ch5 doubts

Comments

• Graham

  March 2021 edited March 2021

  Question 1: Fall 2019 (Q2) part d.--> It asks whether taking avg(current year in-force premium, prior yr in force premium) appropriate for calculating EP for current year. Did not understand the rationale in the sample answer.

  • Consider first the case where the insurer is in steady-state and has been writing annual policies of $100 every month for a several years. At any given time, there are 12 in-force exposures, so the in-force premium is $1,200. Also, the earned premium for every year is $1,200. This would include earnings from policies written both in the prior year ( contributes $600 to current year) and the current year (contributes $600 to the current year). And in this steady-state scenario, the average of the current and prior in-force premium is $1,200 which indeed equals the EP for the current year. In the words, the formula works. This is because there is no growth or shrinkage and writings are uniform. But think about what would happen if, for example, in the following year all policies were 11 month policies each for $100 written on Jan 1. The in-force premium at the end of this year would be 0 so the average of the in-force premium at the end of that year and the prior year would be 600 (average of 0 and $1,200) which wouldn't equal the true EP of $600 + $1100 = $1,700. The example in exam problem is different but the key idea is that the policies are not written uniformly and they are all for different amounts. The "averaging" formula might actually work in certain weird cases even if the writings are not uniform but it won't work in general.

  Question 2: Fall 2019 (Q2) part e. says one use of in-force premium other than to calculate EP. How is in-force premium used in calculation of EP in the first place?

  • One possible answer is actually given in part (d) of this question. If the insurer's writings are stable and spread uniformly over each year then EP can be estimated by the the average of the in-force premium from the current and prior years.

  Answers to other questions to follow...
• Graham

  March 2021 edited March 2021

  Question 3: Fall 2017 (Q3) part b.--> They have assumed that there's no premium audit in sample answer 3 before concluding that WP=EP for PY2015 as of 31.12.2016. What does this assumption mean in general and its context here?

  • The general concept of premium audit is discussed in the wiki here: https://www.battleacts5.ca/wiki5/Werner05.Premium#Adjustments_to_Premium:_Development
  • In this problem, if there is a premium audit after the end of the policy year, the WP could change. This is a subtle point and I think it would have been fine to not even mention this. The first sample answer did not refer to this assumption. I think it was just meant to be a simple problem.

  Question 4: In the Web Based Problem in 1st Mini Battle Quiz, the annual premium column is given and if we want to calculate the in-force premium for a 6-month policy, then do we multiply the annual premium for that policy given by 1/2 ? I'm asking so because it in the cheat answer, the entire (annual) premium has been taken which I think is wrong.

  • I would need to see a specific example to address this question.
  • But note that you also have to multiply by the number of policies. So if the term was 6 months and the annual premium was $500 but there were 2 policies, then WP would be $500 x 0.5 x 2 = $500.

  Question 5: Spring 2015 (Q5) part b.--> What is the assumption taken and calculation behind sample answer 1? (I got it for sample answer 2)

  • Sample answer 1 and sample answer 2 give different results so at least one of them must be wrong.
  • I believe sample answer 2 is wrong. It gives the same answer as part (a) which had uniform writings and that doesn't make sense. Sample answer 2 seems to be making an assumption about the pattern of writings from 2013 and the subsequent earnings that would be produced in 2014.
  • They start by noting correctly that 4.5/12 of the premium written in Q3 would be earned in 2014. This is because the average written date would be Aug 15, which leaves 4.5 months of earnings out 12 months assuming annual policies.
  • Similarly, premium written in Q4 has an average written date of Nov 15, which leaves 1.5 months of earning out of 12.
  • Then they calculate 30% x (1.5/12) + 10% x (1.5/12) = 0.125 which represents the proportion of premium written in 2014 that was earned in 2014.
  • The next step is where I believe the problem lies. They subtract 0.125 from 1.0 to get 0.875 and state that this is the proportion of earned premium written at the old level. This is not necessarily correct. It makes an assumption about how premiums were written in 2013. In fact, the solution in sample answer 2 never even used the given percentages of 10% and 50%.
  • Getting back to your question about sample answer 1: Sample answer 1 seems to be assuming that the given percentages 10%, 50%, 30%, 10% are distributions of earned premium rather than written premium. (Not sure if that's a correct assumption. I think they probably intended the percentages to represent written premium.) Anyway, the idea here is to calculate the average rate level using the given percentages instead of 25%, 25%, 25%, 25% as in the uniform case in part (a). It helps if you draw a diagram that looks like a square for 2014 but with 4 vertical lines that divide the square into tall rectangles representing each quarter. Q1 and Q2 obviously have an average rate level of 1.0. They will contribute 10% x 1.0 + 50% x 1.0 to the ARL for 2014. Then to calculate ARL for Q3, you have to draw the diagonal for the rate change and notice that the diagonal splits the Q3 rectangle into 2 pieces. The top bit is 7/8 of the total (with rate level 1.0) and the bottom bit is 1/8 of the total (with rate level 1.1). The average is then 1.0125 as shown in sample answer 1. Do the same type of calculation for Q4: The top bit of Q4 has an area of 5/8 and the bottom bit is 3/8 so the average is 1.0375 as shown in sample answer 1. Then just follow the sample answer where the Q3 value is weighted 30%, and the Q4 value is weighted 10% to get the final ARL of 1.0075. Once you have that, the final on-level premium calculation is straightforward and results in $1,091.81.
  • Final comment: This problem was not clearly stated. That's why 2 sample answers were accepted but I'm not sure either of them is correct, strictly speaking.

