) = min (1, ) = Therefore revised gross premium = Z 292,683 + (1 - Z) ( ) = 298,932 Note alternative approach: one could strip out the claims cost from the average premium and then blend claims costs and reconstruct gross premium from that (iii) The 5 year historical claims experience may be heavier or lighter than is expected in 2008 Potential large losses in historical data distorting the calculations Competitors pricing levels Insurer may be willing to take a reduced profit or slight loss on this business as the policyholder has other insurance contracts with the company that are highly profitable. Using the insurer s own heavy goods vehicles experience may be inappropriate, for example the account may have a different business mix to that of the client (e.g. age of drivers, location of vehicles). Cover provided in 2008 differs from that in previous years (e.g. increased own damage excess) Different policy wordings/restrictions expected to reduce claims costs/numbers Page 7

84 Subject ST3 (General Insurance Specialist Technical) April 2007 Examiners Report Expected future external events (e.g. changes in legislation) that may impact claims costs, expenses, commission or profit allowances Per policy expense allowance in main account may be disproportionately higher than that required under this fleet contract Influence of broker/customer (e.g. volume of other business offered by broker/customer) Regulators may restrict the price that could be charged Other assumptions not used in the calculation (e.g. investment return, reinsurance) Management decision/growth plans/attitude to risk Position in the market cycle Comments on question 4: In part (i), the examiners solutions provide one answer although alternative solutions were given equivalent marks (e.g. taking an average of each year s burning cost per vehicle). Some candidates applied the profit and contingency loading to the risk premium and not the office premium as stated in the question. Parts (i) and (ii) were fairly numerical questions and these parts were generally well answered by most candidates. However, some confusion arose over the time period to use for the inflation figures. Some candidates also failed to realise that, as the incurred claims development data were as at 10, 22, months there was no need for further adjustments to allow for the data provided being as at 31 October For parts (ii) and (iii) the better candidates identified the external factors such as market, distribution and regulatory influences on the price. For part (iii) most candidates failed to generate enough ideas. 5 (i) Brokers A company which acts as an intermediary between the seller and the buyer of the insurance product without being tied to either party Banks, Building Societies and other financial institutions A company whose main activities include providing financing to small businesses and can therefore cross-sell insurance on the back of loan arrangements Trade Associations A union whose main activity is to provide support and advice to companies of a similar trade who can provide insurance products tailormade to their requirements Internet The insurance company can develop a web-based sales point with the customer entering all the relevant rating information through the internet to obtain a quote for insurance Page 8

85 Subject ST3 (General Insurance Specialist Technical) April 2007 Examiners Report Telesales A call centre arrangement managed by the insurance company to provide in-calls and out-calls to potential clients In-calls can be through advertising in press or telephone directories Out-calls can be through leads generated from commercial tradesmen databases Direct mailshot The insurance company can directly target potential clients through the posting of literature to small business tradesmen Employed staff paid by salary or commission Staff of the insurance company visit the potential clients face to face to discuss their insurance requirements based on their circumstances. Affinity Groups (e.g. Trade Retailers, Training Groups) A company whose main activities are non-insurance related (e.g. a building supplies wholesaler) but whose organisation has a significant Commercial customer database to target sales. (ii) Companies of all sizes (small and large) may use Commercial brokers as they can offer advice on their specific insurance needs. Larger international companies with credible data attract individual underwriting and brokers facilitate this, whereas a standard rating structure approach is used for smaller risks Companies of all sizes could be a part of a trade association The remaining distribution methods are more likely to be used mainly by small businesses due to: the relative speed and ease of obtaining low cost insurance the far greater propensity for clients to use the distributor for other non-insurance activities the commodity nature of small business insurance products makes them more appropriate for direct route cost considerations : lower unit delivery cost of internet when compared to brokers is appropriate for low average premiums (iii) Public Liability The insured is indemnified against legal liability for the death or bodily injury to a third party Page 9

86 Subject ST3 (General Insurance Specialist Technical) April 2007 Examiners Report Or for property damage belonging to a third party Other than those liabilities covered by other liability insurance Employers Liability The insured is indemnified against legal liability to compensate an employee or temporary employee for the death, disease or bodily injury suffered owing to the negligence of the employer during the course of employment. Contract Works Indemnifies insured against loss of or damage to contract works property being worked on and materials Plant insurance (Hired or Own Plant) Indemnifies insured against loss or damage to plant whether it is hired or owned by the insured Employees Tools All Risks Indemnifies insured against loss or damage to tools used in the course of trade Personal Accident/Sickness Indemnifies all people specified under the cover for loss of earnings in an event of an injury or accident, whether temporarily or permanently out of work. Professional Indemnity Indemnifies insured against legal liability resulting from negligence in the provision of a service (e.g. inaccuracies in architectural building design) Vehicle insurance (vans, pickups, goods vehicles, trucks, lorries) Property Damage indemnifies insured against loss or damage to their own vehicles Third Party Liability indemnifies insured against compensation payable to third parties for damage to their vehicle or property or for personal injury Acceptable alternative valid covers : Commercial Fire/Business Interruption/Offices Fidelity Guarantee/Theft by Employees Pecuniary Loss/Credit Guarantee/Third Party Failure Page 10

87 Subject ST3 (General Insurance Specialist Technical) April 2007 Examiners Report Comments on question 5: Part (i) was well answered by the majority of candidates. A few candidates listed distribution channels but failed to describe them as the question asked. Candidates failed to generate many points for part (ii) and thus missed many points on the marking schedule. The better candidates identified the differences between the commodity nature of selling insurance to small businesses and the more bespoke underwriting requirements of selling insurance to large international businesses. In part (iii), candidates who scored well identified the specific property and casualty insurance risks of small construction and engineering businesses. 6 (i) Assumptions All yearly business No reinsurance Risks written uniformly across year Risk is uniform across policy year Assets Company X Y Z Total investments Current Assets Deferred Acquisition Costs Total Assets Liabilities O/S claims reserves Additional URR UPR Current Liabilities Free Reserves Total Liabilities (ii) Assumptions assume GWP = GEP (i.e. business written in 2005 = business written in 2006) assume AURR as at 31/12/2006 = AURR as at 31/12/2005 assume outstanding claims reserves include IBNR Loss Ratio = claims incurred/gep Company X = ( )/50 = 90% Page 11

88 Subject ST3 (General Insurance Specialist Technical) April 2007 Examiners Report Company Y = ( )/2000 = 37.5% Company Z = ( )/250 = 40% Expense Ratio = Acquisition Expense Ratio + Non Acquisition Expenses/GWP Company X = 30% + 5/50 = 40% Company Y = 15% + 250/2000 = 27.5% Company Z = 20% + 30/250 = 32% Underwriting Ratio = Loss Ratio + Expense Ratio Company X = 90% + 40% = 130% Company Y = 37.5% % = 65% Company Z = 40% + 32% = 72% For solvency ratio: Solvency Ratio = Free Reserves/GWP Company X = 57/50 = 114% Company Y = 1680/2000 = 84% Company Z = 190/250 = 76% For return on capital employed: Return on Capital employed = (Earned Premium Claims Incurred Expenses + Investment Income) / Free Reserves Company X = (50 - ( ) ))/57 = -21% Company Y = (2000 ( ) ))/1680 = 48% Company Z = (250 ( ) )/190 = 45% (iii) Comments Company X may have suffered from adverse claims experience due to its higher loss ratio compared to the other companies. Each company may be writing different classes or mix of business, each at a different point in their respective market cycle Company X expense ratio is higher due to higher acquisition expense ratio. The company is smaller than Y and Z and it may be spending money to expand rapidly. Company X solvency ratio is higher than the other companies. This may be the result of a recent capital injection to expand the business. Company Z has the lowest solvency ratio, suggesting that the company is less financed than the other companies. Or it may have more stronger valuation basis for its assets and liabilities Page 12

89 Subject ST3 (General Insurance Specialist Technical) April 2007 Examiners Report Company Z return on capital employed is the highest, supported by a larger relative investment return compared to the other companies Company Y and Z both have high returns on capital employed, supported by a good underwriting results Relevant comment comparing profitability and solvency (iv) Investment Return = Investment Income/(Current Assets + Investments) This provides a comparison of the investment performance of the companies. Gross Claims Paid/Gross Outstanding Reserves This provides a comparison of the relative speed at which reserves are reduced by claims payments Gross Outstanding Reserves/Gross Written Premium This provides a comparison of the relative strength of the outstanding reserves Additional Unexpired Risk Reserve cfwd / UPR cfwd This provides a comparison of the relative profitability of the unexpired risk Current Assets / Current Liabilities This provides a comparison of the ability of each company to meet short term liabilities without the need to realise investments Acceptable alternative valid ratios: Loss Ratio Expense Ratio Profit Margin Total Assets/Total Liabilities Comments on question 6: The examiners were disappointed by the standard of answers to this question. In part (i) a number of candidates made assumptions that were inconsistent with the data provided in the question (e.g. assuming all policies were written on 1 January each year with no UPR at year end even though an AURR was being carried forward at year end). Some candidates thought that share capital was an asset and failed to understand that this formed part of the free reserves of each company. In part (ii), a number of candidates did not know the definition of underwriting ratio with some incorrectly assuming it was derived from the underwriting profit. In part (iii), the better candidates commented on possible reasons for the level of the ratios in part (ii) and compared profitability and solvency levels for each company separately. Most candidates merely commented on whether the ratios were high/low for each company without providing any explanation as to what may be driving the results. In part (iv), a number of candidates defined ratios that could not have been derived from the data as specified in the question (e.g. % reinsured). END OF EXAMINERS REPORT Page 13

90 Faculty of Actuaries Institute of Actuaries EXAMINATION 27 September 2007 (pm) Subject ST3 General Insurance Specialist Technical Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 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. 4. Mark allocations are shown in brackets. 5. Attempt all 6 questions, beginning your answer to each question on a separate sheet. 6. Candidates should show calculations where this is appropriate. AT THE END OF THE EXAMINATION 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 the 2002 edition of the Formulae and Tables and your own electronic calculator. ST3 S2007 Faculty of Actuaries Institute of Actuaries

91 1 A small general insurance company writes only a specialised book of business. The aggregate claims distribution is estimated to follow a compound Poisson distribution where λ = 10% and the claim size distribution is exponential with mean of 0.5m. The company starts with capital of 10m. (i) Show that the loss ratio that the general insurance company must achieve in order to ensure that its probability of ruin is less than 0.5% is 73.5%. Ignore expenses for the purposes of this calculation. [4] The predicted loss ratio for the business next year is 90%. (ii) Comment on whether this is a problem for the general insurance company and list the actions the company might take. [6] [Total 10] 2 You are an actuary working for a newly established general insurance company. It commences writing household contents insurance on 1 September 2006 writing annual policies only. The company sells the following number of policies per month in 2006: Month Policies sold September 1,000 October 1,500 November 2,000 December 2,500 (i) Describe the claims characteristics of household contents insurance. [3] (ii) Calculate the average accident date for accidents occurring during 2006 by considering the company s exposure profile. Assume that policies incept on the first day of the month in which they are sold. State any other assumptions that you use. [4] You have obtained benchmark accident year development factors by analysing a sample of long-established general insurance companies offering similar policies and with similar business mixes as your company. (iii) Discuss the appropriateness of using this benchmark pattern to project the 2006 accident year to ultimate. [4] [Total 11] ST3 S2007 2

92 3 You are the actuary of a large general insurance company that writes all types of property insurance. The management is reviewing the reinsurance programme, which has historically comprised facultative and treaty arrangements and has asked for your comments. (i) Define the terms facultative reinsurance and treaty reinsurance. [2] (ii) (iii) Compare the advantages and disadvantages to the insurance company of using facultative arrangements rather than treaty arrangements. [5] Discuss the factors that you would consider when assessing the effectiveness of the existing reinsurance programme. [6] [Total 13] 4 You are a consulting actuary engaged by a small general insurance company which writes only motor business. The company sells its policies through a broker network and direct to customers. It has been attempting to grow its business and written premium and policy volumes have both increased in the last two years. However, its profit margin has fallen over the same period. The company has asked you to analyse its business and identify reasons for its falling profitability. Describe the actuarial analyses that you would carry out in each of the following areas and discuss the features for which you would be looking in your analyses. (i) Claims [5] (ii) Premiums [4] (iii) Mix of business [5] (iv) Reinsurance [4] [Total 18] ST3 S PLEASE TURN OVER

93 5 You are a pricing actuary of a general insurance company writing employers liability for large companies. An underwriter has given you the following information on a risk that he wishes to renew in Under the proposed terms of the policy there is a limit for each and every loss of 5m and no deductible. Underwriting Year Number of Employees Notified claims ( 000 s) ,100 1, ,600 1, ,400 1, , ,800 The underwriter suggests that the underwriting year incurred development pattern for similar risks is: Underwriting Year % Developed % % % % (i) (ii) (iii) Calculate the risk premium for 2007 using a burning cost methodology allowing for claims inflation of 10% per annum, indicating any assumptions that you make. [8] Explain why the answer that you calculated in (i) may not be an accurate indication of the true risk premium. [5] Further to the points raised in (ii), state what further information you would require to calculate your theoretical office premium for the risk. [3] The actual office premium quoted for the risk is different to the theoretical office premium that you recommend. (iv) Discuss the situations that could give rise to this, other than those already raised in (ii) above, and outline the concerns you would have in each case. [5] [Total 21] ST3 S2007 4

94 6 You are an actuary of a large general insurance company writing private motor business. You are estimating the technical reserves for this class of business as at 31 December You have been given the net paid accident year triangle for the class as a whole, from which you have calculated development factors using the basic chain ladder method, as shown below. Net paid development factors on cumulative amounts Development year Accident year Selected idf s Selected cdf s idf = incremental development factor cdf = cumulative development factor (i) (ii) Suggest reasons why actual ultimate claims paid may differ from those estimated using the paid chain ladder method. [5] Discuss other analyses and projections that you would wish to perform before selecting your undiscounted outstanding claims reserve, including IBNR. [11] (iii) (a) Outline the arguments for and against discounting of reserves. (b) State the factors that you would consider in arriving at an appropriate discount rate. [5] The company has decided to discount its reserves for this class using an interest rate of 9% per annum. (iv) Calculate an appropriate discount factor to apply to the undiscounted reserves for accident year 2004 as at 31 December 2006, stating any assumptions you make. [6] [Total 27] END OF PAPER ST3 S2007 5

95 Faculty of Actuaries Institute of Actuaries EXAMINATION September 2007 Subject ST3 General Insurance Specialist Technical 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 Stocker Chairman of the Board of Examiners December 2007 Comments Individual comments are shown after each part-question or question. Faculty of Actuaries Institute of Actuaries

96 Subject ST3 (General Insurance Specialist Technical) September 2007 Examiners Report 1 (i) Probability of ruin Ψ(U) e -RU (Lundberg s inequality) where U = initial capital = 10 R = adjustment coefficient = aθ/(1 + θ) where a is the exponential parameter i.e. = 1/0.5 = 2 and θ = is the premium loading factor so 1/(1 + θ) = x, where x is the loss ratio Set = e -RU and solve for x to find the required loss ratio R = 2(1 - x) = e -20(1-x) x = 1 + ln(0.005)/20 x = 73.5% Comments on Q1(i). Some students showed that 73.5% loss ratio implies a ruin probability of less than 0.5%. This approach gained equal credit. Many candidates got full marks on this part. (ii) 90% LR implies a probability of ruin much higher than 0.5%, so this may be a problem if the insurance company requires a 0.5% or lower probability of ruin for regulatory solvency/capital requirements, for example or if this would adversely affect insurer's credit rating Lundberg s inequality gives probability of ruin < 13.5% Being a small company, parameter uncertainty surrounding the predicted 90% LR is likely to be greater as it is being estimated on less data Lundberg's inequality is probability of ultimate ruin so concern will depend to an extent on whether the 90% LR is expected to persist; the current position within the insurance cycle may mean that market is currently soft but expected to harden in the next few years The extent to which this is a problem also depends on the level of expenses and commissions as well as the investment return expected on the assets held to back the reserves Possible actions: Investigate why the predicted loss ratio is 90% Consider why insurer requires a probability of ruin of 0.5%. If competitors live with a higher probability of ruin then at a competitive disadvantage Consider reinsurance: might be able to reduce probability of ruin by using reinsurance to reduce variability but will be passing on profit to the reinsurer Reduce expense/commission ratio to compensate for higher LR Tighten claims handling/settlement procedures to reduce payouts Consider diversification into other lines (currently writing specialised book) Enforce tighter underwriting criteria to exclude bad risks Page 2

97 Subject ST3 (General Insurance Specialist Technical) September 2007 Examiners Report Reduce coverage using lower limits and/tighter policy wording/higher excess or deductible Increase premium rates Do nothing; if 90% LR is thought to be the soft part of insurance cycle, management may make a strategic decision to write across the cycle Comments on Q1(ii). Most students were able to list the various actions to bring the loss ratio down. Not so many mentioned the insurance cycle and virtually none pointed out that probability of ruin is to ultimate, not just over the next year. 2 (i) Household contents insurance: Claim event is usually sudden and easily determinable (e.g. burglary, fire) Notification is normally prompt Settlement is usually quick Often just consists of a single payment although total losses (e.g. from fire) may take longer to settle and be settled in parts Claim amount can normally be estimated accurately Claims tend to be fairly consistent in size and distribution Claim amount tends to be low relative to buildings cover Frequency tends to be high relative to buildings cover As a class, can be exposed to accumulation/cat risk As a class, very exposed to the risk of moral hazard Frequencies closely linked to the economic cycle, e.g. theft claims frequencies rise when unemployment rises Claims costs tend to rise in line with price inflation May have nil claims as an excess often applies Comments on Q2(i). Bookwork on which most candidates scored reasonably well. (ii) Assumptions: Even risk profile over the year Identical policies No cancellations Claims occur on average mid-month (In each case, alternative assumptions are valid if correctly applied.) Calculation: (1) (2) (3) (4) Month Policies written Earned exposure = policies on risk (Month 0.5) earned exposure 9 1,000 1,000 8, ,500 2,500 23, ,000 4,500 47, ,500 7,000 80,500 7,000 15, ,000 If a non-constant earnings assumption is used then column (3) needs to be adjusted appropriately. Page 3

98 Subject ST3 (General Insurance Specialist Technical) September 2007 Examiners Report Average accident date = sum(4)/sum(3) = , i.e. two-thirds of the way through November 2006 Comments on Q2(ii). Some silly mistakes such as giving average accident date in 2007 by ignoring the statement occurring during Various approaches are possible, all given equal credit if correctly reasoned and applied. (iii) Long-established => writing business for many years. The benchmark companies portfolios are likely to be quite stable without the rapid growth in volumes that we have experienced. In particular, their pre-september exposure is unlikely to be zero like ours. Their aggregate earnings patterns are therefore likely to be much more even across a year, so their average accident date is likely to be around mid-year and our 2006 accident year will develop later than the benchmark accident year Therefore applying the benchmark development factors is likely to underestimate the true 2006 accident year ultimate So the benchmark is not appropriate for use unless first adjusted for this lag effect. General remarks on why benchmarks development factors may not be appropriate: benchmarks may have faster/slower claims handling procedures; may have different reinsurance arrangements (if considering net); policies though similar won't be identical; business mixes though similar won't be identical; benchmarks could contain large claims/cats which could distort development pattern; benchmarks may use different inflation assumptions; benchmarks might/might not include ALAE may not expect future claims to develop in same way as past. Comments on Q2(iii). Virtually all students were able to recall the standard points for/against benchmarks. Only a few linked the answer back to (ii) and discussed why the unadjusted benchmark would probably under-project in this case. 3 (i) Facultative reinsurance is a reinsurance arrangement covering a single risk, commonly used for very large risks or portions of risk written by a single insurer Treaty reinsurance is a reinsurance arrangement that a reinsurer is obliged to accept, subject to conditions set out in a treaty (ii) Advantages of using facultative reinsurance The insurer can choose the risks that it believes are most advantageous to cede or retain from the point of view of maximising profit and subject to acceptable retention of risk Page 4

