Ratemaking Flashcards
(116 cards)
1
Q
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
A
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.
2
Q
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
A
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.
3
Q
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.
A
• 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.
4
Q
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.
A
• 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.
5
Q
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.
A
• 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.
6
Q
Briefly describe two differences between asset share pricing and pure premium ratemaking when they are used to price property and casualty products.
A
• 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.
7
Q
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.
A
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.
8
Q
Appropriate or not for Ratemaking?
Calendar Year Aggregation for Auto Physical Damage
A
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.
9
Q
Appropriate or not for Ratemaking ?
Policy Year Aggregation for Homeowners
A
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.
10
Q
Appropriate or not for Ratemaking?
Report Year Aggregation for Medical Professional Liability
A
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.
11
Q
Describe a scenario in which a mature claims-made policy would cost more than an occurrence
policy.
A
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.
12
Q
Briefly discuss why a premium trend should be utilized in a rate level indication.
A
Premium trends adjust for premium differences between the historical and future periods based on things like mix of business changes and socio-economic trends.
13
Q
Briefly discuss why it is inappropriate to use written premium at historical rate levels to determine premium trends.
A
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.
14
Q
Assess whether annual or quarterly triangles are more appropriate for a small company selling a long-tailed line of business.
A
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.
15
Q
Identify two reasons an actuary may want to split expenses into fixed and variable components instead of using all variables method.
A
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.
16
Q
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.
A
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.
17
Q
Loss ratio or pure premium ratemaking method ?
A company introduced two new rating variables within the past year.
A
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.
18
Q
Loss ratio or pure premium ratemaking method ?
A company is entering a new line of business.
A
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.
19
Q
Loss ratio or pure premium ratemaking method ?
A company writes a commercial product with multiple exposure bases.
A
The loss ratio method would be better since exposures underlying the pure premium method may not be clearly defined.
20
Q
Fully discuss how an insurance company can “skim the cream” to gain a competitive advantage.
A
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.”
21
Q
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.
A
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.
22
Q
Based on two relevant criteria, propose and briefly justify an appropriate exposure base for a general liability policy for a restaurant.
A
• 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.
23
Q
Based on two relevant criteria, propose and briefly justify an appropriate exposure base for a hospital professional liability policy.
A
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.
24
Q
Briefly describe one advantage and one disadvantage of calendar year data aggregation.
A
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.
25
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.
26
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.
27
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.
28
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
29
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
30
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.
31
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.
32
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.
33
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
34
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
35
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.
36
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.
37
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.
38
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.
39
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.
40
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.
41
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.
42
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
43
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
44
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
45
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.
46
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.
47
Describe how coinsurance provisions promote adequate rates.
Solution 1: no impact on overall rate adequacy
Coinsurance doesn’t help address rate adequacy. It assumes risks insured to the coinsurance requirement are rate adequate, and adjusts losses paid for underinsured risks to have the same loss cost per $1k of coverage as the risks insured to the coinsurance requirement. But it doesn’t address whether the fully insured rate is adequate.
48
Briefly evaluate the number of occupants based on the three criteria of an exposure base for homeowners insurance
Proportional to expected loss: It isn't intuitive that number of occupants in the home is directly proportional to homeowners expected losses.
For instance, I wouldn't expect that having five people in a home versus one makes expected losses five times higher.
Practical: It would be difficult to accurately verify the number of occupants in a home, and furthermore, it can change significantly over time.
Considerate of historical precedence: Since the common exposure base for homeowners is house-years, changing to number of occupants would potentially cause significant premium swings to individual insureds and could require significant IT costs to make this change.
Overall, it is not a good exposure base for homeowners.
49
Briefly discuss an advantage and disadvantage of using the following data to determine loss trend for this state:
i. Competitor filings
ii. Internal company data
i. Competitor filings have the advantage of being easy to obtain if the filings are publicly available in the state.
You could have also said they have a logical relationship to the loss trend for the company itself in the same state/LOB.
Competitor filings have the disadvantage that they may be biased if the competitor book of business is different than the mix of business for the company.
