FALL 2015, Q11
In the 1st solution in the examiner's report, why is the off-balance factor calculated as 1 + 126,164.1/(1164.375(10,000)) = 1.0108 ?
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In the 1st solution in the examiner's report, why is the off-balance factor calculated as 1 + 126,164.1/(1164.375(10,000)) = 1.0108 ?
Comments
The concept here is that once you've calculated the proposed base rate and realized that the (AOI<100K) x (Territory 1) combination does not meet the minimum premium requirement, you have to do 2 extra steps:
Calculate the premium shortfall for the (AOI<100K) x (Territory 1) combination:
Since this shortfall of 126,164.10 must be (somehow) added to the proposed premium for (AOI<100K) x (Territory 1) we must then use the other AOI x Territory combinations to calculate a revised proposed base rate to maintain the required 15% overall increase. This is done by adjusting the base rate by the off-balance factor as follows:
The final step is to reduce the originally proposed base rate of 1,684.45 down by 1.08% as shown in the examiner's report for sample answer 1.
With this new base rate of $1666 how will the minimum premium condition be satisfied? Because $1666*0.5*0.85 for territory 1 x aoi < 100k is still less than $800
Let's break it down:
The formula used, $1666 * 0.5 * 0.85, calculates the premium for the combination (Territory 1, AOI < 100k). This results in:
1666 * 0.5 * 0.85 = 707.05
This amount is less than the required minimum premium of $800.
Satisfying the Minimum Premium Condition:
Since the calculated premium is $707.05 and the minimum premium is $800, the premium for this class is raised to $800. This adjustment ensures that all policies in the (Territory 1, AOI < 100k) combination meet the required minimum premium of $800.
Impact on the Base Rate:
The adjustment creates an excess premium for this class. The difference between the calculated premium of $707.05 and the adjusted $800 (i.e., $92.95 per policy) results in additional collected premium for these policies.
To maintain the overall target of a 15% premium increase, this excess is accounted for by slightly reducing the base rate for all policies. This is done using an off-balance factor to ensure that the total premium across all territories and AOI groups remains in line with the original goal.
Thus, the base rate of $1666 already factors in this excess from the minimum premium adjustment, ensuring that the overall premium target is still achieved.
Oh I think I understand now. Let me confirm my understanding. The base rate is $1666 to account for overall increase of 15%. We had increased the premium for (Terr 1, AOI < 100k) due to minimum requirement and decreased the base rate to keep the overall increase to 15%. So we calculate the premium for other territory and AOI combinations by multiplying the base rate with corresponding relativities and take $800 for (Terr 1, AOI < 100k) combination.
This section is the toughest one I've come across in the whole syllabus. Will have to spend quite a bit of time to understand the whole concept.
Yes, you've got it! Let me confirm your understanding:
I agree that this section can be tricky because it combines multiple concepts—rate relativities, minimum premiums, and balancing overall premium increases. Spending more time on this will definitely help, and it seems like you're on the right track! If you have any more questions as you go through it, feel free to ask!