The median may be a reasonable approximation of the mean accident date. The median accident date is calculated using simple trigonometry assuming premiums and losses are uniformly distributed and the sides of the UPR triangle are set equal to 1.00. The equation to solve for the length of the triangle sides, x, that yields half the area of the triangle or ¼ would be ½ x^2 = ¼ or x = √0.5. Note that the length of the triangle side is defined here as the time from the median accident date to the end of the period or time 1. Therefore, the desired timing from time 0 (or the valuation date) to the median accident date would be the complement or 1 - √0.5 or 0.2929 years.
Page 9 of Premium Liabilities.
However, the mean (1/3) is much easier to calculate and remember. So use that. The previous problems used the median & an adjustment for cumulative claims paid that is no longer part of the "Premium Liabilities" section (so the 0.2929 will not likely be used going forward). Read the Premium Liabilities section (here) for details.
This value of 0.2929, which is actually 1-sqrt(2)/2, is from an old version of the premium liability calculation. You do not have to know this. The new version of premium liability calculation came on the syllabus for the 2017.Spring exam. Any exam from 2016.Fall and prior would have the old calculation, which you can ignore. This is explained in detail in the wiki article:
Could you please provide the final answer with the latest calculation? Makes checking our answers easier/faster... Ideally also the subpart for premium liabilities duration. Could put it in the battle card answer where it currently says "see examiner's report". Thanks!
I've also recalculated the final answer at the link above. The new method changed the capital required for interest rate risk from 1,005 to 975. (And the answer has been included in the BattleCards instead of referring you to the examiner's report.)
We assume Maintenance = 0 due to making problem possible (otherwise impossible).
I'm sure if you assumed maintenance = 200 you'd probably get a technically "correct" answer, but don't make questions more difficult if you don't have to.
Note: APV(Premium Liabilities) could also include costs related to re-insurance (future) or policy maintenance (future) and unearned commissions. But we'll assume those are Zero for this problem.
Will it be correct if we don't take weighted avg of liability (duration) like done in examiner report -> instead find Change (Premium liab), Change (Claim liab) and than Change (liab) = Change (prem liab) + Change (claim liab)
Also for Change (assets) is this ok to do: (40000x2x1.25% + 9000x4x1.25%)
The answer is different if i take the above approaches - so wanted to ensure if it's still valid.
thanks!
Your method looks fine to me. You would normally get the same answer but the examiner's report used the old method for calculating premium liabilities. That should be the only reason you get a different answer with your method.
Comments
Page 9 of Premium Liabilities.
However, the mean (1/3) is much easier to calculate and remember. So use that. The previous problems used the median & an adjustment for cumulative claims paid that is no longer part of the "Premium Liabilities" section (so the 0.2929 will not likely be used going forward). Read the Premium Liabilities section (here) for details.
See Spring 2018 Q14
This value of 0.2929, which is actually 1-sqrt(2)/2, is from an old version of the premium liability calculation. You do not have to know this. The new version of premium liability calculation came on the syllabus for the 2017.Spring exam. Any exam from 2016.Fall and prior would have the old calculation, which you can ignore. This is explained in detail in the wiki article:
Hope that helps!
Could you please provide the final answer with the latest calculation? Makes checking our answers easier/faster... Ideally also the subpart for premium liabilities duration. Could put it in the battle card answer where it currently says "see examiner's report". Thanks!
Hi,
Have you seen this
http://www.battleactsmain.ca/wiki6c/2016.Fall_Q15_Redone
It goes through the modifications that need to be done under the new method. Also question 14 of https://www.casact.org/admissions/studytools/exam6c/sp18-6C.pdf has a full detailed answer under the new method.
I've also recalculated the final answer at the link above. The new method changed the capital required for interest rate risk from 1,005 to 975. (And the answer has been included in the BattleCards instead of referring you to the examiner's report.)
How come the APV of premium liabilities is simply UEP-DPAE=12000-1248=10752? Why don't we need to discount this like it was done in 2018 Spring Q14?
Short answer: Max DPAE is already accounting for all discounting.
OR
The question is merely re-arranged as
Correct Equation:
We assume Maintenance = 0 due to making problem possible (otherwise impossible).
I'm sure if you assumed maintenance = 200 you'd probably get a technically "correct" answer, but don't make questions more difficult if you don't have to.
Note: APV(Premium Liabilities) could also include costs related to re-insurance (future) or policy maintenance (future) and unearned commissions. But we'll assume those are Zero for this problem.
Premium Liabilities = Maintenance (future) + Reinsurance (future) + Claims (future)
In general. Premiums should include unearned (reinsurance) commissions.
Will it be correct if we don't take weighted avg of liability (duration) like done in examiner report -> instead find Change (Premium liab), Change (Claim liab) and than Change (liab) = Change (prem liab) + Change (claim liab)
Also for Change (assets) is this ok to do: (40000x2x1.25% + 9000x4x1.25%)
The answer is different if i take the above approaches - so wanted to ensure if it's still valid.
thanks!
Your method looks fine to me. You would normally get the same answer but the examiner's report used the old method for calculating premium liabilities. That should be the only reason you get a different answer with your method.