Ch 8 Asser Shares

Question 1

Describe the technique of asset shares

Answer 1

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Question 2

explain how an asset share may be built up using a recursive formula

Answer 2

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Question 3

explain the main uses of asset shares.

Answer 3

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Question 4

The asset share is a widely used tool in

Answer 4

management of with-profits business.

Question 5

In a nutshell, the asset share of any policy is

Answer 5

he accumulation of premiums paid rolled up with interest, less expenses and the cost of any cover. It is therefore very similar to a gross premium retrospective reserve. However, when we calculate asset shares we normally use the experience of the policy to date, rather than any assumed basis.

Question 6

The concept of asset share can be applied to individual policies

Answer 6

to a group of policies. We can calculate the asset share for an individual policy just as we can calculate the retrospective reserve for an individual policy. Or, we could consider a group of similar policies all issued at roughly the same time and monitor their progress.

Question 7

Determining asset shares

Answer 7

Asset shares are most commonly used for with-profits contracts, but can also be determined for without-profits contracts. Asset shares (sometimes called earned asset shares) can be evaluated for individual policies or for a block of policies issued with similar terms and conditions.

Question 8

At the most generic level, the asset share for a life insurance policy is

Answer 8

he accumulation of monies in less monies out in respect of that policy. In other words, the accumulated cashflow in respect of a policy.

Question 9

Components of the asset share: The “monies in” for a policy will obviously include

Answer 9

the premiums paid to date, and the investment income. Investment income would include any unrealised capital appreciation on the assets concerned.

Question 10

A less obvious source of “monies in” occurs when

Answer 10

we consider with-profits business. In this context, the life insurance company may be organised so that profits from without-profits business flow into the with-profit fund and become the property of with- profits policyholders. In this case, the profits from such business would be added to the asset shares of the with-profits policies.

Question 11

The “monies out” will include

Answer 11

expenses involved with the contract, and the cost of any cover provided. However, there are several other ways in which the contract can be deemed to cost the life insurance company some money, as introduced in the following Core Reading. We shall then consider what these deductions really mean.

Question 12

The asset share is the

Answer 12

accumulation of premiums less deductions associated with the contract (plus, for with-profits policies, an allocation of profits on without-profits business if appropriate), all accumulated at the actual rate of return earned on investments.

Question 13

Deductions include

Answer 13

all expenditure associated with the contract(s), in particular:
● commissions paid and expenses incurred (net of tax, if appropriate) 

● the cost of providing all benefits in excess of asset share – eg life cover or any other guarantees or options granted – possibly on a smoothed, rather than current cost, basis 

● tax on investment income (if appropriate) including any reserves made for future tax liabilities 

● transfers of profit to shareholders 

● the costs of any capital necessary to support contracts in the early years 

● a contribution to the undistributed surplus in the with-profits policyholder fund which, in turn, support the smoothing of bonuses and the ability to exercise greater investment flexibility. 


Question 14

Commissions paid and expenses incurred (net of tax, if appropriate)

Answer 14

We need to deduct all expenses associated with the policy. This will include acquisition expenses such as commission payable to brokers, and similarly any renewal commission. It would be both normal and fair to deduct all of the expenses incurred in respect of the policy, including its share of the life insurance company’s overheads.

The adjustment made in respect of tax will vary from country to country, and may differ for different types of contract. The important idea here is that the calculation of the asset share reflects how the policies are taxed (where we mean tax that the company pays, not that which the policyholder pays). 


Question 15

The cost of providing all benefits in excess of asset share

Answer 15

The cost of providing death benefits for an individual policy is not an immediately obvious thing to grasp.

Question 16

“The cost of having provided cover for a temporary life policy is obviously zero if there hasn’t been a claim on the policy, and is equal to the sum insured if there has been a claim.” Comment.

Answer 16

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Question 17

It follows from the solution to the above question, that the cost of providing death benefits is

Answer 17

somewhere between zero and the sum assured! The form of this deduction will depend on whether we are calculating asset shares on an individual policy basis or in respect of a group of policies (ie on an aggregate basis).

