Ratemaking Flashcards
A personal auto insurer has a highly-refined classification rating plan. In the calculation of a rate
level indication for this insurer, fully assess the use of the follojwing methods to adjust premium to
current rate level:
i. Parallelogram method
The parallelogram method is simple and doesn’t require detailed policy data. You
would just need overall rate changes and historical earned premium to on-level the premium.
However, this method is less accurate than the extension of exposures method, and the premiums
would be much less reliable when used in classification ratemaking. Furthermore, this method
assumes that policies have been written uniformly over time, and results in inaccurate on-level
premiums if this assumption does not hold.
A personal auto insurer has a highly-refined classification rating plan. In the calculation of a rate
level indication for this insurer, fully assess the use of the following methods to adjust premium to
current rate level:
ii. Extension of Exposures method
The extension of exposures method would be the more accurate method to on-level premium since it
would re-rate each policy using the current rates. Furthermore, this on-level premium would also be
accurate for classification ratemaking. However, the method might be problematic if new rating
variables have been introduced since the experience period as there might not be historical data
available related to those new rating variables. Also, the extension of exposures method requires
detailed data to be available for each policy, and it requires more time to calculate on-level premium.
An insurance market with a fixed number of insureds consists of two insurers - Company A and Company B. Company A intends to charge the true cost 200$ for High Risk insureds, and is evaluating two different prices for Low Risk insureds: $130 or $140. Company B charges $150 for all risks.
Briefly describe two possible strategies Company B could utilize in response to Company A’s
new rate plan.
• Copy company A’s new rate plan and charge different rates for low and high risk insureds. This would prevent adverse selection.
• Company B could exit the market.
• Company B could identify other rating variables not used by company A to segment the market.
• Company B could change its marketing strategy to attract more low risk insureds.
The importance of accurately estimating unpaid claims can be examined from three points of view:
internal management, investors, and regulators.
a.
Briefly describe how a redundant unpaid claim estimate can impact decisions for each of these
three groups.
• Internal Management: It could lead to decisions such as raising rates, tightening underwriting guidelines, exiting a line of business or territory, or purchasing additional reinsurance.
• Investors: It would lower the insurer’s profit, making the company appear worse to investors.
• Regulators: It could result in a regulator restricting the insurer’s ability to write business.
The importance of accurately estimating unpaid claims can be examined from three points of view:
internal management, investors, and regulators.
b.
Briefly describe how an inadequate unpaid claim estimate can impact decisions for each of
these three groups.
• Internal Management: It could lead to decisions such as lowering rates, relaxing underwriting guidelines, pursuing aggressive growth, or purchasing less reinsurance.
• Investors: It would raise the insurer’s profit, making the company appear better to investors.
• Regulators: It could make the company look better than it does, so regulators don’t get involved until it is too late to save the company.
Briefly describe two differences between asset share pricing and pure premium ratemaking when they are used to price property and casualty products.
• Asset share pricing incorporates persistency assumptions while the traditional approach
does not.
• Asset share pricing differentiates between new and renewal business while the traditional
approach does not.
• Asset share pricing looks at a cohort of policies over time while the traditional approach
looks at all policies in a given policy period.
An insurer is considering changing the exposure base for a commercial auto line of business to one
of the following:
i. Annual fuel expense
ii. Number of miles driven
Using three relevant actuarial criteria, evaluate the effectiveness of each of these potential exposure
bases.
Criteria: (any 3 of:)
• Proportional to expected loss (same as “vary with the hazard”)
- Annual fuel expense will have an unclear relationship with expected loss. More driving generally means more fuel expense, but the converse is not true. Higher fuel prices might cause insureds to drive less, reducing expected losses.
- Number of miles driven will be more directly proportional to expected loss than fuel expense.
• Practical
Both are both objective, but they would be difficult and costly to verify.
• Considerate of historical precedence
Both represent a change from the current base of car-years, so it would be costly for the insurer to make the change from an IT standpoint. Changing could also result in large premium swings for individual insureds.
• Verifiable
Both would be difficult and costly to verify.
Appropriate or not for Ratemaking?
Calendar Year Aggregation for Auto Physical Damage
Since APD is short-tailed, there will be a fairly good match between premiums and losses. CY is also the most responsive method. As such, this would be mostly appropriate.
Appropriate or not for Ratemaking ?
