Spring 2015, #25, C
I realize this is a very defective question--still, unsurprisingly, the CAS refused to discard it; instead, they go on with some nonsense about increasing the Bloom's level, although I'm ranting--, but I'm just wondering about the formula the model solution uses for the calculation of the R_5 charge.
Everything in the solution makes sense up until they calculate they basic charge, with a formula I am not familiar with.
I am used to calculating the R_5 basic charge as: NWP_(current year) * [(C x A) + U - 1], where C is the company RBC % and is given, A is the adjustment for investment income and is given, and U is the underwriting expense provision (and, defectively, is not given, but the CAS accepted a number of interpretations for this).
The model solution, however, uses a formula for R_5 that seems to be equivalent to: NWP_(current year) * [(1 + C) * A -1]. I do not know where the CAS gets this formula from, and the examiners report is unhelpful. However, it seems that the CAS accepted my above-mentioned formula for the R_5 basic charge, with an assumption that U = 0. My issue, though, is that using that formula gives me a negative result for R_5, which is not intuitive. Given adjusted premium of 180M (200M given, less the ceded 20M in reinsurance premium), and the other supplied factors, with an assumption that U = 0, I get the following.
R_5 = 180M * ((.25 * .90) + 0 - 1] = -139.5M.
Is this correct? Is this question just so defective that the CAS would have given me credit if I went ahead and used that to calculate the RBC charge and complete the question? It's ridiculous they didn't just throw the question out, but, again, who is shocked at that? I can't imagine proceeding with this question on the exam if I ended up with a negative result for R_5.
Comments
Yeah, that was such a cop-out to claim it inadvertently increased the Bloom's level instead of just admitting they screwed up.
It looks like your answer is what they called "Approach C". They didn't show the calculation corresponding to that approach but apparently they would have accepted it. Of course, it makes no sense to use -139.5 in the RBC formula. I think in that case I would have just set R5=0.
Sometimes when you do a calculation for required capital (in any context) the formulas can't handle the cases that are outliers and you may get a negative answer that doesn't make sense. That could just mean there's no risk so the required capital truly is 0. That definitely isn't the case here, but since there's no good option, I think that's what I would have done. Even if the graders didn't accept 0 for R5, at least they would see you knew the RBC formula and how to get the final ratio.
Regarding the formula to get the base RBC, it just seems dumb to make the "C-term" in the formula slightly different for R4 and R5. But that is clearly what is stated in Odomirok:
A mathematician never would have done it like that. The "C-term" should be defined consistently between the 2 formulas because it represents exactly the same concept. Still, you have no choice but to abide by the source text. And it seems they did accept that, but they didn't explain it in the examiner's report.
The whole thing is very annoying but I think it's wise to prepare yourself for something like this. That's why time management during the exam is very important. I could easily see people wasting far too much time on this question and then running out of time for questions near the end of the exam that they probably knew how to do. If you're managing your time time properly, you would know that you can spend roughly 3.5 minutes per point or roughly 21 minutes on this question. Except calculation questions generally take longer than memory questions, so you could conceivably allocate 30 minutes to this whole question. Even if you don't know exactly how to do the question, you can write down all the relevant formulas and just plug in numbers wherever you can. You would definitely get a bunch of points for that. This is an example of gamesmanship. Forget about getting the exact right answer. Play the odds and do the best you can in the allotted time. It's just a small part of the whole exam. If you see you're coming up to 25 minutes on this question, then you should start thinking about wrapping it up.
You also have to be aware of the psychological toll a stupid problem like this can take on your state of mind. It could very well throw you off balance and negatively impact your performance on other questions. That's why rehearsal is important. If you are well prepared, you'll know how to do most of the questions so something like this doesn't need to sink you. And remember that everyone else is in the same position.
(I also don't know what they mean by "with expense ratio assumption" in Approach B & D. Were you just supposed to make up your own expense ratio???)
Thanks. Yeah, this is a dumb question, and the CAS's response to it is even dumber, but I feel confident enough that, even if I wasn't able to answer it fully, I could get some significant partial credit, which I think is good enough.
Just commenting to say this discussion was very helpful and I came to this forum to specifically ask about this question. Was going crazy looking at their sample solution then looking at their different "approaches" that would give totally different answers. Why in the world does the sample solution use a different formula than the one stated in the text??? They also required you to memorize a random RBC ratio which is the cherry on top.
Hey @Greg, glad this discussion was helpful. Kudos to @rwhiting for starting the thread.