Question 18

If we want to know the asset share of an individual policy at time t+1

Answer 18

then we need to divide this aggregate asset share by the number of policies that are still in force at time t+1

Question 19

this formula shows, when doing individual asset share calculations,

Answer 19

we deduct the death benefit in excess of the asset share. Notice that when doing the aggregate asset share calculations, we deducted the full death benefit sum assured.

Question 20

How might the calculation of the cost of cover be calculated if we are determining the asset share for a very large group of policies?

Answer 20

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Question 21

In addition to death benefits, we should also deduct something in respect of

Answer 21

any guarantees or options.

Question 22

Example

Answer 22

Suppose we are calculating the asset share of an endowment insurance policy and the contract gives the policyholder a scale of guaranteed surrender values.
We should allow for the fact that some policyholders might have exercised the option to surrender when economic conditions were bad and the guaranteed surrender value exceeded the policy’s asset share. This would cause a net loss, which would have to be shared between (ie deducted from) the asset shares of the continuing policyholders.

How we cost such guarantees and options is considered in Chapter 27.

Question 23

Tax on investment income (if appropriate)

Answer 23

Any tax already paid on the investment income that has gone into the positive side of the asset share “equation” should be deducted for consistency. Less obviously, if we have included unrealised capital appreciation as a plus in the asset share then we should also deduct any tax liability that we would incur on realising that capital appreciation. Again, the detail of how this would be calculated will vary from country to country, and possibly between different classes of business.

Question 24

Transfers of profit to shareholders

Answer 24

Clearly if part of the surplus has been transferred to the shareholders then that money is no longer around, and should be deducted from the asset share.

These transfers can be used to compensate shareholders for the provision of capital to support new business strain and the smoothing of payouts to with-profits policyholders. Shareholder assets may be needed to support the payout to with-profits policyholders if the aggregate payout to with-profits policyholders is higher than the aggregate asset share for with-profits policyholders. This could occur shortly after a downturn in the investment markets.

Question 25

Explain what happens to the asset share when surrender profits are made.

Answer 25

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Question 26

Cost of capital

Answer 26

We have already encountered the phenomenon of new business strain, whereby the company makes a loss on writing a new policy. While there are a number of things a company can do to reduce new business strain, such as negative non-unit reserves or actuarial funding (described later in the course), it is very unlikely to be able to eliminate it altogether. Most life insurance companies therefore find that writing business causes some new business strain.
Where does the money come from to fund this strain? In effect, it comes from the surplus built up over previous years from other policies but not yet distributed, and/or from the shareholders’ free assets. These other policyholders, and shareholders, have in effect “invested in” the new policy by putting up the money to fund the new business strain. They therefore require some money back from this “investment”.
We therefore need to deduct from the asset share of a policy the cost of this “loan” provided at inception by other policyholders and/or shareholders. There is then the issue of who should benefit from the returns thus earned on the capital.
The shareholders will naturally get money back from with-profits policyholders via the shareholders’ transfers, and this would normally be designed to provide the necessary return on their capital. But, the capital provided by policyholders and therefore an appropriate return on capital cannot be easily assigned to individual existing policies, because most of the capital will have come from policies that are no longer in force.
For any single policy, therefore, we would expect deductions from asset shares at early durations as compensation for the cost capital being required at those times.
You should note that this is not an exact science, and not all companies do this.
Whatever approach is used, the main reason behind the adjustments made to asset shares is to ensure that the different groups of with-profits policyholders are treated fairly.

Question 27

Contribution to the undistributed surplus in the with-profits policyholder funds

Answer 27

As you will see in later chapters, it is common to smooth payouts on with-profits policies to protect the policyholders from fluctuations in the value of the underlying assets. The payout to a with-profits policyholder shortly after a downturn in the investment markets would normally be greater than the asset share of that policy; while the payout shortly after a market boom would be less than asset share.
This system is going to work only if there is a large amount of undistributed surplus to use to effect this smoothing – if we want to pay more than asset share at times, then we need spare assets (ie capital) to fund the difference.
Additionally, the presence of undistributed surplus also increases the company’s ability to take on investment risk, and so allows greater investment flexibility. This is covered more fully in the investment chapter.
The insurer may wish to reduce (or increase) its existing working capital at times, and so may make further (gradual!) adjustments to existing policies’ asset shares to this effect – ie net deductions (or net additions) to asset shares.
As with the new business strain described above, the providers of capital should be suitably reimbursed for the use of this capital. Unlike that case, however, this capital is required throughout the policy term, and in fact more towards the end rather than at the beginning. For a stable portfolio of policies, it is likely that deductions from and additions to asset shares for the cost of this capital might be expected to cancel out and may quite probably be ignored.