99 Subject ST3 (General Insurance Specialist Technical) September 2007 Examiners Report under an obligatory/obligatory treaty, the insurer is required to cede all risks that meet the criteria of the contract under a facultative/obligatory treaty, the insurer can choose which risks it wishes to cede Facultative reinsurance can cover risks that fall outside treaties fall inside treaties but outside the contract limits Easier for insurers to shop around for best rate/terms in market. Disadvantages of using facultative reinsurance It is a time-consuming and costly exercise to place each and every risk separately The insurer may not be able to accept and provide cover immediately until it has had the opportunity to find appropriate facultative reinsurance cover; under the treaty all risks covered by the contract are ceded automatically This may impact the company s stance in the market with distributors and customers There is no certainty that the cover required will be available when needed; under the treaty the cover is predetermined in the contract Even if cover is available, the price and terms may not be acceptable; under the treaty, the price and terms are all predetermined at the start of the contract (iii) Discussion of Factors: Look at the reinsurance profit and loss accounts (or suitable ratios, e.g. recovery ratios) historically by year to understand the level of profit or losses ceded Analyse separately for each treaty to understand the impact of each arrangement on the overall result Analyse different levels of facultative arrangement (e.g. by size of risk) to determine profitability by amounts ceded Check to see if the period has been atypical in terms of claims experience and adjust accordingly Compare cost of other forms or levels of reinsurance that could have been used. For example, would a Property per risk treaty with a higher or lower retention have proved more profitable for the insurer (or other appropriate example) What are the current reinsurers credit ratings? Is there a need to move cover to more secure companies? What level of financial assistance are the current reinsurers providing? Do these adequately cover acquisition and administration costs? What level of technical assistance is provided by the reinsurers? Can the insurer find more tailor-made solutions elsewhere? Any reciprocal arrangements in operation need to be assessed to determine the profitability of these arrangements and their effectiveness in reducing risk concentration Look at how the reinsurance programme reduces capital requirement Page 5

100 Subject ST3 (General Insurance Specialist Technical) September 2007 Examiners Report Check extent to which reinsurance programme covers accumulations of risk in book Analyse the profit smoothing achieved by the reinsurance programme Consider any regulatory constraints or relaxations that the reinsurance programme has caused Has the reinsurer imposed any conditions, e.g. minimum retention, certain policy conditions? Comments on Q3. Bookwork which was generally well answered. A few students were confused between facultative reinsurance and fac/oblig treaties and some mistakenly answered part (iii) as reasons for purchasing reinsurance. 4 (i) Claims Claims data needs to be collated into homogeneous groups and triangulated Analyse claim numbers and average claim cost separately to identify source of poor experience. This may be a result of increased frequency, increased severity or both. Analyse claims paid, outstanding reported claims reserves and IBNR separately in case one has developed unusually Analyse historic claims inflation to see if claims costs increasing faster than expected Investigate large claims experience. Poor profitability may be explained by a few large claims in the last couple of years. Where there is sufficient data, claims may be analysed by claim type to isolate the claim type(s) developing poorly Where possible, also analyse claims on quarterly/monthly basis to see if any clearer trends emerge Review the company's historic reserving (are their methods appropriate?) There may be errors in their calculations leading to overstatement of reserves Review strength of reserving basis. Are assumptions too conservative? Alternatively, an historically weak basis may have resulted in the need to increase prior year reserves Investigate changes in claims handling procedures. Claims adjusters setting case estimates may have become more cautious over time. Claim settlement controls may have slipped resulting in higher payouts (e.g. due to new claims handling staff being inadequately trained or increased claims volumes and not enough staff to handle workload efficiently or other valid examples) Compare company claims development with external/industry benchmarks Were there any accumulations of risk in the book which have now caused losses? Investigate claims for signs of fraud Compare rate- and inflation-adjusted historic loss ratios to identify trends in underlying risk Could analyse loss ratios for new business and renewals separately to see if experience of one group is worse than the other Page 6

101 Subject ST3 (General Insurance Specialist Technical) September 2007 Examiners Report (ii) (iii) (iv) Premiums Analyse claims together with exposure to determine adequacy of risk premium rates Split by rating factor (age/sex/vehicle type, etc.) into rating cells For each rating cell, compare total cost of claims against theoretical risk premium predicted by company's rating structure Identify particular factor levels where inadequate premiums are being charged which may indicate anti-selection. Where sufficient exposure to perform credible analysis, split by claim type (AD, TPPD, TPBI, etc.) to identify more accurately the inadequacy in the rating structure But company is small so credibility of data may be an issue Consider changes in cover that may have led to increased claims Analyse adequacy of each loading: Expense loading may no longer cover costs (office space, staff costs) arising from increased written volumes Commission loading may be too low, e.g. because commission rates boosted in order to attract more broker business Profit and/or contingency loadings may have been cut to make premiums more competitive Use historic company and market data to investigate position in insurance cycle. Falling profitability may be a feature of the market as a whole Look at historic changes in market share. Changes in share can indicate premiums out of line with market. Mix of business Investigate change over time of: Mix of policyholders: proportion of higher risk policies may be increasing, e.g. young male drivers, high performance cars, more policies in high theft areas? Mix of policy type, i.e. comp/non-comp, as these typically experience different loss ratios. New business/renewal ratio as acquisition costs are higher than renewal costs but usually spread across all policies. Therefore higher than expected volume of new business will mean lower contribution to expenses than expected Source of business: broker/direct as broker business more costly to acquire due to commissions. May have seen broker business increase and direct sales fall. Analyse profitability and persistency by source. Identify sources (phone/internet) or particular brokers where the experience is poor. Analysing lapse rates may indicate rating cells where we have lost profitable business to competitors Reinsurance Analyse historic recovery ratio (RI recoveries/ri premium earned). Has it fallen in the last two years? The company may be failing to structure its RI programme appropriately for the increased business, e.g. aggregate XL limit too low so vertical exhaustion more likely Insufficient reinstatements on treaties causing horizontal exhaustion Page 7

102 Subject ST3 (General Insurance Specialist Technical) September 2007 Examiners Report The price of reinsurance may have risen disproportionately RI recoveries may have fallen due to: new exclusions, tighter policy wording imposed by reinsurers increased deductibles higher attachment points Check for reinsurer failures and disputes. Bad debt provisions may have impacted results. Comments on Q4. Most candidates did not get many of the points available for this question. Better answers covered a broad range of points and also clearly explained why and how the proposed analyses would be useful in investigating declining profitability. Poorer answers tended just to list the various analyses possible without linking these to the specific details of the question. This was especially the case in (iv). 5 (i) Assume that : Employee count definition remains constant No change in structure of company e.g. disposals/acquisitions No change in safety procedures/substances handled No unusual losses in the data No change in the terms and conditions of the policy e.g. limits, deductible Underwriting pattern provided by underwriter is reasonable Future risk profile is same as historic risk profile Calculation: Underwriting year CL Ultimate Inflation index Inflated Ultimate ,333, ,952, ,750, ,329, ,000, ,420,000 1, ,200, ,420, average weighted average average excl weighted average excl Inflated ultimate per employee Make a reasonable selection: average or weighted average Taking e.g. weighted average, risk premium for 2007 is: = 2.66m (ii) Explanation: Frequency-severity approach would provide more information on the risk and might improve accuracy of answer Number of employees may not be the ideal exposure measure. Wage-roll might be better (number of employees okay for frequency) Insufficient data to give full credibility to answer Unlikely to be sufficient large losses in the data to give reasonable allowance for future large losses Page 8

103 Subject ST3 (General Insurance Specialist Technical) September 2007 Examiners Report Or may be heavy experience in the data e.g. unusual large losses Need to investigate trends in the data Any of the assumptions identified in (i) may be incorrect Exposed to latent claims so may need to include a loading Comments on Q5(i) & (ii). There were some strange calculations where students tried to triangulate claims using the development pattern in order to apply the inflation adjustment. Very few discussed alternative methods or exposure measures in (ii). Otherwise the question was generally well answered. (iii) Further information: commission rate expense loading contingency loading return on capital required/profit requirement/ target loss ratio tax rate cost/structure of reinsurance investment return Comments on Q5(iii). Bookwork. Almost all candidates scored full or near full marks. (iv) Situations: Could be a hard/soft market at present so we may be able to charge more/less than the theoretical office premium under present conditions (adjustment for insurance cycle) May make a decision to price over/under the competition (regardless of insurance cycle) Regulations may restrict the premium we can charge We may wish to sell the cover as a loss leader or as part of a combined package Underwriter may have soft information giving him additional information about the risk that enables him to adjust the premium The broker may apply pressure to accept a lower premium Concerns: Need to consider the premium charged for the risk in previous year as customer would compare to this There will be less concern if a higher than theoretical premium is charged in a hard market Although if actual rates are too high this might be an indication that we are losing out to competitors on other profitable business and this may result in volumes insufficient to cover fixed expenses The concern in a soft market will be how low rates will have to go and how long the soft market will persist Charging less than the theoretical premiums may eventually lead to losses and to capital/solvency issues Page 9

104 Subject ST3 (General Insurance Specialist Technical) September 2007 Examiners Report Comments on Q5(iv). Generally well answered. 6 (i) Reasons: Future claims inflation is not a weighted average of past inflation Payment pattern may extend beyond development year 7 (i.e. a tail factor is needed in the projection) Payment pattern may have changed across accident years due to: Change in incidence pattern of claims during each year, e.g. harsher than normal winter causes more claims Change in reporting delay, e.g. postal strike, bad weather New claims handling procedures/systems New legislation, e.g. TPBI settlements change from lump sum to periodical payments Large claims (or the absence of such) may invalidate payment pattern as they usually have a different development pattern to non-large claims The reinsurance program may have varied between accident years Reinsurance recoveries may have been disrupted by defaults/disputes The mix of business may have changed during the period due to: change in balance of comp and non-comp business rapid growth or contraction of business change in mix of policyholders (e.g. age distribution, male/female split) A change in any of these could influence reporting and settlement patterns Random variation The selected development factors may not be appropriate. There is uncertainty surrounding the selected development factors: At later developments they are calculated on relatively little data (one or two years) At early developments they are generally large so a small percentage error in the factor can lead to a large numerical difference in the estimated ultimate Any sensible comment on the development factors given The data may contain errors Comments on Q6(i). Answers were reasonable but students could have gained more marks by systematically going through the possible factors which might invalidate the constant development pattern assumption. (ii) If possible, a better starting point is to project gross claims and then net down as a separate step. This avoids distortions to net patterns caused by changes in RI programme over time. Fit a tail to the net paid projection. Use more historical data if available If not, could try fitting a curve to the development pattern or consult industry/external benchmarks Also project on a monthly or quarterly basis to compare Project gross/net notified claims as a check on the gross/net paid BCL Notified claims includes case estimates so factor to ultimate is smaller. May consider notified claims projection to be more reliable than paid projection Split claims into homogeneous groups and project separately, e.g. by claim type (AD, TPPD, TPBI, etc.), by comp/non-comp, by geographical location Page 10

105 Subject ST3 (General Insurance Specialist Technical) September 2007 Examiners Report Advantages: this gives more homogeneous groups of data which are more likely to develop in the same way. Avoids distortions caused if mix of claim types changes in future Disadvantages: each projection is on a smaller volume of data so less credible, more volatile Large insurer: may write business across several countries, currency may be an issue: conversion of payments at historic exchange rates will distort the development pattern better to compile triangle using constant exchange rate across whole triangle or project currencies separately if enough data for credible projection Large claims (say > 250k) in private motor are usually TPBI. These are likely to be longer-tailed than other claims and have a different development pattern Therefore sensible to remove large claims from triangles and project large and non-large separately. Definition of large should vary (by large claim inflation) between accident years, otherwise you would effectively be removing more claims in earlier accident years Due to low frequency/high severity nature, claims development will be lumpy and irregular so any statistical projection methods for large claims will be problematic. Individual case estimates probably best for outstanding reported large claims reserve. Large claims IBNR: could apply a simple loading to large outstanding if historical data supports this or frequency-severity approach: project numbers of notified large claims to get an IBNR number. Estimate an average cost of large IBNR claims by comparing historic IBNR with reported sizes and allowing for any trends, known changes You need to be consistent in how you treat claims which are large at some point but eventually settle for an amount less than large For 2005 (and 2004) accident years: The chain ladder method is very unstable (factor to ultimate is high for the immature years) The Bornhuetter-Ferguson provides a more stable estimate whilst taking some account of actual development Alternatively could use the Expected Loss Ratio method for these years Other projection methods: Inflation adjusted CL if historic claims inflation has varied considerably over time and/or future inflation is likely to be different to the past ACPC (and/or inflation adjusted version) to study development of frequency and severity separately Need to allow correctly for nil claims here Stochastic methods (e.g. bootstrapping), to get an idea of the reserve uncertainty or if a specified percentile is required Page 11

106 Subject ST3 (General Insurance Specialist Technical) September 2007 Examiners Report The methods and assumptions used will be influenced by the purpose of the reserving exercise Comments on Q6(ii). Generally reasonably good answers.. Most students were aware of the different claim types in private motor and why they need to be studied separately. Some answers simply listed different projection methods without any discussion of why they might be used. Unfortunately, quite a few students seem to think that projected accident year paid amounts do not include IBNR. (iii) (a) Arguments for discounting: In the case of long-tail business investment income can be significant It gives a more realistic position of the financial condition of the insurance company This is particularly relevant for management accounts and for estimating claim costs for rating purposes and allows easier comparison between different classes Arguments against discounting: For short-tail classes discounting makes negligible difference Not discounting provides an automatic margin for uncertainty For long-tail classes, the greater uncertainty justifies the margin provided by not discounting May be seen as a sign of weakness if market practice is not to discount (where regulations allow) not discounting increases reserves and defers the emergence of profit and therefore, tax Where regulations don't specify it, discount rate is a subjective choice requiring extra calculations/time Regulations may prohibit discounting (b) Factors to consider in choosing discount rate: The purpose of the accounts. Management accounts would probably use a more realistic rate than solvency/published company accounts Regulations might dictate or limit the discount rate to use The expected returns from the assets held to back the technical reserves for this class Proportion of non-investible assets held Delay before receiving premiums Investment expenses/tax Consistency with inflation assumptions used for projections Discount rate used last year Any margin to reflect riskiness of class Comments on Q6(iii). An easy question with most students scoring highly. (iv) Use selected idf s and assume no tail (or else select a tail and apply correctly in calculations) Assume payments occur on average mid-way through the year Page 12

107 Subject ST3 (General Insurance Specialist Technical) September 2007 Examiners Report Development yr Selected idf Selected cdf Cum % dev 67.4% 80.8% 88.9% 93.4% 97.1% % 3. Increm % dev 13.5% 8.1% 4.4% 3.7% 2.9% 4. Increm % paid for 2004 acc yr reserve 41.3% 24.8% 13.6% 11.4% 8.9% Time t in years Discount factors (1+i) -(t-1/2) 95.8% 87.9% 80.6% 74.0% 67.9% 6. Payment * discount factor 39.5% 21.8% 11.0% 8.5% 6.1% 7. Discount factor = sum of row % Comments on Q6(iv). Surprisingly few candidates were able to calculate a discount factor correctly. This may be partly explained by a lack of time. Some scripts did show evidence of time pressure towards the end of the exam. END OF EXAMINERS REPORT Page 13

108 Faculty of Actuaries Institute of Actuaries EXAMINATION 17 April 2008 (pm) Subject ST3 General Insurance Specialist Technical Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 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. 4. Mark allocations are shown in brackets. 5. Attempt all 7 questions, beginning your answer to each question on a separate sheet. 6. Candidates should show calculations where this is appropriate. AT THE END OF THE EXAMINATION 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 the 2002 edition of the Formulae and Tables and your own electronic calculator from the approved list. ST3 A2008 Faculty of Actuaries Institute of Actuaries

109 1 Describe the role of the broker in transacting insurance in the London Market. [5] 2 You are an actuary who works for a large general insurance company that has been writing personal lines business for many years and that has kept good marketing records. The marketing director has asked you to model the effect on policy sales of changing each of: the per policy profit loading and the amount spent on advertising. (a) (b) Describe the impact that these two items will have on the company s total profit and Explain ways in which a model may be set up to estimate the future profit arising from changes in these two items. [6] 3 You are an actuary working on secondment overseas in a country that has no guidance in place for the actuarial profession. A member of your team has asked you about the importance of guidance in your home country. (i) State the advantages and disadvantages of having guidance in place. [5] You have been asked to draft a formal report on the year-end reserving exercise conducted by your team. The company s board will also review the report. The board consists of non-actuarial members only. You have been asked specifically to include a detailed section on methodology and assumptions used. (ii) (iii) Describe the sub-sections that you would include in the methodology and assumptions section. [5] List the other key sections that you would include in a formal reserving report. [2] [Total 12] 4 Describe how you would project the various components of the existing overall liability outgo for a motor portfolio in each future time period. [13] ST3 A2008 2

110 5 (i) State the two definitions of burning cost premium and show how they are linked. [2] (ii) You have ten years of premium and individual paid claims development data, gross of reinsurance, for a particular product. Explain the steps you would take to analyse and adjust these data for the purpose of reviewing the risk premium for that product. [13] (iii) For a separate project you have claim data for claims reported between 30 September 2006 and 30 September The average reporting delay is nine months. You are setting the rates for annual policies sold between 1 January 2008 and 30 June Claims inflation was 3% in 2006, 4% in 2007 and is expected to be 5% in 2008 and 6% in Using a claim at the mid-point of the periods given, calculate the inflation adjustment needed for the 2008 rating series stating any assumptions made. [4] [Total 19] 6 (i) State the assumptions underlying the Empirical Bayes Credibility Theory (EBCT) Model 1 and Model 2. [4] X 1, X 2,...X n are the aggregate claims, or the number of claims, in successive periods for a risk. Let a o, a 1,,..., a n be the values which minimise the expression: E[(m(θ) a 0 a 1 X 1 a 2 X 2... a n X n ) 2 ] where m(θ) = E[X j θ] You are given s 2 (θ) = V[X j θ] E[X j m(θ)] = V[m(θ)] + (E[m(θ)]) 2 E[X j X k ] = V[m(θ)] + (E[m(θ)]) 2 E[ 2 X j ] = E[s 2 (θ)] + V[m(θ)] + (E[m(θ)]) 2 (ii) For Model 1 show that the estimate of m(θ) is given by: (1 Z) E[m(θ)] + ZX where: X = Σ n X j / n j= 1 and: Z = 2 n n+ E[ s ( θ)]/ V[ m( θ)] [5] ST3 A PLEASE TURN OVER

