Setting Assumptions - allowing for expenses in premiums

[act_stu]

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

 

[Lynn Birchall]

Hi

Hi
Is my understanding correct or am I missing something?
Cheers

I think you’re missing something

You’ve described the first method fine.

The idea behind the second and third methods, where we don’t have individual calculation of premiums, is that the insurance company would determine some “premium rates” to be used for all policies.

A “premium rate” could be, for example, "£Ppa per £1,000 SA". (There would be a table of different rates for different policy terms, ages at entry, etc).

In method (2), the idea is that you’d combine these premium rates with a policy fee (say £25pa). So, if a policyholder wanted a SA of £100,000, their premium would be calculated as:

Premium = £100 x P + £25

If the company had set the £25 policy fee to be equal to the per-policy expenses and had put all the proportionate expenses in working out the P, this is like the first method.

However, if this would result in uncompetitive high premiums being charged to small policies, the company may have a smaller policy fee (say £15pa) and load some of these per-policy expenses into the premium rates. So, it would have a new set of higher premium rates Q and

Premium = £100 x Q + £15

The premium rates (the Ps and the Qs) would be worked out so that the resultant premiums would be the same amount for a policy with average sum assured. However, bigger than average policies will pay a higher premium under the second method, smaller than average policies will pay a higher premium under the first.

The third method has no policy fee. The premium for a policy is worked out from the premium rates as:

Premium = Sum assured / 1000 x premium rate per £1000 SA

The company makes some allowance for this size of a policy by having different premium rates for different sizes of sum assured. So, it may have premium rates of R for sums assured <£150,000 say and R' for sums assured >=£150,000. In this case R' < R.

Argh, this has ended up being a very long post (sorry!) - hope it helps?

Cheers
Lynn

 

[Avviey]

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.

 

[fischer]

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.

 

[Avviey]

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.

 

[fischer]

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.

 

[Avviey]

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.

 

[fischer]

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.

 

[Avviey]

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.

 

[Lynn Birchall]

Hi

What's been said so far looks good to me

As fischer said in one post - as the sum assured falls, the premium doesn't fall by as big a proportion, so can be left with what look like high premiums for policies with small sums assured.

Cheers
Lynn