A very simple question on the mortality risk and withdrawal risk

[therayofhope]

Hello, I know this sounds like a very basic question and it can trace it roots to as early as chapter 1 or 2 in the course notes. The notes said the mortality risk is the sum at risk, which is the benefit under the contract - reserve, because that is the money that you have not yet had and hence the risk. But when I went onto the withdrawal risk, it said that it depends on the asset share level. I do understand the basic logic, but shouldn't you need to subtract the reserve as well as you will release your reserve too when a withdrawal event happen? Or have I just missed out that the asset share has already included the release of reserve? Shouldn't withdrawal risk be just Withdrawal benefit amount - reserve?

Sorry I know this sounds very basic (and I think so too), but the question has been pondering around for a good while now. So appreciate if someone can help me out...

 

[Lynn Birchall]

Hello

If you have a look at Question 1.12 in the notes it discusses this point.

"Benefit amount - reserve"
and
"Benefit amount - asset share"
both make sense as a definition of profit, even though they're referring to different things!

"Benefit amount - reserve" is the profit/loss (on the supervisory reserving basis) at the time the claim happens.
"Benefit amount - asset share" is the overall profit/loss on the policy.

Imagine a policy has asset share of 500, reserve of 600, and claim amount 800.
If the company has to pay the claim, it makes an overall loss on the policy of 300. However, it only has to come up with an extra 200 of capital to pay the claim (it had already had to provide the other 100 in order to set up a reserve bigger than the asset share).

 

[therayofhope]

Hello

If you have a look at Question 1.12 in the notes it discusses this point.

"Benefit amount - reserve"
and
"Benefit amount - asset share"
both make sense as a definition of profit, even though they're referring to different things!

"Benefit amount - reserve" is the profit/loss (on the supervisory reserving basis) at the time the claim happens.
"Benefit amount - asset share" is the overall profit/loss on the policy.

Imagine a policy has asset share of 500, reserve of 600, and claim amount 800.
If the company has to pay the claim, it makes an overall loss on the policy of 300. However, it only has to come up with an extra 200 of capital to pay the claim (it had already had to provide the other 100 in order to set up a reserve bigger than the asset share).

Hello, thanks again for your reply. Just not sure how much in debt we are to the Act Ed tutor!

I do understand the logic behind Q1.12 and what you said above. However it still doesn't say why there is a difference in determining the mortality risk and the withdrawal risk. Or have I just missed out something here?

Suppose we have 2 examples here...
Example 1:
Supose a policy has asset share of 500, reserve of 600, and death claim amount 800.
So our actual loss will be 800-500, and if you ignore the cost of capital injected, your loss will only be 800-600.

And now if we have an Example 2:
Supose a policy has asset share of 500, reserve of 600, and surrender claim amount 800.
Shouldn't our actual loss remains at 800-500? And again, if you ignore the cost of capital injected, your loss will be 800-600?

If both example 1 and 2 are correct, then where comes the difference that mortality risk is Claim amount - reserve and withdrawal risk is claim amount - asset share?

 

[Lynn Birchall]

If both example 1 and 2 are correct, then where comes the difference that mortality risk is Claim amount - reserve and withdrawal risk is claim amount - asset share?

Both example 1 and example 2 are correct.

The same applies whether it's mortality or withdrawal.

In either case:
200 (ie 800 - 600) is the supervisory loss at the point of claim
300 (ie 800 - 500) is the actual overall loss for the policy. (The reserve doesn’t come into this as it’s not money the p/h has paid and it’s not money the company's paying out.)

I suppose the reading just tends to be referring to one situation (supervisory loss) when it's talking about mortality, and the other when it's talking about withdrawals.

Hope this helps clarify!
Lynn

 

[morrisja]

I think there's a very simple answer here..

It's a principle of supervisory reserves that any guaranteed surrender value should be less than or equal to the reserve (and discretionary amounts are also likely to be accounted for if prudently expected to be paid).

Comparing withdrawal payouts to the supervisory reserve is therefore pointless, we should always see no reserve strain if reserving prudently.

The 2 metrics apply to mortality, but the reserve - payout metric does not apply in the case of withdrawal.