You could also have said they are inaccurate if obtaining filings for a small competitor with limited data.
Internal data has the advantage of having a logical relationship to the desired trend as it would be for the same company.
You could also have said it is easy to obtain (but perhaps not if you already used this for competitor filings). You could also have said it would be accurate if using data from larger states or countrywide data.
Internal data has the disadvantage of being biased as the company has no data for the new state.
50
Explain the loss development and trending overlap fallacy.
There is no overlap between loss development and loss trend. 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.
51
Briefly describe one advantage and one disadvantage of using classical credibility.
Advantage: any 1 of:
- Classical credibility is the most commonly used form of credibility.
- Data (e.g., claim counts or exposures) is readily available for classical credibility.
- Computations for classical credibility are relatively straightforward.
Disadvantage: any 1 of:
- It involves making simplifying assumptions that may not be true in practice.
- It does not take into account the quality of the complement (it is judgmental).
52
Describe one reason to use an excess loss factor when setting property insurance rates.
A long-term average loading of excess losses via an excess loss factor helps reduce the volatility in indications from year to year due to the presence or absence of large individual claims. Without an ELF, inappropriate large premium swings could result.
53
A company is considering whether to use vehicle color as a private passenger auto rating variable for bodily injury coverage.
Evaluate the use of vehicle color as a rating variable using two operational criteria.
Expense: The cost to verify the color of an insured’s car would be relatively inexpensive, so this
criterion is met.
Objective: The color of a car may not be clearly defined, so this criteria may not be met. For example, it isn’t clear whether a turquoise car should be classified into green or blue.
54
A company is considering whether to use vehicle color as a private passenger auto rating variable for bodily injury coverage.
Evaluate the use of vehicle color as a rating variable using two social criteria.
Privacy: The color of the insured’s car is easily seen by anyone, so it does not infringe upon personal privacy. As such, this criterion is met.
Causality: It is not intuitive that the color of the insured’s car has a cause and effect relationship
with losses. As such, this criterion is not met.
55
An insurer is considering changing the exposure base for boat owners line of business from boat-years to the insured value of the boat.
The insurer offers the following coverages for boat owners:
i. Liability coverage pays for damages to another boat or injuries of people not on the insured’s boat.
ii. Physical damage coverage pays for damages to the insured’s boat caused by common risks,
such as sinking, fire, storms, theft, and collision.
Using three criteria for a good exposure base, evaluate the effectiveness of the proposed change in
exposure base for both liability and physical damage coverages and provide a recommendation for
the preferred exposure base.
Proportional to expected loss: The insured value of the boat does not seem to be as relevant to boat accidents as boat-years, so boat-years would be more proportional to expected liability losses. The
insured value would likely be more proportional to physical damage losses.
Practical: Boat-years is very practical as it is only based on the number of boats and policy term length. The insured value of the boat may have to be estimated (especially if insured to replacement cost), so it would be less practical for both liability and physical damage.
Considerate of historical precedence: Since boat-years is the existing exposure base, changing to insured value may be costly and disruptive. So sticking with boat-years would be less costly for both liability and physical damage.
Overall, I’d recommend sticking with boat-years as the overall downsides of switching to insured value are greater than any potential benefit for physical damage proportionality.
56
Two methods of deriving expense provisions in ratemaking include the premium-based projection method and the exposure-based projection method.
a. For each method, briefly describe how both fixed and variable expenses are treated.
Premium-based method: Fixed and variable expenses are divided by historical premiums to get fixed and variable expense ratios.
Exposure-based method: Variable expenses are divided by historical premiums to get variable expense ratios (same as premium-based method). Fixed expenses are divided by historical exposures to get an estimated fixed expenses per exposure, which can then be trended to the future level.
57
Two methods of deriving expense provisions in ratemaking include the premium-based projection method and the exposure-based projection method.
b. Briefly describe one shortcoming (or distortion) of each method.
Premium-based only: at most 1 of:
• If premiums haven’t been on-leveled for rate changes, then fixed expense ratios will be distorted.
