Ch1

Discussion in 'SP2' started by Actuary@22, Aug 27, 2022.

  1. Actuary@22

    Actuary@22 Very Active Member

    Hi

    Please explain why the solution to the question on page 16 of chapter 1 as per Acted 2019 material, states that "
    The determination of [claim cost] – [asset share] might ignore the cost of capital. The actual loss to the shareholders should include the opportunity cost of holding reserves".

    The asset share would already factor in the cost of capital as per my understanding.

    Thanks.
     
    Actuary@22, Aug 27, 2022
    #1
  2. Nico D

    Nico D Member

    An ACTED tutor might be better placed to answer this, but...

    I think the notes are just trying to say IF the cost of capital is NOT factored into asset share, then the difference between claim and asset share not not the same as the profit or loss to the shareholders.

    Generally speaking Asset Share is the level of assets owned by the policy holder.

    Shareholders provide capital to cover any short fall between reserves needed to support the policy and the asset share.
    The return required by the shareholders, i.e. the cost of capital, is a deduction to the asset share.
    { [ (AssetShare t=1) + (Premium @t=1) ] * [1+InvestmentReturns(t1 to t2] } - Cost of Capital = AssetShare t=2

    So for example:
    asset share (t=1) = 1,000
    reserves required = 1,200

    shareholder capital = 200
    cost of capital 5% (ie 10)

    ignoring any premiums, investment returns etc. then
    asset share (t=2) = 1,000 - 10 = 990

    claim (t=2) = 1,100

    thus [claim] - [asset share] = 1,100 - 990 = 110

    pre claim share holder assets (t=2) = 210 (prior to claim, i.e. 200+5%)
    post claim share holder assets (t=2) = 210 - 110 = 100 (i.e. after claim a loss of 110)​

    I think the two sentences you refer to in the notes, means that if the calculation of [claim] - [asset share] ignores cost of capital then we would just have 1,100 - 1,000 = 100, however this is not the actual loss to share holders. They lose the 100, but also the 10 they were expected to gain from supplying 200 in capital. So their actual loss is 110, not 100.
     
    Nico D, Aug 30, 2022
    #2
  3. Lynn Birchall

    Lynn Birchall ActEd Tutor Staff Member

    Hi both

    Yes, the solution in Chapter 1 is just trying to say that if the cost of capital is NOT factored into asset share, then the difference between claim and asset share are not the end of the story when considering the profit or loss to the shareholders.

    As you say @Actuary@22, the asset share could / should already factor in the cost of capital. But this is Chapter 1 and so the course hasn't considered asset shares in detail at this stage, the solution is just pointing out that if the asset share hasn't allowed for the cost of capital, then our assessment of profit/loss should allow or it.

    Keeping our numbers simple: suppose we have a policy that pays a death claim of 10,000 at a point when the reserve is 3,000 and the asset share is 2,000.
    We can say that 10,000 - 2,000 = 8,000 is the loss on the policy.
    If the determination of the asset share allowed for the opportunity cost of having to supply that extra 1,000 of capital to back the reserves, then that's the end of the story.
    But, if the asset share did not include this deduction for the cost of capital, then the loss is actual loss is more than 8,000 (ie we should allow for the cost of capital at this point).

    Hope that clarifies / reassures
    Lynn
     
    Lynn Birchall, Aug 31, 2022
    #3

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