EXAMINATIONS. April 1999

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EXAMINATIONS

April 1999

Subject 302 — Life Insurance

Time allowed: Three hours

INSTRUCTIONS TO THE CANDIDATE

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

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

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

4. Mark allocations are shown in brackets.

5. Attempt all 8 questions, beginning your answer to each question on a separate sheet.

AT THE END OF THE EXAMINATION Hand in BOTH your answer booklet and this question paper.

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

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following bases:

(a) without profits non-linked (b) with profits non-linked

Describe the methods the company has available to limit its exposure to each of the principal risks it faces in issuing these contracts. [9]

2

A life insurance company is repricing its unit-linked whole of life critical illness contract under which no benefit is payable on death or surrender. (i) Describe the sources of data which the life company would have

available for each of the principal elements of the pricing basis, explaining how the assumptions might be determined (a numerical

basis is not required). [20]

(ii) List those items of the pricing basis which would also be needed for the supervisory valuation of the contract and comment how the valuation

basis might differ from the pricing basis. [5]

(iii) List the elements of the pricing basis which are not normally part of the

supervisory valuation basis. [2]

[Total 27]

3

A life insurance company offers a unit-linked single premium whole of life assurance contract for sale through independent advisers. The product design includes the following features:

• sum assured 102.5% of the value of units; • surrender value 100% of the value of units;

• partial surrender option on each policy anniversary, up to 7.5% of the value of units;

• initial commission 5% of the single premium; • maximum age at entry 85;

• no medical underwriting. The only charges made are:

• an initial charge of 5% of the single premium; • a monthly charge of 0.125% of the value of units.

(i) Describe the principal risks to the company associated with this product.

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business:

• guaranteed minimum sum assured equal to the single premium; • guaranteed minimum surrender value, equal to the single

premium, at any time after five years from the date of premium payment.

Describe the new or increased risks to the company associated with

these changes. [4]

(iii) Suggest how the product design could be changed to control the risks

identified in parts (i) and (ii). [4]

[Total 12]

4

(i) Describe how underwriting may be used to manage a life insurance

company’s risks. [4]

(ii) A disease has been identified that potentially affects anyone who has spent time in a specific foreign region — a popular holiday destination. Visitors to this region have a chance of developing the disease, which depends on the duration of their stay. The development of the disease has now been well documented.

In the early years after infection there are no noticeable symptoms. Later, symptoms develop and the health of the infected person progressively deteriorates. The disease is not contagious.

The disease always proves fatal, with death occurring around 20 years after the original exposure. There are no tests for infection with the disease, and there is no cure.

Describe how a life assurance company can reduce the risk of anti-selection from people who are applying for the cover and who have

travelled to the region. [5]

(iii) Describe what terms might be offered to the applicants in the circumstances described in (ii) in each of the following cases:

(a) A person currently showing no signs of the disease who visited the region in 1995 who wants a 25 year endowment assurance for mortgage purposes.

(b) A person showing early signs of the disease, who visited the region in 1990 and who is applying for a five year term assurance.

(c) A couple who want a last survivor whole of life assurance contract. One of the couple is in the final stages of the disease. The partner has never visited the region and is not likely to. [6]

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contracts.

(i) State reasons why the company would want to analyse its sickness

experience. [4]

(ii) The state of the economy in the country where the company is based has resulted in a large rise in the level of unemployment.

Describe what effect this may have on the company’s sickness

experience, and what action the company may take as a result. [6] [Total 10]

6

(i) Describe the principal features of the following methods of distributing surplus:

(a) Additions to benefits (b) Revalorisation

(c) Contribution method [9]

(ii) In a certain country it has been the practice for many years for life insurance companies to invest a significant part of the assets supporting their with profits business in quoted equities.

Discuss the suitability of each of the three methods of distributing surplus given in (i) for life insurance companies in that country. [3]

[Total 12]

7

The surrender value of a with profits policy is normally set by reference to the asset share underlying the policy.

Explain why the surrender value might differ from the asset share. [6]

8

Discuss the suitability of the assets to match the following liabilities for a life insurance company with substantial free assets:

(a) Liabilities: a block of immediate and deferred annuities Assets: a portfolio of medium-dated and long-dated fixed

interest securities

(b) Liabilities: a block of with profits endowment assurances Assets: a portfolio of equity shares

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Assets: the future management charges under the contracts. These charges are at a fixed rate of 1% per annum of the linked funds. No other charges may be levied. [9]

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EXAMINATIONS

April 1999

Subject 302 — Life Insurance

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

1

Mortality

On a without profit basis the only tools to limit risk are underwriting and reinsurance.

Reinsurance passes all, or a portion of, the risk to the reinsurer.

Original terms methods pass on all the risks; risk premium methods only reinsure mortality risks.

Reinsurance also passes on profit making ability.

Underwriting aims to remove substandard lives from the population charged standard rates.

On a with profits basis, the final payment can be determined by consideration of the earned asset share, which can be based on the actual experience of a cohort — although there may be practical constraints e.g. due to guarantees or PRE.

Model, parameter and random fluctuation risk sufficient data needed to reduce risk.

Expenses

On a without profits basis the full risk of expense overruns is borne by the company.

For with profits policies, asset share can reflect actual expense experience. A lot of the risk is passed to the policyholder.

Inflation

For with and without profits, as with expenses. Investment

For a without profits contract the full risk is borne by the company, and the risk can be minimised by matching the assets to the liabilities as closely as possible. In practice matching can be difficult because of the long term of the liabilities.

For with profits policies, asset shares reflect actual experience and so pass the risk to the policyholder.

However, as payouts are smoothed, the company picks up some risk (or benefit) in periods of volatile investment returns.

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Persistency

For without profits products, until the policy has recovered its initial expenses, the risk of higher than expected lapses falls on the company. For with profits contracts, the company is exposed to higher than expected lapses when the asset share is less than the surrender value.

For with and without profits contracts the surrender value scale is not normally guaranteed.

Thus it can be set to recover a desired proportion of expected profit from the contract, and can be altered with experience.