Policy Year Aggregation for Homeowners
PY provides the best match between premiums and losses, but it takes the longest to develop. Since homeowners develops fairly quickly, PY would not be appropriate, and AY would be more appropriate.
Appropriate or not for Ratemaking?
Report Year Aggregation for Medical Professional Liability
Assuming policies are claims-made, this is appropriate since coverage is provided based on the report date of a claim, and RY data develops a little faster than PY data. However, if policies are occurrence, then RY would not allow for easy analysis of pure IBNR, so it would not be appropriate.
Describe a scenario in which a mature claims-made policy would cost more than an occurrence
policy.
If loss costs are decreasing (speedup in settlement like reducing period of report), then the occurrence policy loss costs would experience more of that
negative trend than the mature CM policy due to the report lag of the occurrence policy, so the
occurrence policy would cost less.
Briefly discuss why a premium trend should be utilized in a rate level indication.
Premium trends adjust for premium differences between the historical and future periods based on things like mix of business changes and socio-economic trends.
Briefly discuss why it is inappropriate to use written premium at historical rate levels to determine premium trends.
Using premium at historical rate levels in selecting a premium trend would be inappropriate since the one time rate changes would be picked up by the trend, though we don’t expect these to continue into the future. This could lead to inaccurate projections.
Assess whether annual or quarterly triangles are more appropriate for a small company selling a long-tailed line of business.
Annual triangles are more appropriate in this case. Since the company is small and the line of business has a long tail, the triangles are likely to have low credibility and unstable development. Separating the data further into quarterly triangles would compound this issue, which would make it more difficult to select appropriate loss development factors.
Identify two reasons an actuary may want to split expenses into fixed and variable components instead of using all variables method.
Assuming all expenses are variable when some are truly fixed will overcharge high premium risks and undercharge low premium risks.
Fixed expenses may be impacted by trend, so separating them allows for the application of trend factors to produce a more accurate expense load.
Describe one situation in which it is preferable to use the loss ratio method, and one situation in which it is preferable to use the pure premium method.
The loss ratio method is better when exposures are not clearly defined or not available.
The pure premium method is better for a new line of business since there is no existing premium.
Loss ratio or pure premium ratemaking method ?
A company introduced two new rating variables within the past year.
The pure premium method would be better since it may be difficult to bring the premium to current in the loss ratio method for the new variables, as historical policy data may not exist for those variables.
Loss ratio or pure premium ratemaking method ?
A company is entering a new line of business.
The pure premium method would be better since there is no existing rate for the new line of business to which an indicated change can be applied.
Loss ratio or pure premium ratemaking method ?
A company writes a commercial product with multiple exposure bases.
The loss ratio method would be better since exposures underlying the pure premium method may not be clearly defined.
Fully discuss how an insurance company can “skim the cream” to gain a competitive advantage.
If an insurer identifies a lower risk group that is not being recognized by its competitors, it can
attract more customers from that group using marketing and underwriting guidelines. The insurer
will benefit from the higher profitability of these customers, resulting in a lower overall loss ratio.
This is known as “skimming the cream.”
An insurance company is considering using a rating factor based on a detailed psychological profile.
Identify and briefly explain two of the criteria for desirable classification rating factors.
It should be cost effective to obtain the data necessary to classify risks properly for the new rating variable.
The rating variable should respect personal privacy.
Based on two relevant criteria, propose and briefly justify an appropriate exposure base for a general liability policy for a restaurant.
• Proportional to expected loss: Sales will be very proportional to expected loss since more sales means more customers that could be injured, and busier restaurants may be perceived to have deeper pockets for lawsuits.
• Practical: Sales is practical because it is objective and easy to obtain and verify from company accounting statements.
• Considerate of historical precedence: Since sales is commonly used for restaurant GL policies, it won’t be costly to change (resulting in IT costs and large premium swings for insureds).
• Inflation sensitive: Sales is inflation sensitive, so in times of significant (unexpected) loss inflation, this can help generate additional revenue to help offset the increasing costs.
Based on two relevant criteria, propose and briefly justify an appropriate exposure base for a hospital professional liability policy.
I would choose payroll as the exposure base based on:
• Practical: Payroll is already used and audited for Workers’ Compensation, so it would be easy to use here as well. Also, it is objective and easy to obtain and verify from company accounting statements.
• Inflation sensitive: Payroll is inflation sensitive, so in times of significant (unexpected) loss inflation, this can help generate additional revenue to help offset the increasing costs.