• If premiums and fixed expenses are trending at different rates, then fixed expense ratios will be distorted.
• If countrywide fixed expenses are being allocated to states, then states with higher average premiums will get higher expense allocations, which may not be fair.
Both methods:
• Splitting expenses into fixed and variable is done with a lot of judgment, and perhaps could be more scientific.
• Allocating countrywide expenses to the state level can cause inequities across states.
• Some expenses that are considered fixed actually do vary by characteristics such as new business vs renewal. If the distribution of these characteristics varies by state or is changing over time, then fixed expense allocations may be distorted.
• The existence of economies of scale in a changing book will lead to increasing or decreasing fixed expenses per exposure (or premium). This impacts could be more directly identified and quantified.
58
Briefly discuss three challenges associated with performing GLM analysis on loss ratio data.
• Premiums need to be on-leveled at a granular level
• Actuaries don’t have a priori expectations of loss ratio patterns, as loss ratios depend on thecurrent rates
• Loss ratio models become obsolete when rates are changed
• There is no standard distribution for modeling loss ratios
59
GLM analysis is widely accepted in classification ratemaking. Briefly discuss one reason that
univariate analysis may be more appropriate than GLM analysis.
• Univariate analysis is much simpler to calculate and can be done quickly
• Univariate analysis is simpler to explain and is intuitive
60
Discuss the process by which an actuary would develop new rating territory definitions. Briefly explain a consideration for each step in the process.
• First choose a basic geographic unit, such as zip codes. Large areas like counties may not be
granular enough, but areas like zip codes can have changing definitions over time.
• Next the geographic systematic risk for each geographic unit needs to be estimated. GLMs
are recommended over univariate methods for this, and GLMs can incorporate
geo-physical or geo-demographic variables as part of this geographic component of the
models, as well as a variable for residual geographic variation.
• Spatial smoothing can then be done on the geographic residual variable to smooth results
across neighboring areas and attain greater credibility. One of the 2 basic smoothing
approaches can be chosen: distance-based (better for weather) or adjacency-based (better
for socio-demographic perils like theft).
• Finally, clustering cab be done to group units into territories. Unless a specific constraint is
added to the clustering method, non-contiguous territories can result, which would
generally be undesirable.
61
A company writes homeowners insurance in a large state divided in half by a mountain range. The
company currently uses two geographic rating territories, one on either side of the mountains, as the
range has an effect on weather patterns. Each territory has sufficient exposures for its loss experience
to be considered fully credible.
a.
Briefly discuss two disadvantages of the company’s current territorial rating approach.
Any 2 of:
• The company only uses 2 territories for the entire state, but there is likely much more
geographic variation of loss propensity within the state.
• Competitors might be using more granular territory definitions, which could subject the
company to adverse selection.
• Homeowners losses are due to more than just weather, so basing territorial decisions only
on weather does not recognize how other perils vary across the state.
• There might be a significant change in rates for neighboring homes on either side of the
current territorial boundary.
62
Identify 2 scenarios that could lead to a negative premium trend when analyzing average premium at current level
1. customers could be moving to higher deductibles
2. Customers could be purchasing less coverage
3. Insurer might be writing more lower risks
4. Insurer might be non renewing higher risks
63
State and briefly discuss three ratemaking considerations that have been impacted by the recent rise in worldwide terrorist activity.
i A provision for catastrophes that includes the potential losses stemming from a terrorist attack
should be considered in the rates.
ii The availability and cost of reinsurance should be considered, as terrorist attacks can be
catastrophic and as such insurers may wish to purchase reinsurance coverage.
iii Any relevant legislation that relates to the government’s role in paying for terrorism losses
should be considered, as this may reduce the insurer’s costs in paying for terrorism losses.
64
Your company wants to start writing Automobile Insurance in State X. You have developed rates
and have filed them with the insurance department. The insurance department accuses your company of filing excessive rates because they are significantly higher than your rates for identical insureds in neighboring State Y.
List and briefly describe four external influences that you could cite that justify higher rates in State X.