For PRE reasons it may be necessary to have higher than desired surrender values at early durations which will involve the company in some risk. General

Margins may be built into the pricing of the products for miscellaneous risks. This question was not well answered by the majority of candidates. The differences between with and without profits contracts were not emphasised and candidates tended not to specify which risks could be passed to the policyholder and which were borne by the company.

2

(i) Morbidity / Mortality

Analysis of the company’s experience over a 3–5 year period • long enough to have reliable data and short enough to be homogenous

• males and females separately

• make allowance for any changes in underwriting standards • maybe for unit-linked whole life, or just unit-linked.

In addition — and particularly if company has insufficient data • Industry data (such as CMI Reports in UK)

• Data from reinsurer • Published tables

Published data will probably need adjustment for the particular circumstances of the company and its products

Need to consider trends in experience especially for morbidity Would reconsider illnesses and conditions covered

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Because of doubts over morbidity rates the company is likely to reassure considerably more of this business than of a whole life assurance contract.

If sufficient data may analyse by specific disease.

Rates included in reassurance terms would probably be followed. AIDS projections are available, but only as industry-wide data.

Data need to be interpreted with care. Deaths from the critical illnesses covered will be irrelevant, because a claim will have already been paid.

Other deaths release reserves as no benefit is paid. This is a different situation from the type of policy the data were collected from.

Comparison of the proposed target market and that in the data is important.

Almost certainly likely to use the experience to generate an adjustment to a standard table.

Investment Returns

The purpose of having a unit-linked contract with no surrender value is to pass to the policyholder some of the investment risk.

Reserves will not be large, as there is no certainty that a claim will ever be paid.

The assets backing the unit-linked funds and the historic and expected future return on them will be available.

Low rates are cautious as they reduce the income from management charges.

Interest on sterling reserves will be assessed similarly, using fixed interest returns.

Expenses

The company should have analyses of expenses over recent years. A series of analyses helps to identify trends to use in assessing future rates.

Expenses would be split into acquisition, maintenance and claim, and between contract types. The level of detail would depend on the size of the company.

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Expenses might also be analysed into those which are contract size related and those which are policy related.

If the company’s expense investigation does not provide credible data down to the particular contract type, broader averages may have to be adjusted.

Probably with input from reassurers.

Inflation needs to be allowed for from the date of investigation up to the date the rates will be used and allowance made for any expected trends in future inflation assumptions

Commission

The rates and structure that the company intends to pay can be loaded directly into the basis.

Expense Inflation

National data on inflation of prices and earnings.

Expected future rates of inflation — possibly as measured by the difference in returns on government fixed interest and index-linked securities.

The expense inflation rate will be chosen to be consistent with the investment return assumption.

Withdrawals

The company should have an analysis of experience available relating either to this contract or to broadly similar contracts

Limited industry aggregate data may be available but will have to be adjusted to meet the particular contract and target market.

The analysis may need to be adjusted because it has been affected by unusual economic circumstances over the period the data were collected.

Adjustment may also be needed if the intended target market or sales channel are different from those in the data analysed.

Tax

Suitable assumptions will need to be made taking into account the company’s current and future tax position

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Profit

Risk Discount Rate/Profit criteria set according to the Company’s requirements.

(ii) Items which also appear in the valuation basis:

Mortality: As no payment is made on death, lower rates are more prudent.

Morbidity: The valuation basis would use higher rates than in pricing. This is the most important element of the basis.

Investment Return: Lower rates are prudent because they generate lower management charges. But as reserves are low anyway, the same rates might be used as in pricing.

Renewal and Claim Expenses: Valuation assumptions would be higher than in pricing to provide a margin, and may include an allowance for the impact of being closed to new business.

Expense Inflation: This would also be higher, but as in pricing the key is the difference between interest and inflation rates.

Renewal Commission: Unchanged from pricing basis. Tax may need to be allowed for depending on the tax basis. (iii) Initial Expenses

Initial Commission Withdrawal

Tax may not be needed if taxed on profits only Profit

Candidates who concentrated on answering only the question asked generally did well. Part (iii) was not well answered despite its simplicity.

3

(i) Mortality risk: Death strain of 2.5% of value of units.

No medical underwriting and high ages so mortality will be heavy. Lapse risk: Initial charge pays for commission but only a small margin for other initial expenses.

Company will make a loss on early lapse, or if excessive partial surrenders.

Mix of business/policy size risk: Per policy expenses paid for by fund-related expenses. For small policies this may be insufficient.

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(ii) Increased mortality risk: in early stages of policy, when value of units has not grown to offset initial charge.

Increased risk in later stages too, if investments do not grow and/or partial surrenders are high.

Guarantee of “no loss” on death might lead to anti-selective applications

Increased lapse risk: if investments do not grow and/or partial surrenders are high.

Guarantee of “no loss” on surrender might mean higher use of partial surrenders.

Selective lapse risk: if market values are (temporarily?) low,

policyholders who have SV guarantee may lapse causing a loss to the company

(iii) Reduce maximum age at entry to control mortality risk. Underwriting should be introduced to reduce mortality risk.

Increase initial charge and reduce monthly charge to match expenses better

Set minimum single premium to avoid large volume of small policies. Remove/don’t introduce guaranteed minimum surrender value.

Reduce/remove guaranteed minimum SA if partial surrender option is used.

There was a wide range of standards in answering this question. The candidates who took account of all the information given did well.

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4

(i) It can protect the company from those lives whose health is so seriously impaired that they would have to be declined.

The underwriting process will enable a company to identify lives with a substandard health risk for whom special terms would need to be

quoted.

A company may however aim to accept a large proportion of the business it accepts at its standard rates of premium.

For the substandard risks, the underwriting process will identify the most suitable approach and level for the special terms to be offered. Adequate risk classification within the underwriting process will help reduce the possibility of anti-selection.

Underwriting will help in ensuring that the actual mortality experience does not depart too far from that assumed in the pricing of the

contracts being sold.

For larger proposals, the underwriting process will help to reduce the risk from over insurance.

Lives could be individually underwritten rather than being put into broad risk bands

Claims underwriting will be used for admitting claims on products such as PHI and critical illness.

(ii) Specific question on the proposal relating to travel to the region in the last 20 years, or any known intention to in the future.