Briefly describe one advantage and one disadvantage of calendar year data aggregation.
Advantage: any 1 of:
• No development, so results are final after year is over
• Readily available since used for financial reporting
Disadvantage: provides a poor match in timing between premiums/exposures and losses.
Justify an appropriate data aggregation approach for a risk classification plan for a long-tailed line of business.
Because of the long-tail, policy year would be the strongest answer here. Calendar/accident year or
accident year were also accepted. Report year was accepted if you stated that you assumed the long-tailed
line was on a claims-made basis.
Policy year would be most appropriate since it would provide a perfect match between
premiums/exposures and losses, which would otherwise have a greater mismatch for a
long-tailed LOB as loss transactions can occur for many years after policies are in-force.
Justify using report year data aggregation for a claims-made line of business.
Since the coverage trigger for claims-made policies is the reporting of a claim, it is natural to analyze claims-made policies using RY aggregation. At the end of a year, all claims stemming from coverage provided during that year will be a fixed and known quantity as they need to be reported in order to be covered.
Discuss the appropriateness of applying total limits trend to losses at basic limits for purposes
of ratemaking.
A total limits trend would be inappropriate to apply to basic limits losses since it would ignore that basic limits losses cannot exceed the basic limit. If trends are positive, the total limits trend would overestimate trended basic limits losses.
Identify two non-pricing solutions that could return the fundamental insurance equation to balance to avoid anti selection with unprofitable risks.
• Stop marketing to unprofitable risks and focus marketing to profitable risks.
• Change underwriting guidelines to limit new business from unprofitable risks.
• Reduce expenses (e.g., lay off employees or reduce commission rates).
• Reduce/limit contractual coverage provided to reduce losses (without lowering premiums).
• Accepting a lower target underwriting profit
Identify two non-pricing solutions that could return the fundamental insurance equation to balance to avoid anti selection with unprofitable risks.
• Stop marketing to unprofitable risks and focus marketing to profitable risks.
• Change underwriting guidelines to limit new business from unprofitable risks.
• Reduce expenses (e.g., lay off employees or reduce commission rates).
• Reduce/limit contractual coverage provided to reduce losses (without lowering
premiums).
• Accepting a lower target underwriting profit
Briefly describe two considerations when choosing the maturity age of the tail severity.
Any 2 of:
• Combine data at the age at which results become erratic, since combining the data may provide more stability.
• The influence on the total projections of selecting a particular age. If the impact on the total estimate is very small, more refined analysis may not be necessary.
• The percentage of claims expected to be closed beyond the selected age. Enough claims should be there to provide a more stable severity estimate when grouped, but not too many claims since some should remain to provide estimates for earlier maturities where the age-to-age factors are more stable.
ALAE method
Briefly describe when it is more appropriate to use an additive development approach than a multiplicative development approach.
An additive approach can be more stable if the ratios are very small at early maturities.
ALAE method
Briefly describe one advantage and one disadvantage of the ratio techniques (additive vs multiplicative).
Advantage: any 1 of:
• They recognize the inherent relationship between claims and ALAE.
• The ratio development factors tend to be less leveraged than the development factors based on ALAE dollars.
• The ratios can be used as a diagnostic and a judgmental selection can be made.
Disadvantage: any 1 of:
• There may be claims with no claim payment but substantial ALAE, which may distort
ratios.
• An error in the estimation of ultimate claims will lead to an error in the estimation of ultimate ALAE.
Identify one potential use of in-force premium other than estimating earned premium.
• Managing catastrophe exposure
• Getting modeled catastrophe loads as a ratio to premium for a rate indication
• Calculating the direct effect of a rate change
Identify three other complements of credibility appropriate for first dollar ratemaking.
• Loss costs of a larger group that includes the group being rated (e.g., countrywide)
• Loss costs of a larger related group (e.g., neighboring larger state)
• Rate change from the larger group applied to present rates
• Harwayne’s method (for class ratemaking)
• Competitor’s rates
Briefly describe one difference between occurrence policies and claims-made policies regarding each of the following:
i. Coverage trigger
ii. Loss development
iii. Investment income
i. For CM the trigger is the reporting of a claim
for occurrence it is the occurrence of a claim.
ii. For CM there is only IBNER at year-end since all claims are reported
for occurrence there is both IBNER and pure IBNR.
iii. Investment income is greater on occurrence since there is more time before claims are paid to invest premiums (report lag + settlement lag), while CM policies only have settlement lag.
