The step-by-step guides to exposure rating are comprehensive. After you have mastered the guides, review this sequence of steps.
This is a checklist, not a step-by-step guide. It does not explain the steps or the common errors. It puts together the basic and advanced step-by-step guides and gives an outline of the method.
Check first if any proportional reinsurance insures to the excess-of-loss reinsurer. For a surplus share treaty, compute the reinsurance percentage, which varies with the amount of insurance (or policy limit) on the block of business. Do this for all blocks of business, whether or not the business exposes the treaty.
Some exam problems have two parts. Part A has no inuring reinsurance; Part B has a quota share or a surplus share treaty inuring to the excess-of-loss reinsurer. Compute the reinsurance percentages before solving either part of the problem. This helps organize your work and ensures that you do not make careless errors.
Compute the subject premium. The subject premium includes all blocks of business, whether or not they expose the excess-of-loss reinsurance treaty. You don’t have to determine if a block of business exposes the treaty to compute the subject premium.
The subject premium is after inuring reinsurance; it is not the direct premium. We use the reinsurance percentage to compute the subject premium; we don’t need to know if the block of business exposes the treaty.
Don’t compute the subject premium before checking for inuring reinsurance. If you do this, you may forget to reduce the subject premium for inuring reinsurance.
Draw the coverage tree, with the following layers:
Check first if the primary insurer is an umbrella insurer, an excess insurer, or covers above a self-insured retention or a high deductible. If it is an umbrella insurer, the underlying coverage below the umbrella policy is at the bottom of the coverage tree.
An umbrella policy may drop down above a self-insured retention. A self-insured retention or a deductible is like underlying coverage.
If the umbrella policy drops down, divide it into two blocks of business: one above the underlying coverage and one above the self-insured retention. The exam problem will give the premiums or losses for each part.
The increased limit factors apply to ground-up losses. The underlying coverage affects the increased limit factors. The umbrella coverage and excess-of-loss coverage begin after the underlying coverage.
The limit of the underlying coverage may vary by block of business. The exam problem will give the premiums and the limit of the underlying coverage for each block of business.
If the primary policy is not an umbrella policy, it is the trunk of the tree (the first layer). Write the bottom of the primary policy (zero, a deductible, a self-insured retention, or the underlying coverage) and the ground-up limit of the primary policy. The ground-up limit is the policy limit plus the bottom of the primary policy.
Liability coverage has policy limits; property coverage has amounts of insurance. The amount of insurance or policy limit varies by block of business. Draw a separate coverage tree for each block of business.
Draw the excess-of-loss reinsurance.
The attachment point of the excess-of-loss treaty is a dollar amount above the bottom of the primary policy, which may or may not be $0 ground-up, depending if there is underlying coverage.
The ground-up limit of the excess-of-loss treaty is a dollar amount above the attachment point.
If the attachment point is above the limit of the primary policy, the primary policy does not expose the treaty.
If the limit of the excess-of-loss treaty is above the limit of the primary policy, the excess-of-loss reinsurer does not cover losses between the limit of the primary policy and the limit of the excess-of-loss treaty.
Inuring reinsurance (quota share or surplus share) lies between the primary policy and the excess-of-loss reinsurance treaty. The inuring reinsurance compresses the loss but does not change the attachment point or limit of the excess-of-loss treaty. We undo this compression by expanding the layer of loss. The inuring reinsurance expands the layer of loss but does not change the limit of the primary policy.
If the excess-of-loss reinsurer covers the layer A to B and the inuring proportional reinsurance is P%, the excess-of-loss reinsurer covers (1 – P%) of ground-up losses between A/(1-P%) and B/(1-P%). Memorize this relation.
Determine the costs for the ground-up layers covered by the primary insurer and the excess-of-loss reinsurer.
For liability coverage, the ground-up layers are above underlying coverage or self-insured retentions. If the underlying coverage is 0 to U, a layer from A to B is A+U to B+U ground-up.
For inuring proportional reinsurance with a reinsurance percentage of P%, the layer from A to B is A/(1-P%) and B/(1-P%) ground-up.
For umbrella coverage with inuring proportional reinsurance, the layer from A to B is A/(1-P%) + U and B/(1-P%) + U ground-up.
The inuring proportional reinsurance changes the ground-up layer of loss but does not change the attachment points and limits of the primary policy or the excess-of-loss treaty.
If the limit of the excess-of-loss treaty exceeds the limit of the primary policy, the layer of loss between the limit of the primary policy and the limit of the excess-of-loss treaty is not covered.
