sep 2011 Q4-Embedded value Part ii and iii

[Ivanhoe]

Describe how the approach to determining the embedded value would be
different if the contracts were all conventional with profits contracts with
reserves based on a net premium valuation, and shareholder transfers based on a percentage of policyholder reversionary and terminal bonus declarations.

Solu:

The calculation model now needs to project future bonuses, which will likely
be based on the projection of future asset shares. It will need to make
assumptions as to when profits are distributed as bonuses ....

Where the net assets include the excess of asset shares over the reserves then the value to shareholders for this would be in respect of future projected bonuses from these assets in line with how the company believes these will be distributed to the existing policyholders, and this should be consistent with how the rest of the value of in force is calculated.

Net assets would be the excess of asset shares over the reserves. What else could it be? Also how is the meaning of the second para any different from the first one? I understand that asset shares need to be projected, the bonus outflows need to be assumed in line with PRE. Is there anything else that I am missing?

Describe the impact of increasing the level of prudence in the reserves on the
embedded value of both unit-linked and conventional with profits contracts.

Soln:
...... If the company takes the net assets at face value without any “lock in”, then the overall EV would reduce by the cost of holding the additional reserves, since the discount rate exceeds the earned rate. If the company treats all the net assets as “locked in” already the increased prudence would not make any difference.

What do they mean by "lock in" in this context? Why should it matter to the EV?Why is this argument of lock in not provided for Conventional with profits?


For with profits business, the company should be projecting the expected
bonuses based on asset shares. Any release of prudence in the reserves which are more than required to cover the bonuses driven by asset shares would be subject to management discretion in terms of how or when it is distributed.In effect this is no different to the treatment of the excess of the assets less the liabilities, and is unlikely to make a material difference to the EV.

I would tend to believe that as asset share increases, bonuses will be declared which will increase the liabilities. Now, the liabilities are prudent and so although the argument that it is the management discretion to decide what to do with it does hold, the fact remains that they are released later and so the higher discount rate argument should hold and so the EV should decline. I do not quite understand the last sentence of the para above.

Rgds,

 

[Mark Willder]

Describe how the approach to determining the embedded value would be different if the contracts were all conventional with profits contracts with reserves based on a net premium valuation, and shareholder transfers based on a percentage of policyholder reversionary and terminal bonus declarations.

Solu:

The calculation model now needs to project future bonuses, which will likely
be based on the projection of future asset shares. It will need to make
assumptions as to when profits are distributed as bonuses ....

Where the net assets include the excess of asset shares over the reserves then the value to shareholders for this would be in respect of future projected bonuses from these assets in line with how the company believes these will be distributed to the existing policyholders, and this should be consistent with how the rest of the value of in force is calculated.

Net assets would be the excess of asset shares over the reserves. What else could it be? Also how is the meaning of the second para any different from the first one? I understand that asset shares need to be projected, the bonus outflows need to be assumed in line with PRE. Is there anything else that I am missing?

The assets are the total assets of the company which have been built up over many years, eg from shareholder injections, profits from past policies and asset shares of current policies.

The asset share refers to only the assets built up from the current policies.

So net assets are the excess of the total assets over the reserves. This is bigger than the excess of asset shares over the reserves, because it includes the assets from shareholder injections and past profits.

Describe the impact of increasing the level of prudence in the reserves on the
embedded value of both unit-linked and conventional with profits contracts.

Soln:
...... If the company takes the net assets at face value without any “lock in”, then the overall EV would reduce by the cost of holding the additional reserves, since the discount rate exceeds the earned rate. If the company treats all the net assets as “locked in” already the increased prudence would not make any difference.

What do they mean by "lock in" in this context? Why should it matter to the EV?Why is this argument of lock in not provided for Conventional with profits?

The issue of "lock in" is beyond the course, so I wouldn't worry about it. You wouldn't need to mention it to get full marks, but anyone who works in EV and mentioned it would gain credit.

The idea is that if we increase reserves for unit-linked (or without-profits) the net assets go down but the future profits go up. As the reserves grow with 10% interest, but are then discounted back at 12% RDR, an increase in reserves will decrease embedded value.

This is effectively saying that there is a cost of capital. The shareholders would rather have their profits earlier. They can then invest them to earn their required return of 12%, rather than being tied up in reserves earning 10%.

However, if the net assets are "locked in" then the shareholders cannot take their money out of the insurer. Perhaps the assets are left within the insurer to cover the solvency capital requirements or as working capital. So in the locked in case, it makes no difference whether the profits are released sooner or later, the assets are still invested at 10%.

With-profits is different because the net assets don't belong entirely to the shareholders. Instead the net assets are shared with the shareholders and policyholders. So the net assets are locked in until a bonus is declared and a corresponding shareholder transfer is made.

