S2017 Q11 - Time / Approach / Development Triangles

chrisboersma

What is the best strategy for a problem that has lots of triangles to calculate?

I take one look at this question and roll my eyes. Only because there are just so many calculations to be performed to get the answer, but all the calculations are straight forward and mostly simple addition and subtraction.

It takes about 6 minutes just to put together all the NET triangles required for this problem (incremental, unpaid, APV). that ignores GROSS and ignores the work documenting the answers for each of A,B,C,D,...M.

This problem would probably take me at least 15-20 minutes (it's worth 3.25 points / 69 or about 11 minutes of exam time).

graham

I'm glad you asked this, and I hope other people read this post. The thing I didn't like about this exam question is that if you didn't notice the data is for a reinsurer, you would get it all wrong. Usually, the first paragraph of these types of questions is boilerplate, and the line of business doesn't matter, but that's not the case here. I think they should have emphasized that instead of trying to trick you.

Anyway, there is a wiki article that address time management issues during the exam. Here 's the link:

• https://www.battleactsmain.ca/wiki6c/On_BattleDay

Part of I've noted there is that the calculation problems generally take about twice as long per point as the essay questions. Based on that, you could allocate 11 x 2 = 22 minutes to the problem, which puts it within your 15-20 time frame.

You can read the wiki article for more details, but I recommend you spend the first 5 minutes of writing time on the exam to divide the exam into four 1-hour segments, taking into account that calculation problems take longer. To do this effectively, you have to be aware of the usual layout of the exam. It's very predictable from year to year. (And I've provided an example of what this looks like for an old exam.)

That's the main piece of advice. The second, is that you don't really need calculate the whole triangles because they are only asking for the latest CY. You can get away with just the latest 2 diagonals.

exam6_pass

Thanks Graham: Just a quick follow up question:

I know there is a difference in excess/deficiency for 1 AY vs 1 CY -> For this Q: is there a way to tell if they are talking about AY or CY? E.g. for A/B/C values it’s under “Current year” how do we know it’s calendar year?

Also, for I/J/K -> “net provision for claims of prior years” how do we know if it’s asking for prior CY or AY?

graham

This question asks you to fill in Exhibit 60.30 and you just had to know that these are calendar year values, but that might not really help you.

Generally, if they are talking about AY, it should be clear, either because it's stated explicitly or you're dealing with a situation where it's obvious, like with a development triangle. Most exhibits in the annual statement are CY.

In this problem, they give you development triangles as the given information, which kind of throws you off. But it would be too simple a problem if all you had to do was read the AY values for the most recent AY off the tables. They want you to find the CY across all AYs here.

I hope that helps. It's the kind of thing you get to know after you do enough problems.

bkmlocks

In Schedule 60.30 in the question, from the Examiner's report, why are we calculating the Excess (Deficiency) for CY 2016 ?

1) Does Prior Year End in the last table not mean that we need Excess (Deficiency) in CY
2015 ?

2) In this question, does Provision (Net Provision) mean the same thing as Gross APV (or Net
APV) ?I guess the word PROVISION confused me a lot because it is a component of APV.

As a side note, when we are given Unpaid Claims and asked to calculate APV (not necessarily here but in general), do we always assume that this includes IBNR ?

graham

1)

• The margin calculation is for CY 2015. You can never calculate the excess (deficiency) for the current year because you have nothing to compare the current year-end provision to. You have to wait at least 1 year, then look at that provision versus the original provision. That tells you whether your original provision was too high (excessive) or too low (deficient).

2)

• Yes, "provision" is just a general term. For example, you can talk about provision for expenses, provision for claims, provision for advertising expenses, and many other things. The term "provision" can apply to anything.

Side Note:

• In general, yes. That's because from Exam 5, unpaid = case + IBNR. I know that you sometimes see the phrase UCAE & IBNR, which seems to imply that UCAE does not include IBNR, but unless it's explicitly stated otherwise, you should assume that unpaid does include IBNR.

bkmlocks

Thank you very much for the detailed answer Graham!

I am still not clear about this one though but maybe I am not understanding something properly.

It does seem to me that we are calculating margin for CY 2016 & not 2015.

Since in the examiner's report Sample 2, we are calculating the following :

Margin = APV(beginning) - Paid Claims + Investment Income - APV(ending) where

1) APV(beginning) is the APV at the end of 2015 for all AY's (exclude AY 2016 by default)
2) APV(ending) is the APV at the end of 2016 for all AY's (excluding AY 2016 for the reason you mentioned above)
3) Paid claims is Paid claims in 2016 for all AYs (excluding AY 2016)

However the header on Schedule 60.30 is for Unpaid Claims at **Prior Year End ** so I would think that we actually need to calculate margin for CY 2015 instead and the calculation would be different.

graham

Everything you said is correct except that the answer is indeed the margin for the prior year-end of CY 2015 on Dec 31, 2015. The confusing part is that have to use what was paid in CY 2016 to calculate what the margin was for CY 2015 on Dec 31, 2015. (You also need the investment income for CY 2016 and the APV(end of 2016) for prior AYs.)

