Discussion in 'SP2' started by Ivanhoe, Sep 3, 2013.

1. IvanhoeTon up Member

I am having trouble understanding the following core reading. I apologise for the length of the text, but I am struggling with this

If it adopts a prospective approach then the amount of the profit depends upon the relationship between the assumptions used for the surrender value and those implicit in the calculation of the office premium. Suppose, for the purpose of this discussion, that the allowance for profit is contained solely in margins in the assumptions used to calculate the premium. The profit retained can then be specified as:
(EAS – SV') + (SV' – SV")
where: EAS = earned asset share
SV' = prospective surrender value using same assumptions as used to calculate the office premium
SV" = prospective surrender value using surrender value
basis assumptions.

The first part – (EAS – SV') – represents the profit that has been made to date.
The second part – (SV' – SV") – represents the capitalised value of the profit
that will arise in future from the differences between the premium rate
assumptions and the surrender value assumptions.

If the surrender value assumptions represent exactly future experience then the total profit retained will be the same as if the contract had not been surrendered.

If they are the same as the premium basis assumptions then the company only retains the profit it has made to date.

Also, the part where Acted text says..that Profit B is given up..How can they say that?
Rgds,

2. Mark WillderActEd TutorStaff Member

This is probably one of the hardest parts of the course. Hopefully the following explanation will help.

We make a profit if the money we have (ie the asset share EAS) is more than the money we pay out (ie the surrender value SV"). So

Profit on surrender = EAS - SV" = (EAS – SV') + (SV' – SV")

The course then breaks down the profit into two parts (where SV' is the surrender value that would be paid if we calculated it prospectively using a pricing basis which has margins for prudence but no explicit profit loading):

Profit A = (EAS – SV')

Profit B = (SV' – SV")

To see what these mean, we need to see the picture on page 17.

Profit A is zero at the outset of the contract (as EAS and SV' are equal) and grows over the lifetime of the contract to equal the full profit from the contract (ie the excess of the asset share over the sum assured). So this sounds like a good measure of the profit accrued to date because no profit should be accrued at the start, but all of the profit should be accrued at the end.

Profit B depends on what value we use for SV". If SV" = SV', then profit B is zero (ie profit B is given up as per the ActEd text you quote). So, if the surrender value is calculated on the pricing basis, we only get profit A, ie the profit accrued so far.

However, if SV" is calculated using best estimate assumptions of future experience, then we get the lowest line shown on page 17 (ie realistic V). A realistic reserve at outset (just before the first premium is paid) would be the present value of the benefits plus expenses less premiums. But realistically we expect the value of the premiums to be bigger than the benefits and expenses to make a profit. So at outset (just before the first premium is paid), EAS - SV" = 0 - (-expected profit) = expected profit. So if we pay SV" as a surrender value we keep the full profit expected on the original contract.

I hope this helps.

Mark

3. IvanhoeTon up Member

Thanks for the explanation! Much clearer than before. I just had some follow up questions. Could you please respond?

A realistic reserve at outset (just before the first premium is paid) would be the present value of the benefits plus expenses less premiums. But realistically we expect the value of the premiums to be bigger than the benefits and expenses to make a profit. So at outset (just before the first premium is paid), EAS - SV" = 0 - (-expected profit) = expected profit. So if we pay SV" as a surrender value we keep the full profit expected on the original contract.

When you say the EPV (benefits+Expenses)<EPV(Premiums)at time 0 on a realistic basis, do you mean to say that there is an explicit loading for profit on the right hand side at time zero, i.e EPV(Premiums)=EPV(Benefits+Expenses)+Profit?

I understand that there are no margins when calculating SV", while there is no explicit loading while calculating SV' but the profit is released through the margins? Is my understanding correct? If so, then why the differential treatment for loading profit?

4. Mark WillderActEd TutorStaff Member

In the quotation above, it doesn't matter how we calculate the premium (either with an explicit profit loading or with margins in the pricing basis) it is always true that we would expect the present value of premiums to be bigger than the benefits and expenses when valuing the policy at the outset using realistic assumption.

This is a rather subtle question, but hopefully the following helps.

Yes, the pricing basis used when calculating SV' includes margins in the assumptions which are then released over time.

Alternatively we could use a profit loading to price the contact. This is fine for calculating a premium at outset, but is no use to calculate prospective values at any other time. In order to calculate the surrender value at time t we need to know how much profit loading to include in the calculation at time t. The answer is to instead include the same profit as including a margin in each of the assumptions.

Best wishes

Mark

Thanks

6. User 1234Keen member

Hi Mark

I have a question following to this quoted statement.
If we look at the first line and the last line only on the graph.
Is my understanding in regards of the below three time point correct?!

