EV question Urgent response required

[smSA2]

(a) For unit-linked pension business, can someone please explain the impact on PVIF, net assets and EV overall of each of the following changes?
(i) Increasing the interest rate used in the statutory valuation basis
(ii) Increasing the interest rate used in the projection basis
(iii) Decreasing withdrawal rates both in the valuation basis and projection basis by same amount say 2%(assuming that projection basis assumption is lower than valuation basis)
(b) Repeat (a) for an annuity business but replace withdrawal rates in (iii) with weakening mortality assumptions
(c) Repeat (b) for a without profits endowments business

 

[mugono]

(a) For unit-linked pension business, can someone please explain the impact on PVIF, net assets and EV overall of each of the following changes?
(i) Increasing the interest rate used in the statutory valuation basis
(ii) Increasing the interest rate used in the projection basis
(iii) Decreasing withdrawal rates both in the valuation basis and projection basis by same amount say 2%(assuming that projection basis assumption is lower than valuation basis)
(b) Repeat (a) for an annuity business but replace withdrawal rates in (iii) with weakening mortality assumptions
(c) Repeat (b) for a without profits endowments business

I'd be both surprised and impressed if someone went to the trouble of answering the above without you at least attempting to work through the impacts yourself initially and checking if it's the correct way to think about it.

sa2 tests understanding and the ability to apply knowledge and not on memory of constructed scenarios.

 

[Mike Lewry]

Hi smSA2,

Please can you take any one of your listed changes and explain your current thinking and also where your difficulty lies. Then we can fill in the gaps in your understanding.

 

[smSA2]

I came up with those scenarios to develop my understanding after looking at September 2013 exam paper and question 4.5 of Q&A bank.

Mike thanks for helping out. Below I have attempted few scenarios. If you could fill in gaps in my understanding of only the scenarios I have attempted below, then I should be able to work out other parts of my question. I have pointed out where I am finding the concepts difficult.

For a without profits contract, increasing the interest rate used in the valuation basis will decrease the value of reserves. The net assets will increase because the reserves are lower. The impact on PVIF is less clear: the first thought that comes to my mind is that it will increase as release of surplus will increase. However, if EV is calculated by allocating assets to without profits liabilities up to the value of mathematical reserves plus CRR, projecting the reserves and allocated assets forward using realistic projection basis and taking the 10% of the surpluses as and when they arise (as in question 4.5 of Q&A bank) then I do not understand why PVIF will increase. If the reserves will decrease as result of higher interest rates, the amount of assets allocated will also decrease, so it shouldn’t increase PVIF.

For unit-linked pensions, withdrawal assumptions used both in the valuation and projection basis is reduced by same amount then the unit reserves will be unchanged. Non-unit reserves should decrease. Net assets will increase because of lower non-unit reserves. PVIF will increase as a result of higher future profits. I do not follow the debate about the negative and positive non-unit reserves in the examiners’ report. Surely if we reduce the lapse assumption in reserving basis whether non-unit reserves are positive or negative in both cases non-unit reserves should decrease by the same amount but the examiners’ report suggests that in case of positive unit-reserves these will reduce by a lower amount. In addition, it is not clear to me why the examiners’ report mentions positive non-unit reserves would normally only held for a minority of policies (smaller ones). If this is the case then this would result in overall negative non-unit reserves and my understanding was that negative non-unit reserves are only allowed when overall non-unit reserves are positives.

 

[Mike Lewry]

I came up with those scenarios to develop my understanding after looking at September 2013 exam paper and question 4.5 of Q&A bank.

Mike thanks for helping out. Below I have attempted few scenarios. If you could fill in gaps in my understanding of only the scenarios I have attempted below, then I should be able to work out other parts of my question. I have pointed out where I am finding the concepts difficult.

For a without profits contract, increasing the interest rate used in the valuation basis will decrease the value of reserves. The net assets will increase because the reserves are lower.

Good so far.

The impact on PVIF is less clear: the first thought that comes to my mind is that it will increase as release of surplus will increase.

You're right there is an immediate one-off release in surplus, but this is fully captured by the increase in starting free surplus. This comes at the expense of starting PVIF. Reserves now being lower means less margins in the basis and so LESS surplus to emerge in each future year, irrespective of how it is transferred to s/h. This decreases PVIF and ties in with what you say next.

However, if EV is calculated by allocating assets to without profits liabilities up to the value of mathematical reserves plus CRR, projecting the reserves and allocated assets forward using realistic projection basis and taking the 10% of the surpluses as and when they arise (as in question 4.5 of Q&A bank) then I do not understand why PVIF will increase. If the reserves will decrease as result of higher interest rates, the amount of assets allocated will also decrease, so it shouldn’t increase PVIF.

For unit-linked pensions, withdrawal assumptions used both in the valuation and projection basis is reduced by same amount then the unit reserves will be unchanged. Non-unit reserves should decrease.

Generally, the effect here could be duration dependent. A reduction in early withdrawals before initial expenses have been recouped is good for us and so is likely to reduce non-unit reserves. However, a reduction in later withdrawals might have a different impact. In the Sept 2013 question you're thinking about, the withdrawal assumption isn't duration dependent, so we're just looking at the overall effect, which we can deduce from the fact that the reserving basis assumption is higher than the EV projection basis, ie higher withdrawals is prudent. So, yes, reducing the w/d assumption will cause the non-unit reserve to decrease.

Net assets will increase because of lower non-unit reserves. PVIF will increase as a result of higher future profits.

Your PVIF comment relates to the change in EV projection basis. There's also the reduction due to starting with lower non-unit reserves to consider (same idea as in previous scenario), which will at least partly offset the increase you mention.