111 Company A s records show the claim amounts and number of policies from its household book of business over the last 5 years. You are given the corresponding claim amounts and number of policies from company B, as shown below: Company A Company B Year 000 s Policies 000 s Policies (iii) Using EBCT Model 2 calculate E[m(θ)], V[m(θ)] and E[s 2 (θ)] and hence the expected claim amount for company A, where m(θ) = E[X j θ] and s 2 (θ) = P j V[X j θ]. [9] (iv) Comment on your results given that using Model 1, E[m(θ)] = 290, V[m(θ)] = 60, E[s 2 (θ)] = 700 and the expected claim amount for company A is 287,000. [1] [Total 19] 7 You are a consulting actuary. You have been asked to review and comment on a client s reserving methodology, and to re-project some of the key classes of business, in order to form a view on the client s year-end reserve figures. The client is a large international company with a variety of classes of business being sold in the US and some countries in Latin America. After reviewing their methodology you note the following: Incurred claims data are used for projections. Projections are performed at a net of reinsurance level. For the Bornhuetter-Ferguson (B-F) method, the expected loss ratio (ELR) is calculated as a rolling average of the ultimate loss ratios, using the chain ladder method, for the previous three accident years. The incurred claims data from the Latin American countries is converted into $US prior to projecting. Due to concerns of possible hyper-inflation in these countries, only the latest diagonal is adjusted. All previous diagonals are equal to the data in $US from the previous year reserve calculations. This is done using the latest exchange rates and by converting the movements in paid and outstanding claims only. (i) Comment on the advantages and disadvantages of this approach and highlight any recommendations that you would make to the client. [12] The company is writing some new books of business. For these classes the company has based the latest ELR on the underwriter s view. ST3 A2008 4

112 (ii) State the advantages and disadvantages of this approach, again providing any recommendations that you may have. [3] You have decided to re-project the following data for a motor book of business. You have been told that the claims inflation has been steady at about 5% for each year. You have no information about premium rate increases, but you can approximate this using the increase each year in the average premium per policy. Year Earned Premium $000 s Earned Policy Years Incurred Claims $000 s Incurred Cumulative Development Factor Selected Ultimate Loss Ratio Selected Ultimate Loss ,750 1,150 8, % 8, ,000 1,275 10, % 9, ,500 1,125 9, % 8, ,250 1,050 9, % 8, ,250 1,125 11, % 10, ,650 1,265 9, (iii) (iv) State the key assumption being made when the increase in the average premium per policy is used as the assumed premium rate increase. [1] Calculate the incurred B-F ultimate for the 2007 accident year with the ELR based on the weighted average (by premium) of the last five accident years. [5] When looking at the summary list of reserves by country and class, you notice that there is a book of business called MisMass. You have not been provided with any data for this class; however from the summary list of reserves you can derive that the reserves have been estimated to be 142m and the discounted reserve figure for this book is 86m. (v) Determine the implied Discounted Mean Term (DMT) using a discount rate of 5% per annum and hence comment on what this book of business may contain. [2] You have requested additional data from the company on MisMass to show how the reserve figures were derived. (vi) State what reserving methods would be applicable for projecting the claims data for this book of business, and comment on any limitations of these methods. [3] [Total 26] END OF PAPER ST3 A2008 5

113 Faculty of Actuaries Institute of Actuaries Subject ST3 General Insurance Specialist Technical EXAMINERS REPORT April 2008 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 A Stocker Chairman of the Board of Examiners June 2008 Comments Individual comments are shown after the solutions to each part question that follows. Faculty of Actuaries Institute of Actuaries

114 Subject ST3 (General Insurance Specialist Technical) April 2008 Examiners Report 1 London Market Brokers: Act as specialist intermediaries e.g. Lloyd s broker, reinsurance broker Are agents of the insured Organisational aspects of their work are important as they are often international organisations and clients and the insured are often in different countries/time zones Place business using the slip system Prepare the appropriate slip, which shows the main features of the risk to be insured, in a standard format Prepare additional information relating to the risk at the request of the underwriter and further technical assistance Present the slip to a lead underwriter, who on the basis of the slip and additional information will set the rate and terms Present the lead underwriter s rate and terms to the insured for approval The lead underwriter with the broker indicates the proportion of the risk (line) he is prepared to accept (by signing and stamping the slip) If the insured agrees to the rate and terms, the broker will approach the follow market to place the remainder of the risk on the lead rate and terms Follow underwriters will sign their lines and stamp the slip in a similar fashion to the lead ( they act as co-insurers) The broker continues until the risk has been over-placed The broker, in agreement with the insured, signs down the lines of the underwriters so they total 100% If the broker fails to place 100% of the risk, the insured may retain the remaining proportion or more typically the broker will seek to renegotiate better terms Collecting premiums from the insured and paying claims Advising and negotiating the best terms for the insured The broker also provides an admin role e.g. preparing policy documentation Comments on Q1: A bookwork question on which many candidates scored well. 2 (i) Increasing advertising spend will increase overall expenses However, if it is a successful campaign with high sales volumes then it could decrease expenses per policy as the existing fixed expenses are spread more thinly over the larger book of business. Increasing profit loading will increase profit per policy. However this will result in higher premiums and may reduce volumes of business to a level that results in lower total profit The overall effect on total profit will depend on the effect on the volume of business and hence an assumption around volume of business is needed The overall effect on profit will also be impacted by changes in the mix of business resulting from varying these two items The overall effect on profit will also be different depending on the mix of new business and renewals (ii) In terms of the model total profit is premiums less expenses less claims Also any valid alternative profit formula e.g. (per policy profit load policy volume) Set up the model to give total profit as an output Review past company data on rate changes versus policy volumes Page 2

115 Subject ST3 (General Insurance Specialist Technical) April 2008 Examiners Report In addition, obtain data from comparison web sites to help determine where the premium currently sits in relation to the rest of the market in order to determine sales volumes Other expenses will be fixed or overheads that are independent of sales volume and this will also complicate the total profit calculation Analyse effect on volumes in different groups e.g. age, sales channel or social economic group Consider correlations between the profit loading and marketing spend Produce a set of one-way or two-way analysis tables for each selected profit loading showing how total profit varies by marketing spend, i.e. elasticity and produce a set of one-way or two-way analysis tables for each selected marketing spend showing how total profit varies by profit loading Select the combination of factors which maximises total profit Alternatively given that we have an output which is correlated to two variables we could fit a Generalised Linear Model (GLM) to the model outputs The GLM could then be used to maximise the total profit Set up the model such that the factors can be easily interpreted and monitored Comments on Q2: Most candidates acknowledged that changes in costs and profit loading would affect volumes and many picked up full, or nearly full, marks on part (i). However, in (ii), students tended to trot out the points given in the core reading without thinking through and applying to the specifics of this particular question. 3 (i) + Promotes confidence in actuaries work, by ensuring that actuaries maintain a high level of training and expertise + Being able to demonstrate compliance protects an actuary against litigious criticism + Protects the public by making actuaries accountable + Promotes consistency and greater scrutiny of professional judgments + This in turn can reduce work loads e.g. consistent processes make it easier to review/pick up a predecessor s work + Enables fellow actuaries to be challenged + Provides actuaries with a point of reference for clarification + Consistent with some other professions Above advantages are only applicable if the guidance is well written and not open to interpretation - Guidance will never be fully comprehensive - Guidance can become out of date Additional bureaucracy and time-consuming Infrastructure needed if not already in place, e.g. overseeing boards Additional costs Potentially restricts use of individual judgment Danger of setting standards that are too high/unrealistic, e.g. listing and justifying every incremental development factor assumption in a reserving exercise Comments on Q3(i): ) A few candidates misinterpreted guidance to mean regulation. Many students failed to generate many distinct points and so tended to score badly on this part. Page 3

116 Subject ST3 (General Insurance Specialist Technical) April 2008 Examiners Report (ii) State the methods used when selecting ultimate for each class of business, type of reserves and year of account Detailed description of the methods used A detailed explanation of the methods underlying assumptions A list and discussion of the key assumptions and judgments used A description of the process by which the assumptions have been identified Highlighting any illustrations based on assumptions that the are not regarded as appropriate The rationale for selecting the methods used in producing results and for each method a statement of key assumptions Where the results of different methods or assumptions presented in the report differ significantly, comments on the likely reasons for the differences and an explanation of the basis for the choice of results Sufficient data and other information to understand the key assumptions made and the process by which the assumptions have been identified Comments on Q3(ii): Many candidates failed to restrict their answer to the methodology and assumptions section as required and therefore wasted time writing unnecessary points. (iii) Introduction Definition of terms Purpose and scope Information and data used Analysis of emerging experience (comparison with last year) Business conditions over the year Results Sensitivity testing of assumptions used Uncertainty Comments on Q3(iii): There was a mixed performance for this part of the question with some candidates scoring well and others answering poorly. 4 Claim payments are almost always the most significant item of the liability outgo Ultimate claims and payment patterns can be taken from the reserving calculations Alternatively, project claim amounts forward using standard techniques (e.g. chain ladder) to derive payment patterns This will depend on the basis required for the projection e.g. claim amount are required on a best estimate or prudent basis Perform any adjustments to the data as necessary e.g. large claims, trends, inflation etc. Projecting forward for the full expected run-off period for the book Individual period by period projections are important Model the motor property damage separately from the bodily injury claims As the bodily injury claims will be much longer tailed and may involve periodic payments Page 4

117 Subject ST3 (General Insurance Specialist Technical) April 2008 Examiners Report Calculations should be done on a monthly or quarterly basis to take account of any seasonal effects Split the business into cohorts written in the same period Care needs to be taken to ensure that all types of claim amounts are projected e.g. outstanding, IBNR, URR For example triangles projected using an accident year cohort will not include URR Split the business by currency where appropriate Reinsurance and other recoveries should be included separately as an offset to the liability outgo taking into the reinsurance programme Reinsurance recoveries do not usually coincide with the claim payments and hence a timing difference exists Future known reinstatement premium, and other reinsurance premium, payments will be modelled If large gross claims have been modelled then it may be necessary to calculate the appropriate reinstatement premium with the necessary delay Model expense outgo Fixed expenses can be modelled adjusting for inflation as appropriate Some items may occur at specific times of year e.g. rates or local taxes Allow for any one off expenses Claim handling expenses can be projected with claims Alternatively, claims handling expenses can be projected separately in a triangle Taxes must be calculated on estimated profits and the timing will be known Contributions to the MIB fund for uninsured drivers, or to the Lloyds central fund if relevant should also be allowed for Comments on Q4: Virtually all candidates took note that this question related to a motor portfolio and mentioned the need to split out BI and property damage claims. However, even though the question specified liability outgo, many students wasted time writing about premiums and investment income. Similarly, we are interested in existing liability outgo but some students talked about commission on business which would be written in the future. Some poorer answers failed to discuss expenses, concentrating only on claims outgo, and therefore missed out on some of the easier marks available. 5 (i) BCP = Average Claim Amount x Claims Incident Rate = (Total claim cost / number of claims) / (Total Exposed to Risk / number of claims) Number of claims cancel out to give the alternative form of BCP, namely = total claim cost / total exposed to risk = BCP Comments on Q5(i): Answered well by most candidates, although a small minority didn t seem to know where to start with the definition of burning cost, which is a fundamental concept in General Insurance. Also some candidates defined burning cost as total incurred claims, as opposed to ultimate claims, over total exposed to risk. Page 5

118 Subject ST3 (General Insurance Specialist Technical) April 2008 Examiners Report (ii) Analyse the frequency and severity separately Break into homogenous groups if necessary and possible Check for errors in the data Assuming that we have no outstanding and IBNR data project the number of paid claims to ultimate Estimate an average cost per claim and multiply this by the projected number of claims to obtain the estimated claim ultimate amount Because of changes over time may not want to use all 10 years of data, depending on data volumes Adjust for large claims Truncate, remove, spread or add claims cost to bring claims to an average level Adjust for unusually heavy/light experience Decision depends on the extent to which such claims (or lack of claims) are expected to recur during the exposure period of the new rating series Assume no change in target market or distribution approach Adjust for trends in claims experience bring all data to the mid point of the exposure of the new rating series Decide how historic trends may project into the future to allow for them in the projection of the risk premium Adjust for changes in risk They may show up as trends or as step changes May appear due to changes in the mix of business May be different for different types of claim Adjust for changes in cover They may show up as trends or as step changes The major changes are likely to involve the perils covered and limits or excesses applied to any claim Perils may be excluded hence claim cost reduced or specific claims excluded or new perils added so an estimate of claims cost added Changes in limits or excesses will need the claim cost distribution to be used Data will be incomplete as claims below the excess point are unlikely to be reported Changes in underwriting or claim settlement procedures will result in similar changes to those for changes in cover Adjust for past and future inflation Break down time periods into periods of uniform inflation Adjust for the original period of writing the business and time period of new rating series Page 6

119 Subject ST3 (General Insurance Specialist Technical) April 2008 Examiners Report Adjust for delays between claim notification and individual payments until final settlement, both for claims occurring in the base period and for those expected to occur during the exposure period of the new rates Determine the period of exposure containing the base experience Determine the full period of exposure covering the claims that can arise from the policies written under the new rates and adjust for the timing difference Project exposure values Ensuring that each claim amount corresponds to the premium data To arrive at a risk premium rate, we need a rate of claims per unit of exposure Here these exposure units are expressed in terms of monetary units so the base exposure values need to be projected at an appropriate rate of premium inflation Premium rate increases can be estimated by looking at historic average premium rates (if actual rate increases are not available) Although this assumes that the mix of business, terms & conditions etc. remain the same in all years Comments on Q5(ii): Many candidates tried to answer this part by giving the same answers as in Q4. (Q5 relates to analysing and adjusting past data to make it relevant to the future for the purposes of premium rating whereas Q4 was concerned about the timings of cash flow projections.) Most candidates scored badly because they failed to generate sufficient points for the 13 marks available. The better answers covered the inflation adjustments required for the future rates, which linked into part (iii). Most candidates failed to go into any or enough detail on the projection of exposure values. (iii) Assuming policies are uniformly written over the period Assuming no change in reporting and no settlement delays Assuming claims occur on average mid way through the year Assuming that inflation is uniform over the calendar year For claims: Inflate from the mid point of historic reporting to expected future reporting date Historic claims occur on average on 30/06/06 Historic claims reported on average on 31/03/07 Future claims occur on average on 30/09/08 Future claims reporting date 30/06/09 = = Marks provided for alternative methods for example: Deflate from reporting date to written date = (1/1.04) 0.25 (1/1.03) = Inflation of claim cost between the mid points of writing is = = Page 7

120 Subject ST3 (General Insurance Specialist Technical) April 2008 Examiners Report Inflation from mid point of writing to mid point of reporting is = = So total adjustment = = Comments on Q5(iii): A fairly easy projection calculation which most candidates attempted reasonably well. Marks were lost mainly because the projection dates used were inconsistent e.g. projecting from the average incurred date in the past data to the expected average reported date in the future. A surprising number of candidates expected to pick up a mark for making the assumption that policies are annual, failing to notice that this is specified in the question. Some candidates tried to project the claim data from the average date the claims occurred historically to the average date the claims are expected to occur in the future exposure period despite the fact that the question states that the claim data being projected are for claims reported between 30 September 2006 and 30 September (i) EBCT 1 assumptions The distribution of each X j depends on a parameter, denoted θ, whose value is fixed (and the same for all the X j s) but is unknown. Given θ, the X j s are independent and identically distributed. Where θ could be a real number or it could be a more general quantity such as a set of real numbers. The random variables {X j } are identically distributed. The X j s are not (necessarily) unconditionally independent. EBCT 2 assumptions The distribution of each X j depends on the value of a parameter, θ, whose value is the same for each j but is unknown. Given θ, the X j s are independent (but not necessarily identically distributed). E[X j θ] does not depend on j. P j V[X j θ] does not depend on j. Comments on Q6(i): Bookwork, although many students had not learnt this. (ii) Differentiate equation with respect to a 0 and put the derivative equal to zero. This gives the following equation: Equation 1: E[m(θ) a 0 Σ a j X j ] = 0 j= 1 n Which from the definition of m(θ) gives: a 0 = E[m(θ)] (1 Σ n a j ) j= 1 Page 8

121 Subject ST3 (General Insurance Specialist Technical) April 2008 Examiners Report Next differentiate with respect to a k where k 0, and put the derivative equal to zero. This gives: E[X k (m(θ) a 0 Σ n a j X j )] = 0 j= 1 which gives: V[m(θ)] + (E[m(θ)]) 2 a 0 E[m(θ)] a k E[s 2 (θ)] = 0 n Σ a j (V[m(θ)] + (E[m(θ)])2 ) j= 1 Rearranging this last equation gives: Equation 2: a k E[s 2 (θ)] = (1 n Σ a j ) (V[m(θ)] + j= 1 (E[m(θ)])2 ) a 0 E[m(θ)] This equation holds for k = 1,2,3,., n. An important point to notice is that the value of a k does not depend on k. In other words: a 1 = a 2 =... = a n. Now denote the common value of a 1, a 2,..., a n by Z/n so that: Z = n Σ a j j= 1 and the estimator can be written as: Equation 3: a 0 + n Σ a j X j = a 0 + ZX j= 1 where: X = Σ n X j / n. j= 1 Equations 1 and 2 are now two linear equations in two unknowns, a 0 and Z. The solution to these two equations is: Equations 4 & 5: a 0 = (1 Z)E[m(θ)] Z = n 2 + [ ( θ)]/ [ ( θ )]. n E s V m So, the solution to the problem of estimating m(θ) given is given by the right hand side of equation 3 with a 0 and Z given by Equations 4 & 5, respectively. Page 9

122 Subject ST3 (General Insurance Specialist Technical) April 2008 Examiners Report In summary, the estimate of m(θ) given X given by EBCT Model 1 is: (1 Z) E[m(θ)] + ZX where: X = n Σ X j / n j= 1 and: Z = 2 n n+ E[ s ( θ)]/ V[ m( θ)] Comments on Q6(ii): This also was bookwork. This part was not even attempted by the vast majority of candidates. Of those who did attempt it, many gave up mid-way through. (iii) Company A: Volume mean = ( ) / ( ) = 1,400 / 433 = P ij (X ij - X i ) 2 = [100 ( ) ( ) ( ) ( ) ( ) 2 ] / (5-1) = Company B: Volume mean = ( ) / ( ) = 1,500 / 52.0 = P ij (X ij - X i ) 2 = [110 ( ) ( ) ( ) ( ) ( ) 2 ] / (5-1) = 4.8 Px = (2 5-1) -1 [433 (1-433/953) (1-520/953)] = E[m(θ)] = (1, ,500) / ( ) = E[s 2 (θ)] = (123.2/ /4) / 2 = V[m(θ)] = [100 ( ) ( ) ( ) ( ) 2 ] / ( ) - E[s 2 (θ)] Page 10