For larger cases proof may be required concerning past travel e.g. sight of the applicants passport — although this will be of little help if the passport is relatively new and passports may not be stamped by the country concerned.

For larger cases, medical reports or medical examinations may be requested.

An exclusion clause may be included in the policy.

However, this may cause problems if the disease itself is not put as the actual cause of death, even though the disease lead to the fatal

condition.

It is unlikely that the family of the deceased will allow post mortem investigations by the insurance company if the result is likely to exclude payment.

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Product substitution: it may be that an alternative product may be offered that does not bear the same risk. For example, a shorter term policy may be offered where the contract terminates well before the expected time of death.

Special terms. Higher premiums may be charged based on the probability of infection.

Decline. For those lives seriously affected by the disease.

(iii) (a) If this person develops the disease, then death will occur well within the term of the contract.

An exclusion clause could be included but this has the difficulties noted above.

A shorter duration policy could be offered, but it is unlikely to meet the policyholder’s needs.

Death will occur late in the policy and so the sum at risk will be relatively low. An extra premium is likely to be the most suitable

option.

(b) Death from the disease will occur well after the end of the contract. Ordinary rates can apply.

Provided that there are no continuation or conversion options on the policy.

(c) One of the lives is uninsurable.

However, a joint life last survivor policy can be written using the premium that would apply if the healthy person applied on his or her own life.

A small deduction could be made from the single life premium rate to allow for the possibility of accidental death of the healthy life prior to the death of the uninsurable life.

Again, this would be dependent on there being no conversion options on the policy.

Part (i) and (ii) were answered well.

Part (iii) was answered surprisingly badly: it requires only a careful reading of the question to gain several marks.

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5

(i) The results of the analysis can be used to update the assumptions used to profit test the contracts, to calculate the embedded value of existing contracts and to determine the statutory valuation basis.

The results will enable the company to monitor adverse trends in the sickness experience.

So that it can take appropriate actions, for example tightening claims management or increasing the charges made for the sickness benefit, to rectify the situation.

The results will provide management information on the effects of past decisions, for example as regards initial underwriting or benefit

conditions, on the resulting experience.

This will determine whether premium rate changes are needed. (ii) There could be a rise in claim inception rates.

Under group schemes, (unscrupulous) employers may see the existence of the scheme as a good alternative to making staff redundant.

A similar temptation would also arise under individual contracts, as a form of unemployment benefit.

There would almost certainly be a reduction in claim termination rates. This would be due to a reluctance on the part of claimants to recover if they have little prospect of getting suitable employment.

The company should reconsider the definition of sickness it uses for new contracts.

A change to “inability to carry out any occupation” claims definition, if not already used, would be more appropriate in a situation of high unemployment.

As regards existing contracts, it might need to tighten initial claims management so as to reduce fraudulent claims, and to review actively existing claims.

The cost of doing so needs to be balanced against the resulting increase in claim management costs, and the possible bad publicity which may result.

Checks on existing claimants may need to be increased in frequency or made more stringent, for example all claimants may be asked to provide doctor’s certificates at regular intervals. Alternatively, the company may choose to employ counsellors.

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If the company has the ability to vary its sickness charges and its

experience actually is worsening, it may need to consider increasing the charges.

The adverse competitive effect of doing so would need to be considered. Part (i) is largely bookwork and was answered well. In part (ii) few candidates

covered many of the actions possible.

6

(i) (a) The additions can take the form of “reversionary bonuses”, which usually are given on a regular basis throughout the lifetime of a contract.

There are 3 different types of reversionary bonus which can be used: simple compound or super-compound. These represent an increasing deferral of surplus.

Once declared they become attached to the basic benefits and cannot be taken away.

The additions can also take the form of a “terminal bonus” which is determined when the insured events occurs.

In theory this gives a lot of flexibility to change bonus.

In practice this does not happen, but even so a company will not guarantee to maintain the bonus at any particular level.

(b) The profit to be given to a particular contract is expressed as a percentage of that contract’s supervisory reserve.

The benefit under the contract and the premium payable by the policyholder are then increased by the same percentage.

Where this method is used, it is not unusual for the profit of the life insurance company to be divided into a “savings” profit and an “insurance” profit.

The “savings” profit represents the profit arising from the investments and is distributed to policyholders.

The “insurance” profit represents the profit from other sources and flows to the shareholders.

(c) The dividend given to a particular contract may be calculated using a formula which takes into account that contract’s

contribution to profit from different sources − typically interest, mortality and expenses.

Alternatively, it may be taken as a proportion of the excess of the earned asset share of the contract over its supervisory reserve.

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For this purpose, it may be necessary to use a special earned asset share that avoids new business strain.

The dividend can be paid in cash or converted into an addition to the benefits under the contract.

A terminal dividend may also be given.

(ii) The “additions to benefits” method is eminently suitable as a significant deferral of surplus can be achieved by a suitable split between RB and TB.

Hence market value risk from equities is reduced by the ability to reduce TB.

Under the “revalorisation” method there is no deferral of investment surplus.

Hence significant investment in equities would require significant free assets to be held to cover the investment risk.

Thus it is unlikely that this method would be suitable.

Provided that it is the practice for companies to distribute capital appreciation from the equities as a terminal dividend, the contribution method can also significantly reduce the market value risk.

The bulk of this question is bookwork. It was generally very well answered.

7

Because of the impact of initial expenses, the asset share at early durations may be negative.

Even if it is positive, it may be considered too low to meet policyholders’ reasonable expectations, given the premiums paid. Hence, the surrender value may be set above the asset share.

Competitive pressures may force the company to pay surrender values in excess of asset shares at some durations. This is particularly so where

surrender values appear on the quotation issued to prospective policyholders. The company may have a policy of paying benefits above asset share to with profits policies, in order to distribute part of its Estate, which it considers it no longer requires, or may pay less if it wishes to build it up.

The company may seek to make profits from discontinued policies through a deduction from the underlying asset share.

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Alternatively, it may represent a charge to the company’s Estate for the capital provided during the period the policy has been in force.

The benefits at maturity under a with profits policy are smoothed. The company will probably wish to adopt a similar approach under normal circumstances to the benefits payable on early discontinuance.

