MCT - Interest Rate Risk Sping 2016 Q 13

edited September 2018 in OSFI.MCT

Hi,
I can't seem to figure out how the unearned premium amount of $5000, as well as how why the maintenance cost must be discounted using time 0.292. Could some clarification be provided for this?

Thanks!

Comments

  • The unearned premium amount of 5,000 is based on the written premium of 10,000 and that the exposures are written uniformly over the whole year. They just made the rough assumption that the unearned would equal half of the written.

    The part about the discounting with the 0.292 is based on an earlier version of the premium liability calculation. You can see both this version and the new version in CIA.PrLiab. There is no reason, however, to study the old version. The new reading was put on the syllabus for 2017.Fall, so any exam before that would have the old method.

    This highlights something that can be very frustrating about the examiner's reports. There are solutions from older exams that are no longer valid, but someone studying the material for the first time would have no way of knowing this.

  • Hi Graham,
    Following your discussion with daniell4nan, I have two more questions/findings of the corresponding examiner's reports (please ignore if they are no longer relevant to new version as your CIA.Prliab doesn't mention maintenance calculation):
    1. As the question states maintenance is earned when unearned premium is earned and it takes 4 yrs to collect unearned premium, how come maintenance is collected fully in first year?
    2. When it comes to step (4) of interest rate risk margin calculation, all other items are using APV values while maintenance expense is using an undiscounted value of $300. Why aren't they consistent?

    Thanks

  • Page 8 of premium liabilities:

    Discounting for Time Value of Money....With regards to the time value of money, the cash flows other than losses and loss adjustment expenses (i.e., reinsurance costs and maintenance expenses) would also be considered but are not generally material to the calculation of the premium liabilities.

    So yes you're correct, but it's much simpler to ignore that aspect and not discount those two pieces (reinsurance & maintenance).

  • Thanks chrisboersma for answering about the time value of money on point 2 from christinedu. (Actually, it looks they did discount the maintenance expense in the examiner's report, but I would not have bothered because it isn't material.)

    For point 1, they told you the maintenance was 3% of written premium, so the implication is to use the whole 10,000 x 3% = 300 immediately in 2015. It was a bit confusing for them to then say in the next line that it's paid during the earning of the unearned premium. (By the way, I think it would take just 2 years to earn the premium that was written in 2015 rather than 4.)

    If you look at similar questions in subsequent exams, they definitely got easier. The main things you have to know are:

    • calculating the discount rate from the bond portfolio
    • APV and duration of claims liabilities
    • APV and duration of premium liabilities
    • how to tie it all together to calculate the interest rate risk margin
  • Hi Graham,

    I'd like to validate the new method for discounting the maintenance cost in this question.

    Would the 0.2929 simply be replaced by (0.5 - (1/3)) and the rest of the calculation would stay the same?

    Thank you!

  • edited October 2018

    Not quite. The original calculation is:

    • 300 / (1+discount rate)^(0.2929)

    The new calculation would be

    • 300 / (1+discount rate)^(1/3)

    The reason the exponent is (1/3) not (0.5-1/3) is that you have to adjust the APD, or Average Payment Date, by (0.5-1/3). The APD is 0.5, so the result is:

    • 0.5 - (0.5-1/3) = 1/3
  • The discounting of maintenance expenses using the calculation from the new version of the paper is actually illustrated in the supporting Excel file for CIA.Duration. See sheet 'App A Sh4'.

  • Thx. I've inserted a link to that file in the wiki here:

    (I believe you should still be o.k. not discounting the maintenance expenses though.)

Sign In or Register to comment.