Example: Suppose a company started operations on Jan 1, 2015 and we are now at Dec 31, 2016. If I tell you:

• APV(end of 2015) = 600
• APV(end of 2016) = 400
• Paid(during CY 2016) = 100
• investment income = ii = 40 (earned during CY 2016)

then the margin for CY 2015 on Dec 31, 2015 (but as of the end of CY 2016) is defined to be:

• 600 - 400 - 100 + 40
• =140

This value of 140 means that based on what happened during CY 2016, the APV(end of 2015) of 600 was too high by 140 so that's the margin for CY 2015 on Dec 31, 2015. We have to know what happened in CY 2016 to be able to look back and see whether that value of 600 was high or low or just right.

If I had instead asked you to calculate the margin for CY 2016, you wouldn't be able to do it until the end of CY 2017 because at the end of CY 2016 you would be missing 3 of the 4 items needed in the formula. (Or I guess you just say the margin is currently estimated to be 0 since the APV at the end of 2016 is presumably equal to the actuary's current best estimate.)

With each passing year, you can recalculate the margin for CY 2015 on Dec 31, 2015 and get continually better estimates of that margin. When all claims are settled you would then finally know exactly what the margin was way back on Dec 31, 2015. Note that you could also calculate the margin for CY 2015 on Dec 31, 2016 or Dec31, 2017, or for any other date. But you always need to have some CY information beyond that specific date. That's why it looks like you're calculating the margin for a different year, but you're really not.

bkmlocks

Thank you for all the details, I agree with your explanation and I think it makes sense!

With all this discussion, does it mean that for Fall 2016 Q14 (b). (also discussed thoroughly in the WIKI), we are actually calculating the margin for CY 2014 on Dec 31, 2014 and not margin for CY 2015 as asked in the question. Since we are using the following:

• APV(end of 2014)
• APV(end of 2015)
• Paid (in 2015)
• Invest Inv (in 2015)

On your last note
If we want the margin for CY 2015 on Dec 31 2017, would it be as follows?

APV(end of 2015,AYs 2015 & priors) - APV(end of 2017,AYs 2015 & priors) + Invest Inc (2016 & 2017) - Paid(2016 & 2017)

graham

Yes, now that we've had all this discussion and I've gone back to look at these problems in detail, I think the wording for 2016.Fall Q14(b) should probably have been:

• Calculate the excess (deficiency) amount for CY 2014 as it was on Dec 31, 2014 using data available as of year-end 2015.

This type of problem really needs to specify 3 different dates or time periods to make it clear. Usually there is only one way to proceed based on the given information but the question should really be more precise to avoid this type of confusion. Let's step back from the CY calculation and go back to the basic calculation for just 1 AY. To be completely clear about what to calculate, we would have to say something like this:

• calculate the excess (deficiency) for AY 2015 as it was on Dec 31, 2015 --> using data available as of Dec 31, 2015 (this is 0 by default because you need at least 1 extra year so you can compare back)
• calculate the excess (deficiency) for AY 2015 as it was on Dec 31, 2015 --> using data available as of Dec 31, 2016 (this is what you had to do for 2017.Spring Q11 except for all prior AYs, not just AY 2015)
• calculate the excess (deficiency) for AY 2015 as it was on Dec 31, 2015 --> using data available as of Dec 31, 2017 (This should be a better estimate of the excess/deficiency than the previous case because we now have more knowledge about the claims. This is similar to the "easy version" of this problem in the practice template where there was a 2 year lag. In that version, we always compared back to Dec 31 at the end of that AY.)

I will make a note of this in the wiki and provide a link to this discussion thread.

P.S. For the last part of your question, you need to state what you're looking for more precisely. I believe your formula is calculating this:

• the excess (deficiency) for all AYs 2015 & prior as they were on Dec 31, 2015 --> using data available as of Dec 31, 2017 (so basically CY 2015 as it was on Dec 31, 2015 --> using data available as of Dec 31, 2017)

Let me know whether or not that makes sense.

bkmlocks

I agree with your statements Graham! I think it makes much more sense to have all 3 dates to avoid confusion!

• To be 100 % clear on this, do you mean that for 2016.Fall Q14(b), the examiner meant "Using information available as of end of 2015" when they asked to calculate Excess(deficiency) for CY 2015.

I unfortunately doubt the examiner will specify all 3 dates. But like you mentioned already, there might be only one way to proceed anyway. (except maybe for 2017.Spring Q11 where it could be very confusing I suppose).

Thank you!

graham

Yes, I believe that's what they really meant: total excess(deficiency) for all AYs as they were on Dec 31, 2014 using information available as of the end of CY 2015.

Thank you for taking the time to post about this. It's been very helpful. :-)

suomi

For Spring 2018 Q15, based on this conversation, the proper wording should be: Calculate the excess (deficiency) amount for CY 2016 as it was on Dec 31, 2016 using data available as of year-end 2017.

Please confirm

Staff-T1

Yup that's correct