September 2005 Q11

[Java Jive]

Hi everyone,
I wonder if anyone can guide me through the examiners' report for this question.
When they calculate non-unit fund numbers for the 3rd policy year before the provision is made, they put additional death strain as 0.
But the question clearly states that:

On the death of the policyholder during the term of the policy, there is a benefit payable at the end of the year of death of £20,000, or the bid value of the units allocated to the policy, if greater. On maturity, 115% of the full bid value of the units is payable.

So clearly if policyholder dies during the third policy year, company will have a mortality profit which should be shown in the projected account (as they will pay out death benefit of 100% of the bid value rather than maturity benefit of 115% of the bid value).

Any thoughts?

 

[didster]

The unit fund is the 100% of units.

The non unit fund pays any difference between 100% of units and the full benefit. In the first 2 years, it's to top up the benefit to 20,000.
In the third year no top up to death benefit but top up to maturity of .15 of fund value or 4138.821

(Haven't done these in a long while, so not sure why the maturity cost doesn't have probabilities in it but the death costs do, but its fixed later on in the solution.)

 

[Java Jive]

(Haven't done these in a long while, so not sure why the maturity cost doesn't have probabilities in it but the death costs do, but its fixed later on in the solution.)

Uff, that seems just the other way to ask what I'm asking
They assume in the solution that 115% of bid value will be paid for sure on maturity. However it will be paid with probability (1-qx) and the 'death' scenario which happens with qx leads to the payment of 100% of bid value i.e. just empties the unit fund with no cash movement.

So if we wish to put the whole amount of maturity 'loss' into account ( just as it is done in the solution) we also must add a death 'profit' somehow to balance things out.

Or alternatively we could multiply the maturity benefit by the probability that the policy actually matures and leave the death cell null.

 

[ZebuAlex]

You could think of this as an expected value of the payout for the 3rd year. There are two possible outcomes: death and maturity. Death has probability qx and maturity 1-qx. So the value we should record is:

qx * 0 + (1-qx) * 0.15 * fund

since on death we just pay the unit fund value and there is no extra, and on maturity we pay an extra 15 of the fund value. All that happens is we record the death cost in the death column and the maturity cost in the maturity column. It is all accounted for.

 

[Java Jive]

You could think of this as an expected value of the payout for the 3rd year. There are two possible outcomes: death and maturity. Death has probability qx and maturity 1-qx. So the value we should record is:

qx * 0 + (1-qx) * 0.15 * fund

since on death we just pay the unit fund value and there is no extra, and on maturity we pay an extra 15 of the fund value. All that happens is we record the death cost in the death column and the maturity cost in the maturity column. It is all accounted for.

Thank you,

I understand the basics of constructing projected accounts
But there is NO survival probability multiplier attached to 0.15*fund in the solutions. They just put 0.15*fund as extra maturity benefit (assuming it will be paid in any case). And it spoils further calculations of NPV etc.
I just wonder if this is a mistake in the solution?

 

[didster]

It seems we're all on the same page, ie expecting survival probalities in the table. Perhaps someone more knowledgable could clarify whether this is an oversight or a convention.

As I noted before they fix this later down by adding the mortality profit (from lack of death benefit) so the final answer is OK.

 

[Mark Mitchell]

I agree that the final answer is OK.

I also agree that this seems like a strange presentation. If I were doing this, I'd include the survival probability in the value in the table, rather than fixing it up afterwards. This is the way that this solution is presented in ActEd materials (eg the Revision Notes books).

I don't think the Examiners' Report solutions is either convention or an oversight. It's just a different way of thinking about the problem.

 

[Java Jive]

I agree that the final answer is OK.

Thank you for the clarification.
I usually try to work further than the question asks (i.e. calculate NPV before and after zeroization even if only after-zeroization NPV is asked) to understand the effect. That's why I was so surprized to see this approach in the solutions.