Briefly explain whether a claims-made policy or an occurrence policy would be more underpriced if the actual loss cost trend by report year is 10% instead of 3 %.
The claims-made policy would be impacted very little if at all by the higher trend, while the occurrence policy would have the true cost increase significantly for claims reported in future years but occurring during the policy period.
Briefly explain why a claims-made policy will cost less than an occurrence policy.
Technically, the statement in this question is only true if the loss cost trend is positive If it was negative, then a claims-made policy could cost more than an occurrence policy.
A mature claims-made policy covers losses reported in a year, so going across a row in the given table. An occurrence policy covers losses occurring in a year, so going along down a diagonal of the table. Since the loss cost trend is positive, the occurrence policy will cover losses at higher cost levels.
Explain why trending and developing losses do not result in overlapping adjustments.
Development brings the data from each historical period to its ultimate level, while trending reflects the difference in ultimate levels from one historical period to the next.
In ratemaking terms for losses, loss development makes sure that the future policy is priced to cover ultimate losses, while loss trend makes sure that the ultimate losses are at the cost levels corresponding to the future policy period.
Discuss whether there is a need to explicitly account for the following costs in primary ratemaking:
i. Proportional reinsurance
ii. Non-proportional reinsurance
i. Proportional reinsurance results in the reinsurer assuming the same percentage of premiums and losses, so there is no need to explicitly include it in rate indications.
ii. Non-proportional reinsurance does need to be explicitly included in primary ratemaking since the insurer cedes different percentages of premium and loss. It is often accounted for as a net fixed cost.
Identify two sources of investment income considered in the total profit provision.
• Investment income on investor supplied capital
• Investment income on policyholder-supplied funds
Graders also accepted answers of: unearned premium, loss reserves, IBNR, case reserves, stocks, bonds, mutual funds, real estate, dividends, interest, and capital gains.
Briefly discuss whether trending is necessary for the following:
i. Variable expenses
ii. Fixed expenses when using the exposure-based projection method
iii. Fixed expenses when using the premium-based projection method
i. No trending is necessary for variable expenses since the expenses automatically adjust as premium changes.
ii. Fixed expenses (and exposures if the exposure base is inflation-sensitive) should be trended before calculating the fixed expense provisions.
iii. Fixed expenses and premiums should be trended if they are changing at a significantly different rate.
Briefly describe one similarity and one difference between the purposes of risk classification
and individual risk rating.
Similarity: both attempt to more accurately price individual risks
Difference: Risk classification groups risks and only uses group prior experience, while individual risk rating uses individual risk information/experience
Briefly describe a situation for each of the following:
i. A classification rating plan is more appropriate than individual risk rating
ii. Neither a classification rating plan nor individual risk rating is necessary
i. Any 1 of:
• When risks are small and lack individual credibility
• When risks are very homogeneous
ii. Any 1 of:
• If all risks have the same expected loss cost
• If rates are set by state regulators
• There is no competition in the market
Briefly describe three reasons a rating characteristic might not be included in a classification rating plan.
Any 3 of:
• It is illegal to use
• It is too costly to obtain the data for each insured
• It isn’t correlated with loss experience to a statistical significant degree
• It is statistically significant, but the impact is too small to be meaningful
• Too few insureds have the characteristic to make it worthwhile it implement
• It is hard to define objectively
• It would create affordability issues for insureds if implemented
• It would be controversial/invade privacy, which would create bad press for the insurer
Describe two tests to consider when evaluating the inclusion of a variable in a GLM model.
• Standard Errors - if the predicted relativities have narrow confidence intervals that don’t overlap with the confidence intervals of other levels, then the variable provides statistically significant differentiation between levels.
• Chi-squared (or p-values, or t-tests, or F-tests) - Use a test statistic such as chi-squared to
measure whether the inclusion of the variable is statistically significant at a pre-determined
level (e.g., 5%). If the variable is significant, it should be included.
• Judgment - The implications of including the variable should be considered from both a business perspective and a common sense perspective. If it makes sense (and is predictive), then it should be included.
Describe how coinsurance provisions promote equitable rates.
Coinsurance provisions adjust the amount that insurers pay on claims proportional to the amount of underinsurance. This ensures that after the coinsurance penalty is considered, all risks will have an equal loss cost per $1k of coverage, which makes a single rate per $1k of coverage equitable regardless of varying ITV levels.