Question 28

Asset share calculation

Answer 28

The asset share can be calculated recursively on a year to year basis.

Question 29

Initially the earned asset share is

Answer 29

zero. Each year the cashflows including premiums received, any miscellaneous profits to be allocated, and deductions made (as listed in Section 1.1 above) are recorded. A suitable rate of return on investments is used to accumulate the asset shares plus premiums less deductions plus miscellaneous profit allocations to the year end, to determine the asset share. This process is repeated for subsequent years.

Question 30

Example

Answer 30

A number of with-profits regular premium endowment assurance policies were issued on 1 Jan 2001 with premiums of £1,000 pa paid annually and sum insured of £15,000 under each policy.

Question 31

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Answer 31

As before, you will see that each year we divide by the proportion of policyholders who survive the year. This is because asset shares are, by definition, expressed per policy in force at any given time.
You might find the result for year 1 in this example surprising. We shall discuss the idea of negative asset shares in the next section.

Question 32

Typical asset share developments

Answer 32

For a regular premium policy, one of the most important influences is the incidence of expenses. We normally find very heavy initial expenses, caused by the cost of acquiring the business, and then much lighter expenses subsequent to that. As the policyholder ages, we expect the cost of life cover to increase year by year. Investment income will have a compounding effect, unless deductions due to shareholder transfers are particularly big.
At maturity, we would expect the asset share to exceed the guaranteed sum insured. The excess is the profit on the policy, which would then be distributed to shareholders and/or the policyholder depending on whether the policy is with or without-profits.

Question 33

We can see how the impact of high initial expenses gives

Answer 33

a negative asset share immediately after inception. Thereafter this asset share grows in a compound fashion. (This is not very easy to see in the above graph, but if you place a ruler to line up with the two marked points – for example – you will see that the graph curves away upwards from the straight line as duration increases.)

Question 34

How can an asset share be negative?

Answer 34

This might seem a counter-intuitive idea, but given our definition of asset share, if a policy has incurred expenses to date in excess of the premiums then it seems reasonable to say that the policy represents a negative for the company. The phenomenon of negative asset shares at early duration for regular premium contracts is a big problem for life companies, because of the risk of policies lapsing before the asset share grows above zero. If this happens, the company will have made a loss on that policy.

Question 35

How the asset share moves after inception will depend primarily on

Answer 35

how the three major components of renewal expenses, investment income and cost of life cover all balance out. In the example above, investment income was greater than the other items and so the asset share compounded up. If investment yields had been much lower, or expenses or cost of cover much higher, we might have seen a convex shape where the asset share grows but at a gradually reducing rate.

Question 36

Sketch the asset share development for a regular annual premium temporary insurance contract.

Answer 36

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Question 37

Comment on how the following might affect the individual (per-policy) asset shares for a group of regular premium whole life with-profits policies at the same duration:
. (i) several of the policyholders surrender 

. (ii) the market value of assets decreases by 10% 

. (iii) the shareholders’ required rate of return on capital increases 

. (iv) the supervisory authority strengthens the reserving basis for the policies, so reserves increase 

. (v) one of the policyholders dies. 



Answer 37

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Question 38

Asset shares and surrender values :The asset share will, over a period of time

Answer 38

over a period of time, and allowing for smoothing, be the upper limit on a policy’s surrender value.

Question 39

when a policy is surrendered,

Answer 39

the company makes a profit equal to the difference between the then asset share of the policy and its surrender value. For many conventional life insurance products, the amount to pay as a surrender value is at the discretion of the company. So one thing the company will always do when determining the surrender value is to try to ensure that it is not bigger than the asset share.