I do not follow the debate about the negative and positive non-unit reserves in the examiners’ report. Surely if we reduce the lapse assumption in reserving basis whether non-unit reserves are positive or negative in both cases non-unit reserves should decrease by the same amount but the examiners’ report suggests that in case of positive unit-reserves these will reduce by a lower amount.

The key phrase in the report is "(and zeroises negative non-unit reserves)". In this case, reducing a reserve of 3 by 5 would give 0 (a reduction of just 3 after zeroising), whereas reducing a reserve 0f -2 by 5 would give -7 (a reduction of the full 5 since there is no zeroising here). But if we assumed no zeroising, then you're quite right - it wouldn't matter if we started with positive or negative reserves.

In addition, it is not clear to me why the examiners’ report mentions positive non-unit reserves would normally only held for a minority of policies (smaller ones). If this is the case then this would result in overall negative non-unit reserves and my understanding was that negative non-unit reserves are only allowed when overall non-unit reserves are positives.

For the company as a whole, total non-unit reserves need to be positive. This requirement doesn't apply at product level. So we could have positive immediate annuity reserves covering negative UL pensions non-unit reserves.

 

[qinfen]

Hi Mike,

Referring to the same 2013 Sep Qn, the examiner's report also says, "the increase in future profits from charges wound be expected to exceed the reduction in reserve release".

What's the logic for this? reduction in reserve release is due to lower non-unit reserve. How to compare this with increase in future profits from charges?

Thanks

 

[ActStudent1405]

Further to the thread above, please confirm my understanding that when a company holds positive non-unit reserves, a reduction in lapse assumption will increase PVIF due to:

i. charges being greater than expenses will now be received for a longer duration for those policies which previously were assumed to have lapsed.
ii. reserves being zeroised, the benefit of reduction in reserves is not fully absorbed.

If a company holds positive non-unit reserves for a “minority” of small policies, how come will there be a resulting “material” increase in PVIF? Also this does not seem to tie up with the last paragraph, which states that the high PVIF change suggests that negative non-unit reserves are NOT held. Can anyone please clarify?

Part ii of September 2013 Question 1 – Operating Assumptions
The “experience assumptions” referred to in the fourth paragraph under the heading “Operating Assumptions” on pg 4 of the Examiners’ Report are those used for the realistic evaluation of the EV projection basis. Please confirm? Would it be safe to say that these should be the same as the expected experience assumptions in the Experience Variance?

Is my line of thought correct that when the reserving basis is strengthened, this results in: a higher release in this year’s profits of 0.3m and [ii] higher future profits till run off – reflected in a higher PVIF?

 

[Mark Willder]

Further to the thread above, please confirm my understanding that when a company holds positive non-unit reserves, a reduction in lapse assumption will increase PVIF due to:

i. charges being greater than expenses will now be received for a longer duration for those policies which previously were assumed to have lapsed.
ii. reserves being zeroised, the benefit of reduction in reserves is not fully absorbed.

I think you have misread the solution to September 2013 Q1 (iii). The Examiners Report says that the the majority of non-unit reserves are negative, with few cases of positive non-unit reserves.

So when a company holds negative non-unit reserves (rather than the positive reserves you mention above), a reduction in lapse assumption will increase PVIF due to charges being greater than expenses.

If charges are bigger than expenses then we have no need to hold a reserve (and indeed we can even hold a negative reserve representing the future profits we expect to make). A reduction in lapses means that more policies continue in force and we receive more of these excess charges.

If a company holds positive non-unit reserves for a “minority” of small policies, how come will there be a resulting “material” increase in PVIF? ?

We would get the opposite effect to that I described above for policies with positive non-unit reserves (ie a decrease in PVIF). But as there are few policies in this category we can largely ignore them and focus on the large number of policies with negative non-unit reserves.

Also this does not seem to tie up with the last paragraph, which states that the high PVIF change suggests that negative non-unit reserves are NOT held. Can anyone please clarify?

A good approach with any exam question is to break it down into its component parts. As we are looking at EV we have assets less reserves plus PVIF.

The Examiners Report has started by discussing the impact of the basis changes on the reserves and has tried to draw some conclusions based on this alone. This is the discussion I have refererred to in my earlier comments (where we felt that there may be significant negative non-unit reserves).

The Examiners Report then moves on to look at the impact of the basis changes on the PVIF. We now draw the conclusion that perhaps any negative non-unit reserves have been zeroised, but we cannot be sure as the numbers we are given are at a very high level.

Often we will have factors pulling in opposite directions and cannot be certain which one will win. In the exam its best to describe all these factors as they could all score marks. In practice we would need to do more analysis to conclude which of the possibilities we suggested was correct.

Part ii of September 2013 Question 1 – Operating Assumptions
The “experience assumptions” referred to in the fourth paragraph under the heading “Operating Assumptions” on pg 4 of the Examiners’ Report are those used for the realistic evaluation of the EV projection basis. Please confirm? Would it be safe to say that these should be the same as the expected experience assumptions in the Experience Variance?

Operating assumptions refer to both the EV projection basis and the reserving assumptions. So we have two sets of assumptions for each of mortality, expenses etc.

The experience variance would also look at these same assumptions (mortality, expenses etc) to analyse the difference between actual and projected experience.

Is my line of thought correct that when the reserving basis is strengthened, this results in: a higher release in this year’s profits of 0.3m and [ii] higher future profits till run off – reflected in a higher PVIF?

I think you have this the wrong way round.

The Examiners Report suggested that the valuation basis has weakened. This would reduce the reserves and so lead to the extra 0.3m of net assets.

The report also suggests that changes to the experience basis assumptions have been made to reflect expectations of better future experience, ie the EV projection basis has been weakened so that we now expect more future profits and PVIF goes up by 5.0m.

This was a very tricky exam question, but I hope this helps to clarify the solution.

Best wishes

Mark