123 Subject ST3 (General Insurance Specialist Technical) April 2008 Examiners Report = [( ) / ] / = [ ( )/ ] / = ( ) / = Z = 433 / (433 + E[s 2 (θ)]/v[m(θ)]) = 433 / ( / )) = Hence expected claims = ( ) number of policies in 2007 = = 243.6K Assuming the same number of policies as the latest year or any other reasonable assumption e.g. average of last 5 years, trend in average movements, downward linear trend Comments on Q6(iii): Many candidates scored highly on this part but some failed to realise that the formulae required are in the formulae book. Not giving the number of policies for 2007 in the question may have presented difficulties for some candidates. (iv) The expected claim amount for company A is lower as Model 2 allows for the volume of business which has recently declined for company A. or any other reasonable observation Comments on Q6(iv): For candidates that attempted this part of the question most stated that this was due to Model 2 taking into account the volume of business. 7 (i) Projecting incurred claims data only Projecting incurred claims data only is preferable to only projecting paid data. Incurred projections are useful as paid claims development will be less mature than incurred claims. Paid projections, however, can help identify changes or inconsistencies in the strength of case reserves or possible redundancies. Projecting both bases can therefore reveal features of claim reserves that would otherwise be missed. Need paid claims development if discounted reserves required Would recommend that the client projects both paid and incurred data. Projecting net of reinsurance only Projections at a net level will be robust as long as the proportion of reinsurance recoveries remains stable. It would be preferable to project at a gross level and apply the actual reinsurance program to the projected future claims This may not be feasible in practice. Alternatively project at gross level and analyse the trend in reinsurance to gross ratios for premiums, paid, incurred, outstanding claims in order to select reinsurance IBNR ratios. Page 11

124 Subject ST3 (General Insurance Specialist Technical) April 2008 Examiners Report In addition, understand change to the reinsurance programme and how this will impact the IBNR ratios selected. ELR using 3 -year rolling average 3-year rolling average is good where the historical selected ultimate loss ratios are volatile over time. Using a weighted average by ultimate premium though would smooth out any volatility over the accident/underwriting year (as the years with the largest ultimate premiums will be more stable) Gives credit to the account s own unique experience. Easy to apply but a fairly mechanical approach, which doesn t take into account any possible trends showing in the data/unusual years etc. Claims and premiums are calculated on the same basis. No account has been made to allow for premium rate changes and claims inflation. Would recommend a weighted average where the number of prior year historical selected ultimate loss ratios is based on the data. Would recommend loss ratios are adjusted to allow for premium rate changes and claims inflation. Recommend use of market stats benchmarks, where available for a sense check although need to ensure that the data is on a consistent basis. Exchange rate conversion This exchange rate conversion method would work on paid data but not on incurred. The outstanding need to be treated in a different way depending on whether they are New claims in the quarter/year Prior claims with no movement in the quarter/year Re-stated claims with movement in the quarter (e.g. due to additional information or hyper-inflation) For the first two type of outstanding claims the method is fine, for the last type of claim the entire outstanding amount would need to be converted into US $ s. The method assumes that the movement in exchange rates move in exactly offsetting ways to movements in inflation this is not always the case in practice. Dealing with exchange rates is always complicated. This approach does have its disadvantages but it is not unreasonable therefore no recommendation to change the current method. Comments on Q7(i): Candidates failed to generate many points for the 12 marks available and so tended to score badly. The better answers contained a sensible structure, e.g. they took each of the 4 notes in turn and considered the advantages, disadvantages and recommendations, although there were still an insufficient number of points made. The poorer answers tended to be very muddled. Some candidates were unable to comment fully on why both paid and incurred projections are important and the disadvantages of projecting at a net level only. Hardly any candidates scored marks for the discussion of hyper-inflation and exchange rates, but Page 12

125 Subject ST3 (General Insurance Specialist Technical) April 2008 Examiners Report it was recognised by the examiners that this was a difficult concept under the time pressure of an exam. Many candidates mistakenly considered the BF ELR to be lacking in independence, some even stating that this made the BF method to be the same as the chain ladder method. However, because the ELR related to the previous three years, it was in fact suitably independent. Incorrect assumptions about the independence of the ELR for the BF method have been commented on in previous examiners reports. (ii) + Useful in exceptional circumstances e.g. a very new book of business with no prior data or extremely volatile own history as is the case for this company. + Underwriter has a good knowledge of the business + May reflect market rate changes and inflation effects as well as trends in claims frequency and average cost + Provides independent estimates Underwriter s estimates may be too optimistic and hence not representative of the actual loss ratios. Need to check consistency of the basis used. This approach is reasonable, would recommend the use of market stats data as well, where available, as a sense check Need to ensure consistency with the basis e.g. gross/net commission/reinsurance. Comments on Q7(ii): This part of the question was answered reasonably well. (iii) The mix of business is the same for each year. or other reasonable key assumption Year Comments on Q7(iii): The question asks for one key assumption and so students should only state one assumption. The examiners are not impressed by a scattergun approach in which candidates hedge their bets by stating a number of possible assumptions. (iv) Earned Premium $000 s Earned Policy Years Incurred Claims $000 s Incurred Cumulative Development Factor Selected Ultimate Loss Ratio Premium Rate Increase for 2007 Level Claims Cost Increase for 2007 Level 2007 On- Level Loss Ratio Selected Ultimate Losses $000 s ,750 1,150 8, % % 8, ,000 1,275 10, % % 8, ,500 1,125 9, % % 7, ,250 1,050 9, % % 8, ,250 1,125 11, % % 11, ,650 1,265 9, % 68.3% 13,697 Where premium rate factor for 2002 is (17,650/1265)/(11750/1150) = 1.366, etc. Page 13

126 Subject ST3 (General Insurance Specialist Technical) April 2008 Examiners Report Claims cost increase for 2002 is = 1.276, etc on level loss ratio is 75% (1.276/1.366) = 70.1%, etc IER = ( % % %) / ( ) = 68.3% 2007 Selected IBF Ultimate = (1-(1/1.520)) (68.3% 17650) = 13,697. Comments on Q7(iv): Slightly different answers could be achieved depending on whether candidates used the selected ultimate losses or the selected ultimate loss ratio on which to base the calculation, because of rounding differences. Marks were awarded for either basis and also if premiums and claims were adjusted to same-year values as the question did not specify what weighted premiums to use. Many candidates failed to even attempt to adjust either the premiums or the claims for premium increases or inflation, even though information on these was given in the question. Some candidates also calculated a straight average rather than a weighted average, as required in the question, when calculating the ELR. (v) 142 1/ (1.05) DMT = 86 (1.05) DMT = 142/86 DMT ln(1.05) = ln(142/86) DMT = ln(142/86) / ln(1.05) DMT = 10 years. The DMT is very high. This is likely to be a liability class of business with latent claims e.g. asbestos. Comments on Q7(v): This part of the question was well answered by the majority of candidates. Whilst most candidates recognised that this would be data from a liability class not all candidates realised that a tail length in excess of 10 years would suggest latent claims like asbestos. Some candidates mistakenly tried to calculate the discounted mean term using paid development patterns even though there are no data to do this. (vi) Exposure-based methods but amount and quality of data are often insufficient Paid and incurred survival ratios and IBNR to outstanding ratios. These ratios all use figures that are estimated by the company, e.g. incurred, reserves, IBNR, OS and will differ depending on reserving strength. This also makes benchmark comparisons difficult, as each company will have different reserving basis. Paid survival ratios do at least have paid figures in the numerator (which are not open to interpretation). Comments on Q7(vi): Even though most candidates realised that this was a long-tail book of business, with a small number of claims which would be potentially very large and variable, they were still suggesting the application of chain ladder methods. Only a few candidates scored marks on this part. END OF EXAMINERS REPORT Page 14

127 Faculty of Actuaries Institute of Actuaries EXAMINATION 25 September 2008 (pm) Subject ST3 General Insurance Specialist Technical Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 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. 4. Mark allocations are shown in brackets. 5. Attempt all 7 questions, beginning your answer to each question on a separate sheet. 6. Candidates should show calculations where this is appropriate. AT THE END OF THE EXAMINATION 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 the 2002 edition of the Formulae and Tables and your own electronic calculator from the approved list. ST3 S2008 Faculty of Actuaries Institute of Actuaries

128 1 You are the actuary for a small general insurance company with a low solvency margin. The insurer is considering purchasing excess of loss reinsurance to reduce its claim volatility and hence reduce its probability of ruin. (i) Explain whether the proposed course of action will have the desired effect and state the implications on the insurer s profit. [4] You model the probability of ruin at the end of one year according to a compound Poisson process. According to your calculations the company s profit load is 0.1 θ 0.2, the reinsurer s profit load is 0.15 γ 0.25 and the Poisson parameter is 1,000 λ 1,500. (ii) State, with explanation, which combination of parameters would be worst for the insurer. [2] [Total 6] 2 A general insurance company writes only personal lines business. It would like to build a financial model to provide checks on the business and has asked for your advice. (i) List the requirements that a financial model should meet. [2] For a particular class of business, you have been told that the individual claim amounts have a Gamma distribution with parameters α = 12 and λ = The claim frequency has a Poisson distribution with λ = (ii) Calculate a risk premium for this class of business. [2] You are aware that there is some uncertainty surrounding the bases for calculating both the frequency and the severity and would like to give a range of possible values for the risk premium rather than the point estimate you have already calculated. You would like to add a margin of 5% of the standard deviation for the amounts and 2% of the standard deviation for the frequency. (iii) Calculate the acceptable range. [3] [Total 7] ST3 S2008 2

129 3 You are an actuary in a general insurance company that applies an excess to its motor insurance business. (i) Define the term excess. [1] (ii) Give reasons why the insurance company would use an excess. [3] The motor pricing manager has estimated that the distribution of accidental damage ground up losses for the coming year will be approximately as follows: Loss ( ) Number of claims The excess is currently ,500 1 to 50 1, to to to to to 1,500 3,000 1,501 to 2,500 1,500 2,501 to 7, (iii) (iv) (v) Calculate the amount that the insurance company expects to pay out for accidental damage claims next year. [2] Recalculate the amount that the insurance company would expect to pay if inflation causes ground up losses to double but the excess remains at 100, assuming that the relative distribution of claims stays the same. [2] Given that the losses have exactly doubled, explain why the insurance company s liability has not doubled as well. [1] [Total 9] 4 Describe the following characteristics of marine insurance: (i) Benefits [2] (ii) Insured perils [3] (iii) Exposure measures [1] (iv) Claim characteristics [4] (v) Risk factors [4] [Total 14] ST3 S PLEASE TURN OVER

130 5 You are an actuary at a medium-sized general insurance company. One of the business units writes two annually renewable binding authorities, whereby underwriting authority is delegated to a third party and underwriting risk is 100% retained by the insurer. Contract A incepted on 1 January 2004 and Contract B incepted on 1 April The business unit wants to analyse its profitability over the past three years. You have been given the following information for policies written on the 2004 binding authorities: Contract A Contract B Average premium 265 1,560 Acquisition costs 40.0% 32.5% You have also been given the following information on successive rate changes that were applied to the base rates at each given date between 2004 and 2007: Contract A Contract B 1 May % +2.0% 1 November % +3.0% 1 March % +5.0% 1 October % +1.5% 1 June % +1.5% 1 September % +1.5% The numbers of policies written on the 2004 to 2007 binding authorities were: Contract A Contract B ,000 10, ,000 11, ,040 11, ,824 12,004 (i) Calculate the earned premium (net of DAC) for 2005, 2006 and 2007, stating any assumptions that you make. [12] You have been given the following calendar year incurred claim movement information: Contract A Contract B Current Year Prior Years Current Year Prior Years ,025, ,000, ,625, ,000 5,937,500 1,500, ,126,000 1,593,750 5,475,000 2,700, ,100,000 1,875,000 5,375,000 2,025,000 ST3 S2008 4

131 Claims paid in each year were 35% of GWP for Contract A and 31% of GWP for Contract B. Investment return was 4.5% per annum. Overheads allocated to the business unit were 1.5m in Internal per policy expenses in 2004 were 24 for Contract A and 78 for Contract B. Overheads and per policy expenses increased at 4.0% per annum. (ii) Calculate the pre-tax profit made by the business unit in 2005, 2006 and 2007, stating any additional assumptions that you make. [10] (iii) Comment on the results of your findings in (i) and (ii), paying particular attention to the impact of the two contracts on the overall results. [8] [Total 30] 6 You are the pricing actuary for a general insurance company that writes private motor insurance. You have been contacted by a national cycling club, which is interested in selling bicycle insurance to its members. (i) List the two key insured perils that would be covered in a bicycle insurance policy. [1] The cycling club wants their members to be able to obtain quotes for this insurance very quickly and easily and therefore wants the number of rating factors to be restricted to two. (ii) State the most important requirements of rating factors. [1] (iii) State two rating factors which could be used for this class of insurance. [1] (iv) List the non-standard add-on covers that could be included to give a potentially very comprehensive policy. [8] Your company has not written bicycle insurance before and therefore has no data relating to this. It has been suggested that you could use industry-wide data to help you to set the prices. (v) Explain the difficulties you might encounter in obtaining and using industrywide data. [4] You have been asked to specify the future data requirements for this class of business so that a suitable management information system can be considered. (vi) List the data items for which you would ask in order to help you to develop sophisticated pricing for this business in the future. [8] [Total 23] ST3 S PLEASE TURN OVER

132 7 For a number of years a reinsurer has written a working layer per event risk XL treaty with unlimited reinstatements. The cedant places this treaty to protect the liability element of a large book of private motor vehicle insurance. The reinsurer has recently introduced a stability clause and an aggregate deductible to the layer. (i) (ii) Define each of these new features and explain the impact of their introduction on the expected cost of claims to the layer. [5] State the advantages and disadvantages to both the reinsurer and the cedant of the addition of each of these new features to the layer. [6] [Total 11] END OF PAPER ST3 S2008 6

133 Faculty of Actuaries Institute of Actuaries Subject ST3 General Insurance Specialist Technical EXAMINERS REPORT September 2008 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. R D Muckart Chairman of the Board of Examiners December 2008 Comments Individual comments are shown after the solutions to each part question that follow. Faculty of Actuaries Institute of Actuaries

134 Subject ST3 (General Insurance Specialist Technical) September 2008 Examiners Report 1 (i) Greater risk is associated with greater variability, and hence a larger probability of ruin Purchasing excess of loss reinsurance will reduce claim volatility and therefore reduce the probability of ruin. The effect on the insurer depends on both the retention level and the reinsurer s profit load/cost of reinsurance Consideration of different types of reinsurance (Individual/ Aggregate/ Catastrophe). Layers of reinsurance may be needed to give full coverage / other comment about layers. Buying reinsurance is a trade off between profit and volatility reinsurance will reduce the claims volatility but it will also reduce the company s expected profit. Buying reinsurance will give a more stable profit year on year Reduced profits will worsen the solvency position but reduced claims volatility will strengthen it. Above a certain profit load it will be better for the insurer to retain all the risk and below a certain profit load it will be better for the insurer to cede all the risk. Between these two profit loads the insurer needs to fix the retention level in order to minimise the probability of ruin. Therefore the insurer can set a retention level such that the probability of ruin is less than it would be without reinsurance thus achieving the desired effect. Comments on Q1(i): Generally well answered. (ii) θ = 0.1, γ = 0.25, λ = 1500 Insurer s profit margin is smallest, making less profit Reinsurer s profit margin is biggest, taking more profit from the insurer For a given claim severity distribution the higher the value of λ, the higher the expected number of claims and the variance. Comments on Q1(ii): Generally well answered, but some candidates believed incorrectly that the Poisson parameter does not impact the probability of ruin and some even incorrectly gave λ = 1000 as the answer. 2 (i) Requirements: Valid/appropriate Complete/comprehensive Adequately documented Reflection of the risk profile of the classes of business being modelled Parameter values should be accurate for the classes being modelled / fits the data Outputs and their degree of uncertainty should be capable of independent verification Outputs should be readily communicable/explainable/easy to understand Should not be overly complex/take too long to run Should not be too expensive to run Flexible for the purpose Page 2

135 Subject ST3 (General Insurance Specialist Technical) September 2008 Examiners Report Comments on Q2(i): Bookwork; most candidates scored well. (ii) Severity: E(X) = α/λ = 12/0.02 = 600 Frequency: Ε(Y) = λ = 0.25 Risk premium = = 150 Comments on Q2(ii): Nearly all candidates calculated the risk premium correctly. (iii) Severity: Var(X) = α/(λ 2 ) = 30,000 σ(x) = so E(X) = 600 ± ( ) = (591.34, ) Frequency: Var(Y) = λ = 0.25 σ(y) = 0.5 so E(Y) = 0.25 ± ( ) = (0.24, 0.26) Total Range ( , ) Comments on Q2(iii): This part involved calculating the ranges for the frequency and severity separately and then combining by multiplying. Some students incorrectly tried to add the frequency margin (a number) to the severity margin (as an amount) before applying to the risk premium. No marks were lost by students who calculated a correct one-sided upper range. 3 (i) The excess is the sum, specified in the policy, that the insured must bear before any liability falls upon the insurer. They are widely used in personal lines insurance and may be compulsory (applying to all claims of the type specified) or voluntary (to secure lower premiums). Comments on Q3(i): Many candidates failed to define this term correctly. (ii) Reasons to use an excess To reduce the number of claims To reduce the amount of each claim To eliminate small claims, leading to reduced expenses To encourage policyholders to reduce moral hazard, leading to lower claims To reduce the customer premium (voluntary excess), leading to higher volumes and better retention rates As an endorsement imposed by the insurer to limit their exposure to certain perils To encourage better risk management by customers Comments on Q3(ii): Many candidates failed to pick up easy marks by generating too few examples. Page 3

136 Subject ST3 (General Insurance Specialist Technical) September 2008 Examiners Report (iii) Assume an average claim is at the mid-point of each range/claims are distributed evenly within the range ( ) ( ) ( ) (1, ) 3,000 + (2, ) 1,500 + (5, ) 500 = 6, , , ,700, ,850, ,450,000 = 8,150,000 Comments on Q3(iii): The calculations were straightforward but some students failed to deduct the excess from the average loss. Equal credit was given for candidates using average losses starting at 25.0 or (iv) New Loss Range New Average Loss Number 0 0 3,500 1 to , to to to to 1, ,001 to 3,000 2,000 3,000 3,001 to 5,000 4,000 1,500 5,001 to 15,000 10, ( ) ( ) ( ) ( ) (2, ) 3,000 + (4, ) 1,500 + (10, ) 500 = 37, , , , ,700, ,850, ,950,000 = 16,937,500 Comments on Q3(iv): A simple question but some candidates were unable to apply the excess to obtain the correct result irrespective of having calculated part (iii) correctly. (v) The number of claims hitting the excess is affected as well as the severity. This is a leverage/gearing effect caused by the excess being fixed in terms. If X is the loss and Y is the amount the insurer actually pays out then (Y = X 100) becomes (Y = 2X 100), which is not double Comments on Q3(v): An easy mark picked up by most candidates, even those who did not calculate parts (ii) and (iii) correctly Page 4