At the outset, we keep the full amount of profit because EAS - SV" = 0 - (-expected profit) = expected profit.

During the period, EAS grows (1st line) because of profit from the contract started to accumulate. The SV'' (or we can say realistic reserve here) grows because the reserve we need to hold starts to increase to meet the maturity value at the end.

At the end, EAS - SV'' should be equal exactly to the same as the expected profit at the outset?

Of course, here I assume the actual expeirence (in AS) is the same as best estimate assumptions of future experience.

Thanks a lot!!

7. Lynn BirchallActEd TutorStaff Member

Hi

I think that's 99% correct, yes.

Strictly, in your final point I think it's that the value of the end profit (EAS - SV'') is equal to exactly the same as the value of the expected profit at the outset.

Thanks
Lynn

8. JamaicanJemTon up Member

Hello All,

I've been trying to figure out this part for ages and I think I'm almost there. I'm not sure how to quote so I'll just highlight and hope it works. Why is EAS and SV' equal at the outset of the policy? Also I just wanted to verify that under both the realistic and premium basis, we expect the PV of Prems > PV (Ben + Exp).

Thanks again.

9. Lynn BirchallActEd TutorStaff Member

Hello!

Glad to hear that you're getting there with this (tricky!) part

SV' is defined as being worked out prospectively using a pricing basis which has margins for prudence but no explicit profit loading. So, before the policy is sold, we have an equation of policy value : EPV(all premiums) = EPV(benefits) + EPV(all expenses).

We could expand/re-arrange this to :
0 = EPV(benefits) + Initial expenses (at time 0) + EPV(other expenses) - Premium at time 0 - EPV(all future premiums)
and so
-Initial expenses (at time 0) + Premium at time 0 = SV' at outset of the policy.

We also know that the EAS at policy outset is the cashflows that have occurred on day 1, ie also minus initial expenses + first premium.

We expect PV of Prems > PV (Ben + Exp) on the realistic basis, yes. However with the particular way 'premium basis' has been described here (ie margins for prudence but no explicit profit loading) we expect the two sides to be equal on this basis.

Hope this helps (apologies for any dodgy formatting / notation in my formula attempt!)
Lynn

10. JamaicanJemTon up Member

Thanks so much for the quick reply Lynn. I just want to clarify then the realistic V. The realistic V would be using the office premium but would not have any margins, so is it true that the EPV (B + E) for realistic basis would be lower than the EPV (B + E) under the premium basis, and this is why the realistic reserve is the lowest line of the graph and also why the PV (P) > PV (B + E) on the realistic basis?

Also, an additional question on bases which I think is my problem! For a premium calculated on a prudent pricing basis with margins, these margins would be a source of profit. If the reserves are then calculated with even further prudenece, would this be an additional source of profit (if experience is within margins)?

Thanks again Lynn!

11. Lynn BirchallActEd TutorStaff Member

Yes to both of these!

Yes again to this.

Over the life of the policy, the total profit will depend just on how prudent the premiums were compared to the actual experience. The prudence of the reserving basis will affect the timing of this profit, ie how the profit is released over the life of the policy. The more prudent the reserving basis, the more 'strain' there is early on (due to the need to set up the prudent reserves), but this is compensated by higher levels of profit later on as the prudence in these reserves turns out not to be needed to cover benefits and expenses (hopefully!).

12. JamaicanJemTon up Member

Brilliant Lynn! Thanks again!

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13. Max ClintonMember

[QUOTE="
However, if SV" is calculated using best estimate assumptions of future experience, then we get the lowest line shown on page 17 (ie realistic V). A realistic reserve at outset (just before the first premium is paid) would be the present value of the benefits plus expenses less premiums. But realistically we expect the value of the premiums to be bigger than the benefits and expenses to make a profit. So at outset (just before the first premium is paid), EAS - SV" = 0 - (-expected profit) = expected profit. So if we pay SV" as a surrender value we keep the full profit expected on the original contract.

I hope this helps.

Mark"/QUOTE]

Hi Mark,

So can I just quickly confirm that at any given time, EAS - SV'' = the present value of the future expected profit on the policy if held till maturity?

Thanks,

Max

14. Lynn BirchallActEd TutorStaff Member

Hi Max

Nearly, I think. At any given time:
EAS - SV'' = the total profit made on the surrendering policy (which is equal value to the expected profit on the policy if held to maturity)
= the profit up to the point of surrender + the PV of the future expected profit on the policy of held to maturity.

At time = 0, the first of these to components (accrued profit) is of course 0.

Hope this helps
Lynn

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15. Max ClintonMember

Thanks Lynn, yes that makes sense now!