Spring 2015 Q5b

Comments

• Graham

  January 2022

  Am I looking at the right problem? Spring 2015 Q1 doesn't seem to have a part (b). This exam problem is outdated so you don't have to know how to do it. It was from a reading that is no longer on the syllabus. You can find outdated exam questions using this filter from the website:

  • https://www.battleacts5.ca/BB_byExam.php

  To get to that page from the main page, use the the link "BattleCards - Prior Exams" under "Custom Battles".
• railfan1975

  January 2022

  Sorry, Spring 15 #5b
• Graham

  January 2022

  Sample answer 1 is more methodical. They do the calculations in 2 separate steps. Here's sample answer 1 for reference, with my explanation below:

  

  Step 1: Calculate an area-based weighted average for each quarter in the "normal" way (first 4 lines of solution)

  • Here they calculate the average rate level for each quarter. (See diagram below)
  • The red diagonal represents the rate change of +10% and separates the big square into 2 rate levels. The area above the red line is rate level 1 and the area below the red line is rate level 2.
  • The average rate level for Q1 and Q2 is just 1.0 because the rate change of +10% doesn't occur until Q3.
  • The calculation for Q3 is an area-based weighted average using rate level 1 (which is 1.0) and rate level 2 (which is 1.1). You can see that the red diagonal, which represents the rate change, divides the yellow area (Q3) into 2 pieces with areas 0.875 and 0.125. Similarly, the red diagonal separates the blue area (Q4) into 2 pieces with areas 0.625 and 0.375.
  • Those areas for Q3 and Q4 are used to get an area-based weighted average. Now, if writings were uniform over the whole year, as in part (a), that's all you would have to do. But since the writings are not uniform, you have to do an additional step. See step 2 below.

  

  Step 2:

  • On the 5th line of sample answer 1, they use the results of Step 1 and the 10/50/30/10 distribution to calculate a second weighted average that incorporates these non-uniform writings.
  • Once you have that second weighted average, which represents the ARL (Average Rate Level) for 2014, you can calculate the CRL (Current Rate Level) in the usual way:
  • CRLF  =  CRL / ARL = 1.1 / 1.0075
  • Then the on-level premium is the given premium of $1000 multiplied by the CRLF.

  Conclusion:

  • If you're given a non-uniform writings pattern, you have to first calculate an area-based weighted average, and then a secondary weighted average using the given non-uniform distribution.

  
  
• carrots

  April 2022 edited April 2022

  Hello!

  In this parallelogram example, we assume each quarter's area is 1 to get the weights for each quarter above and below the red line. In chapter 6, when we talk about adjusting historical loss data to current loss level, you attached an example from the werner book, where they use an example of a law change and they split the CY into quarters.

  In their solution, they took the area of the quarter to be at 0.25 instead of 1. I understand that the parallelogram is just for the premium and we aren't doing the same thing for the losses but it is similar... I don't really understand why one uses the area of 1 and the other uses the area of 0.25.

  Or is it the same things because later on in the loss example, they divide back by 0.25, essentially its the same thing? I find it a bit confusing.

  Here is a screenshot of the loss example

  

  
  
• Graham

  April 2022

  If I understand your question correctly, it shouldn't matter what we let the areas be as long as they are all correct relative to each other.

  They are dividing by 0.25 as you highlighted because the total area is 0.25 and the values in parentheses (0.2422/0.2500) and (0.0078/0.2500) are the weights for calculating the ARL (Average Rate Level) for 2010 Q3. (The weights for any weighted average must add up to 1.0.)