The solution in the examiner's report for this question was truly awful.
A problem of this type also appeared in 2015.Fall Q1b. The solution there was explained a little better so take a look at it. In any case, if you get a problem like this again, the first thing you should do is write down the 3 requirements for regulatory approval of territorial changes: (This is covered in the FSCO.PPA wiki article in the section on Approval Process)
[1] direction of [proposed change] must be the same as direction of [indicated change] (both up or both down)
[2] magnitude of [proposed change] must be less than magnitude of [indicated change]
[3] magnitude of [proposed change] must be in the interval (-10%, 10%)
You would definitely get partial credit for at least doing that. The KEY observation is that the 3rd requirement is not satisfied by territory 3. The indicated change is 12% but the maximum allowable change is 10%. So my proposed change for territory 3 would be at most 10%.
Subtle point that wasn't considered in the examiner's report solution:
You don't have to take the full 10% change for this territory since the requirement is that it be at most 10%. So thinking ahead, I would probably just propose 9% because I know I'll have to rebase the changes as the final step. If I took the whole 10%, then I might end up with something higher than 10% after rebasing which would be a problem.
Note that the examiner's report did cap the change at 10% but they got lucky when they rebased the changes because the change for territory 3 actually went down a little bit, so they stayed under the 10% cap.
But now take a look at requirements [1] & [2] for territorial changes. We have to make sure the proposed changes are of the same sign but also less than the indicated changes. So instead of -6.0% and 1.0% for territories 1 & 2, I would take only -5.0% and 0.8% just to be on the safe side.
Anyway, we now have proposed changes for the 3 territories: -5.0%, 0.8%, 9.0%.
The next step is to calculate the proposed differentials by multiplying the current differentials by our proposed changes as follows
territory 1: 0.85 x (1 - 0.05) = 0.8075
territory 2: 1.00 x (1 + 0.008) = 1.008
territory 3: 1.05 x (1 + 0.09) = 1.1445
My numbers above would correspond the column in the examiner's report solution labelled as "Capped Diff. @ 10%".
And the final step is to rebase your changes. To do this, you have to do 2 things:
Calculate the OLEP-weighted average for the proposed differentials above. This works out to 0.9424 (The examiner's report got 0.9412 with their proposed differentials.)
Then adjust the proposed differentials by the factor 0.9401/0.9424 = 0.9976. (The value of 0.9401 is the OLEP-weighted average of the original current differentials.)
Note the adjustment factor in the examiner's report is 0.9401/0.9412 = .9988
So our rebased proposed differentials are:
territory 1: 0.8075 x 0.9976 = 0.8056
territory 2: 1.008 x 0.9976 = 1.0056
territory 3: 1.1445 x 0.9976 = 1.1418
The last step, which is optional because it's just to check your work, is to calculate the OLEP-weighted average of your final proposals. I did this and I did indeed get 0.9401. (That means there is no overall change even though individual territories did change.)
There are many possible acceptable answers to this question. You just have to make sure the 3 regulatory requirements are satisfied. I think the examiner's report solution should have mentioned that.
HI @graham, I think what you have above is very useful, thank you for that!
I would like to clarify my understanding about the 3 requirements above:
direction of [proposed change] must be the same as direction of [indicated change] (both up or both down)
magnitude of [proposed change] must be less than magnitude of [indicated change]
magnitude of [proposed change] must be in the interval (-10%, 10%).
When we refer to proposed change and indicated change, we always are referring to **rebased ** relativities right?
For example for this question, although not explained at all in the examiner's solution, 12 % for territory 3 does not really tell you there has been a violation of point 3 above directly. It is only after rebasing that we get (1.176/0.9455) / (1.05/0.9401) -1= 11.3 % that we know that point 3 has been violated.
Yes, very good point. I just assumed that 12% was far enough outside the (-10%, 10%) range to still be outside after rebasing but I really should have checked. Thx!
Anyone noticed that the rebased final proposed for Territory 2 (1.0088) is higher than the rebased indicated (1.01/0.94555*0.9401)=1.0042? This is not satisfactory for condition 2. Same thing for @graham 's solution (1.0056>1.0042).