137 Subject ST3 (General Insurance Specialist Technical) September 2008 Examiners Report 4 (i) Benefits Marine Property To indemnify the insured against the value of the loss or damage to the marine hull (subject to limits or excesses). Cover can also be for marine cargo and specie and marine freight. Marine Liability To indemnify the insured against a financial loss (subject to limits or excesses). Associated legal expenses may also be covered. Comments on Q4(i): This bookwork question was answered well by many candidates but some failed to mention third party liability. (ii) Insured Perils Marine Property Perils of the sea/other navigable waters eg. storm, tsunami Fire Explosion Jettison Theft of cargo Spoilage and contamination of cargo Piracy Capsizing Stranding Collision (iceberg or other) Actions of the sea (e.g. waves damaging vessel) Running aground Specie (valuables) Marine Liability Damage to 3rd party property Injury to 3rd parties (including death) Injury to employees (including death) Errors and omissions Comments on Q4(ii): Most candidates were only able to reproduce a short standard list and failed to go beyond that. (iii) Exposure Measures Insured value of the hull/ship Tonnage of hull/ship Value of cargo Limits of liability Comments on Q4(iii): Answered well by most candidates. Page 5

138 Subject ST3 (General Insurance Specialist Technical) September 2008 Examiners Report (iv) Claim Characteristics Reporting delays: claims usually reported when the vessel reaches a major port. (May be only a very small delay if claim takes place in the port.) Settlement delays: could be long, especially if there is a dispute over legal liability or the amount that should be paid. Claim Amounts: variable. Relatively small amounts for hull damage to small vessels; very large amounts for complete loss of a large vessel and its cargo. Liability claims very variable; legal expenses element can dominate. Claim Frequency: infrequent for hull but more frequent for cargo Accumulations of risk are possible e.g. geographical concentration (storm/tidal wave); spillage of hazardous material Moral hazard frequency increases in bad economic conditions Salvage and subrogation are often employed Currency issues Comments on Q4(iv): Strong candidates were able to make sensible comments covering a range of claim characteristics of the main marine insurances. Weaker candidates generated few points and made too many unqualified generalisations. (v) Risk Factors Hull Level of cover / excesses and limits Size/tonnage of vessel Type of vessel Condition of vessel Age of vessel Type of industry Classification society Engine type/manufacturer Country of build Experience of captain and crew Detention history Areas sailed in (rough seas/war zones etc.) / locations visited Tonnage of hull Previous claims experience of ship Previous claims experience of owner Insured value / sum insured Cargo Level of cover Value of cargo Nature of cargo How packaged Where stored on ship (deck versus hold) Page 6

139 Subject ST3 (General Insurance Specialist Technical) September 2008 Examiners Report Trade terms Trade routes taken Standard property insurance risk factors apply when warehoused at port Liability Number of passengers and crew Type of work undertaken by the insured (e.g. shipbuilder, marina operator) Limits of liability Comments on Q4(v): Few candidates were able to produce a sufficiently wide range of factors to score well. 5 (i) General Assumptions: Policies attach evenly over any relevant period of time to both Contracts Risk is uniform for each policy and each policy lasts 12 months New policies do not change the risk profile on either Contract (i.e. mix constant) so the average premium is not affected by new business or lapses and remains constant other than for a rate change Endorsements and cancellations are ignored Rate changes applied to policies written on the day of the change Reinsurance is ignored Commission levels constant from 2004 to 2007 In order to answer (iii) properly, best to keep A and B figures separate as far as possible Calculate the monthly average premiums from 1 st January 2004 to 31 st December 2007 by adjusting for the rate changes. Contract A Contract B 1 May , November , March , October , June , September , Method selected based on limited time available and expected to give similar answers to the more accurate tranche method Assumption: annual average premium policies written is an appropriate measure of written premium in an underwriting year Assumption: can use overall proportions for earned/unearned premiums for each year Page 7

140 Subject ST3 (General Insurance Specialist Technical) September 2008 Examiners Report Take a simple average of the monthly average premiums in each calendar year to give annual average premiums for each of the underwriting years: Contract A Contract B , , , , From the definition of the annual accounting basis, it follows that the policies attaching to Contract B after 31 st December 2004 should not be included in the 2004 underwriting year and hence should not be included in the UPR carried forward from 2004 to 2005 Adjust Contract B for policies attaching to the 04 binder, but that are written in the 05 underwriting year (i.e. 75% written in 2004; 25% written in 2005). Repeat for 05 to 07. No adjustment required for Contract A. Adjusted Policy Numbers: Contract A Contract B ,000 7, ,000 10, ,040 11, ,824 11,861 Average Premium Number of Policies Written = Written Premium Written Premiums (000 s): Contract A Contract B Total ,250 11,700 24, ,918 17,198 31, ,768 19,449 34, ,308 21,004 36,312 Calculate the Acquisition Costs as 40% for A, 32.5% for B. Calculate the UPR b/f for 2005 as 50% of the Contract A premium written in 2004 and 62.5% of the Contract B premium written in The 62.5% comes from assuming earning using the 24ths method (i.e. 9/24 earned in 04 and 15/24 earned in 05). Page 8

141 Subject ST3 (General Insurance Specialist Technical) September 2008 Examiners Report For all the subsequent underwriting years the earnings are assumed to be 50%/50%. GWP Acq Cost NWP UPR b/f UPR c/f NEP ,250 5,300 7, ,975 3, ,918 5,567 8,351 3,975 4,175 8, ,768 5,907 8,861 4,175 4,430 8, ,308 6,123 9,185 4,430 4,592 9, ,700 3,803 7, ,936 2, ,198 5,589 11,609 4,936 5,804 10, ,449 6,321 13,128 5,804 6,564 12, ,004 6,826 14,178 6,564 7,089 13, ,950 9,103 15, ,911 6, ,117 11,157 19,960 8,911 9,980 18, ,216 12,228 21,988 9,980 10,994 20, ,312 12,949 23,362 10,994 11,681 22,675 Comments on Q5(i): Most students correctly calculated the premiums following the rate changes for each contract, although a small number of students incorrectly applied each rate change to the 2004 premium, thereby failing to compound the changes. Most candidates attempted to do the calculations by looking at each tranche of rates separately. This was an accurate and valid approach but candidates using this approach were unlikely to be able to finish the calculations in the time available. Because of the limited time available, it was expected that students would split the calculation by year, taking an average premium for each year, rather than by tranche. The examiners gave equal credit to either method. Also, while it is recognised that candidates do not have a spreadsheet available to perform the calculations setting out the workings in the form of tables would have made the calculations easier to perform and to carry forward to later parts of the question. Not many candidates did this thereby making their workings more complex than necessary. While some candidates were able to make the correct calculations for Contract A, most failed to adjust correctly for Contract B. Some candidates did not appear to understand the concept of deferred acquisition costs. (ii) Additional Assumptions: Ignore profit commission, tax and investment return on free assets Ignore reinsurance Incurred claims include IBNR/IBNER allowance No AURR required Sum the calendar year incurred claim amounts for each contract = incurred claims Calculate the paid claims in each calendar year (e.g. 35% GWP for Contract A) Page 9

142 Subject ST3 (General Insurance Specialist Technical) September 2008 Examiners Report Outstanding claims reserve c/fwd = reserve b/fwd + incurred claims paid claims with reserve b/fwd for 2004 = 0 Per policy expenses in 04 given. For each contract for each calendar year, # policies written per policy expenses per policy expense inflation = Expenses (per policy) Allocated Overheads in 04 given. Apply 4% inflation p.a. to get 05 to 07. Split for A, B e.g. pro-rata to incurred claims Calculate total expenses as Expenses (per policy) + Expenses (allocated overheads) Underwriting Result = Earned Premium (net of DAC) Claims Incurred Total Expenses Investment Return is taken as the average UPR b/fwd + Claim Reserve b/fwd + ½ of cash flow times the annual investment return of 4.5% where cash flow is NWP less paid claims less expenses, or other reasonable formula Insurance Result = Underwriting Result + Investment Return Inc Cyr Inc Pyr Inc Clms Paid Claims Res b/f Res c/f A , ,025 4, , , ,375 4,871 1,388 3, ,126 1,594 6,720 5,169 3,891 5, ,100 1,875 7,975 5,358 5,442 8,060 B , ,000 3, , ,938 1,500 7,438 5,331 1,373 3, ,475 2,700 8,175 6,029 3,479 5, ,375 2,025 7,400 6,511 5,625 6,514 Total , ,025 8, , ,563 2,250 14,813 10,203 2,761 7, ,601 4,294 14,895 11,198 7,370 11, ,475 3,900 15,375 11,869 11,067 14,573 Page 10

143 Subject ST3 (General Insurance Specialist Technical) September 2008 Examiners Report Per Pol Exps Per Pol Exps Tot O'heads Total Expenses A , , , , , , , ,436 B , , , , ,853 Total ,785 1,500 3, ,176 1,560 3, ,334 1,622 3, ,602 1,687 4,289 U'wtg Result Inv income Insurance Result A , , , , , B , , , , , , , ,079 Total , , , , , ,011 1,155 4,166 Comments on Q5(ii): Even if students had not managed to complete part (i), it was possible to pick up quite a lot of marks in part (ii), and some students did this. Even without premium figures, claims and expense figures could be calculated and candidates also gained marks for formulae and workings even where the final figures were incorrect. Very few students calculated claims reserve figures or were able to calculate profit. Page 11

144 Subject ST3 (General Insurance Specialist Technical) September 2008 Examiners Report (iii) Comments: Number of policies, average premiums and total premium Contract A average premiums rose in 2005 and 2006, but fell back to 2004 levels in 2007 following a series of rate reductions. Growth in Contract A policy numbers was most prolific as rates decreased Average premium decreases are likely to have been part of a growth strategy (because if the market had been decreasing rates to the same extent, volumes would not have grown at that rate) Contract B average premiums rose from 2005 to 2007 and growth in policy numbers was also strong over the same period. So the market may have been putting rates up at a faster pace than the increases on Contract B or Contract B rates started too low In 2004 the GWP of Contract A was slightly higher than that of Contract B. By 2007 the GWP of Contract B was dominating the mix. As the acquisition costs on Contract A policies (40%) are higher than on Contract B policies (32.5%), Contract B s contribution the total Earned Premium (net of DAC) is greater than its contribution to the GWP Claims The total claims ratio (Incurred Claims/Earned Premium (net of DAC)) has been improving slightly year on year from 2005 to Contract A claims ratio has deteriorated over that period, due probably to falling premium rates and rising claims costs. Contract B claims ratio consistently improves from 2005 to 2007 due, in part, to consistent rate increases over the period. At 2007 the Contract B claims ratio may suggest that further upside potential is limited. So the total claims ratio improvement is being driven by the claims ratio improvement in Contract B and its relative size in (net earned) premium terms compared to Contract A Expenses The total expense ratio (Total Expenses/Earned Premium (net of DAC)) improved from 2005 to Contract B has a much better expense ratio than Contract A. The improvement in Contract B's expense ratio from 2005 to 2007 has been cancelled out largely by the deterioration in Contract A's expense ratio. Contract B total per policy expenses are lower than Contract A total per policy expenses so Contract B has a better per policy expense ratio. Overheads are falling as a proportion of premium as the annual premium growth is well ahead of inflation in overheads. Performance The total combined ratio was less than 100% from 2005 to 2007, so the business unit is making an underwriting profit The profit margin (Insurance Result/Earned Premium (net of DAC)) has improved from 2005 to The contribution to the insurance profit from Page 12

145 Subject ST3 (General Insurance Specialist Technical) September 2008 Examiners Report investment income decreased from 2005 to 2007 as the underwriting results improved. Contract B produced most of the underwriting profit in 2006 and 2007 and significantly outperformed Contract A, so Contract B is cross-subsidising Contract A. This cross-subsidy may be deliberate on the part of the business unit e.g. the unit writes both with the same third party administrator, so losing one contract means losing the other. If the trend in Contract A's underwriting result it will keep upward pressure on the total underwriting result and will increasingly draw on subsidy from Contract B. Contract A requires rate increases/performance review/renegotiation of commission terms if it is to be brought into profitability. Past profitability of Contract B suggests that rates could be dropped to increase volumes while still remaining profitable. However, may become increasingly difficult to grow Contract B volumes while Contract A is underperforming as Contract B is cross-subsidising Contract A. Both contracts produce similar investment income ratios (Investment Income/NEP(net of DAC)). The investment income ratio improved from 2005 to 2007 as there was more cash available for investment in each successive year. If Contract A had not been written, then the total profit would have been higher over the three year period. (Contract A only made a small positive contribution to the insurance profit in In 2005 and 2007 it was a significant drain.) Comments on Q5(iii): Very few candidates recognised that marks could be gained for sensible comments made without having completed part (i) or part (ii). Those who did, tended to score best on this question. 6 (i) 2 key insured perils: Accidental Damage Theft (from insured location/vehicle/within territorial limits) Comments on Q6(i): Most candidates recognised theft as being the key peril. Some candidates did not read the question and listed more than two perils. (ii) Rating factor characteristics: Practical (objectively measurable) Relate to the intensity of the risk/define the risk Do not correlate too closely with the other rating factors Comments on Q6(ii): Surprisingly, the characteristic most frequently ignored by candidates was that a rating factor should reflect the intensity of the risk. Without that, the factor could represent anything. Page 13

146 Subject ST3 (General Insurance Specialist Technical) September 2008 Examiners Report (iii) Rating factors: Value of bicycle Postcode / Age of policyholder / Use (e.g. business/pleasure) / frequency of use Comments on Q6(iii): Again, some candidates did not read the question and offered more than two rating factors. (iv) Non-standard add-on covers: Public liability death or bodily injury to 3 rd party Public liability damage to property belonging to 3 rd party Worldwide cover (rather than limited to home country) Cover while bicycle is away from the home (not always included when a bike is covered under a Household policy) Damage while in transit e.g. on a bike rack on a car, on an aeroplane Hire of a bicycle while being repaired/replaced Personal accident Roadside recovery E.g. to repair a puncture/after falling off and damaging bike Cover while racing Replacement of helmet if you fall off, even if damage is not obvious New for Old cover on bikes up to, say, 3 years old Cover for spare parts & accessories e.g. spare wheels not attached to the bike (if not covered by Household Contents policy) Non-standard bicycles E.g. tandem/unicycle/electric bike Extension to other members of family / other named drivers Cover while child in seat on back Extended warranty Legal protection & assistance following an accident Malicious damage/vandalism Comments on Q6(iv): Poorly answered, with only the strongest candidates offering a range of sensible add-on covers that reflected the nature and cost of the standard insurance policy. Some candidates suggested add-on covers that would not be insurable or would have had disproportionately large premiums when compared to those typical of the standard insurance policy. (v) Difficulties with data: The data supplied by different companies may not be comparable: different geographical section of market different socio-economic section of market differences in cover (exclusions, excesses, policy conditions) differences in underwriting practice differences in claim settlement practice differences in nature of data stored by different companies different coding used for risk factors/rating factors Industry-wide data may not even exist for this class Data may not be detailed enough for pricing Data may be out-of-date (takes time to collect, collate & distribute) Page 14

147 Subject ST3 (General Insurance Specialist Technical) September 2008 Examiners Report Data quality may be poor (depends on quality of data of all contributors) Not all companies contribute so may be unrepresentative Comments on Q6(v): Although this was a fairly standard question, many candidates failed to cover the range of points needed. (vi) Data: Policy Postcode Make/Model of bike Age of bike/year of make Value of bike Excess chosen (if there is an option) Age of policyholder Cover level (UK/Worldwide; leisure/racing; etc.) including use of bike Estimated annual mileage Add-ons chosen Policy number Dates inception/renewal/mid-term change Premium amount Payment frequency (annual/monthly) Payment method (DD/credit card) Unique link between policy and claim, for matching Unique link between this policy and other products e.g. customer number Claims Incident date, reported date, settlement date Claim number Cause of loss Paid date for all claims payments Claim amount paid, by peril Claim amount outstanding, by peril Claims handling expenses Claim status Comments on Q6(vi): Many candidates were able to suggest a wide range of data items that could reasonably feature in the management information system. 7 (i) Aggregate Deductible Introduction of the aggregate deductible means that now the sum of the claims to the layer must exceed the deductible before the cedant can make a recovery so for a given amount of exposure, expect the aggregate deductible to reduce the cedant s expected recovery and increase the cedant s retention The extent of the impact of the aggregate deductible depends on: the size of the aggregate deductible (for a given exposure in vehicle years) the expected number and severity of losses to the layer (for a given exposure in vehicle years) e.g. large aggregate deductible relative to expected number/size of losses means lower recoveries for the cedant (and vice versa for a small aggregate deductible) Page 15

148 Subject ST3 (General Insurance Specialist Technical) September 2008 Examiners Report Stability Clause Before the stability clause applied, the expected amount of total losses to the layer would have increased annually (all else being equal) because of: the effect of TPBI inflation on severity of individual losses to the layer (i.e. the conditional expected value of a loss to the layer increases with inflation) and the gearing effect of TPBI inflation increasing the frequency of losses to the layer (i.e. probability of a loss to the layer increases with inflation) A stability clause means the attachment point and layer limit are adjusted in line with some specified index (e.g. fixed x% p.a. or a healthcare cost index) with the intention of maintaining real values to the layer so the layer widens with each application of the index e.g. 1m xs 1m indexed by 2% is 1.02m xs 1.02m Adding the stability clause has the following expected impact The frequency of losses to the layer may drop over time e.g. a claim that starts in the layer may settle below the layer For a given loss, its actual attachment point depends on the settlement date (i.e. the attachment point will increase in line with the stability clause index until the loss settles) If the deductible is small relative to the expected claims cost without the deductible, the expected claims cost to the layer is simply the cost without deductible less the deductible amount. Whereas if the deductible is relatively large then a straight deduction is not correct and claims to the layer can only be estimated using a distribution and probabilities. The actual impact of the stability clause depends on the cedant s actual claims experience and on the inflation in TPBI claims relative to the index applied to the layer i.e. inflation could be different to the assumed indexation. Comments on Q7(i): Most candidates were able to define a stability clause and explain the effect this would have. Fewer were able to explain the aggregate deductible. (ii) Reinsurer + stability clause ensures alignment of interest by encouraging faster claims settlement (as net retention increases with each year due to the indexation of the attachment point and limit), + stability clause gives some protection against expected future inflation in the claims to the layer + aggregate deductible reduces exposure to the cedant and allows the reinsurer to use capital elsewhere + benefits if the sum of claims to the layer doesn t breach the aggregate deductible or claims settle below the indexed attachment point actual claims inflation may outstrip the indexation thereby eroding the benefit of the stability clause over time (likely in practice) potential increase in expenses for setting up and managing more complex contracts lower premium income with introduction of aggregate deductible more volatility in claims cost to the layer relative to the premium charged Page 16

149 Subject ST3 (General Insurance Specialist Technical) September 2008 Examiners Report Cedant + the aggregate deductible reduces reinsurance spend (especially beneficial if reinsurance rates are hard) + can use the aggregate deductible to manage risk appetite + the aggregate deductible means higher expected profit as ceding less to the reinsurer generally means ceding less profit + cedant can manage total exposure to the reinsurer (reinsurer security impacts capital requirement) + cedant may be able to negotiate a lower premium because of the stability clause aggregate deductible delays recoveries (cashflow implications) greater loss retention, so alternative source(s) of capital required (alternatives may be more costly). greater volatility in the retained losses retains some inflation risk i.e. if the TPBI inflation is lower than the indexation, then more likely that a claim estimated to settle in the layer settles below the layer Comments on Q7(ii): Any advantages and disadvantages given in part (i) were given credit under part (ii). In general, candidates failed to think of enough valid advantages and disadvantages to score highly in part (ii). END OF EXAMINERS REPORT Page 17

