Meaning of "Capitalise future profit" and why using net premium valuation

Discussion in 'SP2' started by Duc Thinh Vu, Oct 23, 2020.

  1. Duc Thinh Vu

    Duc Thinh Vu Active Member

    Hello everyone,
    I'm learning about the difference between net premium valuation and gross premium valuation.
    And I have 3 questions please:

    1. I usually come up with the term "capitalising future profit" and i don't really understand its meaning in the context of net premium valuation and gross premium valuation.
    Could you please explain me ?

    2. For non with-profit traditional life insurance (say, term life for example), I think the Gross Premium Valuation is more prudent because it takes into account the future expense.

    But in other view, the Gross Premium reserve is less than Net Premium Reserve. So in terms of quantity, the Net Premium is more prudent.
    So what type of valuation method should i use in this case ?

    3. For with-profit insurance contract, i am wondering why should we care whether the future profit is capitalised at outset or not ?

    Thank you all for your help!
     
    Duc Thinh Vu, Oct 23, 2020
    #1
  2. Mark Willder

    Mark Willder ActEd Tutor Staff Member

    Hello Duc

    Let's look at your questions in turn.

    1. The office premium that the policyholder pays will include a profit margin. If we use a gross premium valuation, then this is the present value of the claims and expenses less the office premiums. So when we are calculating the reserve at the start of the contract, we are deducting the full value of all the premiums, including the profit margin, from the reserve. Contrast this with a net premium valuation which only deducts the value of the net premiums. Net premiums do not include a profit loading and so are smaller than gross premiums (all other things being equal). This means that net premium reserves are larger than gross premium reserves by an amount equal to the profit loadings. So the gross premium reserve has capitalised the profit loadings on day 1, ie the profits all emerge at the start of the contract. In contrast, if we use a net premium valuation, we've assumed that the small net premium would be paid, but will actually receive the larger gross premium, so each year we make a profit equal to the loadings in the gross premium.

    2. Both valuation methods allow for expenses. A gross premium valuation allows for expenses explicitly. A net premium valuation allows for expenses implicitly because the net premium only covers claims, so each year we have some surplus because the actual office premium received is bigger than the net premium we reserves for, and this difference covers the expenses. So with respect to expenses, it doesn't matter so much which method to use. In practice the method we use should be the one that the regulations specify. Usually this will be a gross premium reserve as they are more realistic - net premium reserves are rather artificial as they don't explicitly allow for expenses or the actual premium paid.

    3. For with-profits contracts, we will use the profit emerging each year to declare bonuses. If all the profit emerges at the start of the contract, then we could in theory declare a very big bonus on day 1 and no bonuses thereafter - this would be wrong in many ways. So a more gradual release of surplus year on year fits well with the idea of declaring bonuses year on year.

    I hope these help, but do let me know if you have other questions.

    Best wishes

    Mark
     
    Mark Willder, Oct 23, 2020
    #2
  3. Duc Thinh Vu

    Duc Thinh Vu Active Member

    Hello Mr. Willder,
    Thank you very much for your help. It enlighted 90% of my problem.

    I would like to confirm with you 2 points:

    1. The meaning of capitalisation of future profit.
    By definition, does it mean "turning the future profit into CURRENT profit?"
    How should i understand its logic ?

    2. The definition of "prudent" between different method of reserving.
    How should "prudent" be defined ? Prudence is to follow the reality as closely as possible, or it should give a higher reserve amount, or should i understand it with different meaning ?

    Thank you very much for your kind support.
     
    Duc Thinh Vu, Oct 23, 2020
    #3
  4. Mark Willder

    Mark Willder ActEd Tutor Staff Member

    Hello Duc

    1. Yes, capitalising future profit means turning future profit into current profit. So a net premium valuation may lead to a profit of 10 each year for 10 years. A gross premium valuation might then capitalise this as a profit of 100 at outset (ignoring the impact of discounting and so on).

    2. A prudent valuation would overvalue the liabilities compared to a best estimate. We could make both net and gross premium valuations more prudent for an endowment assurance by assuming a low rate of interest or high mortality rate. It's impossible to say which valuation method is most prudent without knowing what basis is being used. Your point on the expenses doesn't help us with prudence as both methods allow for expenses either implicitly or explicitly. When I said that a gross premium valuation was more realistic, I didn't mean that it gave a best estimate - I just meant that a net premium valuation is a poor model of reality as it ignores expenses. Ignoring expenses in our model can be a problem as it gives us no control over what allowance is made for expenses, eg we can't increase the expense assumption if inflation turns out to be higher than assumed when pricing the product.

    I hope that helps to clarify things, but do let me know if not.

    Best wishes

    Mark
     
    Mark Willder, Oct 23, 2020
    #4
  5. Duc Thinh Vu

    Duc Thinh Vu Active Member

    Hello Mr. Willder,
    Thank you again for your kind reply.
    There is still 1 point that is not so clear to me.

    It is that there is no profit in the following year when we use the gross premium valuation method.
    Personally, i think, for example, in year 2, the client pays Premium = P. In P, there is a portion of money to cover risk, another portion of money to cover expense and another portion of money to for the profit margin.
    (provided that I calculated the premium P by this equivalent equation:
    Expectation(Total Premium) = E(total claim benefits) + E(total expense) + E(profit)
    and taking profit = (for example) 10% gross premium)

    So I think there will be the profit each year following the first year.

    Am I wrong in something? Please correct me.

    Thank you very much for your help. Have a nice weekend!
     
    Duc Thinh Vu, Oct 23, 2020
    #5
  6. Mateusz

    Mateusz Active Member

    Hi Duc,

    The definition of 'profits' in such a context would normally include change in reserves.

    Prof(t) = P(t) + I(t) - C(t) - E(t) - dR(t), where dR(t) = R(t) - R(t-1) is the change in reserves over period (t-1,t]

    Let's have a look at a single contract assuming gross premium reserves are used and assumptions in the valuation basis are borne out in practice.

    Year 1:
    Change in reserves is just the reserve at t=1, and this can be calculated (ignoring interest for simplicity) as:
    R(1) = [C(2)+...+C(n)] + [E(2)+...+E(n)] - [P(2)+...+P(n)]
    If we now put it into the profit definition above we'll get:
    Prof(1) = Sum of premiums - Sum of claims - Sum of expenses, where we're adding up cash flows over the whole duration of the contract (years 1 to n).

    Year 2:
    Change in reserves is now equal to dR(2) = R(2) - R(1) = P(2) - C(2) - E(2)
    Hence Prof(2) = P(2) - C(2) - E(2) - [P(2) - C(2) - E(2)] = 0
    So in year 2 and beyond we recognise no additional profits; this is all assuming that experience turns out exactly as in the valuation basis (meaning actual premiums, claims, etc are exactly the same as assumed in the reserve calculation).

    There are various reasons why in years 2+ we can have profits higher or lower than 0 (actual vs expected variance, change in assumptions, etc.), but this example is simplistic on purpose and does not cover all important aspects.
     
    Last edited: Oct 24, 2020
    Mateusz, Oct 24, 2020
    #6
  7. Mark Willder

    Mark Willder ActEd Tutor Staff Member

    Thanks for the great explanation Mateusz. Yes, it's all down to the increase in reserves in the profit formula.

    I useful fact to remember is that profit at outset depends on the difference between the pricing basis and the reserving basis. Profit at later times depends on the difference between the actual experience and the reserving basis (the pricing basis is no longer relevant). If actual experience is exactly the same as the reserving basis, then there is no profit.

    Best wishes

    Mark
     
    Mark Willder, Oct 26, 2020
    #7

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