ST2 October 2007 ASET solution

[Alan2007]

I don't understand the part of the solution on page 21 of the October 2007 ASET solution to the exam question 6. The solution explains how well this principle is met "The calculation method should allow profit to be recognised in an appropriate way over time and should not be subject to discontinuities arising from arbritary changes to the valution basis"

Here is a basic theme of the question 6.
The company intends to hold a reserve of min(single premium paid, unit reserves). The policy pays a maturity bonus on top of the units. The surrender benefit that the company pays out is 90% of unit fund.

The solution reads "At least 10% of reserve is released on surrender, more if the fund value is below the single premium. If a non-zero maturity bonus is paid, there will be a supervisory loss at maturity. ....."

Can someone please explain this solution.

Many Thanks

 

[Lynn Birchall]

Hi

I'm assuming it's the highlighted red/brown sentence that's the problem - ie why the profit/loss is the amount quoted? (Of course, do say if that's not the issue )

At the point a benefit is paid , the profit recognised is:

Amount of benefit paid - Amount of reserve that was being held at that time

For surrender:
SV = 90% of unit fund
reserve = max (unit fund, premium paid)
so profit recognised is >= 10% reserve

For maturity:
MV = (100% + bonus%) x unit fund
reserve = max (unit fund, premium paid)
so, assuming that bonus% > 0 and that by matuity the unit fund has grown to > premium paid, profit recognised <0.

Hope that helps?
Lynn

 

[Alan2007]

Re: Reserving principle

Hi

I'm assuming it's the highlighted red/brown sentence that's the problem - ie why the profit/loss is the amount quoted? (Of course, do say if that's not the issue )

At the point a benefit is paid , the profit recognised is:

Amount of benefit paid - Amount of reserve that was being held at that time

For surrender:
SV = 90% of unit fund
reserve = max (unit fund, premium paid)
so profit recognised is >= 10% reserve

For maturity:
MV = (100% + bonus%) x unit fund
reserve = max (unit fund, premium paid)
so, assuming that bonus% > 0 and that by matuity the unit fund has grown to > premium paid, profit recognised <0.

Hope that helps?
Lynn

Thanks for the reply.

I don't understand why the profit recognised = Amount of benefit paid - Amount of reserve that was being held at that time. I understand the profit of the unit linked policy being net cashflows from the non-unit fund + increase in reserves

For surrender if this equation was used, then this would give a loss ie 90% of unti fund - max (unit fund, premium paid)

For maturity, we would get a loss using the equation

Could you explain why reserving method max (unit fund, premium paid) would not be consistent with the principle "the method of calculating reserves should be set so that an appropriate pattern of surplus emerges during the life time of the contract?

Thanks:

 

[Muppet]

"I understand the profit of the unit linked policy being net cashflows from the non-unit fund + increase in reserves"

if you increase reserves, you will reduce profits so it should be minus increase in reserves.

in the SV example
net cashflow = -90% unit fund
increase in reserve = 0-unit fund = -unit fund (assuming UF> prem)

so profit = + 10% UF

 

[Lynn Birchall]

Absolutely. If you make your profit formula be:

net cashflows from non-unit reserve - increase in non-unit reserves

then the profit or loss you'll calculate at surrender or maturity are the same as the amounts in my first post.

As to why that's not an appropriate pattern: it's not appropriate for there to be a loss at maturity - this suggests your reserves weren't sufficient to meet your outgoings (see Principle 1 in the solution).

Lynn

 

[rishanb]

Hi

At the point a benefit is paid , the profit recognised is:

Amount of benefit paid - Amount of reserve that was being held at that time


Lynn

Hi Lynn

A quick check to make sure I understand you correctly:

The profit (in this case loss) released st the point the benefit is paid is as described above.

but

If the policy was priced correctly (had the correct experience assumptions and a profit margin) then overall the policy would be profitable. We could see this by calculating the [Asset Share - Final Benefit]. In this particular example this would mean that profit was made in earlier years when too small a reserve was set up - enough profit was made in earlier years to counter the outflow at the end.

so

overall profit on policy = asset share - benefit paid
profit at point of benefit = reserve - benefit = capital cost at point of benefit?

 

[Lynn Birchall]

Hello

Yes, that looks good to me.

The overall profit on a policy doesn't depend on the reserve : as you say it's asset share - benefit paid. (This makes sense as it's the difference between "what the company's got over the life of the policy" and "what the company pays out".)

The reserve (ie the amount the regulator requires the company to hold at any point in time) just affects how this overall proft is spread over the life of the policy. A the time of the benefit payment, this reserve is "released" and the profit at this point is "reserve - benefit" as you say.

(I could have just left that as "yes, you're right" couldn't I )

Best of luck for Thursday
Lynn