150 Faculty of Actuaries Institute of Actuaries EXAMINATION 23 April 2009 (pm) Subject ST3 General Insurance Specialist Technical Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 1. Enter all the candidate and examination details as requested on the front of your answer booklet. 2. You have 15 minutes before 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. 4. Mark allocations are shown in brackets. 5. Attempt all six questions, beginning your answer to each question on a separate sheet. 6. Candidates should show calculations where this is appropriate. AT THE END OF THE EXAMINATION 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 the 2002 edition of the Formulae and Tables and your own electronic calculator from the approved list. ST3 A2009 Faculty of Actuaries Institute of Actuaries

151 1 List regulatory restrictions that could be applied to a general insurance market, briefly explaining the reason for each. [12] 2 A general insurance company selling personal lines insurance policies is considering removing the excess from future policies and replacing it with a deductible of the same magnitude. (i) (ii) (iii) Explain the terms excess and deductible, highlighting the main difference between them, and giving an example to support your answer. [4] Discuss the effects that this change could have on the company s future operations and profits. [4] Describe how the company should model the potential impact of this change on profit. [4] [Total 12] 3 The following data are provided for a general insurance class of business: paid claim amounts by accident year and development period incurred claim amounts by accident year and development period settled claim numbers by accident year and development period reported claim numbers by accident year and development period ultimate premium data by accident year (i) (ii) (iii) Give examples of the checks that you would carry out during a reserving exercise, explaining what each of these would show. [5] Suggest, with examples, reasons why the actual run-off of outstanding claims may at times be higher than the estimated amounts when monitoring the claims reserve figures for mortgage indemnity business. [7] List other reasons why a general insurance company would analyse claims data. [4] [Total 16] ST3 A2009 2

152 4 A general insurance company arranges a layer of excess of loss reinsurance for 4.0m excess of 1.0m for individual claims. There is also an annual aggregate deductible of 4.0m. The reinsurer charges an initial premium of 1.0m with a first reinstatement premium of 120% of initial premium, a second reinstatement premium of 150% of initial premium, and no further reinstatements. The actual claims in the year are shown below in the order that they occurred: Claim Claim size 1 2.5m 2 3.5m 3 6.0m 4 4.2m 5 1.8m 6 3.0m 7 5.0m (i) Calculate the claim amounts paid by the reinsurer and the reinstatement premiums payable after each claim. [6] (ii) Define aggregate excess of loss reinsurance. [1] (iii) (iv) (v) (vi) Explain how stop loss reinsurance is different from aggregate excess of loss reinsurance. [3] Explain why stop loss cover is generally quoted in terms of claim ratios rather than monetary amounts. [1] Suggest possible risks relating to the direct writer s operations that a reinsurer would face if stop loss cover were made available. [3] Describe the conditions that a reinsurer providing stop loss cover is likely to impose on the business covered. [1] [Total 15] ST3 A PLEASE TURN OVER

153 5 An individual claim amounts distribution, F(x), is a discrete distribution on the positive integers, and the number of claims, N, has a binomial, Poisson or negative binomial distribution. The probability functions for individual claim amounts (X i ) and aggregate claim amounts (S), respectively, are: f k = P(X i = k) k = 1, 2, 3,. g k = P(S = k) k = 0, 1, 2,. Constants a and b are such that the distribution of N, P(N = r) = p r satisfies the following equation: and p r = (a + b/r) p r 1 for r = 1, 2, 3,... n E X1 Xi = r = r/ n i= 1 m r E X X = r = jf i i= 1 j= 1 ( n 1)*. f / 1 j r j r 1 n* ( n 1)* n r = ( + / ) j n 1 r j j= 1 p f a bj r f p f f n* r (i) Derive a recursion formula for the aggregate claim distribution G(x). [6] The number of claims follows a Poisson distribution with mean 125. The claims are assumed to be random variables, independent of each other and independent of N, with a Pareto distribution with mean 750 and standard deviation 1,750. The PDF for the Pareto distribution is: αλ f( x) = x > 0 α+ 1 ( λ+ x) α (ii) (iii) Show that E[S] = 82,523, given that S = X 1 + X 2 + X X N, if a policy excess of 100 is introduced. [6] Calculate suitable values for the parameters of a translated gamma distribution to approximate the distribution of S given that the standard deviation is 23,480 and coefficient of skewness of S is [3] [Total 15] ST3 A2009 4

154 6 A country has experienced a significant increase in insurance premium rates in recent years. The regulators believe that the major factors contributing to this are a significant increase in the level of bodily injury court awards as well as the proportion of claims cost spent on legal expenses. Although solicitors only charge a fee if the case is successful, fees can account for up to 40% of damages awarded. As a result, the regulators are planning to introduce a Bodily Injuries Compensation Authority (BICA), with the principal aim of reducing premium rates, which will operate as follows: Disputed bodily injury claims less than two years old will automatically be referred to the BICA before they are allowed to be processed through the court system. Any disputed bodily injury claims not notified within two years of injury will be referred to the court system. The claimant will be charged a small fixed fee, regardless of the outcome of the claim. General insurance companies will be charged a fee in proportion to their market share based on total GWPI to cover the additional running expenses of the BICA. The initial application will be made by post on a standard form completed by the claimant s doctor. The claimant will not meet the BICA staff in person and therefore legal representation will not be possible. Damages awarded by the BICA will be based on standard amounts by type of injury. A single amount will cover pain and suffering, medical expenses and loss of earnings. Any associated property damage claims will not be processed by the BICA. The claimant will be notified of the damages awarded by post. The BICA will aim to settle claims within 90 days of notification. If the claimants are dissatisfied with the level of compensation, they may reject the award and continue with the claim through the court system. (i) (ii) (iii) Discuss the advantages and disadvantages to the claimant of this system of claims resolution. [7] Describe the adjustments that a private motor pricing actuary would need to make to the existing premium calculation assumptions and methodology as a result of the introduction of the BICA. [13] Suggest improvements that could be made to the proposed system, giving reasons for these. [10] [Total 30] END OF PAPER ST3 A2009 5

155 Faculty of Actuaries Institute of Actuaries Subject ST3 General Insurance Specialist Technical EXAMINERS REPORT April 2009 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. R D Muckart Chairman of the Board of Examiners July 2009 Comments Individual comments are shown after the solutions to each part question that follows. GL Faculty of Actuaries Institute of Actuaries

156 Subject ST3 (General Insurance Specialist Technical) April 2009 Examiners Report 1 Restrictions on the type/ amount of business a general insurance company can write / classes of business it is authorised to write. Ensures companies have appropriate expertise/ sufficient capital to write the business classes Initial authorisation of new insurance companies.. Ensures companies have appropriate expertise / sufficient capital to write the business classes Limits on premium rates that can be charged. Ensures premium rates are sufficient to meet future claims/ ensure policyholders not overcharged Restrictions on information that may be used in underwriting and premium rating. For ethical / anti-discrimination reasons. The requirement to deposit assets to back claims reserves. To ensure the company has sufficient funds to pay claims. The requirement to maintain a minimum level of solvency. To ensure if claims are significantly worse than expected the company will still remain solvent. Restriction on the type or amount of certain assets allowed to demonstrate solvency. To prevent high-risk assets from backing liabilities. Restrictions on the currency, domicile and duration of assets allowed to demonstrate solvency (or mismatching reserves). To ensure that assets match liabilities by term and currency so that short term changes in exchange rates will not have an impact on solvency margins. The use of prescribed bases to calculate premiums, asset values and liabilities to demonstrate solvency. To ensure accurate estimates of liabilities and uncertainty. Licensing agents to sell insurance and requirements on the method of sale. To ensure company has necessary expertise and that insured is well informed. The requirement for risk-based capital calculations & ICA analyses. To ensure accurate estimates of liabilities and uncertainty. Requirement to pay levies to consumer protection bodies. To protect policyholders and maintain faith in insurance market. Legislation to protect policyholders should general insurance companies fail, e.g. Financial Services Compensation Scheme. To protect policyholders and maintain faith in insurance market. Cooling off period, e.g. fourteen day cancellation rules on policies issued. To protect policyholders and promote confidence in the industry. Regulations with respect to treating customers fairly. To protect policyholders and promote confidence in the industry. Restriction on countries a general insurance company can write business in. Prevents exposure to volatile risks and unfamiliar legal systems and regulations. Restrictions with respect to anti-competitive behaviour Prevents formation of cartels, concentration of risk, and protects policyholders. Requirement to file / publish premium rates before they can be used. Prevents anti-competitive practices and therefore protects policyholders. Page 2

157 Subject ST3 (General Insurance Specialist Technical) April 2009 Examiners Report Mandatory restrictions on cover e.g. no deductible on EL To protect policyholders and claimants and to ensure consistency of cover. Requirements to offer cover e.g. even in high-risk flood areas / motor 3 rd party liability. For social responsibility and helps economy as a whole. Statutory requirement to offer certain cover e.g. EL & Motor 3rd Party Liability. For social responsibility and helps economy as a whole. Disclosure / transparency of reporting requirements To help regulators, investors, capital providers and policyholders assess the soundness of the company. Requirement for a Statement of Actuarial Opinion to be produced by an approved actuary. Promotes confidence in the level of reserves and helps to prevent the failure of a general insurance company. Requirements for management to be fit and proper. Promotes confidence in the industry and helps prevent fraud. Restriction on the type of reinsurance that may be used. To prevent exposure to risky reinsurers or reinsurance products. Restriction on discounting of liabilities and discounting rates that can be used To ensure consistency and that reserves are sufficient. Prohibiting illegal products from being sold, e.g. kidnap insurance. To discourage illegal practices. Requirement for general insurance companies to be audited. To give regulators and investors confidence in the company and to prevent fraud. Comments on Q1: This question was reasonably well answered by the majority of candidates but some students did not give enough distinct points or specific enough reasons. 2 (i) Deductible Amount deductible from claim amount, payable by policyholder. Sum insured = S. Deductible = D. Loss = L. If L > S insured pays L S + D, insurer pays S D. If L < S insured pays D and insurer pays L D. Excess Sum specified by policy which insured must bear before any liability falls on insurer. Sum insured = S. Excess = E. Loss = L. If L > S + E, insured pays L S and insurer pays S. If L > E but L < S + E insured pays E and insurer pays L E. Therefore effect differs in the case where L > S. The primary difference is that the deductible eats into the sum insured whereas the excess sits below the sum insured. Hence for a policy with a deductible the maximum the insurer will be liable to pay is the sum insured less the deductible. Page 3

158 Subject ST3 (General Insurance Specialist Technical) April 2009 Examiners Report Example (this has to be realistic). sum insured of 30,000. Policy A has an excess of 5,000, policy B has deductible of 5,000 Each policy experiences loss of 40,000 Policy A: loss to insurer = sum insured = 30,000, loss to insured = 40,000 30,000 = 10,000 Policy B: loss to insurer = sum insured deductible = 30,000 5,000 = 25,000, loss to insured = 40,000 25,000 = 15,000. An explanation without using L, S, D etc. which is correct is acceptable. Comments on Q2(i): This was well answered by the majority of candidates. However, some candidates did not understand how a deductible worked with some getting the excess and deductible the wrong way round. Some students did not give an example even though this was specifically requested in the question. (ii) Replace excess with deductible Effect of change will be small as this is personal lines business. Any valid reason explaining why change will be small All else being equal insurers profits will increase as claims cost will decrease so profit per policy will increase Depends on change in policy volumes Option of reducing premium rates to compensate for potential loss of volume. Policyholders may not realise that there is a difference Although will be obligation to clearly explain policy changes to clients (treating customers fairly) Policyholders may realise that there is a difference and demand a reduced premium. Possible change in mix of business as a result. Effect depends on mix of renewal / new business. Also depends on factors such as advertising and distribution channels. Significant increase in costs associated with communicating changes to brokers and policyholders, and updating policy documentation. Increase in costs associated with system changes & retraining of staff. Expenses will most likely increase by more than any benefits gained. Comments on Q2(ii): Better candidates picked up on the key points for this part. Candidates that did not understand the term deductible failed to answer this part of the question correctly. Also, many students did not comment that the claim cost impact would be small, particularly since it was personal lines business, and some students did not consider the implications for expenses. (iii) Model Set up the model to give total profit as an output Review company data on past changes in excess and effect on policy volumes and profit Review past company data on any deductibles (if available) otherwise review industry data on effects of deductibles on policy volumes and profitability Page 4

159 Subject ST3 (General Insurance Specialist Technical) April 2009 Examiners Report Allow for other factors such as distribution channels, advertising Allow for any changes to mix of business e.g. age, social economic group Allow for level of expenses, both fixed and variable Allow for possible changes in premium rates Allow for correlations between excess / deductible and other rating factor Fit Generalised Linear Model to model outputs. Alternatively, fit a stochastic / deterministic model. Use results to maximise profits Sensitivity test model - test the goodness of fit. Set up so that factors can be easily interpreted and monitored Comments on Q2(iii): Most candidates struggled to answer this part well with many candidates talking about choosing a base period and modifying the data, rather than tailoring the answer to the question and discussing what specific modifications to the data would be needed and what the actual output of the model should be. 3 (i) Check consistent with the data from the previous development period to check for any errors, e.g. compare diagonals. Check any anomalies / large movements in the data. (If large claims etc. are mentioned it must be because they have seen anomalies in the data) Cumulative paid to incurred ratios to test for a change in the case reserving strength or claims settlement practise. Look at the ratios by accident and development period. IBNR to outstanding ratios to test for a change in the reporting process. Look at the ratios by accident and development period. Average outstanding case estimate again to test for a change in the strength of case reserves. Look at the ratios by accident and development period. Trends in ultimate loss ratios by accident year for consideration against market benchmarks and knowledge of the underlying market conditions. Settlement claims divided by reported claims to check for changes in the claims handling process. Average cost per claim as a sense check for reasonableness. Claim frequency again for consideration against market benchmarks and knowledge of the underlying market conditions. Check development patterns by accident year to check consistency between accident years and compared to the prior analysis Sense checks e.g. the relationship between paid and incurred is as you would expect Compare results of different projection methods to see if the results are consistent Survival ratios if class of business includes latent claims. Check actual versus expected for the latest development period to identify any large movements / changes in reserving strength any other reasonable diagnostics, based on the available data given, with explanation, are acceptable Page 5

160 Subject ST3 (General Insurance Specialist Technical) April 2009 Examiners Report Comments on Q3(i): This was poorly answered by the majority of candidates. Better candidates mentioned points including: checking for errors and unusual developments but most candidates did not consider any diagnostic checks (looking at specific ratios) or benchmarking results as a sense check. Some candidates gave answers that required additional data although the question specifically stated what data were provided. (ii) Unusually heavy experience e.g. increase in central bank base rates leading to increase in number of claims Random fluctuations / volatility. Large or exceptional claims e.g. factory closing down leading to local unemployment with one regional mortgage lender leading to increase in number of claims Trends in claims experience numbers due to economic factors e.g. rising unemployment/falling house prices leading to increased number of claims. Trends in claims experience amounts due to economic factors e.g. increase in the level of repossessions leading to higher costs for the insurer. Changes in risk. e.g. switch to endowment mortgages from repayment mortgages implying higher claim severity. Changes in cover e.g. increase in amount by which mortgage exceeds normal advance. Unexpected changes in law e.g. introduction of new government legislation stating that insurers must still pay out when the lender has failed to apply any required underwriting. Quality and amount of reinsurance cover may have varied e.g. reinsurance review. Inadequate claims reserving process e.g. inappropriate assumptions tail selection, future inflation may differ to that assumed Change in mix of business e.g. policies sold to people with low job stability MIG business has a strange risk profile (uneven with a long tail) that will need to be taken into account. Therefore very difficult to reserve this class. Systematic fraud e.g. developers artificially inflating official market prices through the use of incentives, mis-selling through increasing prevalence of self-certification loans. Payment patterns may differ e.g. due to system changes or settlement patterns may differ e.g. postal strike. Comments on Q3(ii): Better candidates understood the impact of the economy on this class of business but could have generated more points. Some candidates did not appear to understand what the question was asking for. (iii) monitoring the adequacy and use of reinsurance comparing the relative profitability of various parts of the account reviewing present premium rates pricing new or amended products determining rating factors Page 6

161 Subject ST3 (General Insurance Specialist Technical) April 2009 Examiners Report experience rating financial planning and management information Assessment and allocation of capital monitoring the insurer s asset/liability position giving investment advice based on the liability profile monitoring actual versus expected for both claims and premiums for statutory accounts establishing the need for other reserves e.g. URR identification of unexpected claims sources to tighten up policy wording / testing efficiency of the claims management teams and loss adjustors plus any other sensible suggestions Comments on Q3(iii): This was bookwork and was well answered by the majority of candidates. 4 (i) Claim Claim size Claim size in layer Reinsurer pays RI Premium 1 2.5m 1.5m 0m m 2.5m 0m m 4.0m 4.0m 1.2m 4 4.2m 3.2m 3.2m 1.2m 5 1.8m 0.8m 0.8m 0.3m 6 3.0m 2.0m 2.0m 0m 7 5.0m 4.0m 2.0m 0m Total 26m 18m 12m 2.7m Comments on Q4(i): Many candidates answered this completely correctly with other candidates making minor mistakes when calculating the reinstatement premiums. Some candidates however misunderstood the impact of the annual aggregate deductible with a few mistakenly assuming this was aggregate excess of loss even though individual claims cover is specified. (ii) A form of excess of loss reinsurance that covers the aggregate of losses, above an excess point and subject to an upper limit, Sustained from a single event or from a defined peril (or perils) over a defined period. Comments on Q4(ii): This is bookwork and was reasonably well answered by the majority of candidates. (iii) Aggregate XL only provides cover for either one peril over the year or one event. Stop loss extends cover to all claims, arising from all perils or all events, in a class or classes over the defined period Stop loss is broader in that it covers not only catastrophe events but also unforeseen accumulations of losses Page 7

162 Subject ST3 (General Insurance Specialist Technical) April 2009 Examiners Report Stop Loss reinsurance directly relates to the primary insurer s underwriting results In general, Stop Loss reinsurance is difficult to obtain and is usually limited to only a few lines of insurance Comments on Q4(iii): This is bookwork and most candidates did understand the difference between the two types of reinsurance although many students did not give enough differences between the two. (iv) By using claims ratios the limits (and premiums charged) rise in proportion to the amount of business written by the direct writer. If this was not the case then the direct writer could, after taking out cover, write lots more business by cutting premiums and hence trigger the stop loss limits in that way. Comments on Q4(iv): Most candidates got this point. However, some candidates did not understand why a reinsurer would not use monetary amounts. (v) Direct writer s premium generally under-priced (e.g. a competitive market) Poor underwriting by direct writer Poor premium rating structure leading to adverse selection Unusually heavy claims experience (e.g. catastrophes and/or large claims) Generally adverse claims experience (i.e. random event) Poor claims handling control particularly after deductible reached i.e. moral hazard Risk insurer targets more volatile but profitable business for higher expected returns once downside risk is removed. Comments on Q4(v): Most candidates mentioned poor underwriting and claims handling with better candidates generating more points. (vi) Only reinsure a proportion of the risk e.g. 90% so that the insured retains an interest in the risk (can be described as a participation clause / coinsurance / deductible if used in the correct context) Ensure stop loss cover has an upper limit Maintain some control over underwriting and claims Comments on Q4(vi): This was reasonably well answered with most candidates suggesting that the insurer retains some interest in the risk via some sort of participation clause/deducible/co-insurance. Page 8

