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Asset Share

Discussion in 'SP2' started by sadie1990, Apr 23, 2013.

  1. sadie1990

    sadie1990 Member

    Can someone describe to me what the asset share of an annuity and deferred annuity would look like?

    I gather it would be largely positive initially due to a significant single premium payment?

    Thks for any help.
     
    sadie1990, Apr 23, 2013
    #1
  2. Iori_

    Iori_ Member

    I would imagine so?

    Asset share build-up initially would look something like [Single premium - initial expenses] x (1+i) - First month annuity payment] / (1-q(x+1))], assuming annuity is paid at end of month?
     
    Iori_, Apr 23, 2013
    #2
  3. Mark Willder

    Mark Willder ActEd Tutor Staff Member

    Iori's formula looks good.

    So for an immediate annuity, the asset share will start off large. Over time it will gradually fall as the annuity payments and expenses will exceed the interest earned. Hopefully when the last person in the cohort has dies, the asset share will be slightly positive reflecting the profit to the insurer.

    For a deferred annuity, the asset share will start small (particularly if regular premium) and then grow over time with investment return. Then when the annuity starts to be paid the asset share will fall (in the same way as an immediate annuity).

    Best wishes

    Mark
     
    Mark Willder, Apr 24, 2013
    #3
  4. sadie1990

    sadie1990 Member

    Thanks for replies, makes sense!
     
    sadie1990, Apr 24, 2013
    #4
  5. Helloall

    Helloall Very Active Member

    Hi Mark,

    I was just wondering if i could query this equation -

    [Single premium - initial expenses] x (1+i) - First month annuity payment] / (1-q(x+1))]

    why wouldn't the equation be -

    [Single premium - initial expenses] x (1+i) - First month annuity payment*(1-q(x+1))] / (1-q(x+1))]

    or written another way

    Single premium - initial expenses] x (1+i) - First month annuity payment*(1-q(x+1)) +AS*q(x+1)

    which would mean that the asset share is equal to the single premium minus initial expenses - payment made at the end of the year + the asset share released at the end of year on policyholders who die minus the annuity payment these dead policyholders didn't receive.

    Does this make sense or am i way off the mark?
     
    Last edited: Mar 23, 2022
    Helloall, Mar 23, 2022
    #5
  6. Mark Willder

    Mark Willder ActEd Tutor Staff Member

    Hi

    Yes, your equation is better. If the annuity is paid in arrears then we should have the 1-q_x term to allow for the benefit only being paid to survivors. I think it should be q_x rather than q_(x+1).

    Best wishes

    Mark
     
    Mark Willder, Mar 24, 2022
    #6

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