Chapter 19 - Models (2)

Question 1

A life insurance company sells a wide range of products through insurance intermediaries. It is about to perform a profit test to assess what premium rates would be appropriate for its without profits non-linked whole life assurance business.

i. List the assumpttions that would be required to carry out this exercise [4]

2007_s1_uk

Answer 1

List of assumptions required:
* Mortality
* Initial administration expenses
* Ongoing administration expenses
* Claim expenses
* Investment expenses
* Expense inflation
* Initial commission
* Renewal commission
* Clawback of commission
* Surrender / paid up rates
* Investment return
* Tax
* Reserving requirements
* Solvency margin requirements
* Rate of reinsurance recovery
* Profit criteria e.g. IRR
* Or profit margin at specified risk discount rate
* Average case size
* Volumes of business
* Business mix, e.g. age / sex / sum assured etc

Question 2

Describe the profit criteria a company could use to assess the profitability of its products and when each of these criteria may or may not be appropriate [7]

2006_s1-uk

Answer 2

Internal rate of return (IRR)

• This is the rate of return earned on initial capital invested in writing the policy.
• It is calculated as the rate of interest at which the value of discounted future profits equals the value of initial outlay
• IRR may not exist or may not have a unique value for certain policies, for example single premium policies.
• IRR shows the return earned on capital invested so it is a useful measure when capital is scarce

Discounted payback period (DPP)
* This is the length of time it takes for any initial capital outlay to be repaid.

• In the calculation future cashflows are discounted at a chosen risk discount rate.
• IRR and DPP do not show anything about monetary profit levels or about future cashflow profiles.
• DPP is useful as it will demonstrate when scarce capital is fully repaid.

Net present value of profit (NPV)
* This represents the monetary value of future profits from the contract discounted back to the start date of the contract at a chosen risk discount rate.
* The NPV is often expressed as a percentage of premium income or inital commission.
* The NPV shows total profit levels achieved.
* Economic theory states that an investor would choose the option which gives the highest NPV.
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* NPV is subject to the law of diminishing returns.
* If it were not - then a company that could sell one policy with a positive NPV could sell an unlimited number of policies and increase the company value without limit.
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* However, NPV does not indicate anything about how effectively any initial capital required has been used.
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* In practice - a combinaiton of targets and other criteria is often used.

Question 3

(i) State what is meant by dynamic solvency testing [2]

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(ii) Discuss the main assumptions which need to be made when carrying out dynamic solvency testing for a proprietary life insurance company which has recently closed to new business and has written only unit-linked business. [8]

2000 - s2 - uk

Answer 3

(i)

Dynamic solvency testing means assessing the ability of an office to withstand changes in both the external economic environment and the particular experience of the office.

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It involves projecting the office’s revenue account and balance sheet forward, and then changing the important assumptions in turn to establish the sensitivity of the office to changes in that particular assumption or assumptions.

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This could involve stochastic modelling to assess the probability of ruin.

ii.

• Expenses levels and rate of expense inflation will be particularly important because there is no new business to cover overheads.
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• Also the difficulty of reducing costs as the inforce business decreases will have a large impact on the future surpluses arising.
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• There will be costs relating to closure as redundancies are made and, for example, branch offices are closed.
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• Rates of unit growth - possibly varying by fund types, as fund management charges are a source of surplus - and especially as there may be guarantees on some policies.
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• Lapse rates and paid-up rates are important as the future profits and margins are dependent on the volumes in force
• and future lapse rates may be quite volatile depending on the reasons for the company closing to new business.
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• Mortality / morbidity is unlikely to be too important provided charges are reviewable.
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• Taxation - the future tax position of the office may change as the result of closure
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• Allocation of profits to shareholders - the amount of profits distributed to shareholders will affect the capital strength of the company.