163 Subject ST3 (General Insurance Specialist Technical) April 2009 Examiners Report 5 (i) g 0 = p 0 This holds as the minimum claim size is 1 g r = = = n* pnfr n= 1 ( n+ 1)* 1 r + n+ 1 r n= 1 r 1 n* a+ b p0 fr + a+ bj r fjpnfr j n= 1 j= 1 pf p f ( ) ( / ) = ( a + b) g = = r 1 0 f r + ( a + bj / r) f j p n j= 1 n= 1 r 1 0 r j r j j= 1 ( a+ b) g f + ( a+ bj/ r) f g r j= 1 ( a+ bj/ r) f g j r j f n* r j Above is slightly different from core reading where equations incorrectly contain (a + bj) / r) not (a + bj / r) Comments on Q5(i): This is bookwork but was poorly answered by the majority of candidates. (ii) E[S] = E[N] E[X ] where X = 0 X 100 = X 100 X > 100 E(X) = λ / (α 1) = 750 V(X) = αλ 2 / (α 1) 2 (α 2) = α / (α 2) = V(X) / E(X) 2 = / = α = (α 2) α = / = 2.45 λ = = ( x 100) EX ( ) = αλ 100 α+ 1 ( λ+ x) α dx dx x x + α λ = αλ 100 α α 1 ( λ + ) ( λ + ) α λ =αλ + α 1 α ( λ+ x) ( α 1) ( λ+ x) α 100 Page 9

164 Subject ST3 (General Insurance Specialist Technical) April 2009 Examiners Report α 1 1 =αλ α 1 α 1 ( λ+ 100) ( α 1) ( λ+ 100) α α = λ 1 ( λ+ α 100) ( α 1) = Note 2 nd line of derivation of E(X ) was to simplify integration by splitting numerator in 1 st line as (λ+x) (100+λ). The alternative is to do integration by parts which is an equally valid approach, as follows: ( x 100) α EX ( ) = αλ dx 100 α+ 1 ( λ+ x) α 1 x = αλ. + dx α α α α ( λ x) α ( λ x) α ( λ + x) α = αλ +. + α + α α α λ α ( α 1) 1 ( 100) ( λ + x) α ( λ + 100) 100 α α 1 1 = αλ. α ( α 1) α 1 ( λ + 100) = λ 1 ( λ + α 100) ( α 1) ES [ ] = = 82,523 Comments on Q5(ii): Most candidates were able to determine the values for α and λ and wrote down the correct integral to be solved but not many were able to solve it. (iii) Let Y + k be a gamma random variable with the same first three moments as S. Then equating parameters: Skewness = = 2 / α Variance = 23,480 2 = α / λ 2 Mean = 82,523 = k + α / λ So α = λ = k = 13,848 Comments on Q5(iii): This was correctly answered by the majority of candidates who attempted it, although some who did badly on parts (i) and (ii) did not attempt this part. Page 10

165 Subject ST3 (General Insurance Specialist Technical) April 2009 Examiners Report 6 (i) Advantages Possible reduction in premium rates if the claimant is the policyholder. Settlement delays should be significantly less. No legal fees (if they are deducted from damages). Simpler process. More consistent / predictable Can still use court system If the injury is not severe the overall payout should be higher. If no medical expenses or loss of earnings incurred then the overall payout should be higher. If claimant has lower than average earnings the payout would probably be higher. Awards may be inflated initially to promote confidence in the system. Disadvantages Process will not be specific enough for certain more complicated cases. Fee that is non-refundable. If the injury is severe the overall payout will be too low. If no medical expenses or loss of earnings incurred then the overall payout will be too low. No representation. Two separate claims will need to be processed if there are property damages as well i.e. 1 through BICA and 1 through insurer. May have to go to court anyway so overall costs / delays longer. Postal strike will delay the process BICA aims to reduce premium rates so may give lower awards If the claimant has above average earnings the payout would probably be lower. Comments on Q6(i): Most candidates answered this part of the question well although a few candidates incorrectly talked about the advantages and disadvantages from the insurer s perspective. (ii) Adjustments to pricing model Divide injury claims by type of injury Base assumptions on claim amounts published and used by BICA rather than on own experience. Therefore results have less reliance on rating factors However if claims go to court awards will not be based on BICA. Therefore need an assumption about the rate of claims to court and the nature of the claims to court. Divide claims by severity of injury need to make an assumption on potential savings or losses as a result of average damages. Divide injury claims into general damages and special damages e.g. medical expenses, loss of earnings need to make an assumption on potential savings or losses as a result of average damages. Page 11

166 Subject ST3 (General Insurance Specialist Technical) April 2009 Examiners Report Possible changes expected to number of claims: Possible increase in number as may be simpler to claim Possible decrease as more difficult for solicitors to encourage claims with no win no fee offers Possible decrease in fraudulent claims. Significant changes in average cost per claim due to standard damages regardless of severity of injury or level of medical expenses etc. Possible initial increase in average cost as BICA will want to promote confidence in system. In long run possible decrease in average cost as claims inflation decreases. Amend assumption about future claims inflation. Could be due to rejection of BICA damages. or a delay of longer than 2 years before notification. Amend expected notification delays. Include possibility of longer delays due to claimants waiting 2 years to enter the court system. Amend settlement delays. e.g. 30 days for small claims 90 days for larger claims. Include longer settlement delays for claims entering court system. Refer to industry data from any countries that have a similar system in place to support your calculations. Adjust large claim loadings where these are no longer felt to be appropriate due to the change in the data groupings. Adjust for any proposed changes in cover following introduction of new system. Adjust for any proposed changes in mix of business / target market / distribution channel following introduction of new system. Include assumption about the proportion of combined damage and injury claims as this will result in an increase in claims handling expenses as more than one claim will need to be set up. Include assumption about the reduction in claims handling expenses as a result of most bodily injury claims being processed by the BICA. Include assumption about any longer term reduction in fixed costs that may be possible as a result of this. Amend assumption about the level of legal expenses. Change reinsurance loadings where appropriate` Include assumption about the BICA fees based on forecast market share. Amend investment return assumptions to reflect the change in the expected duration of the liabilities. Factor in pressure from regulators to reduce premium rates. Consider possible changes to competition in the market. Amend any profit loadings that may have changed following the introduction of the new system. Page 12

167 Subject ST3 (General Insurance Specialist Technical) April 2009 Examiners Report Comments on Q6(ii): Most candidates did not generate anywhere near the number of points on the marking schedule. Better candidates had a more structured answer considering the claims that would be settled by BICA and those that would go to court separately. (iii) Changes to system Add severity of injury as this will result in fairer awards. Severely injured claimants will be less likely to reject the award. Employ a group of independent doctors to process the application forms. This will reduce fraudulent claims and ensure consistency of diagnosis. Make the fee refundable if the claim is successful and the claimant accepts the award. This is fairer to legitimate claimants and will also discourage fraudulent claims as there are different costs involved depending on the outcome of the claim. Include claims older than two years e.g. less than five years old. This could further increase the savings on legal expenses Introduce other injury compensation e.g. medical expenses, loss of earnings. This will result in fairer results and claimants who have incurred significant costs will be less likely to reject the award. Introduce standard property damage awards calculated by a pricing actuary. This will reduce claims handling expenses for the insurers and make the process simpler. Introduce a deterrent for going through the court system e.g. the BICA award is no longer available regardless of the outcome of the court case. This will reduce settlement delays and legal expenses. Introduce face-to-face meetings if required. Allow additional documentation if necessary. This will result in fairer diagnosis and ensure claimants are happier with the outcome. Introduce an arbitration / appeal process. This will ensure that claimants are happier with the outcome and make it less likely that they will go to court. Allow claimants to opt out of BICA. This will save costs relating to those claimants who have no intention of accepting the BICA award. Add the option of legal representation if requested but with fees covered by policyholder. This ensures that less educated claimants (or any with other issues) will still be well represented, but still deters the majority of claimants from engaging a solicitor. Refer more complicated cases or those expected to settle above a certain threshold to courts. This will result in a more appropriate outcome for complex cases that cannot be properly addressed by the BICA. Page 13

168 Subject ST3 (General Insurance Specialist Technical) April 2009 Examiners Report Ban no win no fee practices. This will reduce fraudulent claims and will also reduce the number of claims that are unlikely to be successful. Amend the insurer s BICA fee so that it is based on market share by line of business or on a claim-by-claim basis. This will more accurately charge those insurers with a higher proportion of bodily injury claims. Process applications by fax / internet / .. This will speed up the process and avoid postal strikes.. Be more specific with which claims the BICA will apply to i.e. only future notifications or current IBNR claims. This will help pricing actuaries to more accurately calculate their prices and prevent any unnecessary delays in the process. Comments on Q6(ii): Most candidates made a reasonable attempt at this question, although some of the reasons given for suggested improvements were questionable e.g. removing the small fixed fee as some claimants may not be able to afford it would have the opposite effect on fraudulent claims. Some students did not give specific enough reasons and some tended to focus on the insurance companies points of view rather than considering the claimants as well. END OF EXAMINERS REPORT Page 14

169 Faculty of Actuaries Institute of Actuaries EXAMINATION 2 October 2009 (pm) Subject ST3 General Insurance Specialist Technical Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 1. Enter all the candidate and examination details as requested on the front of your answer booklet. 2. You have 15 minutes before 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. 4. Mark allocations are shown in brackets. 5. Attempt all six questions, beginning your answer to each question on a separate sheet. 6. Candidates should show calculations where this is appropriate. AT THE END OF THE EXAMINATION 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 the 2002 edition of the Formulae and Tables and your own electronic calculator from the approved list. ST3 S2009 Faculty of Actuaries Institute of Actuaries

170 1 A small upmarket supermarket has approached a large general insurance company directly and has enquired about insuring a promotional product. They sell a range of luxury food hampers that are delivered all over the world. They would like to offer purchasers a guarantee that if a hamper is lost in transit then a replacement will be dispatched within seven days of the loss being accepted. The supermarket sends the hampers uninsured via national postal services and couriers depending on destination country and the weight of the hamper. For every hamper lost the insurance company will pay the supermarket the replacement cost. Explain what data would be required in order to rate this business, including the likely source of these. [6] 2 The following data have been extracted from the accounts of a medium-sized general insurance company which writes mainly motor and household business. The company prepares its accounts on an accident year basis with a financial year end of 31 December. (All figures in millions) Net written premium Net earned premium Net incurred claims Increase in DAC Expenses paid Commission paid Investment income on insurance funds Other investment income Total assets at 31 December Total liabilities at 31 December Net in the above table means after allowing for reinsurance. (i) Calculate the following for each of 2007 and 2006 (a) (b) (c) (d) Loss ratio Expense ratio Operating ratio Solvency ratio [5] (ii) Comment on the ratios calculated in (i), giving possible reasons for the features observed. [8] [Total 13] ST3 S2009 2

171 3 A general insurance company has been asked to tender to provide insurance cover for the organisers of a major sporting event to be held in 2012 at a number of venues across the United Kingdom. At the moment approximately half the venues have been completed while it is anticipated that those remaining will be complete by early in In addition to the sporting events the competition will be preceded by a series of concerts featuring top musicians. The proposed cover will be a three year policy commencing on 1 January 2010 with the premium payable in three equal annual instalments. It is intended that the cover will be on an all risks basis that will meet the organisers insurance needs. (i) (ii) (iii) (iv) Describe the different types of cover that would be required, including the claims characteristics of each. [14] List the exposure measures that would be required to determine the appropriate exposure for rating the cover in part (i). [4] Discuss other risk considerations that would be considered when rating this particular product. [7] State reasons why a general insurance company may choose to model claims, other than to calculate the risk premium. [4] [Total 29] 4 (i) State the main objective regarding the investment of the free reserves of a general insurance company. [1] The following information has been extracted from the management accounts of two proprietary non-us general insurance companies, A and B. Company A Company B Value of assets 600m 55m Value of liabilities 400m 40m Largest class of business written UK Motor Commercial Property (USA) An actuary is advising on the best investment strategy to use for the assets of each company. (ii) (iii) Discuss the strategies that the actuary would recommend and the factors that should be considered when giving advice. [10] Describe the extra information that would be needed before a more informed level of advice could be given, explaining why this information is important. [3] [Total 14] ST3 S PLEASE TURN OVER

172 5 The actuarial team of a large accountancy firm is currently working on the audit of a medium-sized general insurance company. The company writes a number of different lines of business. The following is the only information that has been provided. XYZ Insurance Plc Year Ending 31 December 2008 Summary of written premium Class Amount Territories Commercial Property 250m 50% USA, 25% EU, 25% Asia Motor Reinsurance 70m 50% local, 50% Turkey Household 65m 100% local Product Liability 60m 75% North America, 25% EU Marine 100m Mixed global coverage Professional Indemnity 55m Large global law firms Other 50m Various TOTAL 650m Summary by accident year from internal actuarial reports Class 2005 ULR* 2006 ULR 2007 ULR 2008 ULR Commercial Property 200% 45% 50% 75% Motor Reinsurance 50% 45% 50% 55% Household 75% 70% 86% 80% Product Liability not written not written 55% 65% Marine 125% 50% 55% 35% Professional Indemnity 52% 43% 52% 65% Other 80% 80% 80% 80% *ULR = Ultimate Loss Ratio = ultimate claims/ultimate premiums High level summary of reserves and methods adopted Class IBNR Reserves** Method Commercial Property 250m 520m Based on run-off triangles Motor Reinsurance 160m 300m Based on contract by contract review Household 20m 80m Based on delay tables Product Liability 55m 60m Based on case estimates and pricing loss ratios for IBNR Marine 120m 300m Based on run-off triangles Professional Indemnity 190m 320m Based on report from US parent Other 27m 100m Run-off triangles if data allow ** Reserves include IBNR (i) Outline with reasons the areas where the team should concentrate its review providing justification for your choices. [7] The team is invited to attend a meeting with the company s chief actuary. (ii) Describe the key information that the team would wish to obtain from this discussion on the methodology and assumptions used by the company. [7] [Total 14] ST3 S2009 4

173 6 A general insurance company writes direct household insurance. For the last eight years its reinsurance programme has consisted solely of catastrophe excess of loss reinsurance renewing on 1 January each year. This gives cover of 0.5% in excess of 0.05% of the total sum insured for the book at the date of loss and one free reinstatement. The cover has always been 100% placed with the same reinsurance company. The insurance company has experienced the following results. Accounting year (beginning 1 January) Sums insured 1 Jan ( bn) * 99* Gross written premium ( m) * 422* Gross earned premium ( m) Net earned premium ( m) Gross claims incurred ( m) Net claims incurred ( m) * = forecast 1bn = 1,000m In Years 12 and 13 the company suffered an unusually high number of large subsidence, fire and liability claims. In Year 17 a severe windstorm and a widespread flood resulted in additional claims of 19.3m and 33.7m at the start of February and October respectively. If the weather events had not occurred, the gross loss ratio for Year 17 would have been 67.0%. It is now halfway through Year 18 and you are deciding on the reinsurance programme for Year 19. The Board of Directors has questioned whether the existing reinsurance programme is still appropriate. (i) (ii) (iii) (iv) List the potential benefits to the company of purchasing this type of reinsurance cover. [3] Calculate the total gross and net claims incurred and gross and net loss ratios for Year 17, stating any assumptions made. [5] Suggest reasons why the Board of Directors has challenged the reinsurance programme. [6] Outline the options available to the company regarding its reinsurance programme, giving their relative merits. [10] [Total 24] END OF PAPER ST3 S2009 5

174 Faculty of Actuaries Institute of Actuaries Subject ST3 General Insurance Specialist Technical September 2009 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. R D Muckart Chairman of the Board of Examiners December 2009 Comments for individual questions are given with the solutions that follow. Faculty of Actuaries Institute of Actuaries

175 Subject ST3 (General Insurance Specialist Technical) September 2009 Examiners Report 1 Manufacturing cost, retail price of the hampers shipping costs to set claim cost per hamper Obtained from supermarket and retailers Historic sales volumes of each type of hamper. and sales forecasts for exposure measure from the supermarket Past hamper loss frequency to estimate loss frequency & hence loss cost Data could be obtained from postal service Hampers sent worldwide and so the weights to apply to different territories will have to be estimated, using client past data if available Data splits (e.g. territories) Internal claims data unlikely unless you have written this type of business before Costs of administering this business, policy issuance costs, claim administration costs. Need to know by how much to load the policy to recover expenses. Exclusions (e.g. territories/strikes) including deductibles Length of contracts Recoveries (e.g. from postal services) or subrogation on damage Available internally. Need company profit targets, and any relevant taxes to know how to load the policy. Available internally Competitor information and other market research Page 2

176 Subject ST3 (General Insurance Specialist Technical) September 2009 Examiners Report to assist in setting the premium at a level appropriate for current market While students were generally able to generate a reasonable number of points on data sources required to estimate future claims, very few clearly explained why these data would be required as per the command word of the question. Many candidates spoke as if the product has been around for some time using phrases such as full policy download or "full list of rating factors". Although these forms of data could be available, the question is fairly clear that this a new product, and therefore other sources of data would be needed, and a fairly simple approach to pricing was needed. Many candidates did not clearly identify the sources of data as requested. Few candidates went beyond the claims information to consider the wider data required such as expenses and commission in order to complete the rating process. 2 (i) Loss ratio = Claims Incurred/Earned Premium 2006: 17.3/25.5 = 67.8% 2007: 36.5/38.2 = 95.5% Can give expense ratio credit if commission excluded explicitly or calculated in separate ratio Expense ratio = Expenses Paid (including commission) /Written Premium 2006: ( )/26 = 13.5% % = 34.6% 2007: (4.5+7)/40 = 11.3% +17.5% = 28.8% Alternatively, if calculated using earned premium: Expense ratio = Expenses Paid (including commission) less change in DAC /Earned Premium 2006: ( )/25.5 = 29.4% 2007: ( )/38.2 = 23.6% No credit for operating ratio if commission excluded Operating ratio = claims ratio + expense ratio 2006: 102.5% (or 97.3% if expense ratio is on an earned basis) 2007: 124.3% (or 119.1% if expense ratio is on an earned basis) Solvency ratio = (Assets Liabilities) / written premium Page 3

177 Subject ST3 (General Insurance Specialist Technical) September 2009 Examiners Report 2006: 14.5/26 = 55.8% /40 = 33.8% Generally well answered although a few mistakes by either using incorrect formulae or in calculation (ii) General comments Ideally we would want to consider more than two years worth of data before reaching any firm conclusions about possible trends. Ideally we would want to calculate the ratios for each class separately, which would help to analyse performance at sub-account level. Loss ratio The loss ratio has worsened substantially. This is most likely to be a result of a catastrophe in However, premiums have also risen substantially at the same time which could indicate that the company is writing poorer quality business. Further causes could include: Generally very poor claims experience, such as many large liability claims. Poor underwriting. Inadequate premiums. Severe deterioration in claims controls. A strengthening of reserves for outstanding claims or IBNR. A change to the level of reinsurance cover Failure of one or more reinsurers. Expense ratio The expense ratio has improved particularly the commission element. Administrative expenses could be lower as a proportion of premium because of: An increased volume of business over which the expenses have been spread. Cost reduction initiatives. Page 4