Any four of the following:
• The judicial environment could be different between states. For example, there could be a higher tendency for lawsuits in State X.
• There could be regulatory or legislative differences between states. For example, the laws in State X might require more coverage to be provided than in State Y.
• There could be a difference in how the states handle guaranty funds. For example, State X might have more insurer insolvencies, and thus might require more money to be taken from the remaining insurers to help pay for the insolvency costs.
• There could be differences in economic variables between states. For example, parts or labor costs might be higher in State X, which means claim costs will be higher as well.
65
Identify four adjustments made to historical losses in projecting losses for a future policy period for
ratemaking. Briefly describe the purpose of each.
• Development: project losses to their ultimate levels when all claims are paid and closed. This will ensure rates will cover the ultimate losses coming from those policies.
• Trend: adjusting losses to expected levels of frequency and severity in the future policy period.
This will ensure rates will cover the expected costs at the future trend levels (e.g., inflation).
• Benefit level changes: adjusting losses to the levels of benefits expected in the future policy period. This ensures rates will be priced for the benefit levels expected in the future period.
• Catastrophes/Shock Losses: adjust historical losses to remove any catastrophes or large losses, and replace them with a longer term average loading. This ensures rates will be smoother over the long run, and not overly impacted by the presence or lack of large individual events.
66
List two methods that are used to adjust earned premiums to a current rate level basis.
1. EoE
2. Parallelogram
67
Explain why using average premiums is better than total premiums when analyzing premium trend.
Total premiums can change over time due to changes in exposures in addition to changes in the average premium. Average premium is not affected by changes in exposure, so it more closely relates to the premium trend.
68
Give one argument for using average earned premiums in the premium trend analysis and one
argument for using average written premiums.
An argument for using EP is that EP is used in the rate indications (it is what needs to be
trended). An argument for using WP is that WP allows for the use of more recent data.
69
Identify a situation in which the excess limit trend will be less than the basic limit trend.
If loss trends are negative, the basic limits trend will be closer to 0 than the more negative excess loss trend.
70
Explain why an actuary should use written premium, rather than earned premium, to analyze premium trend.
Using WP instead of EP for premium trends allows you to incorporate more recent data into the analysis. Trends that show in WP are expected to eventually show up in EP.
71
Explain why an actuary should use premium adjusted to current rate level to analyze premium
trend.
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.
72
Fully explain the overlap fallacy between loss development and loss trend.
There is no overlap between loss development and loss trend. 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. Historical losses are trended from the
average accident date of the historical period to the average accident date of the future period, and
loss development takes losses from the average accident date of the future period to their ultimate
level.
73
List two reasons the underwriting profit provision might differ between companies with the same loss, LAE and expense experience.
Any 2 of:
• The investment income might vary between companies.
• One company may be pricing more aggressively to write more business.
• One company might be viewing profit from a lifetime value perspective.
• One company might have more reinsurance protection, so would tolerate a lower target
profit margin.
• One company might be more conservative in its estimation of the contingencies piece of the
profit provision.
74
3 Causes of loss development
• Development on known claims: i.e., case reserves are too low or too high on existing claims.
• New claims being reported: i.e., late reported claims
• Closed claims being re-opened: i.e., additional payments needed on existing claims
75
Briefly explain why it is appropriate to both trend and develop losses (i.e., why there is no overlap).
There is no overlap between trend and development. Trend takes losses from the midpoint of the experience period to the midpoint of the future period. Development takes losses from the midpoint of the future period to their ultimate level.
76
Ratemaking method : Loss Ratio or Pure premium ?
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.
77
Ratemaking method : Loss Ratio or Pure premium ?
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.
78
Ratemaking method : Loss Ratio or Pure premium ?
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.
79
Briefly explain why claims-made rates are both more accurate and more responsive to changing conditions than are rates for an occurrence policy.
