(The attached PDF file has better formatting.)

Loss corridors are similar to sliding scale commissions. A loss corridor can be converted to the analogous sliding scale commission. For optimal exam preparation:

Loss corridors are like sliding scale commissions in that

Exam problems on loss corridor and sliding scale commissions are of several types. The easiest types test your understand of the contract provisions: Given a direct loss ratio on the subject premium, and a loss corridor or a sliding scale commission, what is the net loss ratio after reinsurance?

Many candidates understand sliding scale commissions and are confused by loss corridors. They say: "Sliding scale commissions are easier, so I will study them. I don’t have time to master loss corridors." This exam strategy is flawed.

Clark’s study note deals with reinsurance pricing. The effects of loss corridors and sliding scale commissions depend on the loss ratio distribution. The exam problem may give a discrete distribution with the average of each range or a continuous distribution, the provisions of the loss corridor or the sliding scale commission, and ask for the net loss ratios of the reinsurer and the primary insurer.

Step #1: Parameters

A loss corridor or a sliding scale commission with a constant percentage has three parameters:

A sliding scale commission with different percentages in two or more ranges is like a set of loss corridors. For exam study, focus on a single loss corridor, which is like a sliding scale commission with a minimum, a maximum, and a single sliding scale percentage (Z%).

The difference between the sliding scale commission and the loss corridor is

The difference is affects statutory accounting, not the cash payments.

The loss corridor changes the loss recoverable; the sliding scale commission changes the premium due the reinsurer or the commission due the primary insurer. They give the same net result of premium minus losses minus expenses, so the cash flow is the same.

Step #2: Loss Ratios Before and after the Loss Corridor: Reinsurer

The exam problem may ask for the expected loss ratio after a Z% loss corridor, either for the reinsurer or the primary insurer. Calculate first the loss ratio for the reinsurer.

Divide the loss ratio distribution into three ranges:

We need the mean loss ratio in each section, not the distribution of loss ratios within the range. The loss corridor effect is linear, so mean in the range gives the mean effect for the distribution in the range. (The term mean is the mean in the range.)

Step #3: Illustration of Loss Corridor

Memorize this heuristic illustration. If you know the procedure for this illustration, you can solve almost any exam problem.

A primary insurer buys a 75% quota share treaty with a 20% ceding commission and a 60% loss corridor from 65% to 80%. The direct loss ratios are uniformly distributed from 50% to 100%.

Part A: We divide the loss ratios into three sections.

For loss ratios within the loss corridor, the primary insurer takes 60% of the portion in the loss corridor. For a loss ratio of 72.5%,

For loss ratios above the loss corridor, the primary insurer takes 60% of the width of the loss corridor. For a loss ratio of 90%,

The expected loss ratio for each insurer is the weighted average. For the reinsurer:

30% × 57.5% + 30% × 68% + 40% × 81% = 70.05%

Of the ceded business, the primary insurer pays

30% × 0% + 30% × 4.5% + 40% × 9% = 4.95%

The sum of these is the overall 75% expected loss ratio on the ceded business.

(1) Reduce the loss ratio above the loss corridor by Z% the width of the loss corridor. A common error is to adjust only the loss ratio within the loss corridor. This loses full credit.

(2) A Z% loss corridor means the primary insurer takes Z% of the loss ratio points in the loss corridor, not that the reinsurer takes only Z% of the loss ratio points in the loss corridor. Reduce the reinsurer’s loss ratio by Z%, not by (1 – Z%).

Step #4: Loss Ratios Before and after the Loss Corridor: Primary Insurer

Part B: For the primary insurer, the premium is from retained business and the losses are from both retained and ceded business.

The 75% quota share treaty means the 4.95% loss ratio to ceded premium is like a 4.95% × 75% / (1 – 75%) = 14.85% loss ratio to retained premium. We multiply the loss ratio points by P% / (1 – P%).

The total loss ratio for the primary insurer is 75% + 14.85% = 89.85%.

We verify with a weighted average of the primary insurer and reinsurer loss ratios:

Total loss ratio = 25% × 89.25% + 75% × 70.05% = 75.00%

(1) Do not add 75% and 4.95% to get the loss ratio for the primary insurer. You must multiply 4.95% by P% / (1 – P%) to adjust for the percentage retained by the primary insurer.

(2) Do not multiply 4.95% by 1 / P% or 1 / (1 – P%). These adjustments may seem logical at first, but they are not correct. See the step-by-step guide to sliding scale commissions for more explanation.

Step #5: Equivalent Sliding Scale Commission

Part C: We convert the loss corridor to a sliding scale commission:

A Z% unbounded loss corridor is Z% is equivalent to a quota share reinsurance percentage of (1 – Z%) × P%. This is also a P% quota share treaty with a Z% sliding scale commission that has no maximum or minimum.

Step #6: Likely Exam Problems

After working through a practice problem, review the likely exam problems: