Part 2 - Part 4 vs. Part 2 - Part 3 - Part 4
I'm a bit confused by the "restate Schedule P triangles for a new year" problems. In the battle quiz for that section, the practice template provides Schedule P Parts 2, 3, and 4, so I'm able to calculate the new paid triangle, new IBNR triangle, and new case reserve triangle (Part 2 - Part 3 - Part 4) and add them all together for the new Part 2.
In Fall 2016 #12, only Part 2 and Part 3 are provided, and the solution calculates Unpaid as Part 2 - Part 3. Does that Unpaid figure include IBNR?
Comments
Yes, it does include IBNR. Schedule P, Part 2 is labelled as "Incurred Loss" but it's actually "Ultimate Loss". That's why Part 2 - Part 3 includes IBNR. (It's confusing, but that's the way it's done in the annual statement.) So you don't actually need to have Part 4 to do this kind of problem.
For 2016 Spring 13a, the average unpaid claim severity is the same meaning for average case outstanding? I think unpaid should be P2-P3. BUT the solution is P2-P3-P4.
First, a correction for the CAS examiner's report: IBNR is included in Part 2, not Part 3. Their calculation in the answer justifies this.
I find the scenario drawn in the question to be inconsistent. They continue to assume that Part 4 states IBNR, but the average IBNR in their newly introduced schedule does not reconcile to Part 4.
Having said this, it seems they expect you to defer to the newly introduced schedule for the IBNR figure.
The question asks for "average unpaid." This is (case+IBNR)/outstanding count. It also states that there is no IBNR claims on 2011 as of 12/2014, so that you know you only have to have outstanding counts in the denominator.
You use your knowledge of the ordinary Schedule P to derive case as Part 2 minus Part 3 minus Part 4. Dividing this by outstanding counts from Part 5 gives the average case. Average IBNR is given in the new schedule. And average case plus average IBNR is average unpaid, given that there are no IBNR claims.
They also give an alternative answer of deriving case as above, deriving IBNR as the average IBNR from the new schedule times the open claims from Part 5, summing these two, and dividing by the open claims. Notice that they do NOT use Part 4 for the IBNR, but they do use it for the derivation of case. This is the inconsistency I find in the question.
Maybe I got lucky, but here's how I made sense of this:
For case o/s, this is not changed due to the regulation change, so we calculate it in the familiar way: case o/s = p2 - p3 - "old" p4 = 80M - 54M - 12M = 14M.
But then, the question asks us to use the "new" p4 as required reserves per open claim x open claims = 6000 x 1400 = 8.4M
So our numerator becomes: "old" case o/s + "new" p4 = 14M + 8.4M = 22.4M.
The denominator is given in the table, then just finish taking the ratio.
Yes, what you did is reasonable. By "inconsistency," I was referring to the simultaneous use of "old" and "new p4's for IBNR.