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Revalorisation method

Discussion in 'SA2' started by PhamThinhLe, Nov 17, 2019.

  1. PhamThinhLe

    PhamThinhLe Member

    Under the revalorisation method, the profit, or surplus, to be distributed to a particular contract is expressed as a percentage of that contract’s supervisory reserve. Does this implicitly mean that the supervisory reserve requirements of that particular jurisdiction has to have some particular properties in order for the method to actually achieve the goal of sharing the "investment" profit of the contract?

    Let's say we have for example a contract that has 2 years term, pay 1 if the policyholder dies, no expense, no surrender... Suppose actual experience of the company in year 1 is 0.5 premium, 0.5*0.07 = 0.035 investment income, 0.3 claim, in year 2 is 0.7*0.5 = 0.35 premium, 0.35*0.05 = 0.0175 investment income, 0.1 claim. Suppose at the start of year 1, the reserve requirement is 0.6 and at the end of year 1, the reserve requirement is 0.42. So immediately from the pure numbers alone, it is not very clear what is the "investment profit" of the fund is supposed to be here. For "actual investment return", I imagine it is the 0.07 but what exactly is supposed to be the "expected investment return"? In the first place, there is no reason why a reserve requirement has a "expected investment return" concept to begin with, for example it might well be just SA multiplied by a set probability of death, or simply a requirement to hold exactly the annual premium. Also, apparently the reserve requirement must be such that the increasing premium and SA by x% leads to exactly an x% increase in reserve --> this might not be necessarily the case. For example, the reserve calculation can be to simply hold the Asset Share, or E[ max((Asset Share + Premium) * return, SA) ].

    Also why is it that "insurance profit is defined as the surplus arising on actual experience being better than expected in the valuation basis"? Again, the reserve requirement can be just to hold the annual premium in which case there is no "expected" concept to begin with. Even if there is an "expected", it can be totally arbitrary.
     
    PhamThinhLe, Nov 17, 2019
    #1
  2. Em Francis

    Em Francis ActEd Tutor Staff Member

    Hi
    Whenever we talk about expected in this content, we are referring to the valuation basis. Even if the reserve is approximated, by holding x% of asset share for example, it would still have been initially calculated with an expected basis, otherwise how would the company know how much to set aside to meet the corresponding liabilities?
    For example, for an assurance product: V = SA x (Assurance factor) - Prem x (annuity factor):
    The expected investment return would be whatever is assumed within these factors. A company could always use the investment return assumption within its pricing basis (so long as this is prudent) as this is expected and should be close to the reserves which need to be held.
    The reason why a company would only distribute the difference between actual and expected is that the expected return will be needed to cover the reserves, any excess can go to the policyholder (subject to the k factor).
     
    Em Francis, Nov 21, 2019
    #2
  3. PhamThinhLe

    PhamThinhLe Member

    My apologies but "valuation basis" here does not mean anything. Every jurisdiction has a different valuation basis. Even your own course notes have different "valuation basis"! Are the assumptions best-estimate? Are the assumptions best-estimate with margin? Are the assumptions specified by the government? Active valuation? Passive valuation? Are the investment return assumptions risk neutral or real world? Are you telling me that the revalorisation method will work regardless of what exactly is the "valuation basis"?
     
    PhamThinhLe, Nov 24, 2019
    #3
  4. Em Francis

    Em Francis ActEd Tutor Staff Member

    Hi

    Hi

    Revalorisation is used in conjunction with a traditional prudent prospective valuation. So even if now companies have moved to Solvency II using best estimate, the existing policies would likely have been written under pre Solvency II rules.
    Historically the pricing basis and valuation basis were always the same in mainland Europe.

    Hopefully a numerical example will help:
    The products are often endowment assurances used primarily for savings. So expenses and mortality costs are relatively small compared to the investment component and so we'll ignore expenses and mortality for simplicity.

    Imagine an endowment with 2 years to go, with sum assured of 10,000 and annual premium of 450. We will assume a prudent investment return of 2% in our valuation. The reserve just after the premium has been paid is then:
    Reserve start of year = 10,000 / (1.02)^2 - 450 / (1.02).
    If we actually earned 2% on these reserves we would have:
    {10,000 / (1.02)^2 - 450 / (1.02)} x 1.02 =10,000 / (1.02) - 450
    which is exactly the right amount of money to set up the reserve just before the premium is paid at the end of the year.
    So if actual experience is the same as that expected on the valuation basis we have no profit or loss.

    However, as the reserves are prudent we might actually get 3% investment return giving us:
    {10,000 / (1.02)^2 - 450 / (1.02)} x 1.03 = end of the year reserve x 1.03/1.02

    So we have approximately an extra 1% more of assets, so we can afford to increase the reserve by 1%. The reserve will go up by 1% if we increase both the sum assured and the premium by 1%. So the new reserve will be:
    10,000 x 1.01 / (1.02) - 450 x 1.01

    Hope this helps.
    Thanks
    Em
     
    Em Francis, Nov 28, 2019
    #4

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