Actuarial Present Value of Ultimate (S2016 Q14b)

chrisboersmachrisboersma
in CCIR.ARinstr

At a glance this question makes a lot of sense. But later I realized we are never given a formula for Actuarial Present Value of paid claims. (paid + unpaid = ultimate)

What is the Actuarial Present Value of Paid claims?
PV(Paid) + PfAD's
PfAD = 0

PV(Paid) would need to be INCREASED to account for timing of payment.
If @ age 12 mo we would need to calc: Paid x (1 + i)^0.5

APV(paid) is not discussed in materials.

Additional problems (14b):
1. Years in solution are incorrect (2013, 2014 vs 2014, 2015).
2. there should be some investment income on unpaid claims for year 2013 (2750 - 1500)/2 * 0.045 = $28 (half of initial APV unpaid estimate)

Comments

  • grahamgraham
    edited September 2018

    As you noted, PfADs would be 0 for paid amounts. I believe PV(paid) = paid though because you can't earn investment income on paid amounts. That money is no longer in your possession. You might argue that it should be adjusted for inflation if you wanted to know the value of the claim in current dollars. But the actual paid amounts are in the context of the revenue in the time period so there isn't any mismatch or uncertainty in the same sense as there would be for the unpaid if the unpaid were not adjusted for PV & APV.

    You're correct that in 2016.Spring Q14 they mislabeled the investment income calculation. I made a note in the wiki about that.

    On your second point, the investment income for 2013 isn't included because you're evaluating the excess(deficiency) of the unpaid at the end of 2013. It's true there was investment income earned during 2013 but that's now in the past and it doesn't affect the adequacy of the current reserve. (You would only include that if you were calculating the excess(deficiency) for AY2013 as of the end of 2012. But that wouldn't make sense because there are no claims for AY2013 at year-end 2012.) By the same reasoning, if you were calculating excess(deficiency) for AY2013 at the end of 2014, you would not include investment income earned during 2014.

  • yz20190101yz20190101

    Hi Graham,

    in 2016 Spring Q14 Part b): AY 2013, investment income for CY 2013 isn't included in accumulative II asof 2015 YE

    in 2015 Spring Q25: AY2013, Investment income for CY 2013 is included in accumulative II asof 2014 YE

    I'm confused a little here ... so AY of Current CY's "Investment Income" should be included in current CY's calculation or not? I may understand the questions/concept wrong, but could you please verify?

    Thanks

  • javidjavid

    Hi,

    In general, the investment income in the first CY should be included, as was done in Spring 2015.

    When the CAS did the 2016 solution, I think their initial intention was to have a more natural flow from part b) to part c) (the excess/deficiency). The excess/deficiency does not use the first CY investment income, so that's why their part b) did not include that first CY investment income (had they included it, it would have meant that they would have to back it out when they get to part c)).

    So long story short, I would follow Spring 2015 and just lay out any assumptions accordingly.

  • jptardif2jptardif2

    Hi Graham,

    Just to summarize some of the things that are going on here:

    1. Actuarial Present Value Ultimate = Discounted Ultimate?
    2. We are using discounted unpaid to calculate Investment Income?
    3. What is the difference between discounted and undiscouted unpaids?

    Regards,

  • grahamgraham
    edited July 2019

    Hey @jptardif2,

    I think you sort of have it, but you need to be a little more precise:

    1. Let APV = Actuarial Present Value of the claims liabilities, and PV = Present Value of the claims liabilities. It isn't quite right to refer to an ultimate amount as APV because the ultimate amount includes paid amounts, and paid amounts are not given PfADs or discounted. (There is no uncertainty with paid amounts - that money is already out the door. ) You should refer instead to APV of claims liabilities and discounted claims liabilitiies. (The same reasoning applies to premium liabilities.) Also, your statement that APV equals discounted isn't quite accurate. APV includes discounting for the time value of money as well as PfADs but PV includes only discounting of the time value of money. Those 2 quantities are then related by the forumla: APV = PV + PfADs.
    2. To calculate investment income, we're using APV of claims liabilities. Again, this includes both discounting for the time value of money and PfADs.
    3. The difference between discounted and undiscounted unpaids is best demonstrated by a simple example. Suppose the undiscounted unpaid claim liability (also called claim reserve) is $100. Suppose also that it is expected to be paid out 6 months from now and the discount rate is 5%. Then the discounted claim liability is $100/(1.05)^0.5 = $97.59. If you then want to calculate the APV for this liability you would add on an amount for PfADs. This would include claims PfAD, investment return PfAD, and reinsurance PfAD.

    I think sometimes you might see references to discounted liabilities where it's understood this includes PfADs but technically this is not correct. There is a very clear distinction between PfADs and discounting for the time value of money, and they are related by the formula APV = PV + PfADs.

  • jptardif2jptardif2

    You're the man, thank you so much.

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