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2008 September SA4 Q2

K

Korach

Member
The ActEd solution to this question (ASET 2010) explains logically that the sum at risk for someone dying is equal to the
funding reserve minus the value of the death benefits

However, it then keeps saying that the underfunding of the plan means that the funding reserve should be reduced (but not the death benefits).
The main death benefit is the spouse's pension, which will also be affected by the funding of the plan.
In addition, the issue here is the effect on the deficit, which will depend on the total change in liability and not some adjusted version.

For example, if I have a scheme with one member, with funding valuation
Liability - 1 million
Assets - 0.8 million
If the death benefits together, on the funding basis, are worth 0.9 million, what is my sum at risk?
I would say that there is no sum at risk, since the death will cause a reduction to the deficit in the scheme.
The ACTEd solution suggests, though that the funding reserve here is only 0.8 million (since that is the amount of assets held) and therefore there is a sum at risk of 0.1 million.

Please explain if I am missing something.
 
Sum at risk

Hi Korach

What does sum at risk mean? Really, it's an insurance idea.

For example, a DC scheme but has a death benefit that's defined benefit in nature.

What's the risk? The risk is that the member dies and the accumulated DC fund does not cover the defined death benefit.

So what should be insured? The value of the death benefit less the accumulated fund.

This is the same idea. Here we hold:

X = the lesser of the funding reserve and the assets

and so may want to insure anything above this, ie:

the value of the death benefits - X.

For the numbers in your example I would consider insuring up to:

0.9 - min (1, 0.8) = 0.9 - 0.8 = 0.1m

because if there is a claim for death benefits right now, I am 0.1m short of being able to pay it, ie it is at risk.

Hope that helps

Best wishes
Stuart Underwood







Korach said:
The ActEd solution to this question (ASET 2010) explains logically that the sum at risk for someone dying is equal to the
funding reserve minus the value of the death benefits

However, it then keeps saying that the underfunding of the plan means that the funding reserve should be reduced (but not the death benefits).
The main death benefit is the spouse's pension, which will also be affected by the funding of the plan.
In addition, the issue here is the effect on the deficit, which will depend on the total change in liability and not some adjusted version.

For example, if I have a scheme with one member, with funding valuation
Liability - 1 million
Assets - 0.8 million
If the death benefits together, on the funding basis, are worth 0.9 million, what is my sum at risk?
I would say that there is no sum at risk, since the death will cause a reduction to the deficit in the scheme.
The ACTEd solution suggests, though that the funding reserve here is only 0.8 million (since that is the amount of assets held) and therefore there is a sum at risk of 0.1 million.

Please explain if I am missing something.
Click to expand...
 
Thank you - maybe you will agree that..

Thank you very much for your reply.
Now I understand sum at risk in the context.

However, in this case, since most of the death benefit here is a widow's pension for life - maybe for the next 50 years - the idea that there is a real qualitative difference here between the death benefit and the normal pension benefit whereby one is to be insured and the other is underfunded seems a little artificial.
I would suggest that both are underfunded and it makes little or no difference.
Anyway, now I see the logic of the answer.
I guess I could write that theoretically the underfunding should affect the sum of risk, but actually this is arguable.
I can split that into two points and get a whole mark!

This makes me think of another issue: is it really true that it is worth bringing up issues that could theoretically be but clearly are not relevant in this case and then explaining why they are not relevant? The Mock A paper solutions are full of examples of this.
I never thought of that as a useful actuarial skill, but I am beginning to change my mind. It can help communication, since unfortunately people need things spelled out clearly, including an explanation of why some points are not relevant.
 
Exam technique

Hi Korach

How should your answer look in the exam?

At the start of the answer, you want to cover the key issues relevant to the question, and as they are the most important issues, spend longer on them.

Then the bulk of the rest of the answer should be spent discussing other issues more briefly, issues that are fairly important, but not so important as the key issues.

You should rarely then need to spend time saying
"X is not an issue as ..."
or
"Y is not important because ..."
as you already should have lots to say.

I'm not sure that I agree that in this question that the issue of sum at risk is not an important issue to discuss as in a question about insuring death benefits I think it is important to know:
- what the amount and timing of the liability is under the most likely scenario (ie surviving to retirement)
- how that would differ if instead the member dies
- and what money is available vs the cost of the benefits in either case.

If the conclusion is that all the numbers are fairly close together, great, but we can score marks for showing the examiner our process.

A important skill in SA4 is to avoid being too dogmatic. It's easy to think an issue clearly isn't important now, but if for example market conditions were to change, would it become important then - eg setting terms for guaranteed annuity rates is a great example.

I don't think it'd be a good use of your time for you to create a list the parts of the solution you feel are less relevant and then my time to justify why they might be (as it seems you feel there are quite a few of these, and you may still disagree with me anyway!).

So instead, it might be more useful for you to play devil's advocate yourself, if you feel some of the points in the solutions don't seem immediately and initially relevant, have a think about scenarios where they could become relevant - you may be surprised what you come with!

Good luck!

Best wishes
Stuart
 
Thanks again

Thank you for your reply - I see that you consider it an important issue and that you gave me some good tips.
I have culled the following tips from what you write:
1) Don't be too dogmatic what is relevant - situations can change and I would add that the case in the question is rarely described fully - for example, ActEd solutions are willing to countenance that there may be a DC section of the plan even though this is not in the blurb of the question - a logical possibility, particularly with auto-enrolment on its way!
2) Show the examiner our process - this is very difficult for me and may be for others who love mathematics, since the mathematical way of thinking commonly jumps to the answer (and then goes back and proves it if forced to).

Thanks again!
 
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