Practice Problems: Clark Reinsurance

[i++]

Note: I did not write any questions for Section 5 (Catastrophe Ratemaking) or Section 6 (Calculating the Final Price)



1. You are a young, brilliant, and stupid actuary at Mega Reinsurance Company. You tell your boss that you just read some really jazzy classification ratemaking material and want to implement a classification rating plan for the insurance companies that you reinsure. Evaluate the appropriateness of your reinsurance company using a classification ratemaking plan for insurance companies. (1 point)

Spoiler:

A reinsurance program is generally tailored closely to the buyer. There is no such thing as the “average” reinsured or the “average” reinsurance price. Each contract must be individually priced to meet the particular needs and risk level of the reinsurer. As such, the risks are too heterogeneous to apply a classification ratemaking approach to them. The plan is not appropriate.

2. Explain why the basic ratemaking tools are inadequate for pricing reinsurance. (1 point)

Spoiler:

Insurers generally only reinsure business for which the experience is not stable enough for them to make a precise expected loss estimate. The assumptions of basic pricing models are generally not met on such volatile business where the data is thin and the loss distribution is skewed.

3. A reinsurer is participating in a surplus share treaty with the following parameters:
Retained Line: $100,000
1st Surplus: 4 Lines

Calculate the insurer and reinsurer loss ratios from the following risks: (1 point)

Spoiler:

4. You are pricing a surplus share reinsurance treaty. Describe the six steps, as instructed in Clark’s “Basics of Reinsurance Pricing”, for determine a rate for the treaty using the past experience of the insurance company. (3 points)

Spoiler:

Step 1: Compile the historical experience on the treaty. Assemble historical premium and incurred losses on the treaty for five or more years. If this is not available, the gross experience should be adjusted “as if” the surplus share had been in place to produce a hypothetical treaty experience.

Step 2: Exclude catastrophe and shock losses. Catastrophe losses are due to a single event, such as a hurricane and earthquake, which may distort experience. Similarly, shock losses are large losses due to a single risk or a single large settlement on a single policy, which may also distort experience.

Step 3: Adjust experience to the ultimate level and project to future period. Losses need to be fully developed based on loss development factors using either company or industry data. Adjustments for reporting lag to the reinsurer may also need to be performed. They also need to be adjusted for changes in benefit levels and inflation. Premium needs to be adjusted to the projection period by adjusting for rate changes, changes in pricing factors (e.g. schedule mod), premium trend, and possibly an exposure inflation factor.

Step 4: Select the expected non-catastrophe loss ratio for the treaty. If the data in step 3 is reliable, then the expected loss ratio is simply the average of historical loss ratios adjusted to the future level. It is worthwhile comparing the experience to the annual statement and industry loss ratios.

Step 5: Load for catastrophe loss. Typically there will be insufficient credibility in the historical loss period to load for catastrophe potential. Therefore you may use an alternative approach such as using a catastrophe model to estimate the catastrophe loss provision. Or you can use the average catastrophe load by state, from ISO circulars, weighted by the premium by state.

Step 6: Estimate the combined ratio given the ceding commission and other expenses. After the ELR is estimated, add in provisions for ceding commission, reinsurer general expenses, and brokerage fees. The reinsurer must evaluate whether the projected combined ratio on the treat is acceptable, taking into account potential investment income and the riskiness of the treaty.

5. A reinsurer and insurer are in discussions regarding the ceding commission on a reinsurance treaty.

The insurer is calculating the expected ceding commission using an expected loss ratio. The reinsurer is calculating the expected ceding commission using a loss ratio distribution described as below, using the expected loss ratio by the insurer as the mean.

