The section on "Loss Capping Ratios" on pages 624 through 627 assumes knowledge of Table M. For instance, to fully master this section, you must know what the "insurance charge" refers to (page 624), and you must know what an "entry ratio" is, or what the phrase "to enter Table M" means (page 625). If you have already taken Part 9, these items are trivial. Most Exam 6 candidates are initially stumped by them. The terms are defined in the paper, though the definitions are concise.
The following paragraphs elaborate on some of the terms and concepts discussed in the text. Complete understanding of these concepts requires knowledge of Table M; exam questions requiring detailed knowledge are unlikely. The following explanations should suffice for Exam 6.
The "net insurance charge" is defined as the "charge at max" minus the "savings at min" (page 624) This definition is shorthand for "the amount of premium that the insurer loses because of the maximum premium limitation" minus "the amount of premium that the insurer gains because of the minimum premium limitation."
The "entry ratio at the max" is defined on page 625 as "(loss ratio at max/actual loss ratio)." When you first read this, this seems like gobbledegook. Table M works by entry ratios, not by loss ratios. When you study Table M, this is very confusing, since the entry ratios look like loss ratios, they behave like loss ratios, and some candidates even hear them talking like loss ratios. Suppose that the actual loss ratio for a book of business is 60%. At this loss ratio, there would be no premium limitation, either maximum or minimum. Suppose that if the loss ratio were instead 90%, then you would hit the maximum premium limitation. The "entry ratio at the max" is 90% / 60% = 150%.
Candidates who have experience with Table M may wonder at the use of "actual loss ratios" here instead of "expected loss ratios." Table M normally is used with ultimate loss ratios. Teng and Perkins are extending the use to reported loss ratios at interim development points. The "actual loss ratios" which they use are the ultimate loss ratios multiplied by the expected reporting percentages at each development date.
The comments above help you understand the terms. The text of this section is still obscure to most candidates. You must understand how Table M works. This is complex; here is a brief summary. Table M determines the insurance charges by positing a loss ratio probability distribution function. For instance, 10% of the time, the overall loss ratio will exceed 100%; another 20% of the time, the overall loss ratio will be between 90% and 100%; and so forth.
Think now of the Pinto and Gogol paper, and especially of the explanation of this paper in the recommended study schedule. Pinto and Gogol, using the ISO data, show that the loss severity probability distribution function changes shape as the losses develop. That is why excess loss development factors are greater than total loss development factors. Teng and Perkins assume that the "loss ratio probability distribution function has the same shape throughout all development stages." Make sure you understand the difference between Pinto and Gogol versus Teng and Perkins. Pinto and Gogol actually checked the ISO data to see how the severity p.d.f. changes shape as losses develop. Teng and Perkins are not saying that the loss ratio p.d.f. stays the same. They are saying that the changes are probably not material to their analysis, so one can get sufficiently accurate results by assuming that the p.d.f. stays the same. See the paragraph in the middle of page 625: "If it is assumed that the loss ratio probability distribution function has the same shape throughout all development stages, then at each retro adjustment one may enter Table M by defining two entry ratios."
On page 627, Teng and Perkins note that this assumption may not be correct:
By using Table M to calculate the loss capping ratios, one major assumption is that the loss ratio probability distribution function underlying Table M is appropriate for all retro adjustment periods. This may not be true. The procedure can be refined by using a loss ratio distribution that is more appropriate for each retro adjustment period. Such distributions may be calculated from empirical data at the proper evaluation dates, and be used to replace or modify the Table M distribution, depending on the credibility of the empirical data.
Now look at page 626, second paragraph from the bottom. Table M assumes that the loss ratio p.d.f. differs by size of policy. This makes sense. A large policy with a standard premium of $200 million would have a very compact loss ratio p.d.f., since most random fluctuation is eliminated by the enormous size of the policy. In contrast, a small policy with a standard premium of $20,000 would have a very diffuse p.d.f., since there is much random fluctuation. Teng and Perkins have to assume an average policy size for their analysis; they use $750,000. This seems like a lot, but it is reasonable. Most Fortune 500 companies have workers’ compensation premiums well in excess of a million dollars.