Claims-made rating is more accurate and responsive because there is a shorter forecast period for trends for claims-made policies compared to occurrence policies because occurrence policies have a longer report lag. Since trends are uncertain, applying the trends over a shorter period of time reduces the uncertainty compared to occurrence policies. Also, trend selections can be updated sooner because of the shorter forecast period, so claims-made policies are also more responsive to changes in trends.
80
What is the purpose of an Expense Constant?
An Expense Constant accounts for fixed expenses that do not vary by policy size.
81
Why is an Expense Constant important for small policies?
The premium for small policies may be so small that it may not cover the expenses of writing the policy. Without the expense constant, insures may not want to write small policies.
82
What is the purpose of a Loss Constant?
A Loss Constant is added to the premium for either small policies or to all policies to account for the fact that small risks have worse expected loss experience than large risks.
83
Briefly discuss three methods for calculating complements of credibility in first dollar ratemaking.
Comment on the effectiveness of each method as a complement of credibility.
• Loss costs of a larger group including the group being rated. The advantages of this approach
are accuracy, availability, being easy to compute, and a logical connection to the subject experience. If the subject experience is excluded from the complement, then the complement may also be independent. The disadvantage of this approach is that it can be biased, since there is a reason the subject group has been separated from the larger group.
• Trended present rates where the complement is the present rate adjusted for the residual indication and trended from the target effective date of the last filing. This complement may or may not be accurate based on stability of indications, it is unbiased, it may or may not be independent, it is readily available, it is easy to compute, and it has a logical relationship to the
subject experience.
• Competitor’s rates can also be used. This can be biased, inaccurate, and difficult to obtain.
However it is independent, easy to compute, and has a logical relationship to the subject experience.
84
ISO Commercial General Liability Experience and Schedule Rating Plan.
Explain why the plan uses basic limits losses, and limits losses and allocated loss adjustment
expenses to a maximum single loss limitation (MSL).
The limits prevent any large individual claims from overly influencing the experience mod.
They also make the plan more responsive to the frequency of losses rather than the severity.
85
ISO Commercial General Liability Experience and Schedule Rating Plan.
Explain why the MSL increases as the size of the risk (as measured by premium or credibility) increases.
The larger the risk, the larger expected losses, and the less impact a loss of a given size will have on the mod. As such, the MSL will increase to allow for more credibility to be given to the actual experience.
86
Contrast the asset share pricing model to traditional techniques for calculating rate relativities.
Traditional ratemaking techniques only consider the experience of a single period of time. As such,
they fail to consider differences in persistency between risks. Persistency can have a significant impact due to loss and expense differences between new and renewal business. The asset share pricing model accounts for this by introducing multiple periods, persistency, and different assumptions for new and renewal business.
87
Werner and Modlin state that "It is important to consider the [fundamental insurance] equation at the individual or segment level" in addition to the aggregate level. Discuss two reasons it would be acceptable to maintain an imbalance in the fundamental insurance equation at the
individual or segment level.
One reason to have an imbalance at the individual or segment level would be because of a regulatory constraint. For example, a regulator might place limits on rate changes or rate differentials across segments.
Another reason would be if the insurer was using an asset share pricing approach, in which the insurer would look at a longer term view of profitability. In that scenario, the initial costs of writing the policy would be potentially outweighed by future profits on the policy.
88
Reconcile an imbalance in the fundamental insurance equation with the following quote from the Statement of Principles Regarding Property & Casualty Insurance Ratemaking: "A rate provides for the costs associated with an individual risk transfer."
An actuarially sound rate may not always be implemented since the insurer needs to balance
other objectives, such as marketing or regulatory considerations. Also, asset share pricing approaches could be used, which may result in rates that are considered inadequate using traditional methods. At the end of the day, it is the actuary’s role to produce the best estimate of an indicated rate, though management can choose to deviate from using that rate.
89
Explain why the off-balance factor is necessary.
The off-balance factor is necessary because the average relativity underlying the indicated rates is different from the average relativity underlying the current rates, which causes an impact to the total premium. The off-balance factor is used to offset this impact to premium by modifying the base rate.