Evaluate which method of calculating the expected ceding commission is superior. (2 points)



Provision Commission: 30%

Minimum Commission: 25% at a 65% loss ratio
Sliding 1:1 to 35% at 55% loss ratio
Sliding .5:1 to a Maximum 40% at a 45% loss ratio

Spoiler:

6. You are assisting with the renewal of a quota share reinsurance treaty. The treaty has a sliding scale ceding commission based on the loss ratio of the ceded business. In addition, the contract contains a carryforward provision. Describe a procedure for determining the effect of the carryforward provision. Evaluate the appropriateness of your given method. (1.5 points)

Spoiler:

Answer 1: Include any carryforward from past years and estimate the impact on the current year only. This amounts to shifting the slide by the amount of the carryforward. The problem with this approach is that it ignores the potential carryforward beyond the current year. For example, in the first year of the program we would calculate the expected commission for the current year as though the program would be cancelled at the end of the year. The same price would result with or without the carryforward provision – which does not seem right.

Answer 2: Look at the “long run” of the contract. The sliding scale is modeled as applying to a longer block of years rather than just the single current year. This means that the variance of the loss ratio distribution would be reduced on the assumption that bad years would be smoothed out by good experience on other years. A problem with this approach is that the method for reducing the variance is not obviously. Additionally, it ignores the fact that the contract may not renew the following year, potentially leaving the reinsured with no carryforward benefit.

7. You are an actuary working on a property excess treaty. You are asked to price the $1M xs $1M and $3M xs $2M layers.

For the $1M xs $1M you have decided to use experience rating to determine the loss cost.

Since no historical losses trend into the $3M xs $2M layer, you have decided to use the experience rating of the $1M xs $1M layer to price the $3M xs $2M layer.

Given the following information, determine the selected loss costs for both layers. (2 points)

Spoiler:

8. You are an actuary working on a homeowners property excess treaty.

You are asked to price the 500,000 xs 500,000 layer using exposure rating.
Given the following information, determine the expected losses for the reinsurer using exposure factors.

In addition, evaluate the appropriateness of using the same exposure curve for each size of insured. (2 points)

Spoiler:

9. You are an actuary working on a homeowners property excess treaty.

The insurer currently has a surplus share treaty with a different reinsurer. The insurer retains a maximum of 500,000 on any one risk.

The insurer wants to purchase a 250,000 xs 250,000 to protect against their net retention

Determine the expected losses to your company (the reinsurer). (2 points)

Spoiler:

10. Casualty excess treaties are often separated into three categories: Working Layer, Exposed Excess, and Clash Covers. Briefly describe each type of treaty. (0.75 points)

Spoiler:

Working Layer: Low layer attachment which is expected to be penetrated, often multiple times in each annual period.

Exposed Excess: Excess layer which attaches below some policy limits on the underlying limit. Typically these losses will be less frequent and there will be some years in which the treaty layer is not penetrated.

Clash Covers: High layer attachment. Typically a single loss will not penetrate the treaty layer. It will be penetrated due to multiple policies suffering a loss on a single occurrence, or when extra-contractual obligations (ECO) or rulings award damages in excess of policy limits (XPL) are determined in a settlement.

11. Describe two additional complications that arise in pricing casualty excess treaties (as opposed to property treaties). (1.5 points)

Spoiler:

• Auto losses on a split limit rather than a combined single limit basis may need modification in order to separately cap losses for bodily injury and property damage.

• Workers compensation losses will not have an explicit limit associated with them. However, because large workers compensations losses are often shown on a discounted case reserve basis, a request should be made for these losses on a full undiscounted basis.

• The selection of loss inflation is difficult. Theoretically we should use an unlimited trend factor derived from large losses only, but this may be unavailable or the data may be too thin. Using losses capped at the underlying policy limit as a source may understate the final results. There is also an implicit assumption that the same trend factor applies to all losses regarding of size.

• The trended losses must be capped at applicable policy limits. This presents another problem. Theoretically we want to cap losses at the limit that the policy would have if written today. However, what is that limit? You can use the historical limit, but insureds generally choose higher limits as inflation occurs over a period of years. If you use a limit greater than the historical limit, then you must adjust premium for the additional premium you would receive from the increased limit. There is no generally accepted solution for this problem.