As I said, my answer goes beyond the ST2 syllabus here, but hopefully it helps the Examiners Report to make sense.

For with profits business, the company should be projecting the expected bonuses based on asset shares. Any release of prudence in the reserves which are more than required to cover the bonuses driven by asset shares would be subject to management discretion in terms of how or when it is distributed. In effect this is no different to the treatment of the excess of the assets less the liabilities, and is unlikely to make a material difference to the EV.

I would tend to believe that as asset share increases, bonuses will be declared which will increase the liabilities. Now, the liabilities are prudent and so although the argument that it is the management discretion to decide what to do with it does hold, the fact remains that they are released later and so the higher discount rate argument should hold and so the EV should decline. I do not quite understand the last sentence of the para above.

You have described how reserves will increase over time as bonuses are declared each year.

However, the question is asking what would happen if we increased the reserve today.

The shareholders get their money when a bonus is declared. This is completely different to the unit-linked/without-profits case where shareholders get their money when a profit is made.

Inreasing reserves will delay the emergence of profit, but is unlikely to delay the declaration of reversionary bonuses (we normally hold back a big chunk of surplus to declare a terminal bonus at the end of the contract anyway).

This was a tricky question. Embedded value questions on without-profits are much more straight forward. I hope these comments help.

Best wishes

Mark

 

[Helloall]

Hi, I was doing this question in the revision booklets and I couldnt understand the answer to the with profits component (iii).

Please could someone explain. (Perhaps with a mathematical solution if possible).

 Current asset shares and cost of guarantees should be unaffected, so the free surplus should be unchanged.
 If assume regular bonuses are unchanged, their projected (reserving) cost would rise causing an increase in projected shareholders’ transfers.
 The higher transfers will reduce later asset shares and so later transfers would be reduced.
 Overall, transfers would be paid out earlier, but may be similar in total amount to before.
 As RDR is higher than the earned rate, this change in timing would increase the PVIF, and hence increase the EV.

Thanks in advance.

 

[Mark Willder]

Hi, I was doing this question in the revision booklets and I couldnt understand the answer to the with profits component (iii).

Please could someone explain. (Perhaps with a mathematical solution if possible).

1) Current asset shares and cost of guarantees should be unaffected, so the free surplus should be unchanged.
2) If assume regular bonuses are unchanged, their projected (reserving) cost would rise causing an increase in projected shareholders’ transfers.
3) The higher transfers will reduce later asset shares and so later transfers would be reduced.
4) Overall, transfers would be paid out earlier, but may be similar in total amount to before.
5) As RDR is higher than the earned rate, this change in timing would increase the PVIF, and hence increase the EV.

Thanks in advance.

I've numbered your points so I can refer to them more easily.

I'm sorry for the confusion with this question. I wouldn't agree with some of the points made in the solution.

1) The asset share is a retrospective calculation, so will be unaffected by the change in valuation basis. I'm surprised that the revision books say the cost of guarantees is unaffected - the examiners report doesn't say this - a stronger valuation basis might increase this cost, depending on how it is calculated.

2) It's common practice for shareholders to get one-ninth of the cost of bonus where the cost is calculated using the valuation basis. So a stronger valuation basis, eg a lower interest rate, will make the bonuses look more expensive and so shareholder transfers go up.

3) Shareholder transfers are deducted from asset shares.

4) I'm not convinced this is right. The shareholder transfers are likely to be bigger due to 2).

5) If shareholder transfers occur earlier then this is good news for shareholders who would prefer to get their money quicker. Funds within the insurer are likely to earn a lower rate (probably based on bonds) than the shareholder's required return (the RDR).

Best wishes

Mark

 

[Helloall]

ii) Describe how the approach to determining the embedded value would be
different if the contracts were all conventional with profits contracts with
reserves based on a net premium valuation, and shareholder transfers based on
a percentage of policyholder reversionary and terminal bonus declarations.
[No calculations are required.]

I really dont understand the level of detail involved in the answer to this question. Just wondering if you could clarify.

My understanding is simply that the embedded value for with profits is the shareholder share of net assets and pv of shareholder transfers.

So I would agree that we need to do this, as we need to know when bonuses are paid/shareholder transfers are made -

"
The calculation model now needs to project future bonuses, which will likely
be based on the projection of future asset shares. It will need to make
assumptions as to when profits are distributed as bonuses and in particular
whether they are distributed as regular annual bonus or as a terminal bonus,
which could make a difference to the timing and hence the value. The future
bonus assumptions will need to take into account policyholders’ expectations
(for example smoothing), which may be influenced by past practice.
"

This would give us the shareholder transfers I think. Take the PV of this. Then I think we just need to determine the reserves. So we determine the reserves based on our modelling above and subtract from our initial assets. We then take a share holder share of this and + to PV of shareholder transfers.