Question 40

Asset share and bonus distribution

Answer 40

Asset shares are a key element in the process of determining profit distribution: this is described in the next chapter.

Question 41

The asset share of a policy is the accumulation of

Answer 41

● premiums, 

● investment income, and 

● miscellaneous profits 
less 

● commissions and expenses, 

● cost of all benefits in excess of asset share, 

● tax, 

● profit transfers to shareholders, 

● cost of capital required to support new business strain, and 

● contribution to the undistributed surplus of the with-profits policyholder fund required to support smoothing of bonuses and increase investment freedom. 
The calculation can be summarised by the following recursive formula: 
(AS +P-E)(1+i)-Sq¢¢
t t t x+t 
1-q¢¢ x+t 


Question 42

If we had a very large group of policies (say at least several thousand) then we could get

Answer 42

meaningful results for the asset share of that group by taking “total claim payments in
the year” as the cost of cover in any particular year, ie in the aggregate asset share
calculation deducting “number of actual deaths ¥ S ” rather than S n q ¢¢ . However, the x+t
group would have to be very large for there not to be any noticeable random fluctuation from year to year.
In practice, even large life companies would not follow this approach but would first
use their claims data to determine crude mortality rates, graduate these rates and then
calculate the cost of cover using these smoothed rates, ie the q¢¢ rates. (So this is x+t
what the Core Reading is meaning when it says that the cost of benefits is deducted on a “smoothed, rather than current cost, basis”.)

Question 43

The asset share is initially

Answer 43

negative because of very high initial expenses.
It then grows because each year’s premium exceeds the cost of life cover in the early years. Then, later on, as the policyholder ages, the cost of cover rises above the level of the premiums and the asset share decreases.
At the end of the policy’s term the asset share is small and positive. There is no maturity benefit to provide, but the company should be making some profit on the contract.
To give an idea of the relative values involved, the annual premium used for the above example was £900, the sum insured was £100,000.
Note also that, in real life, most term assurance policies have monthly premiums. This will make the steps much closer together and smaller, and producing a graph looking more like the overall trend in appearance.

Question 44

Surrender of policyholders

Answer 44

The impact on the asset shares for remaining policyholders depends entirely on how the surrendering policyholders were treated. If they were paid surrender values equal to asset share less the administration costs of the surrender then the asset shares of the remaining policyholders will be unaffected. If, on the other hand, they were paid surrender values lower than that, the company will have made some profit from their surrender and this should be reflected in higher asset shares for the remaining with- profits policyholders.

Question 45

Market value of assets down 10%

Answer 45

The immediate answer would be “asset shares down by 10%”. However, if the fall in market values also reduces the tax liability on total unrealised capital gains, then asset shares will fall by less than 10%.

Question 46

Shareholders rate of return increase

Answer 46

This will increase the cost of the shareholders’ capital. As a result, the shareholders’ share of the distributed profit may be increased, increasing the amount of shareholders’ transfer each year (although the extent to which this can be done may be heavily restricted by regulation). This will reduce asset shares.

Question 47

Reserves increased

Answer 47

At an immediate level, there will be no change because asset shares are affected only by
cashflows, and the level of the reserves is therefore irrelevant. However, a number of second-order effects may occur.
● A strengthening of the reserving basis will mean that the capital required to sell a policy will now be higher. Larger deductions should therefore be made from asset shares at early policy durations, to pay for the increased cost of capital, for all policies that require more capital than before. This will reduce the future asset shares for such policies. 

● An increase in reserves will reduce the insurer’s investment freedom. This will reduce the future investment return potential, which will in turn result in lower asset shares ultimately.

Question 48

Policyholder dies

Answer 48

If the group asset share is being calculated by totalling actual cashflows for the group, then the asset share will clearly go down a little. If the approach taken is that of determining the mortality rates experienced by the group, and then using those rates to calculate asset share, then asset share will go down if our estimate of mortality rates increases as a result of the death. In practice, one death would have no influence on our rates and so the asset share would not be affected.

Question 49

If we pay a benefit on surrender that is bigger than the asset share, then

Answer 49

the overall financial effect on the company of that policy’s existence is to cause it a loss, equal to the excess of the surrender value over the asset share as at the date of surrender.