90
An insurer proposes to increase rates by 6.0% where many individual policy impacts will be above
10%. The insurer proposes a capping rule that will restrict premium changes at the policy level to
plus or minus 10.0%.
Identify two problems that a capping rule may cause for an insurer.
1. Insurer will not be charging what they should be to keep the fundamental insurance equation in
balance and earn their target underwriting profit.
2. Systems limitations-need to program this rule into computer systems. Can get complicated as to
what gets capped and what doesn’t and how this changes the rating algorithm
OR
1. May cause need for premium transition
2. Insurer may not get all the rate needed
OR
1. Can cause rates to be inadequate
2. Can be subject to adverse selection
91
Explain why an insurer would propose a capping rule
May have a concern that they will not retain policyholders if they raise rates substantially at
renewal-may cause insureds to shop- Also might be regulation reasons-restrictions on the amount
of rate increase a policyholders can see at each renewal
OR
Keep customers from getting shocked at renewal and shopping.
92
When aggregating data for ratemaking purposes, two of the three general objectives are:
• To accurately match losses and premiums for the policy.
• To use the most recent data available.
Briefly discuss how well the following methods of data aggregation achieve these two general objectives.
a. Calendar year
CY provides a poor match of premiums and losses, especially for longer tailed lines of business.
Losses in the CY may come from policies that were written in earlier CYs.
CY does use the most recent data available, and the data is not subject to development.
93
When aggregating data for ratemaking purposes, two of the three general objectives are:
• To accurately match losses and premiums for the policy.
• To use the most recent data available.
b. Calendar/accident year
Cal/acc year provides a better match of premiums and losses than CY, since losses occurring during the year are compared to premiums earned during the same year.
AY losses are subject to development, so using the most recent data requires estimation of future development.
94
When aggregating data for ratemaking purposes, two of the three general objectives are:
• To accurately match losses and premiums for the policy.
• To use the most recent data available.
c. Policy Year
PY provides the best match of premiums and losses, since losses are matched with premiums from policies written during the year.
PY data takes longer to develop than AY data, so using the most recent information will also result in greater uncertainty due to the longer development period.
95
Assess whether an accident year approach or a report year approach is more appropriate for reserving auto liability insurance.
AY is more common, but report year is more appropriate if a change in social or legal climate causes severity to correlate more with report date than accident date
96
The loss provision in the indicated rate for next year is calculated as historical reported loss divided by exposure.
Using historical reported losses divided by historical exposures would not be appropriate for
several reasons:
• Losses used in the rate indications should be at ultimate levels, so that rates are adequate to cover ultimate losses in the prospective period. To correct for this, reported losses for prior accident years should be developed to ultimate.
• Historical losses (and exposures if they are inflation-sensitive) may be at different trend levels than losses (and exposures) in the prospective period. To correct for this, trend losses (and exposures) to the prospective period.
• Historical reported losses may contain actual catastrophe or shock losses, which may introduce volatility into the rates. To correct for this, the actual catastrophe and shock losses can be removed and replaced with expected catastrophe and shock loss loads.
97
The indicated rate for next year is calculated using projected losses and loss adjustment expenses based on historical experience. In the next month, the company will be revising its underwriting guidelines, increasing the minimum deductible from $500 to $1,000.
If the current deductible relativities are perfectly priced, then the product manager’s proposal would be appropriate. This is because moving a policy from the $500 deductible to the $1,000 deductible would result in the same exact expected profit load, so no adjustment to the base rate would be needed.
98
Is it appropriate that The indicated rate for a classification is calculated based on one year of historical data that includes 25 earned car years.
This would not be appropriate due to the volatility in the limited amount of data. The data should be supplemented by using additional years of data and credibility-weighting the class data with an appropriate complement of credibility.
99
The indicated rate change is calculated using the ratio of developed, trended historical losses capped at $100,000 to on-level total earned premium. Loss trend factors and loss development factors are determined using data limited to $100,000. The company has a significant number of claims in excess of $100,000.
Using the capped losses would not be appropriate without adding in a loading for losses in excess of $100,000. Since the company has significant data in excess of $100,000, it may be best to just use an indication based on uncapped losses.
