2013.Fall 14
If E = Expected Losses, and ELR = 0.7 of SP, then ELR = Exp L / Exp Prem = E/Exp Prem.
ELR = 0.7*SP
E/Exp Prem = 0.7*SP
So how does E = 0.7?
If E = Expected Losses, and ELR = 0.7 of SP, then ELR = Exp L / Exp Prem = E/Exp Prem.
ELR = 0.7*SP
E/Exp Prem = 0.7*SP
So how does E = 0.7?
Comments
This is one of the more confusing aspects of the Fisher reading. You can switch back and forth between using losses and expense dollars or loss ratios and expense ratios within the retrospect rating formula. Essentially, you get a second version of the retrospective rating formula by dividing through by the standard premium. It's critical to remain consistent throughout though and since it's not a different formula, it's best to remember this technique rather than memorizing another set of equations.
In this question we're given ratios to standard premium so as we apply the retrospective rating formula we will get a ratio of the retrospective premium to the standard premium. This is okay because they didn't give standard premium and luckily it's all they asked for. So in this case E is the ratio of expected losses to standard premium, which is the 70% given in the question.
I also have one question about this one. In the CAS sample solution, they said, for Model Solution 2:
The following solution can be used IF AND ONLY IF the candidate stated that it’s a balanced plan
However, Model Solution 1 is always equivalent as Model Solution 2, right?
This is a good example of the CAS writing a question where they intended candidates to answer in a particular way but left a shortcut available.
Yes, Model 1 is equivalent to Model 2. However, note you must have a balanced retrospective rating plan in order to derive the equation used in Model 1. (Refer to https://battleacts8.ca/8/wiki/index.php?title=Fisher.Visualization#The_Balance_Equations for more detail.)
I believe the CAS required candidates who used Model 2 to state the equation there holds only when the retro plan is balanced because otherwise the candidates aren't demonstrating they know how to price a retro plan because they're applying a guaranteed cost method. This is a good example of always taking a short amount of time to acknowledge assumptions given in the question, in this case that the plan is balanced.
In the reading we are given the formula used in Step 1 in terms of E[A]:
But it looks like their solution is in terms of E[L]. How do you know which one you should use?
Nevermind, after much algebra I figured out that what we're calling E[A] is what they're calling E[L].