The asset share is likely to fluctuate from day to day. For practical reasons, the company will want to maintain a more stable surrender value.

Hence, even if the surrender value is targeted to be equal on average to the asset share, it is likely at times to depart from it.

The asset share may not make allowance for profits from miscellaneous sources.

This question is fairy straightforward. It was generally well answered but few candidates got most of the relevant points.

8

(a) The liability outgo is fully guaranteed in monetary terms.

A company will ideally want to invest so as to ensure that it can meet the guarantees.

This means investing in assets which produce a flow of asset proceeds to match the liability outgo.

This will involve taking into account also the term of the liability outgo, and hence the probability of the payments being made, so as to indicate the term of the corresponding assets.

It will probably be impossible in practice to find assets whose proceeds exactly match the expected liability outgo.

A best match is all that can normally be hoped for because of the uncertain cash flows and the length of the liabilities.

Modelling techniques will help to assess what such a best match may be.

(b) The liability outgo is partly guaranteed in monetary terms (the basic sum assured and reversionary bonus, once declared) and partly discretionary.

Considerations for the guaranteed part of the liability are as for (a) above.

The aim of the company will be to maximise the discretionary benefits and the investment strategy should aim to do this.

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This means investing in assets that will produce the highest expected return.

The policyholders will usually expect the proceeds of these contracts to maintain their value in “real” terms.

Equity shares meet the criteria outlined above.

The existence of free assets enables the company to depart from the matching strategy required for the guaranteed benefits to improve the overall return to policyholders.

Thus a portfolio of equity shares would be appropriate if the free assets were sufficient to provide the necessary cushion.

(c) Here the liabilities depend on the operating efficiency of the company, and on future inflation of prices and salaries.

Although the liabilities are not guaranteed in money terms they have to be met and are effectively index-linked.

The assets depend on the performance of the funds in which the contracts are invested.

Although in general terms there is an expectation that the income from equity-type assets will increase, over the long term, in line with or in excess of inflation, the theory of matching or immunisation cannot be applied to this situation.

The risk is that future expenses will increase at a rate faster than would be covered by increases in the management charges.

A resilience test approach is required to assess whether additional assets would be required and this would normally be done as part of the calculation of the non-unit reserves for the linked contracts.

This question caused some difficulty. Part (i) was well answered; part (ii) less so with many candidates missing the relevance of the free assets. Part (iii) was not well answered with many candidates missing the link between inflation and fund growth for equity-type investment.

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EXAMINATIONS

September 1999

Subject 302 — Life Insurance

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model used to assist in the financial management of a life insurance

company. [7]

(ii) Describe the steps that should be followed when using a model to set the charges under a new single premium unit-linked product. [9]

[Total 16]

2

A mutual life assurance company writes only with profits endowment

assurance contracts. The experience for the last year has the following features:

• a once-off increase in expenses due to the purchase of a new computer system

• an increase in yields on the fixed interest assets from 7% per annum to 9% per annum

• a large increase in unrealised gains due to the revaluation of the company’s property portfolio, which now makes up 25% of the company’s assets

Describe how this experience would impact on the bonus declaration if the company distributed surplus using:

(i) additions to benefits [5]

(ii) contribution method [4]

[Total 9]

3

A life company is about to calculate its supervisory reserves using a net

premium valuation method. The company writes both with and without profits policies.

(i) State the principles that should be followed when setting the bases for each of:

• interest rate • mortality

• expenses [8]

(ii) Discuss how the bases might relate to those used to price the products. [2] [Total 10]

4

A life insurance company wishes to launch a new regular premium unit-linked whole of life product. This will provide benefits on the first event of death or diagnosis of a critical illness stated in the policy documents. The charges in the product will be guaranteed.

(i) Describe the major areas of risk which the company will face as a result

of introducing this product. [10]

(ii) Discuss the actions the company could take to limit and control these

risks. [6]

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endowment products.

(i) State the principles that should be followed in determining the lump

sum discontinuance terms under these products. [5]

(ii) A consumer group has suggested that life insurance companies should be required to pay on discontinuance a lump sum equal to the reserve being held for supervisory purposes.

Discuss how this suggestion fits in with the principles given in (i). [8] [Total 13]

6

A small life insurance company has recently repriced its product range. As a result, it is selling significantly higher volumes of new business.

Describe the sources of risk to the company that may result from this. [4]

7

A life insurance company writes a significant volume of group life cover benefits associated with the death-in-service element of occupational pension schemes.

(i) Describe how the company might review its retention limit for this

portfolio. [5]

(ii) The company establishes a one-third quota share reassurance

arrangement with Reinsurer A. For the balance of risk it establishes a surplus treaty with Reinsurer B. This provides surplus cover in excess of £80,000 up to a maximum reinsured of £600,000.

Calculate how the claim payment would be apportioned between the company and its two reinsurers in the event of a total claim on a single life of

(a) £90,000 (b) £290,000 (c) £1,000,000

(d) £1,200,000 [2]

(iii) Describe the reinsurance methods available to the company to protect

itself against very large claims. [3]

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require an investigation by an actuary into the financial condition of each life company. Only non-linked business is written in this country.

A summary of the valuation of liabilities using a prospective gross premium valuation is to be presented to the regulatory authorities each year together with a valuation of assets at market value. It has been proposed that statutory regulations governing the valuation of assets and liabilities should be

incorporated into the legislation.

Describe the main rules that would be expected, assuming the purpose is to demonstrate solvency:

(i) for the valuation of assets [5]

(ii) for the valuation of liabilities [12]

[Total 17]

9

State the principles which should be taken into account when setting the demographic pricing assumptions for a new life assurance product. [5]

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EXAMINATIONS

September 1999

Subject 302 — Life Insurance

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General Comment (comments on individual questions appear at the end of each solution):

In general, this was a fair examination, testing some basic principles.

Candidates who were well prepared should not have found it too difficult. Most questions were reasonably attempted with no particular question proving to be more difficult than the others.

As usual, easy marks appear to have been lost by candidates simply stating a number of general points rather reading and answering the questions put. More commentary rather than a list of bullet points is required when the question states “describe” or “discuss”.

