Spring 2016 Q22 - Part a & c

Comments

• Graham

  March 2022

  Here are a few general comments before I get to the actual solution:

  • The examiners report did say this was a difficult problem and that candidates scored poorly with many not even attempting it. There are usually 1 or 2 problems like that on every exam so don't let it worry you too much.
  • This is a good example where time management is very important. Assuming 60 total points on a 4-hour exam (240 minutes), you can allocate 240/60 = 4 minutes per point. This question is 2.25 points so you should spend roughly 9 minutes on it. Even if you can't solve the problem completely, you can probably get something, even if it's only 0.25 pts. But make sure you don't spend more than 9 minutes because that would take time away from other problems which may be easier. YOU HAVE TO AT LEAST ATTEMPT EVERY PROBLEM ON THE EXAM.

  Anyway, In part (a) this problem, the key is somehow incorporating the fact that the legal fees in the ALAE triangle are 50% lower starting Jan 1, 2015. I think the second answer is the most clever because it gets right at the heart of the issue. I probably would have explained it more fully as follows: Without the 50% reduction, the ALAE triangle would have looked like this:

  

  You can see pretty easily that the ultimate ALAE for each AY would have been 2,700. The question also gives you the paid ALAE for each AY, so you can calculate what the unpaid ALAE would have been as (2,700 - latest diagonal) and you get:

  

  Now you can easily incorporate the 50% reduction by dividing all of these unpaid ALAE amounts by 2. Or even simpler, just divide the total by 2 to get 3,850/2 = 1,925. The reason this works is the problem tells you that going forward, all these (original) unpaid ALAE amounts will be 50% lower. It might take several minutes to realize all this, but I think that's the best solution. I suspect the examiners did not think of that solution because it seems too short for 1.0 points. I suspect they had in mind sample answer 3.

  I will do another post for part (c).
• Graham

  March 2022 edited March 2022

  (See above for part (b). For part (c) where you have to comment on the reasonableness of the ULAE estimate, here's how I thought through it:

  • The standard assumption for the classical ULAE method is that 50% of the cost is incurred when the claim is opened and 50% when the claim is closed. Here they tell you explicitly that prior to the change, this assumption holds.
  • When they ask you to evaluate the reasonable of the ULAE estimate from part (b), they are really just asking you to evaluate whether this 50/50 assumption still holds.
  • There are essentially 3 possibilities: (1) The 50/50 assumption still holds and the estimate in part (b) is ACCURATE. (2) The 50/50 assumption does not hold, and the estimate is TOO HIGH. (3) The 50/50 assumption does not hold, and the estimate is TOO LOW.

  So you have to figure out which is those is correct:

  • Let's focus on claims that were opened prior to the change but not closed until after the change.
  • When these claims were opened, the 50/50 assumption still held so let's just say for the sake of argument that it cost $50 in ULAE to open a claim. If there had been no change in operations, it would then have cost another $50 in ULAE to process and close the claim.
  • But under the new system, ULAE has increased due to greater use of internal legal resources. So it will now cost MORE than an additional $50 to process and close the claim. So the 50/50 assumption no longer holds.
  • Even if you try to adjust the ULAE ratio to account for the 30% increase in overall ULAE costs as the sample solutions in part (b) did, the classical method still has the 50/50 assumption embedded in it and will likely produce an estimate that's too low. (Of course, if you chose a REALLY high ULAE ratio in part (b) you could possibly get an accurate unpaid ULAE estimate but I don't think any of the sample answers from part (b) did that.)

  Hope that helps.
• StudyFor5

  March 2022

  Thanks Graham, that was super helpful! I feel much better. I think I got so accustomed going to the ratio approach for ALAE reserve questions that I didn't even consider the possibility of just using the Paid ALAE triangle. So I fell into the exam committee's trap :-)
• judyoh

  August 2023

  "Even if you try to adjust the ULAE ratio to account for the 30% increase in overall ULAE costs as the sample solutions in part (b) did, the classical method still has the 50/50 assumption embedded in it and will likely produce an estimate that's too low."

  Does this mean that the RATIO has increased by 30% but the overall ULAE has increased by more than 30% due to changes in the 50/50 assumption? Is it then accurate for the question to state that ULAE has increased by 30%?
• Graham

  August 2023

  The question doesn't provide any information on the ULAE ratio (which is the ratio of paid ULAE to paid claims). All they tell you is that the paid ULAE increased by 30% but you don't know anything about the paid claims. (If the paid claims didn't change then the ULAE ratio would indeed increase by 30% also.)

  The point of the change in operations was to reduce ALAE by more than any subsequent increase to ULAE.