Analysis of surplus ch 16

Discussion in 'SA2' started by nikita agarwala, Mar 30, 2022.

  1. nikita agarwala

    nikita agarwala Keen member

    Hi,

    I'm getting a but confused with practice exam (Q16.1, iv) solution in the acted book pg 23, in particular the answer for change in basis surplus.
    How is Change in basis surplus = 5,658,822 - 5,114,959 = -543,863? How is it showing negative results when it looks like it should be positive.
     
  2. Em Francis

    Em Francis ActEd Tutor Staff Member

    Hi

    It is because we are looking at a change in liabilities.
    To write this out in full:

    Assets stay the same as haven't changed so change at this step =
    5,347,720 - 5,658,822 = -311,102
    we then have to isolate the impact so deduct the previous step:
    deduct 5,347,720 - 5,114,959 = +232,761

    -311,102 - 232,761 = -543,863
     
  3. kze

    kze Keen member

    Can anyone help me to understand the calculation?

    1. Why do we project forward asset and liability to the end of year using start of year valuation assumptions? Looks like these figures are not used for the surplus breakdown?
    2. In part (ii) the liability at the start of year is 4.09m. Why is this figure used as the value of asset at start of year when calculating the value of asset allowing for actual expense? (first calculation in page 23)
    3. Why there is no change in liability when allowing for actual expense and investment return but only for liability?
     
  4. Lindsay Smitherman

    Lindsay Smitherman ActEd Tutor Staff Member

    Hi

    Re Q1: projecting assets and liabilities forwards to the end of the year on the start of year valuation assumptions gives us the 'expected year end surplus'. This is then the starting point for the next steps of the analysis, which allow us to understand why actual year end surplus differs from that.

    Allocating total assets held at the start of the year into {start year surplus assets} + {assets = start year liabilities} can be a really useful starting point. This is because we can now calculate the {investment return earned on surplus assets} component directly and because if we roll forward {assets = start year liabilities} to the year end using the 'expected' basis, we can check that this amount (roughly) equals year end liabilities. So it helps to validate the analysis.

    The above also addresses your Q2. The {start year surplus assets} are dealt with under the heading 'Start-of-year surplus' near the start of the solution (page 22). This leaves us with just the {assets = start year liabilities} to consider for the rest of the solution: for each step, this is the amount of assets that we project forward, changing one element from expected to actual at a time. [We can see at the bottom of page 22 the point in the paragraph above about checking that the 'expected' roll forward of {assets = start year liabilities} roughly equals the year end liabilities.]

    Q3: A liability valuation looks forward: how much is needed to cover the expected future net outgo on the business being valued. What the company happened to spend as expenses during the past year and what investment performance it happened to achieve doesn't impact that, noting that this is without-profits business. Of course, the company might decide to change its valuation basis as a result of actual expense and investment performance - but this is included in the 'Change in valuation basis' item.

    On the other hand, actual mortality experience during the year will impact the year end liability, because it impacts how many policies there are in-force (and therefore the number of policies for which a liability has to be held).

    Hope that helps clear this up.
     
  5. Tu Doan

    Tu Doan Member

    Hi,

    I want to ask a couple of questions regarding the analysis of surplus and question 1 in this chapter of ActEd book.
    1, The surplus should arise also from the profit margin loaded into the premium, right? I can't find it as a source mentioned in the core reading.
    2, Where is the return on opening surplus in the process defined on pages 9 and 10? I suppose it belongs to bullet number 4 - it is a constituent part of the total economic variance.
    3, On page 23, the solution to question 1 states that 325 is due to a lack of decimal places in the commutation functions. I'm not really satisfied with this statement. The two calculations performed are two different calculations:
    • One uses a retrospective approach (5,107,7647)
    • The other uses a prospective approach (5,107,422)
    Assuming that there is no change in the valuation methodology, I believe that it includes the approach used, i.e., if the liability is currently calculated using the prospective approach, that approach should be used to calculate the liability in the next valuation date unless there is a change in the valuation methodology (which is captured by opening adjustments).
    The retrospective approach and the prospective approach will only be perfectly equivalent if the premium is calculated using the equilibrium principle and the calculation can cover all components loaded into the premium. It is actually not the case for profit margin as gross premium valuation will normally not reflect it into the calculation, which makes the retrospective and prospective approaches different. This difference represents the actual profit margin released over time.
    Therefore, from my point of view, I think the premium of 800 is not the equilibrium premium, covering only mortality and expense. The 325 should be better regarded as the release of profit loaded in the premium.

    My full attempt at this question is as follows:
    https://ibb.co/JB6h1kX
    https://ibb.co/9VKmgQS
    https://ibb.co/thkFKFh

    (I don't know how to attach a doc file here :( )
     
  6. Lindsay Smitherman

    Lindsay Smitherman ActEd Tutor Staff Member

    Yes - I agree.
    An alternative approach which is often used is to do the roll forward process only for an amount of assets equal to the start-period liabilities, and then to determine the return on opening surplus separately.
     
  7. Lindsay Smitherman

    Lindsay Smitherman ActEd Tutor Staff Member

    No, this is not a separate item in the analysis.

    For new business (either regular or single) sold during the analysis period, the profit loading impact is captured in the 'new business contribution' item.

    For single premium business that is in-force at the start of the period, the premium has already been received and so we have also already received the inherent profit loading.

    For regular premium business that is in-force at the start of the period, then (assuming that a gross premium valuation approach is being used) the value of the profit margins have already been recognised in the establishment of the liabilities. The liability value has the present value of all future premiums deducted from it, and thus is reduced by the value of profit loadings within these future premiums - hence contributing towards surplus as soon as the liability is set up. If the liabilities are valued on a best estimate basis, no future surplus would be expected to arise. If they are valued on a prudent basis, future surplus would be expected to arise to the extent of the prudential margins being released. This would be expected to happen as actual experience turned out to be better than had (prudently) been allowed for in the liability valuation, and is included in the experience variances item of the analysis. [Of course, there would also be experience variances in either case, if actual experience turned out to differ from the best estimate.]
     
  8. Lindsay Smitherman

    Lindsay Smitherman ActEd Tutor Staff Member

    I haven't looked at your workings as we can only provide high-level assistance on this forum. However, this seems to be related to the misunderstanding about profit margins, as I have attempted to address in the previous post.

    What this point in the solution is saying is that:
    If we start the year with exactly the right amount of assets to meet our liabilities at that point in time ...
    ... and if everything happens during the year exactly in line with the assumptions made in the liability valuation ...
    ... then we will have exactly the right amount of assets to pay what has to be paid out during the year (net of premiums received) ...
    ... and to cover the year-end liabilities.

    This inherently makes sense: if we hold the right amount of assets to meet our future obligations under a set of assumptions and everything happens the way we expect it to under those assumptions, we should still have the right amount of assets to meet the remaining future obligations.

    In this case, it doesn't quite balance exactly due to rounding and approximations in the factors used.
     
  9. Tu Doan

    Tu Doan Member

    Thanks for your replies, Lindsay. It has been much clearer now :)
     

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