CAS Sample Questions 18 and 20

MarianneCMarianneC
in General

Hi,

A few questions on the CAS sample IFRS17 Questions

Sample 18 : part c) : why is the average accident date = 1/3
Sample 20 : Can you provide more explanation of the formula to obtain BoY capital, which is the initial capital/1.5 * 2*Remaining future cash flows?

Thanks!

Comments

  • Staff-T1Staff-T1
    edited April 27
    Sample 18: 0.333 is just the average accident date adjustment for premium liabilities/LRC. There is a derivation for this in one of the old premium liability papers under IFRS4 using some integration, but you just need to know the output.
    Sample 20: The firm's operating target is an MCT ratio of 200%. The capital required provided is at an MCT ratio of 150%. This means that you'd divide by 1.5 to get to a 100% MCT ratio, and then multiply by 2 to go to a 200% operating target for the MCT ratio
  • sofiagiubilasofiagiubila

    So is the 1/3 because there are 3 time periods?
    If there were 4 time periods then would the average accident date be 1/4?

  • Staff-T1Staff-T1
    What are you referring to by time periods?
  • NycxBattleNycxBattle

    @Staff-T1, are you saving the 0.333 in question 18 is a typo? Can we just use average time of 0.5 to discount for first year and 1.5 to discount fir second year and so on?

  • Staff-T1Staff-T1
    No I'm not saying that. If you're discounting premium liabilities or LRC in this case, you need to "shift" the accident date by subtracting (0.5-0.33). The derivation relies on sole calculus that you do not need to know but is basically because you're expected to incur claims that on policies that have not been written yet slightly quicker than those that have already been written
  • NycxBattleNycxBattle

    I see. I briefly read the source text and its basically using integral of x f (X) over integral of f (x) and when there is different valuation date its different.

    Just to confirm a few things
    1) the AAD (Average Accident Date) concept is only applicable to LRC (not LIC)
    2) we are not expected to the integral calculations and just assume its always 1/3 and use 1/3 directly.

    Are my two assumptions correct?

  • NycxBattleNycxBattle
    edited April 27

    @sofiagiubila

    But the reason is not due to the 3 periods.

    Basically its:

    Let x = future accident date underlying the unexpired coverage relating to 12-month
    policies
    Let f(x) = the loss exposure earned on a given future accident date

    And in this case we are just assuming uniform distribution. So the function is just

    f(x) = 1 - x,
    This is 1 because our policy is 1 year long. If our policy was only 6 months it would be 0.5-x

    The idea is that the earlier the accident happens, the longer our our claims will be.

    For example if the accident happened on Jan 15, 2024. Than claim will start accumulative on Jan 15, 2024. Assuming the liability builds uniformly, it will have 11.5 months / 12 months to accumulate. So for accidents dates that are earlier, it will be bigger. Since we are calculating weighted average accident date. Earlier dates will have a bigger weighting.

    We are simply taking the weighted average of the accidents. But because the accidents in the beginning has a bigger weight, the average accident date ends earlier than the halfway point in this case its 1/3

    Here is visual derivation of the 1/3 from the source text

    The formula to calculate this is just an expression:
    The numerators is
    integral of (x* f(x)) from 0 to 1 (1 because our policy period is 1 year, if it was 6 months this would take the integral from 0 to 0.5)
    The denominator is just integral of (f(x)) from 0 to 1.

    In this case our formula for f(x) is just 1-x by making a simplified uniform distribution. But in reality the function doesn't always have to be 1-x

    @Staff-T1, I know now it's only for LRC. since its for accident date for LIC the accident already happened so its irrelevant.

    Hopefully they only give us 1 year periods that ends on Dec 31. I would hate to do integral calculation on the exam.....

  • JConceicaoJConceicao

    CAS Sample Question 20 on the new IFRS material:

    Why is the 14% cost of capital being multiplied by the cumulative unpaid future cashflows?

    Shouldn't it be multiplied by incremental cash flows? Aren't we otherwise double counting capital needed to be held?

    If I apply this to an extreme example: if insurer pays off 1% of capital per year, they would need to initially hold 100x the capital (excluding discounts).

  • JConceicaoJConceicao

    Is it because the CoC is based on RoE?

  • NycxBattleNycxBattle

    No this is correct, incremental is for margin method. You are mixing the two concepts.

  • Staff-T1Staff-T1
    Regarding the time AAD adjustment:
    1. It is only applicable to the LRC
    2. Yes that's correct. I doubt they would require you to perform this calculation, what more for policies with terms > 12 months. I think it's safe to just memorise that it is going to be 0.33 and then move on.
    Regarding the CoC method:
    1. CoC is based on the ROE method. Using incremental capital as the denominator does not make sense. You're looking for the return on capital deployed here at each time period to calculate your risk adjustment, which is the cumulative remaining capital employed here, not the incremental capital released. Also, this is not unpaid cash flows but capital which is an important distinction to make
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