13. Describe difficulties with using the Reinsurance Association of America’s published loss development factors. (1 point)

Spoiler:

• The reporting lag from the occurrence of an event to the establishment of a reinsurer’s case reserves varies by company. Included in the data is retrocessional business which may contain several levels of reporting lag.

• The mix of attachment points and limits is not cleanly broken out. RAA has started to release triangles by attachment point ranges, but this data is less stable than the total triangle.

• The RAA requests data exclusive of Asbestos and Environment claims which could distore patterns. It cannot be known if all members have done this exclusion consistently

• For workers compensation claims, members may not handle the tabular discount consistently. If the ceding company reports a loss on a discounted basis and the reinsurer establishes a reserve on the discounted value, the resulting development factor may be very high.

14. For general liability and auto liability, the industry has generally following ISO in using the truncated Pareto distribution for loss severity. The form is of E[x;L] is given by:



Where
T= Trunction point
P= Probability of small loss
S =Average small loss severity
B=scale parameter for Paretro distribution
Q=shape parameter for Pareto distribution

Give one advantage and two limitations of this formula. (0.75 points)

Spoiler:

Advantage: Scale of distribution can be adjusted easily for inflation, by multiplying T, S, and B by the same amount.

Limitation: The formula only applies for losses above the truncation point T.

Limitation: The excess factors for high layers become very dependent on the Q parameter. This parameter must be watched very carefully when curves are updated.

15. You are given the following information:

The limited (ground-up) expected values of losses X at limit Z is:



Expected Loss on Umbrella Policies = $5,000,000
ALAE = 20% of loss


A ceding company sells umbrella policys with $1M limits excess of $1M underlying

The umbrella policy provides "drop down" coverage. The probability of this coverage is 10%.

You are asked to price an umbrella reinsurance treaty covering the $500k xs $500k layer.

Determine the expected loss and ALAE assuming ALAE is covered pro rata
(2 points)

Spoiler:

16. You are given the following information:

The limited (ground-up) expected values of losses X at limit Z is:



Expected Loss on GL Policies = $5,000,000
ALAE = 20% of loss


A ceding company sells general liability policies with $2M limits.
You are asked to price a reinsurance treaty covering the $500k xs $500k layer.
a) Determine the expected loss and ALAE assuming ALAE is included with loss (1.5 points)
b) Evaluate the appropriateness of assuming ALAE is a constant percentage of loss. (0.5 points)

Spoiler:

17. Experience rating for a workers compensation excess of loss reinsurance treaty may be distorted depending on how tabular discounts are taken into effect. Describe a way to avoid distortions (1 point)

Spoiler:

Collect sufficient information for individual claimants to project their expected costs into the treaty layer. For claims with potential for penetrating the layer, all future payments should be determined. For those payments that fall into the treaty layer, an appropriate mortality factor should be applied to determine the expected amount in the treaty layer.

18. To determine the loss to a reinsurance treaty, a single distribution model can be used to project aggregate losses. Describe two advantages and two disadvantages to the single distribution model. (1 point)

Spoiler:

Advantages: Simple to use. Reasonable fit provided even when frequency and severity are unknown.

Disadvantage: If you use a single distribution such as the lognormal, there is no allowance for the loss free scenario. There is no easy way to reflect changing per occurrence limits on aggregate losses.

[TwoStep]

Thanks, this paper is my biggest pain point.

[FourKicks]

Originally Posted by i++

1. You are a young, brilliant, and stupid actuary

how'd you know?

[rj_rattigan]

Originally Posted by i++

Note: I did not write any questions for Section 5 (Catastrophe Ratemaking) or Section 6 (Calculating the Final Price)

Section 6 isn't on the syllabus, FYI.

[i++]

Originally Posted by rj_rattigan

Section 6 isn't on the syllabus, FYI.

Thanks. I did not read the syllabus carefully enough. While reading section 6, all I was thinking was "uh oh... it's exam 9 all over again".