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Calculating PVIF for with-profits endowment assurance business

A

ActuaryEye

Member
Good day

Can someone help me understand the calculation of the present value of in-force business (PVIF) for with-profits endowment assurance policies. The profit participation rule is 90/10 - where 90% of the profits go to policyholders and 10% is for shareholders. So what I really want to understand is how the future shareholder transfers are calculated through the bonus distribution.

For example let us say we are projecting cashflows to arise in year one of the projection period. So, for a single policy, we have Premium - Expenses - Cost of benefits (surrenders, death claims, maturities) + investment income - increase in reserves. Does this give us the profit that should then be split 90/10? I am thinking the policyholder has already benefited by the increase in reserves, so it is not making sense to give them 90% of this profit.

Should the cost of benefits in my example above include the bonus for the year? I understand how this would work when the policy is not a with-profits policy.

Please help
Regards
 
Hi - this is described under the heading 'With-profits business' in Section 2.3 of Chapter 18 and is also covered in Practice Question 18.2. There is also an example in the SA2 Online Classroom that works through calculating the EV for a 90/10 WP fund.

Basically: shareholder transfers under WP business are typically triggered by bonus declarations. So to calculate the PVIF (= PV of future expected shareholder transfers) we need to project future bonuses. For example, we could project future RB by assuming continuation of the current rate or gradual movement towards the long-term sustainable rate. And we could project future TB by projecting asset shares.

In a 90/10 fund, shareholders are eligible for 10% of the profits and WP policyholders 90%. Therefore shareholder transfers equate to 1/9 of the cost of bonus. Hence we project future bonuses, take 1/9 of that, discount it ... and that's the PVIF.

There are other complications, such as profits arising on without-profits business written into the 90/10 fund. This is also described in that part of the Course Notes.
 
Lindsay Smitherman said:
Hi - this is described under the heading 'With-profits business' in Section 2.3 of Chapter 18 and is also covered in Practice Question 18.2. There is also an example in the SA2 Online Classroom that works through calculating the EV for a 90/10 WP fund.

Basically: shareholder transfers under WP business are typically triggered by bonus declarations. So to calculate the PVIF (= PV of future expected shareholder transfers) we need to project future bonuses. For example, we could project future RB by assuming continuation of the current rate or gradual movement towards the long-term sustainable rate. And we could project future TB by projecting asset shares.

In a 90/10 fund, shareholders are eligible for 10% of the profits and WP policyholders 90%. Therefore shareholder transfers equate to 1/9 of the cost of bonus. Hence we project future bonuses, take 1/9 of that, discount it ... and that's the PVIF.

There are other complications, such as profits arising on without-profits business written into the 90/10 fund. This is also described in that part of the Course Notes.
Click to expand...
Thank you very much for that. Very helpful indeed!
 
Hi Lindsay. If one was to price a With-Profits contract, would the cashflow method be followed to the above? I.e setting a premium that meets the s/h's profit requirement by discounting future profits (taken as transfers to shareholders) at the risk discount rate?
 
Hmmm - this is actually quite a tricky question! We have to be a bit careful when talking about 'pricing' a with-profits contract. What exactly does that mean?

For example, for unitised with-profits business where explicit charges are taken and the shareholder is eligible for all expense / mortality etc (ie non-investment) surpluses, then 'pricing' means setting the charges to be sufficient to meet the expenses and excess benefits and to generate a profit margin.

For conventional with-profits business, 'pricing' effectively means setting the premium rate to purchase the basic sum assured. As described in Subject SP2, this amount is normally set well below the total expected affordable benefit, and the calculation would be done using very prudent assumptions. This then enables the majority of the premium to form a 'bonus loading', allowing future surpluses to emerge from which bonuses and shareholder transfers will be paid. For example, if the company expects future investment returns of 5% pa it might 'price' the basic sum assured to be what could be afforded on a future investment return of 1% pa (and similarly for other assumptions such as expenses, mortality). So the premium charged would be much higher than would actually be expected in order to meet that basic sum assured, allowing future surpluses to emerge (eg 4% pa expected investment surplus in this example) to generate the bonuses. So there wouldn't really be the same kind of profit testing approach needed for this process, it's more a case of deciding how much to 'hold back' for the bonus loading. Having said that, the company may well check that the present value of expected shareholder transfers is reasonable.

For the revalorisation & contribution methods, there would be similar determination of an appropriate premium rate for a particular sum assured, but using a basis that allows there to be some expected emergence of surplus for the distribution of bonuses / dividends. (And of course the shareholder share may be defined differently for these methods.)

Hope that helps a bit - might be worth reviewing some SP2 content as a reminder.
 
Hi Lindsay, thank you very much for your very detailed reply! What you have described there makes a lot of sense to me, I just wanted to make sure I wasn't missing anything set in stone about With-Profits pricing as the idea is kind of dodged in Sp2/Sa2 rather than the line you quote around using prudent assumptions.

Does it sound reasonable that if asked about pricing for a conventional with profits contract, one's answer could be based on the third paragraph you have written above? And then depending on the amount of marks, one could expand on your last line (PV of shareholder transfers) by giving the details described under the heading 'With-profits business' in Section 2.3 of Chapter 18 ?
 
Sounds good to me - it's what I would do! :) [Although if there were a lot of marks, I might be inclined to expand more on how the premium rate for the basic sum assured was determined.]
 
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