1

(i) The model should be rigorously designed and adequately documented. This minimises the risk of an undetected error being present.

The model points used should represent adequately the underlying business. Thus, the output from the model will be a reliable indicator of the likely outcome in practice.

The parameters present in the model should allow for all the features that could have a bearing on the purposes for which the model is being used.

This enables the advice given from using the model to address all likely eventualities.

The values assigned to the parameters when using the model should take into account the particular features of the company in question and those of the environment in which it is operating.

Thus, the results from the model will reflect accurately the actual position of the company.

The results from the model should be capable of independent

verification. This provides additional reassurance as to the accuracy and reliability of the advice given.

The results should be readily understood by the model’s users. If they are confusing or ambiguous, inappropriate conclusions may be drawn, and may be difficult to review.

Whilst it is important to achieve an acceptable level of accuracy, the model should not become overly complex.

Otherwise, it may take too long to run and be too expensive to maintain.

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(ii) The following steps should be taken:

• Set a suitable group of model points to represent the business under consideration. These would either be based on an existing product, or set by reference to the characteristics of the target market.

• Set suitable values for the parameters used in the projection, such as unit growth rates, expense levels, decrement rates and, where

appropriate, a basis for determining non-unit reserves. • Determine a trial charging structure and profit criterion. • For each model point, assume a tranche of identical policies are

issued. Project the policies into the future allowing for decrements through death and surrender.

• Use the projection, the trial charging structure and the input

parameters to obtain projected cashflows. These include transfers to and from non-unit sterling reserves.

• Discount the cashflows at the required risk discount rate and compare the result with the target profit criterion.

• Vary the charges until the profit criterion is met.

• Repeat the exercise for the other model points to obtain a comprehensive charging structure.

• Then consider the profitability of the product as a whole, using appropriate weightings for each model point. It may be necessary to accept lower levels of profit for some model points, provided the product meets the profit criterion overall.

• Check impact on overall tax and capital position of company based on expected business volumes

• Discuss the results with the Sales and Marketing area to assess the product’s marketability. Hopefully, it will be possible to derive a marketable product which generates the required level of profit. Otherwise, it may not be possible to launch it.

• Consider the sensitivity of the profit to variations in the principal parameters that influence it.

Comment: This question contained a large proportion of the marks available and candidates clearly spent an appropriate amount of time on it. Whilst the principle requirements were well covered, the application of the model in setting charges were poorly attempted.

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2

(i) Additions to benefits — reversionary/terminal bonuses It would be inequitable to charge the whole of the cost to current policyholders when the new computer system will also benefit new business.

Part of the cost could be absorbed by charging future asset shares for the benefit of the computer through an annual depreciation charge — this will have a marginal impact on future reversionary bonuses. Part of the cost could be offset against free reserves, but this would reduce the ability to use them for other purposes.

The anticipated long term yield from fixed interest investments is normally used as the basis for setting the reversionary bonus rate. If the increase is expected to be permanent, RB rates will increase but the full amount may not be reflected in the current year as the bonus rates tend to be changed only gradually.

Unrealised gains which can vary from year to year tend to be paid out through terminal bonuses.

Again the terminal bonus rates tend to be smoothed but would be increased at least partly to reflect these gains.

(ii) Contribution method

These expenses will be converted into a per policy expense but again the cost would probably be spread over several years.

This would lead to a reduction in dividends for those contracts the system is used to administer.

The increase in investment income would increase investment surplus which would lead to an increase in the investment component of the dividend.

The income is applied in proportion to the reserves for each contract. The investment gains could be paid out in part as an increase in the investment dividend — possibly over a number of years.

This could also be used to increase terminal dividends.

Comment: Few candidates achieved a high mark with this question. There seemed to be a view that the rules for the contribution method are “set in stone” and that no judgement is involved.

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3

(i) A prudent basis, rather than a best estimate, should be used and should include appropriate margins for adverse deviations.

Interest rates:

The rate of interest used in the calculation of reserves should: • take into account the currency in which the policy is

denominated

• have regard to the yields on the corresponding existing assets

• have regard to the yield that is expected on sums to be invested in the future

Where no explicit allowance is made for future bonuses, a rate of interest should be used which is lower than that suggested above by an appropriate amount.

A low interest rate is prudent. Mortality:

Should be chosen prudently, having regard to: • sex of the insured

• the type of insurance • underwriting policy

• the territory of the person insured

A high mortality rate assumption is prudent except for annuity and PHI business, where a low rate is prudent.

Expenses:

Should be chosen prudently having regard to expected levels of administration costs and commission.

The net premium method defines the allowance for expenses to be the difference in value of the net and company premium. This amount should not be less than the expected expenses determined above.

If a Zillmer is used, the allowance should not be more than the initial expenses actually incurred.

The overall reserve should have sufficient margins to allow for future inflation of expenses, which may be partly covered by a margin in the valuation interest rate.

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(ii) In some countries it is standard practice to price using prudent assumptions and then to use the same assumption for supervisory purposes.

This is suitable for with profits contracts as surplus will emerge from actual experience being better than the prudent assumptions.

This is less justifiable for without profits contracts, although it may still be used.

However the difficulties with this are from a pricing point of view rather than from the supervisory side.

In other countries a best estimate basis is used for pricing, incorporating a risk discount rate.

Such a basis would not be appropriate for supervisory reserves. Comment: No major problems.

4

(i) Mortality/Morbidity

On death or when a critical illness claim is made a sum assured will be paid out which will be considerably greater than the unit fund.

In addition, the premium will be set such that on a set of assumptions the premium will be sufficient to support the benefits for whole of life. The company will base the rates it will use for charging on any previous experience it has, on industry rates it they are deemed appropriate and probably with advice from reinsurers.

The extent to which the company can move from any “standard” rates will depend on:

• the volume of data and experience that the company has • the standard of underwriting that the company uses and • the type of salesforce and marketing being targeted.

The company will have to take into account future trends in medical treatments which could significantly alter the claims experience in the future, and the likelihood of epidemics.

If the company does not set the tables at the correct level it leaves itself at the risk of paying out more claims than it has costed for.