Does this make sense or is there a flaw above?

 

[therayofhope]

I think there's a very simple answer here..

It's a principle of supervisory reserves that any guaranteed surrender value should be less than or equal to the reserve (and discretionary amounts are also likely to be accounted for if prudently expected to be paid).

Comparing withdrawal payouts to the supervisory reserve is therefore pointless, we should always see no reserve strain if reserving prudently.

The 2 metrics apply to mortality, but the reserve - payout metric does not apply in the case of withdrawal.

Does this make sense or is there a flaw above?


Also, on an unrelated topic, it appears people can edit their posts without vetting during the exam period - risk that people could get posts through and then edit them to talk about exams. Probably not going to happen. But might want to introduce some underwriting on alterations..

Thanks to both Lynn and morrisja! I think morrisja has got a point there as well. But basing on your logic I will still wonder why isn't mortality risk = payout amount - asset share. Wouldn't that be a fairer comparison with the withdrawal risk defined?

Anyway, thanks for all of your help. You guys have made me way more confident to the exam as I am the only guy doing IOA in my office - hence having nobody to discuss with. Hope they didn't annoy or bother you. I am happy to stick with Lynn's suggestions that I will leave it as it is.

 

[morrisja]

Always happy to help if I can!

I think mortality risk is defined as payout - reserve as the cost of increasing the reserve beyond the asset share has already been booked in another period. I think Lynn mentioned this below.

I'm trying to think why the payout - asset share is not as appropriate as a measure of mortality risk (if that is the case). I think the inconsistency you've pointed out must have some reasoning behind it..

When someone withdraws from a policy the payout that is made has to be based on the duration into the policy and asset share is the way we would measure the accumulated contribution here.

For mortality the payout is based on the sum assured which is the same (simplest case) throughout the policy and the reserve is based on this Sum Assured.

The reserve and sum assured are both prospective measures and the asset share and withdrawal claim are both retrospective measures.

So while you can look at Sum Assured less asset share on death, it would not be as appropriate a measure of the risk that we experience more death claims than expected.

I'm not sure if I've clearly explained myself above or if my idea is even accurate. Any thoughts Lynn/therayofhope/anyone?

 

[Lynn Birchall]

Hi again

I agree that the rules about supervisory reserves might affect which comparison (against asset share or reserve) is most useful.

As you say morrisja, when a GSV is acting as a minimum reserve, we're not going to get a capital strain if the policy withdraws. There is potentially a big death strain however, as the reserve could be much lower than the death benefit.

Also, the idea of the gap "asset share - reserve" being a measure of how much profit/loss we've incurred so far makes sense to me. I think "death benefit - asset share" is appropriate as a measure of overall mortality risk. The "death benefit - reserve" is just the bit we make at the time of the claim.

(I'm not sure I really follow the prospective / retrospective idea? Withdrawal benefits aren't always worked out retrospectively, eg lapses with 0 payout, even though asset share may be negative.)

Best wishes
Lynn

 

[morrisja]

(I'm not sure I really follow the prospective / retrospective idea? Withdrawal benefits aren't always worked out retrospectively, eg lapses with 0 payout, even though asset share may be negative.)

I may have been looking for something that isn't actually there. I take your point on the retrospective/prospective part in calculating withdrawal terms as well.

It's possibly just convention to use payout - reserve for mortality risk. I can see that both are useful metrics in this case.

If we were looking from an internal management accounts view, where reserve could be less than GSV, presumably the 2 metrics would be interchangeable for withdrawal risk also.

I get the feeling it won't matter a whole lot on Friday in any case..

 

[therayofhope]

I may have been looking for something that isn't actually there. I take your point on the retrospective/prospective part in calculating withdrawal terms as well.

It's possibly just convention to use payout - reserve for mortality risk. I can see that both are useful metrics in this case.

If we were looking from an internal management accounts view, where reserve could be less than GSV, presumably the 2 metrics would be interchangeable for withdrawal risk also.

I get the feeling it won't matter a whole lot on Friday in any case..

I have a feeling though for every uncertain topic it is bound to come up in my exam...

Anyway, thanks so much for the discussion. I think it helps me understanding the topic, so best of luck on friday!