302 April 2003 Question 5

[tatos]

The question and solution can be found here:

http://www.actuaries.org.uk/researc...e-insurance-exam-papers-and-reports-1999-2004

However, it's basically that we need to compare two designs of unit-linked pension schemes. The only difference between the 2 designs is in the charges.

In design A, there is a low allocation rate in the early years, a variable monthly policy fee guaranteed not to increase by more than the rate of increase in national average earnings, and an annual management charge expressed as a percentage of the value of units.

In design B, there is only an annual management charge, assumed to be expressed as a percentage of the value of the units.

We are also told that the charges have been set so that profitability of the 2 designs is the same.

The solution in the examiners' report and in ACTED revision notes says that in order for the profitability to be the same, B must have a higher annual management charge (unless there is a higher allocation rate for A in the later years). Fine, I get that.

Where I'm confused is with what is mentioned under marketability:

It says that A has a lower surrender value early on, but higher in the later years. I understand that it should have a lower surrender value in the early years. But why does it have a higher surrender value in the later years. Surely, the surrender value should only just be catching up to B's surrender value at maturity?

It then says that A should have a higher maturity value. As I suggested above, why aren't the maturity values the same? I was thinking that the surrender value should only JUST be catching up to B's surrender value as they contracts approach maturity. And at maturity the values should be the same in order for the same profit to be realised? But I seem to be confusing something really badly

 

[tatos]

I think I might be understanding this now somewhat :

Just looking at the examiners' report again they reason that A will have a lower capital requirement at the outset (because of the low allocation in addition to the other charges, policy fee and annual management charge) and therefore it has a lower cost of capital.

So it must be that in order to have the same profitability design A should offer a higher maturity value to compensate for the fact that it's allocating less of the premium initially to the unit fund. So the expected present values of the 2 designs will appear to be the same. I think that makes sense?

I still don't get why the surrender value of A should be higher in the later years though. Unless the solutions are saying that A's surrender value is higher in later years than it is in early years (not that its surrender value is higher than B's surrender value)? That seems to make sense to me in that the allocation increases in the later years so A is always surrendering a subsequently higher and higher value of the premiums paid. And by contrast B has a constant surrender value. I think I'm possibly terribly confused and/or need to sleep on this and/or need to read up on unit linked contracts again and/or need someone's help..

 

[jollyfakey]

Hi Tatos,

I put figures in a spreadsheet to see what unit fund values would be at different times. Although my calculations are very crude, it shows that fund values would be higher for Design A towards the end of the contract term, hence higher maturity values.

I think this flows from the examiner's comments that 'This is because the effect of the lower annual management charge eventually outweighs the initial low allocation of units and the fixed expense charge'

 

[tatos]

Thanks Jollyfakey! This is all making sense today. How did I write that much though

 

[jollyfakey]

Thanks for writing much. I picked up valuable points from your reasoning which made me question myself and hence use spreadsheet to discard any doubts.