I went to the report of 2015 Fall 01b, there we compared % change of rebased indicated vs rebased proposed just like I did. so I think the red No in Col [9] is the same thing. Right?
yes, i noticed it too.. don't think the 2nd condition is fulfilled (%change proposed < %change indicated) using rebased values. doesn't seem to be true for terr 2, if we compare rebased values for proposed and indicated.
That is an astute observation. I did not do the extra step of checking that all the rebased values still satisfied the conditions.
I had proposed a change of 0.8% for territory 2 (even though up to 1.0% is allowed) because I knew the percentages could change after rebasing. I just did the problem again in Excel and found that choosing 0.5% will work.
Then my proposed changes:
That's a lot of work for 1.25 pts and apparently the examiners did not notice the issue you raised either.
hi Graham,
one small thing - in your comment above you said "I had proposed a change of 0.8% for territory 2 (even though up to 1.0% is allowed)" i.e. value of 1% is allowed.
in the Wiki it says: territory criteria is: "proposed change is less than indicated change" should it be "less than or equal" ?
It should probably be less than or equal, but I couldn't find any specific reference in FSCO's PPA guidelines. The answer in the examiner's report says "lesser" but in practice there would be no difference between "less than" and "less than or equal". (It isn't like a mathematical theorem where such differences could be very important.)
for this question why does overall change have to be revenue neutral? why cant we just cap the indicated differential change for each territory at 10% and call it a day.
If you look at the statement of the problem, the TOTAL for "One-Way Analysis Indication" is 0.0%. It's true they didn't specifically say the overall change had to remain at 0.0% (which is the same thing as revenue-neutral) but if you didn't have to maintain the 0.0% change, then your proposed differentials would only have to satisfy the 3 FSCO conditions. You could make up any old numbers to satisfy this without even doing any calculations. Generally, when doing a territorial analysis you have a target overall rate change. It doesn't have to be 0%, but whatever it is, your proposed territory differentials should maintain this target.
Yup this seems a bit right - Although you don't have to rebase the current and proposed differentials so you can save some time there. But there is nothing wrong with what you just did
@graham why do we not compare the actual % change after re-basing for both proposed and indicated change? In your November 2020 comment, you show the "Actual % Change " after rebasing the proposed but not for the indicated.
Another way to solve this is to determine the premium change for each territory and the capped premium change, then allocate the excess of the cap to another territory. You'll then have the target proposed premiums to calculate the territory differentials by dividing against (OLEP/Current differentials). No need to fiddle around with rebasing or checking if the changes are within range.
I don't like how the answer provided states that an off-balance (rebase) is needed when using the indicated rate change (average factor of 0.9455 indicated vs 0.9401 current).
Their mistake is to use OLEP after differential (instead of backing out w/o differential)... also, the question mentions that the overall change is 0.0%, so no rebase should be needed...
This is too deep into ratemaking if you ask me A random selection within boundaries should be accepted!
Comments
The solution in the examiner's report for this question was truly awful.
A problem of this type also appeared in 2015.Fall Q1b. The solution there was explained a little better so take a look at it. In any case, if you get a problem like this again, the first thing you should do is write down the 3 requirements for regulatory approval of territorial changes: (This is covered in the FSCO.PPA wiki article in the section on Approval Process)
You would definitely get partial credit for at least doing that. The KEY observation is that the 3rd requirement is not satisfied by territory 3. The indicated change is 12% but the maximum allowable change is 10%. So my proposed change for territory 3 would be at most 10%.
Subtle point that wasn't considered in the examiner's report solution:
Anyway, we now have proposed changes for the 3 territories: -5.0%, 0.8%, 9.0%.
The next step is to calculate the proposed differentials by multiplying the current differentials by our proposed changes as follows
My numbers above would correspond the column in the examiner's report solution labelled as "Capped Diff. @ 10%".
And the final step is to rebase your changes. To do this, you have to do 2 things:
So our rebased proposed differentials are:
The last step, which is optional because it's just to check your work, is to calculate the OLEP-weighted average of your final proposals. I did this and I did indeed get 0.9401. (That means there is no overall change even though individual territories did change.)
There are many possible acceptable answers to this question. You just have to make sure the 3 regulatory requirements are satisfied. I think the examiner's report solution should have mentioned that.
HI @graham, I think what you have above is very useful, thank you for that!
I would like to clarify my understanding about the 3 requirements above:
When we refer to proposed change and indicated change, we always are referring to **rebased ** relativities right?
For example for this question, although not explained at all in the examiner's solution, 12 % for territory 3 does not really tell you there has been a violation of point 3 above directly. It is only after rebasing that we get (1.176/0.9455) / (1.05/0.9401) -1= 11.3 % that we know that point 3 has been violated.
Thank you very much
Yes, very good point. I just assumed that 12% was far enough outside the (-10%, 10%) range to still be outside after rebasing but I really should have checked. Thx!
Hi,
Anyone noticed that the rebased final proposed for Territory 2 (1.0088) is higher than the rebased indicated (1.01/0.94555*0.9401)=1.0042? This is not satisfactory for condition 2. Same thing for @graham 's solution (1.0056>1.0042).
I went to the report of 2015 Fall 01b, there we compared % change of rebased indicated vs rebased proposed just like I did. so I think the red No in Col [9] is the same thing. Right?
Thanks
yes, i noticed it too.. don't think the 2nd condition is fulfilled (%change proposed < %change indicated) using rebased values. doesn't seem to be true for terr 2, if we compare rebased values for proposed and indicated.
That is an astute observation. I did not do the extra step of checking that all the rebased values still satisfied the conditions.
I had proposed a change of 0.8% for territory 2 (even though up to 1.0% is allowed) because I knew the percentages could change after rebasing. I just did the problem again in Excel and found that choosing 0.5% will work.
Then my proposed changes:
That's a lot of work for 1.25 pts and apparently the examiners did not notice the issue you raised either.
Thank you @graham ! I agree and I also don't like this question.
hi Graham,
one small thing - in your comment above you said "I had proposed a change of 0.8% for territory 2 (even though up to 1.0% is allowed)" i.e. value of 1% is allowed.
in the Wiki it says: territory criteria is: "proposed change is less than indicated change" should it be "less than or equal" ?
thanks
It should probably be less than or equal, but I couldn't find any specific reference in FSCO's PPA guidelines. The answer in the examiner's report says "lesser" but in practice there would be no difference between "less than" and "less than or equal". (It isn't like a mathematical theorem where such differences could be very important.)
for this question why does overall change have to be revenue neutral? why cant we just cap the indicated differential change for each territory at 10% and call it a day.
If you look at the statement of the problem, the TOTAL for "One-Way Analysis Indication" is 0.0%. It's true they didn't specifically say the overall change had to remain at 0.0% (which is the same thing as revenue-neutral) but if you didn't have to maintain the 0.0% change, then your proposed differentials would only have to satisfy the 3 FSCO conditions. You could make up any old numbers to satisfy this without even doing any calculations. Generally, when doing a territorial analysis you have a target overall rate change. It doesn't have to be 0%, but whatever it is, your proposed territory differentials should maintain this target.
Sounds good, thanks Graham!
Hi Graham, can you help verify if my calculation in the picture for 2019 Q4.a is correct? Thanks!
Lastly, verity that the rebased proposal change satisfying the 3 FSCO conditions by comparing it to the indication % (which is not rebased)
Yup this seems a bit right - Although you don't have to rebase the current and proposed differentials so you can save some time there. But there is nothing wrong with what you just did
@graham why do we not compare the actual % change after re-basing for both proposed and indicated change? In your November 2020 comment, you show the "Actual % Change " after rebasing the proposed but not for the indicated.
There's no need to because you can see that the proposed is clearly between 0 and the indicated
Another way to solve this is to determine the premium change for each territory and the capped premium change, then allocate the excess of the cap to another territory. You'll then have the target proposed premiums to calculate the territory differentials by dividing against (OLEP/Current differentials). No need to fiddle around with rebasing or checking if the changes are within range.
Below is an exhibit of what i mean...
@felixc5 I did same as you
I don't like how the answer provided states that an off-balance (rebase) is needed when using the indicated rate change (average factor of 0.9455 indicated vs 0.9401 current).
A random selection within boundaries should be accepted!
Their mistake is to use OLEP after differential (instead of backing out w/o differential)... also, the question mentions that the overall change is 0.0%, so no rebase should be needed...
This is too deep into ratemaking if you ask me