  Answers to other questions to follow...
• Graham

  March 2021 edited March 2021

  Question 6: Is there any trick to apply parallelogram method in general where policy distribution is uneven throughout the year, (For eg- in questions like Spring 2015 (Q5) part b. and Spring 2014 (Q1) part b.), because I couldn't correctly distribute the CYs in correct areas for ARL calculation in either of the questions even after seeing the answers?

  • There isn't really a trick. These problems are challenging because you have to apply general knowledge to the specific situation that isn't like the standard method.

  Question 7: One reason for change in premium levels is distributional shift. An example of distr. shift is when an insurer purchases an entire portfolio of business from another insurer (may cause a 1-time shift upward or downward depending on how the characteristics of the current book compare to the new book) What does this mean?

  • If the insurer's original book of business had an average policy premium of $500 and they purchased a new book of business that had an average policy premium or $700, there would be a sudden increase in premium to something between $500 and $700. In other words, there would be a distributional shift from less expensive policies to more expensive policies. (Maybe the new policies were more expensive because they were centered on an urban geographical area versus a rural area. Or maybe the new policies had higher limits and thus were more expensive.)

  Question 8: Why do we use average EARNED premium in the formula ==> latest AWP@CRL / historical AEP@CRL (for step 1 in 2-step premium trending)? This formula itself isn't quite intuitive as the first choice for doing step 1. If you could give some rationale behind that too.

  • EP is used in the denominator because it is the earned premium that we want to adjust. In other words, EP is the basis from which we want to make our projection. Then the question becomes: why do we use WP in the numerator? The reason AWP is used in the numerator is that we want the ratio to adjust this historical AEP forward to the average written date of the latest quarter (or year) available in the trend data. If we used AEP in the numerator, we wouldn't be fully using the latest available data since EP for a period also depends on writings prior to that period.

  Question 9: Fall 2017 (Q1) part a.--> Sample answer 5 is unclear. Why taking simple yr-on-yr average directly and that too of EP and WP changes together?

  • The examiner's report solutions show there is no single correct way to perform the trending. The first 4 sample answers used standard 2-step trending where the step 1 trend was the ratio of latest AWP to historical AEP
  • Sample answer 5 did something more direct. It calculated a trend in the more straightforward way by looking at year over year changes and then made a judgmental selection. (Actually, you could use any kind of regression analysis to come up with a selected trend based on this historical data.) Here, they selected a step 1 trend of 6.1%, then separately projected each historical quarter to the latest period available in the data. This required separate trend periods for each historical quarter, so it was a bit more complicated than the step 1 trend used in sample answers 1-4.

  Answers to other questions to follow...
• keshav1996

  March 2021

  Q5: Can you please send over the diagram for area calculation either here or over email? I am still not able to make it. Probably that would make your explanation easier to take in.

  Q8: Why are we projecting taking EP from the historical period as our basis of projection and not WP?

  You may want to answer these follow up doubts only after you have answered all the questions to avoid any confusion here.

  Thanks
• Graham

  March 2021

  Question 10: Fall 2017 (Q1) part b.--> . Shouldn't aging insureds receive higher age factors and thus have higher premiums and so, how does this scenario lead to a negative premium trend in average premium @ CRL?

  • If we're talking about car insurance, rates are highest for young drivers. As they get older and have more driving experience, their expected losses are lower so they get lower age factors in the rating algorithm. A particular cohort of insureds all aging together would then exhibit a negative premium trend.
  • This trend generally continues well into middle age. (At some point, maybe around age 70-80, loss experience starts getting worse again.)

  Question 11: Fall 2018 (Q3) part c.--> Not clear.

  • You need the overall rate change broken out by class. For example, the rate change of 10% on Oct 1, 2017 is for the overall book of business. If you want to calculate indicated class factors you first need on-level EP by class factors, but to to get on-level EP by class factors, you need rate changes by class factors so you can apply the parallelogram method at the class factor level. In other words, this overall 10% rate change needs to be broken down into separate rate changes for each of classes X, Y, Z. (Maybe class X got a 7% change, class Y got 9%, and class Z got 14%, or something like that so it averages out to 10%. But the problem doesn't provide that level of detail.)

  Question 12: Spring 2015 (Q2)--> There's no mention of the current exposure base being used in the question. So, why have the sample answers assumed that the current exposure base is car years at all places?

  • It is almost universal that car-years is used as the exposure base for auto insurance. Still, they probably should have mentioned that in the statement of the problem.

  Question 13: Pricing problems Set1 (Q3) —> EP calculated for CY 2022 maybe wrong due to area wrongly calculated in the solution spreadsheet. Also, Q5's solutions seem to be wrong as per the ques. Kindly confirm if that is the case. I have put solving further Excel problems on hold for the time being.

  • I looked at this and I don't immediately see what's wrong. You have to be more specific because I'm not sure I'm looking at the same thing you're looking at. Please give me the chapter, set, problem #, and explain which calculations you think are wrong and why.

  
  
• Graham

  March 2021

  I have copied your follow-up questions below:

  Q5: Can you please send over the diagram for area calculation either here or over email? I am still not able to make it. Probably that would make your explanation easier to take in.

  Q8: Why are we projecting taking EP from the historical period as our basis of projection and not WP?

  For Q5, I sent you a message. Check the little envelope under your name in the top left of the screen.

  For Q8, that's just the way it's done according to the procedure in Werner.