Reserves

Discussion in 'CA1' started by barney, Apr 5, 2009.

  1. barney

    barney Member

    how do you know if a contract has low reserves or large reserves?

    e.g. in questions on Assumptions, it says term assurance contracts have low reserves so investment return isn't very important. but what if, say endowment assurances, came up? do they have low or high reserves and how do you know?
     
    barney, Apr 5, 2009
    #1
  2. fischer

    fischer Member

    I think we would need to look at the benefits being paid out. If there is a benefit on maturity then the contract will have a high reserve. This I believe holds true for both conventinal and unit-linked products.

    So,
    Term assurance - low reserve as only death benefit within term of contract.

    Endowment - increasing from low to high reserve as death benefit within term of contract but also a maturity benefit on survival to end of contract.

    Whole life - increasing from low to high reserves as only death benefit is paid. At higher ages, probability of death is higher (i.e. higher mortality) so more likely to make a payout and so higher reserves at later durations.

    Immediate annuities - not sure. I think the reserve = the PV of all future annuity payments. So, as you move through time this PV will reduce and so reserves will decrease.

    Hopefully someone can throw some more light on this.
     
    fischer, Apr 6, 2009
    #2
  3. Anna Bishop

    Anna Bishop ActEd Tutor Staff Member

    I find it helpful to think about how you would calculate a reserve.

    Term assurance, 100K sum assured, 20yr term

    Net premium reserve = PV future benefits - PV future premiums

    = 100,000 [prob die in Year 1 + prob survive Year 1 and die in Year 2 + prob survive Years 1 and 2 and die in Year 3 + ... + prob survive Years 1 to 19 and die in Year 20] - PV future premiums

    In the formula, although 100,000 is a big number, the probabilities of dying (the q factors) will be small, unless you are looking at someone very old or infirm. So the reserve ends up being quite small.

    Now consider an endowment assurance, 100K sum assured, 20 yr term

    Net premium reserve = PV future benefits - PV future premiums

    = 100,000 [prob die in Year 1 + prob survive Year 1 and die in Year 2 + prob survive Years 1 and 2 and die in Year 3 + ... + prob survive Years 1 to 19 and die in Year 20 + prob survive Years 1 to 20] - PV future premiums

    Note the extra term in the formula: prob survive Years 1 to 20. This will be quite large unless you are looking at someone very old or infirm. So the reserve ends up being quite big.

    An annuity gets paid on survival, so again, reserve will be big. I'll leave you to try and work out a formula for it.

    UL policies work a bit differently. You have a unit reserve = bid value of units and a non-unit reserve, which is effectively the PV of future expenses less the PV of future charges.

    In general though, there are fewer guarantees involved with UL policies so less need for caution, margins in assumptions. This tends to reduce the capital requirements relative to non-linked policies.

    Hope this helps.
     
    Anna Bishop, Apr 6, 2009
    #3
  4. saurabh_act1984

    saurabh_act1984 Member

    Reserves for new business??

    If Reserves are just equal to the 'PV of future benefits - PV of future Premiums' then why do we need to hold large reserves for writing new business.... because the above eqn should not give big value unless the basis is very prudent?

    Also if the basis of valuation of liabilities is same for pricing and the reserving..then the reserves requires should be zero. because the premiums are also calculated by the above formula(and loadings on top of that)

    Can anybody help?

    Thanks
     
    Last edited by a moderator: Apr 8, 2009
    saurabh_act1984, Apr 8, 2009
    #4
  5. phantom

    phantom Member

    on Day Zero, when the policy is written:

    i. PV(premiums)>PV(benefits) – by an amount equal to the profit you expect to make – if valued on pricing basis which is usually best-estimate
    ii. PC(premiums)<PV(benefits) – by an amount you would need to hold reserves for – if valued on reserving basis which is usually prudent

    yes you are right, if reserving basis is weak, so that it is best estimate, then reserves will not be required – as rather than expecting a loss, you will expect to make a profit
     
    phantom, Apr 8, 2009
    #5
  6. Gordon Gekko

    Gordon Gekko Member

    The insurance company is more like a bookie than an exchange. The "less" risky subsidize the "more"risky. Mathematics and real life do not always relate so rate makers have to have sufficient solvency capital just in case the "unexpected" negative events happen.
     
    Gordon Gekko, Apr 10, 2009
    #6
  7. Mark Willder

    Mark Willder ActEd Tutor Staff Member

    The regulator is looking to protect policyholders. So the valuation basis will need to be very strong/cautious to ensure that the reserves are large enough to cover the claims even if adverse events occur.

    The premium basis will be much less cautious. Hence the first premium is generally insufficient to cover the costs of the initial expenses and setting up the reserves. So the insurer incurs a loss at outset (referred to as new business strain). However, we expect that the actual experience will turn out to be much better than the valuation basis and profits will emerge in later years.

    Best wishes

    Mark
     
    Mark Willder, Apr 15, 2009
    #7
  8. saurabh_act1984

    saurabh_act1984 Member

    Thanks to all guys who have replied to my query.
     
    saurabh_act1984, Apr 15, 2009
    #8

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