Chapter 14: Best estimate reserves

Question 1

In SAM, the best estimate is characterised as:

Answer 1

• A point estimate
• Not inherently optimistic or pessimistic
• Based on sound and appropriate actuarial or statistical techniques
• Based on current and credible information
• Nothing is said in the requirements about the skewness of the underlying distribution or its volatility

Question 2

Data required for reserving:

Answer 2

• Dates of reporting and occurrence
• Paid claims (gross and net of reinsurance)
• Case estimates
• Premiums
• Number of claims
• Other measures of exposure (e.g. turnover, payroll and vehicle years)
• Expenses (direct and indirect)

Question 3

Advantages of grouping data according to accident year in run-off triangles:

Answer 3

• All claims stem from the same exposure cohort and thus subject to the same risk environment

Question 4

Disadvantages of grouping data according to accident year in run-off triangles:

Answer 4

• Full amount of claims in the cohort is not known until the last claim is reported
• Relies on detailed claim record being maintained

Question 5

Advantages of grouping data according to underwriting year in run-off triangles:

Answer 5

• We can follow the total outcome of all policies written in each year
• Can follow claims that arise from a particular group of policies that are subject to the same set of premium rates and use the results to test the adequacy of premium rates
• Terms, rates and conditions are more stable
• Projection will ensure IBNR, recoveries and reopened claims are automatically included, provided emergence of newly reported/reopened claims are allocated to correct underwriting year

Question 6

Disadvantages of grouping data according to underwriting year in run-off triangles:

Answer 6

• Takes more than a year before all the claims under this cohort have occurred and reporting delays will extend this further

Question 7

Advantages of grouping data according to reporting year in run-off triangles:

Answer 7

• No further claims will be added to the cohort after the end of the origin reporting period
• Can help us monitor the development of notified claims to assess the delay before reliable estimates can be observed for claims once they are notified to the insurer

Question 8

Disadvantages of grouping data according to reporting year in run-off triangles:

Answer 8

• Projections won’t allow for IBNR. A separate allowance for IBNR claims will be needed
• Claims would have come from many different exposure periods, each of which may have differed in volumes of business, cover applying, claim settlement patterns and claim environments
• Won’t pick up changes in exposure or risk profile
• Difficult to find an exposure base that would correspond to the definition of risk under the claim being developed. Possibilities include average premium and current year’s premium

Question 9

Considerations when grouping data for reserve estimation purposes:

Answer 9

• Materiality
• Homogeneity of data
• How to deal with large/catastrophic losses
• How to deal with latent claims

Question 10

We can apply benchmarks in different ways, including:

Answer 10

• Age to age development factors
• Ultimate to paid/incurred factors
• Ultimate loss ratios
• IBNR as a percentage of paid: outstanding or incurred
• IBNR as a percentage of premium

Question 11

Issues that may affect the stability of the claims’ development patterns:

Answer 11

• Changes in terms and conditions
• Distortions in the data
• Changes in the claims handling processes
• Market wide initiatives
• Claims reviews
• Seasonality
• Changes in the commencement of writing policies
• Changes in average policy length
• Changes in reserving policy – the way case reserves are set influences the incurred claims development
• Developments in the business, economic and legal environment – future inflation, recession/economic upturn, legislation, accounting changes

Question 12

Methods of calculating reserves:

Answer 12

• Basic Chain Ladder method
• Inflation-adjusted Chain Ladder method
• Expected loss ratio method
• Bornhuetter-Ferguson method
• Average Cost per Claim (ACPC) method

Question 13

Assumptions of the Basic Chain Ladder method:

Answer 13

• The future pattern of claims development derived from past experience should remain stable
• There should be enough data available that can be grouped into homogenous reserving classes
• Unusual development factors or trends in development factors need to be understood and judgement applied in selecting appropriate development factors
• The most developed cohort is assumed to be fully developed. If this isn’t the case, then a tail factor needs to be applied
• The data used in the BCL calculations should be accurate and reconcile to the financial statements

Question 14

Problems that arise when using the Basic Chain Ladder method:

Answer 14

• Analysis of development factors for trends, usual values or cohorts which appear unusual compared to others. Understand the underlying reasons and consider whether the development factors are appropriate to include in projections
• The need for judgement to understand the factors underlying the development factors and ensure data anomalies are queried and understood
• In some cases, full triangles may not be available. In these cases, we need to make approximations
• In theory, paid and incurred ultimate claim amounts should converge, but in practice they likely wont
• There may be development factors with values less than one and the appropriateness of this needs to be considered

Question 15

Method for carrying out a Basic Chain Ladder calculation:

Answer 15

1. Tabulate claims on a cumulative basis by development year/origin year
2. Calculate development ratios
3. Apply these ratios to complete the table
4. From the cumulative results, find the amounts expected to be paid in each future development year/origin year cell

Question 16

Strengths of the Chain Ladder method:

Answer 16

• Can be applied to a variety of sets of data
• Provided the data can be arranged into a development triangle, the chain ladder method can be used to project it to ultimate
• The basic method can be easily modified to allow for any distortions
• The method is conceptually straightforward, and it is relatively easy to relate results back to the pattern of development
• The method can be developed to serve as a starting point for a number of other methods

Question 17

Weaknesses of the Chain Ladder method:

Answer 17

• Results can be distorted by unusual experience
• Limited use for recent cohorts, particularly for longer-tailed classes
• Considerable care is needed in applying the method to prevent unusual features in the data having a significant impact on the results

Question 18

Methods related to the Chain Ladder method:

Answer 18

• Berquist-Sherman method
• Curve fitting
• Trend analysis

Question 19

Strengths of the Expected Loss Ratio method:

Answer 19

• Not distorted by anomalous data which has a particular impact on longer tailed business and at early durations

Question 20

Weaknesses of the Expected Loss Ratio method:

Answer 20

• Ignores the pattern of claims development to date
• It is difficult to adjust for large claims
• If loss ratios are derived from past years, the method may replicate past biases
• The benchmarks used may not be appropriate as the business written may be different from that to which the benchmarks relate
• The ultimate loss ratios for previous years may be understated or overstated because of fluctuations in experience. Changes in the underwriting/claims environment may make them unsuitable for use
• The underlying assumptions can be subjective, especially when based on the underwriters’ opinion
• Where premium rate changes are introduces, these are often only for renewed business and not for new business

Question 21

Strengths of the Bornhuetter-Ferguson method:

Answer 21

• Can be used when the claims data is at a very early stage of development

Question 22

Weaknesses of the Bornhuetter-Ferguson method:

Answer 22

• Can be difficult to gather the information for the prior estimate for the claims

Question 23

Problems that arise when using ACPC method:

Answer 23

• Claim number:
  o Projected reported claims can provide a short-tailed projection of the ultimate numbers of claims as claims are often reported more quickly than settled
  o The definition of a settled claims is important to consider when using settled claims to project ultimate number of claims
  o Define carefully how reopened claims are treated so they don’t distort the number of settled claims and hence the average cost per claim
• Claim amounts:
  o Data needs to be adjusted for inflation
  o Allow for large claims that may or may not have been notified or recognised as being large

Question 24

Strengths of the ACPC method:

Answer 24

• Easy to understand and communicate
• Provide information on how claim numbers and amounts are expected to develop in future
• The data is generally available, especially for direct business
• Can be used alongside other projection techniques
• Helps explain volatile data and results when data contains only a small number of claims
• Can be applied to settled claims when claims reserving protocols have changed over the development history
• Can be useful as a basis for estimating latent claims because we can make explicit assumptions about the average claim size, long-term effect of inflation and expected number of claims

Question 25

Weaknesses of the ACPC method:

Answer 25

* Can be distorted by reopened claims, nil claims or partial repayments * Assumes the distribution of claims is the same for each origin year or settlement year * Needs more detailed information, which may not always be available * Small data samples may lead to volatile results (common with other projection techniques)

Question 26

Distortions which invalidate the underlying assumptions of reserving methods are often caused by:

Answer 26

* Errors in the data * Large claims * Inflation * Latent claims * Catastrophes * Changes in procedures * Changes in the mix of business * Lack of data