Setting Assumptions - allowing for expenses in premiums

Hi
Ch18 Setting assumptions (1) talks about allowing for expenses that do not vary by contract size in premiums in 3 different ways
1. Individual calc of prems or charges
2. Policy fee addition to prem
3. Sum assured differential

I am not sure what the difference is between the 3 as all 3 appear to lead to the first point of individual calc of prems.

Consider this example: Conventional (non-linked) term assurance contract, term=5yrs, age=20yrs, sum assured = £50,000 and initial and renewal expenses = £10.

So, to allow for these (fixed) expenses in the prems, I would use
P.a.due.20:5 = 50,000.A.20':5 + 10.a.due.20:5

This is consistent with 1 - individually work out prems as sum assured varies (but expenses are still fixed).
This is also consistent with 2 - where 10.a.due.20:5 can be seen to be a policy fee charged at the start.
Finally, also consistent with 3 because different prems charged depending on sum assured banding.

Is my understanding correct or am I missing something?

Also, while on expenses,
am I correct in saying that all direct expenses are variable? Example - commission.

and indirect expenses can be variable or fixed?
Example of indirect fixed expense - wage of staff (does not vary depending on vol of business {in the short term atleast})

Could you please give me an example of an indirect but variable expense?

Cheers

 

Hi, I understand the 2nd and the 3rd way, but could you please give me an example of the 1st way. ie. individual calc of premium rates? And why small policies priced on this basis would end up paying a very large % of their premium as expense loading? Many thanks for your help.

 

Consider this example: Whole life conctract for person aged x.
I have chosen some random annuity and assurance factors
annuity factor = 10
Assurance factor = .5
Expenses = £10 each year starting from first.
Premium = P (need to work this out)

So formula used is:
P.annuity factor = 1000.Assurance factor + 10.annuity factor

Contract A: Sum assured = £800
Px10 = 800x0.5 + 10x10
P = £50

So, of the £50 premium paid, £10 goes toward expenses. So, 20% of premium is used to cover expenses.

Contract B: Sum assured = £600
Px10 = 600x0.5 + 10x10
P = £40

So, of the £40 premium paid, £10 goes toward expenses. So, 25% of premium is used to cover expenses.

So, the smaller the contract, the smaller the premium and so larger the % of the premium used to cover expenses.

Hope this helps.

 

Thank you, Fischer. Gotcha.

There is this last sentence saying,'...the premium rate would then seem unreasonablely large'. How to interpret this?

Thank you again.

 

Okay, I'm going to guess here. If you look at Lynn's definition of premium rate above (or below?)- it says "£P per £1,000 SA" {i.e. formula for premium rate is
(actual prem paid x 1000)/(actual sum assured)}.

So, in my example:
For Contract A (the larger policy) - the premium rate is:
(50 x 1000)/800 = 62.5

For Contract B (the smaller policy) - the premium rate is:
(40 x 1000)/600 = 66.7

So, the premium rate is higher for the smaller policy. This difference might be even more if the policy size reduces and so will become "unreasonable".

Hope this helps.

 

Hmm, I tried to replace sum assured of 800 by 10,000 and 600 by 1,000 and the equations gave premium of 510 and 60 respectively based on your example, then premium rates are 0.051 and 0.06, so they dont differ unreasonably altho premium rate does appear greater for small policy than big one. I'm not sure now.

 

Yes - I agree, not the most "unreasonable" increase in premium rates.
Having said that - I think the example highlights the fact that the premium rates are higher for a smaller policy if pricing is done using fixed expenses only.
So, it might not be seen as "fair" to PH's who have smaller contracts.
Like in your example - the sum assured falls by 90% from 10,000 to 1,000, but the premium does not fall by the same amount.
I don't think we are expected to get caught up in the details of the core reading (unless they are lists) but would need to get the concept and be able to apply them in questions. Numerical examples help me and so I use them to get a hold of things.
That said, it is my second attempt at ST2, so not sure of what level is required to pass.
Good luck anyway.

 

Yeah, I'm trying to understand it. I hope the tutor can come to have a look to see if our understandings are correct.
Thanks very much for your help, Fischer.