Illustration: The limit of the primary policy is $5 million. The reinsurance treaty is $3 million excess of $2 million.
With no inuring proportional reinsurance, the excess-of-loss reinsurer cover the layer from $2 million to $5 million.
With a 60% quota share treaty, the ground-up attachment point and treaty limit are $2 million / (1 – 60%) = $5 million and $5 million / (1 – 60%) = $12.5 million. The excess-of-loss reinsurer covers nothing.
The exposure rating percentage is the cost of the layer covered by the excess-of-loss reinsurer divided by the cost of the layer covered by the primary insurer.
With inuring proportional reinsurance, both costs are multiplied by the complement of the reinsurance percentage. This does not affect the ratio.
Pure premiums
Determine the pure premiums from the increased limit factor table (or function) for liability coverage and from the first loss table for property coverage.
The increased limit factors are ratios to the basic limits pure premium. They are 1.000 for basic limits and higher ratios for higher limits.
An exam problem may deal with the effect on inflation on increased limit factors; this is covered in a separate step-by-step guide.
The exam problem will not tell you the basic limits pure premium. The basic limits pure premium varies by the rating characteristics of the insureds. We use ratios, not dollars.
The exam problem may ask you to compute the pure premium for the block of business at the basic limit.
The exam problem will give the gross premium, the policy limit for the block of business, the expected loss ratio, and the increased limit factor table.
Divide the gross premium by the expected loss ratio to get the pure premium.
Divide the pure premium by the increased limit factor at the policy limit to get the basic limits pure premium.
We do not need the pure premium at the basic limit for exposure rating.
You have the factors needed in most exam problems. Do this computation if it helps you visualize the pure premium for each layer of loss.
The exam problem may give an increased limit factor table or a function. If the exam problem gives a function, you must compute the factors. The exam problem is likely to give a function if the problem deals with umbrella coverage over an underlying policy or with inuring proportional reinsurance. By using a function, the exam problem gives no hint what limits to use.
If you compute the factors from a function, be sure the factors are reasonable. All factors should be positive, the factors increase at a decreasing rate as the policy limit increases, and the factor at basic limits is one.
If any of these conditions are not true, check your work. It is easy to mis-read the function. If you mis-read the function, further time spent computing the exposure rate is wasted.
The factors in a first loss table are ratios to the pure premium for full coverage (the sound value of the property). This is the amount of insurance for commercial coverage and about 180% of the amount of insurance for Homeowners.
Property coverage may have deductibles. Most losses are small, so a deductible raises the exposure rating percentage.
For an exposure rating problem, the deductible may be a percentage deductible, such as 5% or 10% of the sound value, or a dollar amount that converts to a round percentage, such as a $5,000 deductible on a $100,000 property.
Liability coverage may have underlying coverage, a self-insured retention, or a large deductible. The liability deductible is a dollar amount, not a percentage.
The pure exposure rate is the ratio of pure premiums for the excess-of-loss reinsurer to the primary insurer. The reinsurance rate is the ratio of gross premiums.
We use four items to convert the ratio of pure premiums to the ratio of gross premiums.
The expected loss ratio of the primary insurer.
The exam problem may give the expense ratio and the underwriting profit provision, from which we derive the expected loss ratio.
The exam problem may give fixed vs variable expenses for the primary insurer; this is not likely.
The expenses for the reinsurer. The expenses may be of three types, all of which are likely in an exam problem.
A variable expense ratio, which is a function of the gross reinsurance premium
Fixed expenses per treaty
Loss adjustment expenses that are a function of the reinsurer’s losses
The adequacy of the primary insurer’s gross premium.
We are setting rates for the reinsurer. We assume we are setting adequate rates, and the reinsurer’s profit margin is in the variable expense ratio.
For each block of business that exposes the treaty:
Divide the subject premium by the complement of the primary insurer’s premium adequacy. The subject premium is after inuring proportional reinsurance.
Multiply the adequate subject premium by the primary insurer’s expected loss ratio.
Multiply the subject pure premium by the exposure rating percentage.
Multiply by the reinsurer’s ALAE to loss ratio.
Add the reinsurer’s fixed expenses.
Divide by the complement of the reinsurer’s variable expense ratio.
We now have the reinsurer’s gross premium. Divide this gross premium by the primary insurer’s subject premium to give the reinsurance rate. The subject premium includes blocks of business that do not expose the treaty, but it is after inuring proportional reinsurance.
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