Premium based projection method assumption
Hi,
Under premium based proj method, when we apply historical Fixed Expense ratio to higher avg. premium then it leads to overstatement of fixed expense and it's a disadvantage of this method. But, you have also pointed out that when taking a multi-year avg. premium (incorporating a distributional shift in book of business) and then applying old fixed expense ratio to it would aggravate this overstatement problem further.
I didn't get the last point. For example, say we have a historical fixed exp ratio of 20%. If we apply this to only latest year's higher avg. premium (due to distr. shift), we are overstating fixed expense dollars. But, if we use a 3-year avg premium instead (with distr shift still increasing premium in latest year), the fixed expense dollars would be still be overstated but by a lesser magnitude according to me.
So how is this a worse case than using only 1 year's (higher) average premium after the shift, as mentioned in the article?
Thanks.
Comments
Hi Keshav,
I hope your studying is going well. If I understand your question correctly, here's an example that illustrates the point. Suppose:
Then the fixed expense ratio based on 1 year would be $10/$150 = 6.7%
But suppose average premium has been increasing so that the multi-year average is lower and that:
Then using the 3-year average, the fixed expense ratio = $10/$140 = 7.1%, which is too high. If you were to apply 7.1% to the current average premium of $150, you would get fixed expenses of $10.65, an overestimate of $0.65.
(Note that by similar reasoning, using the 1-year average premium to calculate the fixed expense ratio will still result in an overestimate of fixed expense dollars if the average premium is still increasing with that 1-year time frame. But the error will be less than if the 3-year average premium is used to calculate the fixed expense ratio.)
Graham
Hi Graham,
Thank you for asking. I am trying to revise the syllabus asap now.
In the example you gave, I think the premium based method assumes that the historical fixed expense ratio (say 10%) applies to a projected period too. In your case, say 10% is my historical ratio so 10% * 150 = $15 must be my fixed expense as per the method.
But $150 is my current (increased) premium after the distributional shift and just as you stated, the ideal fixed expense ratio given that i know the fixed expense $s must only be 6.7%.
But, as the method applies a historical fixed expense ratio (which is 10%), so in such a case if I apply this to 3-year average premium ($140), then my fixed expense would be 10% * 140 = $14 which is still overstated but by a lesser magnitude.
Anyways, I guess the doubt is not as material considering the rush hour. 😅
Well, you still have a month to go. I think you studied pretty thoroughly last time even though you didn't sit for the exam. It should all come back quickly.
For your question, I think they are talking about how you come up with the ratio in the first place. And the idea is if there is a trend, then the prior year's data is essentially outdated. So the more prior years you use, the worse your estimate of the ratio is going to be.
But you're right, that particular discussion is probably less important. The most important thing is to be able to do the calculations and have some basic idea of advantages and disadvantages of each method. If you know that, you will get most or all of the points on a question on this topic. You can return to this later if you have time.