Chapter 8 - Asset shares

Question 1

A proprietary life insurance company sells monthly premium conventional with profits endowment assurance policies

Consider one such policy that was in-force at both the start and the end of a calendar year, and for which the asset share was known at the start of the calendar year. An inexperienced actuarial student has been asked to write a formula for the calculation of the asset share of that policy at the end of the calendar year.

He has proposed the following formula:

Asset share at end of calendar year =
+ + Asset share at start of calendar year × (1 + Investment return)
+ + Total annual premium
– Per policy renewal expense loading
– Commission
– Cost of guaranteed death benefit
+ + Annual bonus
+ + Transfer of profit to shareholder

Where:
* “Investment return” is the total domestic equity market return over that calendar year, derived from indices.
* “Per policy renewal expense loading” is obtained from a detailed expense allocation model that splits direct salary, property and computer costs between products and between initial, renewal and termination expenses
* “Cost of guaranteed death benefit” is defined as the guaranteed minimum sum assured multiplied by qx (where x is the age of the policyholder at the start of the year).
* The company uses an “addition to benefits”
approach to profit distribution.

Describe the improvements that could be made to this proposed formula [12]

2008 - s2 - uk

Answer 1

Investment returns

• It is acceptable to base the return on indicies, but it would be preferable to use the actual return achieved on the underlying asset.
• The return should be based on all of the types of asset in which the with profits fund is invested, not just equities.
• The assets are also likely to include overseas equities, property and fixed interest investments.
• The precise allocation of assets appropriate to this policy might take into account its duration in force and / or accrued level of guarantees.
• The investment return may need to be netted down to reflect tax
• Other items in the formula need to be increased by investment return
• For example, premiums and expenses could be assumed to occur halfway through the year and therefore should be increased by a half a year’s investment return.
• Alternatively, premiums and expenses can be allowed for monthly including the appropriate increase for the investment return
• Smoothed investment return may be allowed for since some companies may use this approach.

Premium

• It would be need to check that this policy does not become paid up during the year.

Expenses

• It is not clear that allowance has been made for investment expenses, this should be explicit.
• The same is true for overheads
• Allocating expenses completely on a “per policy” basis might not be appropriate.
• The expenses and commission may both need to be netted down for tax
• Need to ensure that the expense loading allows for an appropriate period of inflation.

Death benefit

• The treatment of the cost of the death benefit is inaccurate.
• It should not be based on the whole guaranteed minimum sum assured, but the excess of the actual death benefit of the death benefit over the asset share.
• It should also be divided by (1 - qx) to reflect the fact that the cost can only be shared across those policyholders that survive the year.
• The table from which qx is to be taken should be defined
• Alternatively - the cost could be based on actual mortality experience during the year,

Annual bonus

• This should not be included in the calculation as it has not impact on the asset share, which reflects the build up of actual assets underlying the policy rather than the build-up of the benefits that are communicated to the policyholders.

Shareholder transfer
* This should be a deduction from the asset share, not an addition

Other items

This formula should also include:

• cost of providing any guarantees or options
• the cost of any capital necessary to support contracts in the early years
• a contribution to the free assets, which support the smoothing of bonuses and investment freedom
• an allocation of profits on without profit business, if appropriate
• an allocation of profits on surrenders of other with profits contracts.