In the revision notes it states -
"Liabilities would be the sum of the (possibly smoothed) asset shares plus cost of guarantees"
Are liabilities used here to describe the reserves?

Also in the past paper it writes this? What does this mean?

"Where the net assets include the excess of asset shares over the reserves then
the value to shareholders for this would be in respect of future projected
bonuses from these assets in line with how the company believes these will be
distributed to the existing policyholders, and this should be consistent with
how the rest of the value of in force is calculated"

 

[Mark Willder]

ii) Describe how the approach to determining the embedded value would be
different if the contracts were all conventional with profits contracts with
reserves based on a net premium valuation, and shareholder transfers based on
a percentage of policyholder reversionary and terminal bonus declarations.
[No calculations are required.]

I really dont understand the level of detail involved in the answer to this question. Just wondering if you could clarify.

My understanding is simply that the embedded value for with profits is the shareholder share of net assets and pv of shareholder transfers.

So I would agree that we need to do this, as we need to know when bonuses are paid/shareholder transfers are made -

"
The calculation model now needs to project future bonuses, which will likely
be based on the projection of future asset shares. It will need to make
assumptions as to when profits are distributed as bonuses and in particular
whether they are distributed as regular annual bonus or as a terminal bonus,
which could make a difference to the timing and hence the value. The future
bonus assumptions will need to take into account policyholders’ expectations
(for example smoothing), which may be influenced by past practice.
"

This would give us the shareholder transfers I think. Take the PV of this. Then I think we just need to determine the reserves. So we determine the reserves based on our modelling above and subtract from our initial assets. We then take a share holder share of this and + to PV of shareholder transfers.

In the revision notes it states -
"Liabilities would be the sum of the (possibly smoothed) asset shares plus cost of guarantees"
Are liabilities used here to describe the reserves?

Also in the past paper it writes this? What does this mean?

"Where the net assets include the excess of asset shares over the reserves then
the value to shareholders for this would be in respect of future projected
bonuses from these assets in line with how the company believes these will be
distributed to the existing policyholders, and this should be consistent with
how the rest of the value of in force is calculated"

Hi

This was a very tricky question as the Core Reading doesn't give much detail about the calculation of EV for with-profits. So we need to work it out from the information given in the question.

We need to give enough detail to score 6 marks. So just covering the Core Reading will not be enough.

Yes, I agree that "shareholder share of net assets and pv of shareholder transfers" is a good starting point. This is going to be complicated though as the fund is owned by both the policyholders and the shareholders.

The question tells us "shareholder transfers based on a percentage of policyholder reversionary and terminal bonus declarations". This is actually very common for with-profits, and a common split is that policyholders get 90% of surplus and shareholders get 10%. There are other ways to determine shareholder transfers though for with-profits, so don't assume that this will always be the case in future questions.

Let's take the shareholder's share of the net assets first. This would be easy for without-profits contracts as the shareholders own all of the net assets - so we would take the net assets to be equal to the assets minus liabilities, where the liabilities are the reserves.

But for this with-profits company, the shareholders do not own all the net assets. All we know is that the shareholders get a share of any surplus distributed. This surplus could be generated by the policyholder's asset share or from distributing the free assets. So in the end it doesn't really matter whether we allocate assets to the net assets calculation, or the present value of future profits calculation. We still end up having to project the whole fund forwards to determine bonuses and hence shareholder transfers. For this reason the decision of what constitutes the liabilities is rather arbitrary - this explains your last quotation where the examiners discuss allocating more (less) to the net assets and consequently less (more) to the present value of future profits. So in answer to your question, no, we are not saying that liabilities are (necessarily) the reserves in the solution.

Perhaps the easiest way to do the calculation is to split the assets into two parts: the asset share (to give the present value of future profits) and the assets in excess of the assets share (to give the net assets). To value both of these parts we will need to project these assets forward to determine the bonuses and hence the payout to shareholders in each case.

A numerical example might help. We'll assume all bonuses are terminal bonuses and are paid immediately for simplicity and that shareholder's get 10% of the surplus. Assets are 100, guarantees are 60, asset shares are 70. We'll take liabilities as the asset share.

So net assets are 100 - 70 = 30. We declare TB of 27 and the shareholders get 3, ie 10% of the total surplus of 30. So shareholder's share of net assets is 3.

Guarantees are 60 and asset share is 70. So we distribute surplus of 10 and declare a TB of 9 and a shareholder transfer of 1. So present value of future shareholder transfers is 1.

So overall the EV is 3 + 1 = 4.

I hope this helps.

Best wishes

Mark

 

[Helloall]

Thanks very much for the reply. Helpful.