This is probably the biggest risk of this type of contract, given the uncertainty of future claims experience.

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Expenses

When profit testing the contract, the level of charges will be set to recover the expected level of expenses.

These contracts will involve higher costs at the underwriting stage. For critical illness, high claims cost when determining if the claim is legitimate.

Again any underestimation will involve reduced profits.

If the sales of the product are lower than expected, development costs may not be recouped.

Investment

As above, a premium will be calculated that will support the benefits in the future.

As part of this calculation the fund will be projected.

The investment rate actually earned over time will have to be at least as high as the rate used in the premium calculation or profits will be affected.

Persistency

Higher lapse rates at early years than that assumed in profit testing can affect profitability depending on the charging and surrender structure.

Capital strains

This class of business usually involves heavy costs at the start of the contracts due to both commissions and underwriting costs.

Higher sales than expected may put a strain on the company’s resources.

Marketing

The company will have to be sure that the market understand the contract and in particular the concept of critical illness or sales may not be as high as expected.

(ii) Mortality/Morbidity

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The risk can also be reduced by reinsuring some element of the sum assured.

For critical illness a clear definition of what is a claim would be required because of the impact of advances in medical treatment and the difficulty of identifying what a particular client is suffering from. It could remove the guarantee and put a review in this contract whereby the premium could be increased or the sum assured be reduced due to actual factors being different to those assumed in the premium calculation.

Expenses

A tight control over expenses needs to be maintained together with regular reviews to ensure that the actual expenses are consistent with loadings.

The clear definitions for critical illness claims described above would also assist in keeping claims expenses down.

Investment

It would be appropriate to put a review in this contract whereby the premium could be increased or the sum assured if required due to actual factors being different to those assumed in the premium calculation.

Persistency

Careful monitoring of the lapse rates particularly by sales channel and agent is required.

The surrender basis may have to be amended, or commission scales adjusted, due to lapses being inconsistent with those used in the pricing.

Capital strains

Reassurance finance could be used if the profits flow through in the early years of the contract to repay that finance.

This is particularly true if the charging structure is such that the profits emerge in the early years in force.

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Note this capital will possibly be more efficiently accessed than shareholder funds or money from the Estate.

Comment: This question tested candidates understanding of actuarial risk. Those doing well here tended to do well elsewhere.

5

(i) The principles that a company would follow are as follows:

The lump sum paid should not consistently be greater than the earned asset share at the date of discontinuance.

The method and basis used to calculate the lump sums should enable the company to retain a level of profit that is consistent with that retained on non-discontinued contracts

and is consistent with the company’s philosophy on how profit accrues over the lifetime of a contract.

At early durations in force, the lump sums should appear reasonable compared with the premiums paid, after making some allowance for expenses.

The scale of values should be consistent with the amount due to be paid on the maturity of the contract, that is there should be no discontinuity at maturity.

The scale used should be consistent with any values disclosed either in the company’s literature or specifically to the policyholder at the point of sale.

A company may not wish to appear to be too out of line with the practice of its competitors with regard to the amounts paid on discontinuance.

A company may wish to consider the auction value of its contracts, if such exist. The company would probably not wish to pay out more than these.

The scale of lump sum values should not change too frequently, due to the administrative work involved.

Although the values will usually be calculated by computer, it is desirable that they should not be excessively complicated to calculate. (ii) Given that the company will be holding, in respect of a particular

contract, assets equal to its reserve, one can see the logic behind the consumer group’s suggestion.

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BUT this logic is flawed as the reserve will be calculated so that the probability that the liabilities cannot be met is less than some adequately small figure.

Hence the reserve does not represent a realistic value.

In particular, the reserve will be much greater than the earned asset share for most non-linked contracts near to entry, mainly due to the inability fully to allow for acquisition expenses in calculating reserves for supervisory purposes.

For many contracts the reserve may even exceed the earned asset share for a large part of the term.

Hence, the first two principles will not be met.

The third principle will clearly be met, but the values will look highly attractive to policyholders.

This could lead to significant losses being made by the company from early discontinuances.

The lump sum values will be automatically consistent with maturity values for most contracts.

The main exception will be with profits contracts where surplus is distributed using the “additions to benefits” method and a terminal bonus is given.

The reserves for such a contract could be significantly less than its realistic value and will not be consistent with the amount that would be paid at maturity.

Provided that appropriate disclosure is made, the scale of values would be consistent with disclosure information.

Differences between companies in their reserving bases would be automatically reflected in the lump sum discontinuance terms. Hence, competition could lead to problems for a company in choosing its reserving basis.

Given that reserves would usually be higher than realistic values under the proposal, there is unlikely to be an auction market.

The last two principles are likely to be met without problem. Comment: Generally well attempted.

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6

There may be a significant change in the mix of business by nature or size leading to changes in the risk profile or capital needs of the company. The company may not have the resources to meet these changes.

A change in the mix may cause a mismatch between the expense allowances within the charging structure and its actual expenses.

There may be a change in the mix by distribution channel.

This could invalidate the pricing assumptions such as mortality, morbidity and expenses.

The office will have finite resources to cover capital and administration requirements.

The volumes of new business sold may exhaust the available resources. Comment: There were only a few marks available but a number of candidates missed out on fairly easy marks regarding new business strain.

7

(i) The first step is to analyse the distribution of the mortality costs on various assumed retention levels.

The main difficulty is normally the lack of detailed data. The company will typically know the number of lives covered by each scheme and the total sum insured, but may not know the distribution of sums insured. It will however have fuller details of risks exceeding its current retention limit, and will have underwriting information on lives exceeding each scheme’s free cover limit.

One approach is to keep the probability of insolvency below a specified level.

A model of the business together with stochastic models of claim rates and the company’s assets and liabilities is built. Allowance would be made for any changes in underwriting costs and profit commission as a result of the change in retention.

Paucity of data may make determination of the model points fairly subjective.

Using simulation techniques a retention limit that leads to a ruin probability of say less than ½% can be determined.

An alternative approach is to consider the sum of the cost of:

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(b) obtaining reinsurance — which allows for the reinsurer’s expenses and profits.