178 Subject ST3 (General Insurance Specialist Technical) September 2009 Examiners Report Commission rates may be lower due to: Renegotiation of rates with the distributor. Increased use of a different sales channel. An expansion in one of the classes that has a lower commission rate. Reduction in profit-related commissions due to deteriorating results. Operating ratio The operating ratio has worsened, primarily due to a worsening loss ratio. The fact that the denominators for the loss ratio and expense ratio may be different can lead to a distorted picture if the business is growing or shrinking rapidly. However, there does not appear to be significant distortion in this case. Written and earned premium have grown similarly, which suggests that the bulk of the growth took place in late 2006/early Solvency ratio Solvency has worsened significantly. The level of free reserves may not support the rapid increase in business going forward. This is because net assets have reduced whilst written premiums have increased The poor claims experience has probably contributed to this Generally well answered with the best answers being those that worked methodically through the four ratios, commenting on each in turn and generating a wide range of ideas for the reasons for the changes in ratios from 2006 to Some candidates did not appear to have read the question thoroughly, and commented more generally on all of the figures provided rather than just the four ratios specified. Some labelled their ratios by year correctly in part (i) but then reversed the direction (i.e. seemed to assume that 2006 came after 2007!) in their comments in part (ii) although would have gained some credit for valid observations. 3 (i) Employers Liability Very large number of employees/volunteers will be working on the event Page 5

179 Subject ST3 (General Insurance Specialist Technical) September 2009 Examiners Report Bodily injury claims of various sizes depending on nature of accident These could be very large e.g. in the event of the permanent disablement of a high earning employee. and can take a long time to settle due to litigation/medical evidence May be reporting delays as the injury may not deteriorate for some time..therefore the claims cost will be impacted by level of inflation In the extreme, could be latent claim issues such as exposure to toxic substances Possibility that liability claims are re-opened Public Liability Large number of attendees (or other people near venues) at the events so possible claims for slips/trips or more significant injuries Also claims for damage/theft of property from negligence of organisers; these will be settled more quickly Frequency may be expected to be higher than for EL as a very large number of spectators expected Accumulation of claims as same event will impact many people Financial Protection Losses could arise from non-performance/insolvency of subcontractors Or the failure of a commercial sponsor of the event Potential could be very large and lead to lengthy legal actions as contracts likely to be complex Directors & Officers Could be significant claims against the organisers for maladministration of the event Likely to be large and potentially notified long after the event Construction If organiser is responsible for construction of venues, likely to be claims for damage/delay to unfinished stadia Commercial Property Potential for catastrophe losses from weather event e.g. flood Page 6

180 Subject ST3 (General Insurance Specialist Technical) September 2009 Examiners Report Significant potential for terrorist attack as high profile event could give rise to significant damage/injury claims especially if negligence proved Variable cost distribution extreme case: loss of stadium Much shorter reporting and settlement delay as cause likely to be identifiable quickly..but still potential for disputes e.g. damage due to negligence of architect rather than storm If cover included for business interruption this will be longer tailed Contingency Non-appearance of pop stars at concert could lead to significant losses if event cancelled Sponsors losing revenue from events Likely to be very short tailed as will know of loss very quickly and cost of making refunds etc. Motor Both bodily injury and property damage claims could arise as the organisers are likely to operate motor fleet PD claims small, consistently distributed, injury claims subject to delays but less so than EL Likelihood of seasonality of claims as more accidents in wet weather Competitors PA & Belongings Cover Fixed benefit for athletes competing at event Amounts high depending on event and extent of athlete s earnings Goods In Transit Covers for delivery of merchandised items/equipment to venues around the country Possibility of moral hazard if economic conditions worsen Product Liability Indemnifies against loss caused by defect in event-branded merchandise Computer Cover Indemnifies against loss caused by virus/criminal hacking of the event website Page 7

181 Subject ST3 (General Insurance Specialist Technical) September 2009 Examiners Report..or losses arising from failure of event-booking engine Fidelity Guarantee Loss caused by theft/criminal act of employee The better answers were those which worked through a thorough list of relevant insurance covers plus descriptions of their characteristics tailoring each carefully to the specific scenario described. Students were expected to demonstrate understanding of the relative importance of different types of cover in such a situation and some wasted time giving a lot of detail on relatively minor covers. Many of the claims descriptions were too vague. (ii) Number of venues Number of competitors Number of employees Number of concerts Length of sporting event Cost of rebuilding venues (including sum insured) Size of motor fleet Payroll Capacity of venues Number of attendees at the concert/event Expected ticket price of concert Turnover of organisers Number of subcontractors Cost of work undertaken by subcontractors Total merchandising sales Website traffic Number of sponsors Amount paid by each sponsor The best answers were those that worked methodically through their list of covers in part (i) realising that more than one exposure measure could be applicable for each. Some candidates wrote the same exposure measure repeatedly for different covers rather than identifying a range of factors. (iii) Amount of risk that will be retained by organisers cover might only be required for really large losses Page 8

182 Subject ST3 (General Insurance Specialist Technical) September 2009 Examiners Report Extent of support from government they may provide cover for any losses related to terrorism Expert reports from surveyors or health & safety consultants The projected value of completed venues against those still under construction at 1/1/10 Reinsurance cover available Capital availability/margins Investment (in risk context) Expense risk (in context) Diversification/how the product fits in with rest of business written While premium is paid over three years, the risk is much higher during the period of the event itself Experience of organisers in holding similar events though due to scale may not be appropriate comparison Could use data from previous events to determine historic claim costs..but likely to be difficult as not publicly available or covered by state Could consider previous reliability of performers at concert and if event has enough so that one or two withdrawing would not matter Location of buildings (including aggregations) would impact cost of rebuilding/repair Future economic growth projections could be used to judge likelihood of supplier insolvencies Fire prevention measures installed in venues Number of security personnel/technology available to prevent possible terrorist attacks Size of event could lead to skilled labour shortage and therefore cost of carrying out repairs could be much higher than anticipated Any aggregation within sectors of the event sponsors e.g. if they are all banks will increase risk A challenging question that required candidates to think widely round the problem. It was generally poorly answered with many missing that the product is over three years which would be expected to be a key consideration. Other simple things were missed, e.g. what data are available to price. (iv) To select rating factors To determine premiums using experience rating procedures To estimate the effect of changing the level of cover by changing the level of deductibles Page 9

183 Subject ST3 (General Insurance Specialist Technical) September 2009 Examiners Report To demonstrate the effect of reinsurance To estimate likely variability of claims experience For reserving (including estimating possible effect of industrial diseases on reserves). Statutory requirements To assess the degree of solvency To determine and allocate capital to different classes/categories of business To value portfolios for purchase/sale To estimate cash flow to determine investment strategy Investigations to draw out trends that may impact profitability Budgeting and business planning for future years, including staff planning This was well answered by those who had learned the bookwork thoroughly. The question is written generically (stating "a GI company ), not about the specific scenario and it also clearly asks for the reasons to be stated. However, some students did not appear to have read the wording carefully and instead gave a discussion of claims modelling under the scenario described previously in the question. 4 (i) To maximise the long-term return for policyholders/shareholders Subject to meeting future liabilities and solvency requirements..subject to satisfying the company s risk appetite e.g. covering any shortfall in assets A bookwork question that was well answered by those who knew the Core Reading but very vaguely and imprecisely answered by many. Page 10 (ii) A 200m free reserves is significant so more investment freedom to invest in riskier assets Could invest 400m in secure assets to match liabilities by term Suitable assets include cash/short bonds/index-linked gilts Free reserves could be placed in higher risk investments to maximize return Some examples could include equities or property Mixture of long and short term investments good match for liabilities arising from motor business Consider matching the nature of the liabilities

184 Subject ST3 (General Insurance Specialist Technical) September 2009 Examiners Report Use longer term assets to match bodily injury claims Short term assets appropriate match for property damage claims B Less investment freedom as low free reserves of 15m in absolute terms and relative to liability Commercial property claims can be volatile.. and need value of assets > value of liabilities so avoid volatile assets Writes cat exposed business so may need more liquid assets Largest class of business is in US so consider matching by currency Suggest mainly short-dated assets (to match liabilities by term) Some longer delays arising from business interruption claims Suitable examples are secure assets e.g. cash/short bonds Possibly small proportion in equities/indirect property/longer bonds For both companies need to consider: Investment expertise available (may be less for B as small) The company's risk appetite Level of investment expenses of alternatives The impact on each company s tax liabilities Availability of assets to purchase in the market Level of reinsurance held by each company Future growth plans (availability of premium income) The level of non-investible assets that each company holds The influence of the supervisory authority on investment policy The need to invest the statutory minimum margin short Economic Outlook Diversification of assets The better answers here were those that considered each of Company A and Company B in turn, and then general factors that would impact both. Students were expected to tailor their answers to the detailed information provided, so those that simply stated generically e.g. that investment mix should depend on financial strength would not have gained any credit. Many students wrote about the short- tail versus long-tail nature of different liabilities written, but did not always clearly relate these to the need to invest in short and longer term assets respectively. Despite the heavy hint in part (i) of the question, Page 11

185 Subject ST3 (General Insurance Specialist Technical) September 2009 Examiners Report relatively few students clearly identified a strategy for the investment of the free reserves separately from the investment of the assets backing the liabilities. (iii) What basis has been used for calculating Assets and Liabilities if too cautious, could constrain investment policy too much What premium income is expected in the future? if high then could use income stream to help pay out liabilities, meaning greater investment freedom Are companies A and B stand-alone or part of a larger group? If they have access to funds from a larger parent, this may give more investment freedom What is the required Statutory Minimum Solvency Margin? What modelling has been done for the future liability outgo? gives assurance that taxes, dividends and timing issues have been considered What assets competitors are investing in Other classes of business written Split out the figures to provide more detail (e.g. split of Motor PD & BI) Marks given were generally low but most candidates made some comments about the additional information that may be desirable. 5 (i) Ensure a certain percentage of reserves are reviewed Commercial Property class covers a significant proportion of the premium written (38%) so important Historic loss ratios show likely to be cat exposed significant source of uncertainty for class And USA and Asia exposure that might be particularly prone to cats Large proportion of the Motor RI account written in Turkey possibly very different claims profile Also non-standard technique used (contract by contract approach) so worth investigating IBNR is significant part of reserves for both Motor RI, PI and PL classes so value added from actuarial investigation Marine 2008 ULR looks unusually low compared to recent years Review classes of business that have large reserves Look at PI class as potential concentration of risk by industry (all global law firms) Page 12

186 Subject ST3 (General Insurance Specialist Technical) September 2009 Examiners Report..and relying on someone else's report Investigate inconsistency between reserve amounts and WP in PI class Product Liability class has only been written for two years so uncertainty due to little historic data Review the long-tailed/liability classes such as Product Liability and PI as claims may emerge over a long period Suggest spending less time on Household business as relatively small class with stable results The results from the other class look unusual as the same loss ratio booked on all years worth further investigation especially as method is vague General Points Expertise of the team that has produced the results if new actuary looking at some classes may need to review more Any issues with currency conversions If an external actuarial consultant has reviewed reserves may give more comfort in these areas The time available and resources to complete audit in professional manner Any issues that senior management have raised regarding individual classes or the actuarial function in general Any other significant inconsistency observed The best answers were those that worked methodically through each of the classes of business, identifying two or three specific areas of concern for each using the information provided. Many candidates ignored virtually all the information in the question despite many marks being available for pulling the key points from both the numerical data and the descriptions. Very few queried why the ULR for Other was 80% for all years. Page 13 (ii) Basis that the reserves are calculated on best estimate or prudent Are the reserve figures quoted IBNR + outstanding or do they include UPR, AURR or other contingency reserves? Have ranges been calculated in addition to point estimates? What risks are written in the other class of business? Is the report from the US parent for the PI class of a reasonable quality?..are the figures used reviewed in any way by the UK team? Have inflation and premium rate changes been incorporated in methods? Are appropriate checks carried out on the data before use? What reserving methods are used for the classes based on CL techniques Actual vs Expected analysis - including any changes in methodology If the BF method is used, how are the IELR assumptions derived?

187 Subject ST3 (General Insurance Specialist Technical) September 2009 Examiners Report Is the analysis split between large and attritional losses as the development of these can differ? The actuary s opinion of any trends in the loss ratios Are the results presented net or gross of reinsurance/retrocession? Ask for reinsurance resumé (i.e. provide details of the programme) Have any of the reserves been discounted for investment income? How have changes in the mix of business or terms and conditions been represented in the methods chosen Are there any known large losses that are not yet reflected in the data? Is any separate allowance made for IBNER in Household class as delay table method does not automatically provide this Are claims and other specialists within the company involved in determining the reserves Has GN12/appropriate professional guidance been followed Any more detail considered necessary on data splits and data sources Any other significant request This should have been tackled by thinking "what could possibly have gone wrong within the reserving?" and "what is not completely clear from the information provided already?" Reasonably well answered by the better students but many concentrated their answers on just claims issues, such as development patterns, when a broader approach was needed. Few candidates managed to generate a sufficiently wide range of points to score highly on this question. Writing a page about each of three points rather than making a large number of much briefer points is not generally a successful approach in ST level examinations. 6 Page 14 (i) Smooth financial experience over time by reducing claims fluctuations. Particularly since the retention is not very high. Reduce the capital requirement due to the reduction in claims variability. Particularly since the upper limit is fairly high. Alternatively, increase capacity to write more risks through better use of capital. Diversify or further stabilise the portfolio by writing more risks. Protect the company s solvency by truncating the effect of catastrophes. Protect against accumulations if there are concentrations of risk in certain geographical locations. Technical assistance from reinsurance broker.

188 Subject ST3 (General Insurance Specialist Technical) September 2009 Examiners Report This type of cover may be good value compared to other options Cover grows with the business as directly related to Sum Insured..therefore saves admin costs as don't need to renegotiate Improves market standing (rating agencies/regulator/policyholders) The free reinstatement gives protection against second and possibly subsequent events Although asked regularly, few candidates managed to score full marks. (ii) Gross claims incurred = = Assume the sum insured at any point is the weighted mean of the sums insured at the 1 Jan before and after that point (linear change in SI during each year). Assume that the flood event triggered a reinsurance recovery under the terms of the contract (no RI disputes or defaults). Assume that the quoted figures for the windstorm and flood losses are ultimate estimated costs and are gross of reinsurance. Sum insured ( bn) at start of Feb = ( ) 12 = Sum insured ( bn) at start of Oct = ( ) 12 = Retention ( m) Feb = = Retention ( m) Oct = = Recovery ( m) = = 1.95 (no recovery from Feb event) Net claims incurred = = Gross loss ratio = 245 / 287 = 85.5% Net loss ratio = 243 / 271 = 89.8% Most candidates were able to determine the gross claims incurred and gross loss ratio correctly, but relatively few performed a thorough calculation of the net claims. Almost all assumed that the sum insured would be constant over the year, but given the information provided this is not a realistic assumption and so would not have gained full credit. Loss ratio calculations often had the wrong denominator. Some candidates did not fully answer the question, calculating only the claims amounts and not also the loss ratios. Some students were not able to interpret the reinsurance layer correctly. Very few gave the assumptions they were making. (iii) The business has moved on over the years but is still using the same programme, which may make it appear that it has not been re-evaluated properly each year. Written premiums are projected to grow rapidly over the next two years, Page 15

189 Subject ST3 (General Insurance Specialist Technical) September 2009 Examiners Report which may mean the insurance risks need to be re-evaluated. The Board s risk appetite or performance targets may have changed with the growth of the business. The company s capital position may have strengthened recently, lessening the need for reinsurance. The following are the net loss ratios achieved in years Year Net loss ratio 75.5% 87.1% 83.5% 72.6% The loss ratios in years 12 and 13 are poor compared with surrounding years...so there may not be enough protection against individual large claims. Despite buying reinsurance protection, the net loss ratio in year 17 was still poor compared with other years. The company has spent around 15m each year on reinsurance but has only recovered 2m over the 7 years. With two weather events fresh in the mind, the Board may be worried about continued poor experience if these events become more severe or frequent. The price of this form and level of reinsurance might rise following industry-wide weather losses. The company might not be getting the best price if cover is always with the same reinsurer. The company may be paying too high loading in the premium for the reinstatement element. There is a concentration of default risk with a single reinsurer. Most could see that the programme was not good value, but then couldn t explain further problems with the programme. The fact the company was expanding rapidly should have indicated that the risk profile was changing. (iv) Raise (lower) the attachment point. Reduces (increases) the reinsurance premium. Increases (reduces) the capital requirement. Reduces (increases) the recovery from catastrophes above the Page 16

190 Subject ST3 (General Insurance Specialist Technical) September 2009 Examiners Report attachment point. Reduce (increase) the upper limit Reduces (increases) the reinsurance premium. Increases (reduces) the capital requirement. Reduces (increases) the recovery from extreme catastrophes. An alternative is to include an annual aggregate deductible in the contract A further alternative to the above is to place less than 100% Similar impacts to the above. Remove the reinstatement. Reduces the reinsurance premium. Could leave the company with insufficient cover remaining following a severe event. This would require replacement cover, which may be difficult or expensive to obtain. Pay a reinstatement premium rather than having it free. Defers or removes part of the expected reinsurance premium because the reinstatement premium is only paid if the cover is used. Reduces the effective cover because the recovery will be net of the reinstatement premium. Purchase additional reinstatements. Increases the reinsurance premium and may be overkill. Avoids having to purchase replacement cover following severe losses. Stop reinsurance altogether But leaves company open to very large catastrophe losses Purchase risk excess of loss. Increases the cost of the programme. Increases the company s capacity to accept larger risks. Protects against a cluster of individual large claims that fall outside the catastrophe treaty. Purchase quota-share cover. Eases expansion by increasing underwriting capacity from the same capital base. Cedes profit. Consider stop-loss cover. Protects against adverse experience, regardless of cause. Page 17

191 Subject ST3 (General Insurance Specialist Technical) September 2009 Examiners Report May be unavailable or prohibitively expensive. Negotiate a better price with the current reinsurer Cuts costs. May drive the reinsurer to stop offering as much cover. Negotiate a better price with an alternative reinsurer Cuts costs. Breaks the relationship with the former reinsurer. Use several reinsurers on the programme. May be able to obtain a better price. May weaken the relationship with the former reinsurer. Use reinsurers of different strength (credit rating). Enables the company to balance price with risk appetite. Consider alternatives to reinsurance, such as raising more capital/parental bail-out or capital market solutions (alternative risk transfers) May cut some costs but ART likely to be expensive for a class this size. May not be consistent with the company s risk appetite Students did not appear to have left themselves sufficient time to complete this question part, given the number of marks available, and often covered only a relatively narrow range of different options. The examiners were looking for a wide range of possible alternatives although many candidates opted for a scattergun approach of listing other types of reinsurance, whether appropriate or not. Few considered options related to adjusting or re-broking the existing arrangement. END OF EXAMINERS REPORT Page 18