2019 Spring Q13

Tony88passTony88pass
in OSFI.MCT

The Net premium liabilities duration of 1.8 given in the question seems to be the effective duration rather than modified duration, the solution used it directly in calculating the interest rate risk margin, is that correct, shouldn't we use the modified duration?

Comments

  • grahamgraham

    Either is acceptable according to the CIA.Duration source text. See the following section of the wiki:

  • Tony88passTony88pass

    Thanks!

  • sant93sant93

    a few questions:
    1) Might be a silly question, but shouldnt we also have t = 3.5 in the table to account for payments during year 36-48?

    2) Why do we need to calculate the PV @2.5% in the table? It looks like we use it to determine the unpaid claim liab?

    3) I thought capital requirement calculation will use discounted claim & prem liab but will exclude PFADs. However, in the solution... we have multiplied the claim liabilities by 12% MFAD factor?

  • grahamgraham

    Hi,

    question (1)

    • There are no silly questions here! This reading is long and complicated and you really have to grind to learn it well enough for the exam.
    • The reason there is no t = 3.5 is that the discounting takes the unpaid amounts back to age 12, not age 0. That means the 12-24 interval uses t = 0.5 to get from the midpoint of the year back to age 12.
    • Then 24-36 uses t = 1.5 and 36-48 uses t = 2.5.
    • (But note that for premium liabilities, it's different. If you had that same payment pattern for premium liabilities, you do want to discount back to age 0, so you would indeed have t = 3.5 for the 36-48 interval.)

    question (2)

    • The reason for the PV@2.5% column is so you can calculate the interest rate PfAD (investment return rate is the same thing as interest rate.)
    • The given rate is 3.0% and the investment rate MfAD is 0.5% so you also need the PV at (3.0% minus 0.5%) or 2.5%
    • When they calculate APV = 96,383 + (95,690 x 12%) = 107,866, they used PV@2.5% which might be confusing because they are doing 2 steps at the same time.
    • The 96,383 is the PV@2.5% but you could also have calculated the APV as:
    • APV = 95,690 + (96,383-95,690) + (95,690 x 12%) which is the same thing. The quantity (96,383-95,690) = 693 is just the investment return PfAD, but you don't calculate that directly. Instead you calculate PV@2.5% and it automatically incorporates the investment return PfAD.

    question (3)

    • The MCT calculation requires the APV (Actuarial Present Value) of the unpaid claim liability.
    • The APV can be expressed as PV + PfADs, and there are 3 PfADs: claims development, investment return rate, and reinsurance.
    • This company didn't seem to have any reinsurance for 2017 and no reinsurance MfAD was provided so the APV for unpaid claims incorporated only claims development MfAD and investment return MfAD.
    • (This company did however use reinsurance for 2018 but that part of the calculation pertained to the premium liabilities, which is covered later in CIA.PrLiabs. In this problem, you were given the premium liabilities so you didn't have to go through that very long calculation.)
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