And to set the retention limit to minimise this cost.

To determine (a) it would be necessary to build the simulation model described above.

The levels adopted by competitors would be taken into consideration.

(ii) Total Claim Direct Writer Reinsurer A Reinsurer B

(a) £90,000 £60,000 £30,000

(b) £290,000 £80,000 £96,667 £113,333

(c) £1,000,000 £80,000 £333,333 £586,667

(d) £1,200,000 £200,000 £400,000 £600,000 L4

(iii) Assuming life cover of four times salary the surplus treaty will only become exhausted at claims of £1.02m, implying a salary of £255,000. Thus we are dealing with a handful of individuals in each employer — possibly only the top executive.

The company could seek a second surplus treaty with another reinsurer covering claims in excess of £600,000.

Alternatively, if the number of affected risks is few, facultative reinsurance could be sought for each case as it occurs.

The relative costs of the alternative arrangements compared with the administrative work involved will drive the decision.

Comment: This question proved quite difficult as it tested more understanding and application rather than pure bookwork knowledge.

8

(i) The question states that assets be valued at market value. This would need to be specified in more detail as

• for listed securities these will normally be a spread between buying and selling prices — mid-market value could be used

• for many assets there may not be a market value so further guidance is needed, e.g. property to be valued by professionals or by using PE ratios

Certain assets would be deemed inappropriate for life companies to hold to meet their liabilities, e.g. collectibles, yachts, time-share properties, precious metals as their value is too volatile/risky. Such investments could be deemed illegal or discouraged by not allowing a value to be placed on them.

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There would be rules for depreciating capital assets.

The legislation should try to restrict the concentration of risk. This would be done by limiting the values (as a proportion to the liabilities of the company) which can be placed on certain types of assets, individually and/or collectively.

The risk of default would also be limited by restricting the values which can be placed on assets which depend on a particular counterparty. (ii) Mortality/Morbidity — A requirement for prudent assumptions

including allowance for future adverse changes in experience (e.g. AIDS for assurances or mortality improvement for annuities)

taking account of the country of residence of the policyholder. Interest Rates — A maximum interest rate

depending on yields on existing assets

less some prudential margin (say 5–10% minimum but more for high risk assets) to allow for the risk of reduction in yield obtained.

Also have conservative assumptions about the (unknown) investment return on sums to be invested in future in each relevant currency, with possible blending in over 2–5 year period

• an overall limit to yield on existing assets less a prudential margin could also be applied

• hypothecation of assets to different groups of contracts could be allowed for the purpose of this assessment of interest rates. Bonuses — Declared bonuses would be valued as part of the guaranteed benefits.

The valuation should have regard to the custom and practice of the company with regard to the manner and timing of the distribution of profits.

It would normally be quite unreasonable to require explicit allowance to be made for current rates of reversionary bonus in conjunction with a valuation interest rate that is much lower than the rate of investment return currently being earned.

A solution might therefore be to reserve for the level of future bonus that could be reasonably expected on new policies issued on equivalent premium rates, assuming future rates of investment return equal to the valuation interest rate assumed.

Taxation — Allow for reduction of interest rate (and expenses) as appropriate in line with current and future expected rate of taxation in the country.

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Expenses — Allowance required for expected costs (including

commission) of maintaining business including future inflation, likely to be on a run-off rather than a going concern basis and with allowance for transitional expense overrun period.

Resilience — Consider effect of changes in investment conditions (e.g. fall in equity and property values or changes in interest rate) on ability of the company to set up adequate reserves and meet liabilities. Also, allow prudently for any currency mismatch.

Surrenders/Lapses — Ignore unless likely to increase liability, as level of surrenders and effect on the company is uncertain especially if surrender values discretionary.

However, any guaranteed surrender value within say 12 months should be covered by reserve at valuation on assumption of 100% surrenders. Negative Values — Eliminate

Options — Allow for effect of options exercisable by policyholder Reinsurance — Offset allowable, subject to assessment of financial strength or adequate security

Calculation — Individual policy by policy, but approximations and generalisations may be allowable if it can be demonstrated

satisfactorily that results are at least as high

In addition — the statutory valuation rules are likely to be

supplemented by appropriate mandatory professional guidance notes which deal in more detail with certain technical aspects.

Comment: Some easy marks were lost by not considering all of the points effecting the liability calculations but only concentrating on mortality/interest and expenses.

9

The values assigned to the parameters should reflect the expected experience

of the lives who will buy the contract.

These values should be based on adjusted standard tables where available. If the company data is adequate the values should take account of past

company experience, adjusted for any known factors which are not relevant for the future.

Company experience of a similar class of business may be a suitable substitute. Any data used will need to be based on a credible data sample and allow for future trends.

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Standard tables produced by industry sources such as the Continuous Mortality Investigation Reports in the UK or life reinsurance companies should be considered.

Levels of underwriting will affect the experience so should be considered particularly if it is changing from existing levels.

The sales method should also be considered as different sales methods are usually associated with different social groups who may experience different demographics.

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EXAMINATIONS

12 April 2000 (am)

Subject 302 — Life Insurance

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maintain a specified level of solvency capital. [2] (ii) Discuss the relationship between the strength of the supervisory

reserves for a life insurance company and the level of solvency capital

required. [3]

[Total 5]

2

Describe the key factors that influence the adequacy of an actuarial model,

used for projecting cash flows to assess the profitability of a life insurance

contract. [7]

3

A life insurance company is considering entering the market for long-term care contracts which cover the costs for an elderly person of home or nursing-home care.

Describe the factors the company must consider in designing this new contract to ensure a successful launch can be made. Your answer should consider

benefit and claims definitions as well as the normal profitability

considerations. [10]

4

A life insurance company is launching a ten year regular premium unit-linked endowment assurance with a wide range of investment links and a guaranteed minimum maturity value.

Discuss the risks for the company in offering this product. [10]

5

(i) Describe the contribution method for distributing any surplus which

may arise from a with profits life insurance contract. [5] (ii) Describe the principal practical difficulties that may need to be

overcome. [3]

(iii) State the formula commonly used to distribute surplus via the

contribution method, defining any notation used. [2] [Total 10]

6

A life insurance company offers a without profits term assurance contract. (i) Describe the reasons for underwriting a client’s application for the

contract. [4]

(ii) List the sources of information that a life insurance company can use to establish the level of mortality risk for a particular applicant. [3] (iii) Describe the options open to the company if the underwriting process

shows an applicant to have a higher expected level of mortality risk

than that priced into the product terms. [4]

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linked endowment assurances.

(i) List the data required for the analysis and discuss the level of detail to

which the analysis might be performed. [11]

(ii) Describe why the current experience may not be indicative of the future.

[5] (iii) Describe how the results of the analysis might be used. [6] [Total 22]

8

A life insurance company markets single premium without profit immediate annuities. The premium rates include an allowance for the company’s administration costs equal to 1% of each cash annuity payment.

(i) List the features that could be offered under the contract. [3] (ii) Describe the principal risks the company faces in relation to the

contract. [8]

(iii) Discuss the actions available to the company to limit the impact of each risk identified in part (ii) on its financial position. [14] [Total 25]

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EXAMINATIONS

April 2000

Subject 302 — Life Insurance

EXAMINERS’ REPORT

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1

(i) The solvency capital provides an additional level of protection to the policyholders over and above that provided by the reserves alone. The objective is to reduce the likelihood of the insurance companies becoming insolvent in reasonably foreseeable circumstances. In practice the SC provides additional protection by acting as an early warning system, and/or triggering powers of intervention for the regulator.

Note: “Solvency Capital” = Required Minimum Margin in UK terminology; not RMM + mathematical reserve.

(ii) When considering the adequacy of the reserves that have been set up it is important to do this in the context of the solvency requirements and not in isolation.

Similarly when setting the solvency capital requirements it is important to consider the level of reserves already set up.

The balance between the two components can.

However countries where reserves are on a relatively weak basis tend to have a substantial level of solvency margin and vice versa.

This question was answered adequately by most candidates.

2

One must minimise the risk of the model not representing the products The model being used must be valid, fully tested, rigorous and completely represent the business being modelled.

The parameters being used for demographic, investment, expense and product details must be relevant, accurate and appropriate for the business being modelled.

This includes the fact that these must represent the experience of the company. The model must be capable of sensitivity testing using different parameter values.

The data being used to represent the expected portfolio of business and the premium/sum assured relationship must be accurate and fair.

The outputs from the model should be capable of independent verification for reasonableness and should be communicable to those whom the advice will be given.

Failure to comply with these basic principles will mean that the model may be inappropriate and misleading as a tool in managing the finances of the business.

In particular an actuarial model would be a tool that would be used to assess both the future profitability and expected solvency position in future years.

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An inappropriate model may lead to lower profits or the need for more capital or at worst threaten the solvency position of a life company

On top of the above, a model would be expected to be inexpensive to operate and not overly complex.

This question was answered adequately by most candidates.

3

The most important feature the company will need to consider is the form of the benefit and the circumstances under which it will be paid.

These need to be attractive to the market in which it is intended to operate and the distribution channels open to the company.

A benefit paid as a lump sum will avoid longevity risk, or the cost of care increasing. If benefits are defined as “meeting the costs of care” rather than in cash terms, the company must assess the costs of care to be covered, and test the sensitivity to the level of those costs.

This will reduce overall costs, but may generate a marketing risk in that the benefits may not be enough to cover the eventual cost of care.

Similarly the more conditions that need to be fulfilled before the benefit is paid the lower the cost. This may be good or bad from a marketing point of view. Good because premiums will be lower; bad because claims may not be paid when some policyholders think they ought to have been.

If the definition of the insured event is loose, the company will incur additional costs in disputing claims and will find it difficult to obtain reinsurance.

Answering by means of an example of “loose definition” is OK

Similarly, highly unusual benefit changes might make obtaining reinsurance difficult. The company will require new underwriting abilities and additional underwriting staff. Both for point of sale underwriting and claims admission. And will need to develop new underwriting guidelines and rules.

Although in general the company will not want the structure and level of charges to depart too far from those of competitors, a novel definition of the insured event may differentiate the contract sufficiently in the market so that competitiveness on price is less significant.

In order to make adequate profit, premium rates must be adequate to cover benefits and expenses (including inflation of claims costs and expenses) in most foreseeable circumstances. Profitability conflicts with marketability and

competitiveness.

It is also desirable to have a design that minimises sensitivity of profit to changes in experience. The available experience data for this type of contract is still limited, and this company has no data of its own. Assistance may be sought from reinsurers. Overseas experience can be used but one needs to adjust it for the

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different risks, benefits and state social benefit schemes, all of which will affect the experience. The expected cost of claims will be affected by the target market and the type of distribution.

Consideration will need to be given to the financing requirement and the solvency margin that needs to be established. A design that reduces these also reduces the overall cost.

The extent to which premium rates and early termination values are guaranteed or reviewable will influence both the overall cost and the market perception of the contract.

The company needs to consider the extent of any cross-subsidies between e.g. large and small contracts.

The marketing advantage of simplicity conflicts with the desire to avoid cross subsidies and associated anti-selection.

It is necessary to ensure that the contract as designed can be administered on the office’s systems.

Benefits may need to dovetail with State social benefit schemes.

The plans may need to take account of any government initiatives in this area. The question indicated that answers should specifically consider benefit design and claims definitions. Most candidates did not give these issues adequate attention.

4

Investment Returns

· There are significant investment risks for the company in offering this product due to the maturity guarantee.

· The policyholder can choose his own investment links, which implies the company has little control over the risk.

· Risks could be reduced by limiting the fund choice.

· The company is exposed to reinvestment risk-current investment returns may be high but as the product is regular premium the future level of investment return is unpredictable.

· Volatile assets such as equities mean the risks of not attaining the necessary return are greatly increased.

· The ability of the policyholder to switch investments from one fund to another may increase the risk that the policyholder may make inappropriate changes in investment.

· Indeed towards the end of the term, if the guarantee is likely to bite, the policyholder may deliberately switch to a more volatile fund to gain possible reward without any downside risk. The cost of the guarantee will depend on the level at which it is set.