100
The chief actuary is concerned about the credibility of company data in this state and would like to begin using credibility weighting with the company’s countrywide loss costs. Assess this approach, considering two desirable qualities of a credibility complement.
Any 2 of:
• Accurate: The countrywide data is a larger group so it should result in more stable (accurate) estimates.
• Unbiased: The countrywide loss cost would be expected to be different than the state loss cost, so it would be biased.
• Independent: Countrywide data would only be independent if the state data was excluded
from the countrywide data. If the state only represents a small portion of the country, it will be mostly independent.
• Available: Countrywide data for the same company should be readily available for use.
• Easy to compute: Countrywide loss costs should be easy to compute.
• Logical relationship: Countrywide data has a logical relationship to the state data since it is for the same company.
101
Retrospective Premium Question
Briefly describe 2 elements that the basic premium is intended to cover for a retrospectively
1. The total expenses including profit but excluding LAE and taxes
2. The net insurance charge for limiting premiums by the maximum and the minimum
102
How are experience rate changes and law amendment rate changes different in their purpose and their effect?
The purpose of experience rate changes is to adjust rates so that future experience will be different than currently projected. The purpose of law amendment rate changes is to adjust rates to match statutory changes in benefits.
Experience rate changes impact existing policies as they renew, while law amendment rate changes impact existing policies on the date of the law amendment rate change.
103
If the company decides to use a different permissible loss ratio due to a territorial cap, the fundamental insurance equation will not be in balance. Describe an alternative to pricing changes the company can take to achieve balance in the fundamental insurance equation.
Prem = Loss + LAE + UW Expense + UW Profit
Need to increase premiums or reduce losses, LAE, expenses, or target profit through (any 1 of):
• Trying to reduce expenses by finding more operational efficiencies or laying off employees(UW expense or LAE)
• Reducing commissions to agents (UW expense)
• Accepting a lower target UW profit
• Taking a longer term view of profitability using a Lifetime Value Approach
• Increasing insurance-to-value (assuming this is property insurance) as premiums will go up more than losses
• Reducing coverage via policy endorsements
• Revising underwriting guidelines to be more restrictive
104
Explain the general role of credibility in ratemaking.
Credibility complements are used in order to make indications more actuarially sound. If data is too sparse or erratic, it shouldn’t be used by itself when creating the indication for your rate review. It protects the insurer (and insureds) from creating rates that are excessive or inadequate.
105
There are several ratemaking techniques that can be used to recognize the differences between large
risks and small risks for Workers’ Compensation insurance. Select two of these techniques and
explain how they account for these differences.
• Loss Constants attempt to equalize the loss ratios between small and large risks by adding a flat dollar amount to either small risks alone or to both small and large risks.
• The premium discount applies a percentage discount to larger policies based on their standard
premium to recognize that expenses are a lower percentage of their premium than for small risks.
106
Identify and briefly explain two issues that arise when using empirical data to construct increased limit factor tables.
• Data often isn’t captured for what claims would have cost in the absence of actual policy limits, so the data is censored.
• Data may need to be developed to ultimate at trended, as higher limits often experience higher development and trends.
107
Briefly discuss two reasons why occurrence policy ultimate loss estimates are more volatile than claims-made policy ultimate loss estimates.
• Occurrence policy estimates also include pure IBNR, which creates additional uncertainty relative to claims-made policies.
• Sudden, unpredictable changes in underlying trends will have more impact on occurrence
policies than claims-made policies.
• Sudden, unexpected shifts in reporting patterns will have more impact on occurrence
policies than claims-made policies.
108
Briefly describe a situation where negative profit and contingency provision may be
appropriate.
1. Long tailed line of business where there is a significant amount of investment income
2. When a company want to be more competitive and gain profit in the future (lifetime value)
3.Company forced by regulation to set the profit at this amount
109
Describe a shortcoming of the method of implementation : Approximated Rate differential
It ignores the impact of exposure correlation between different variables .
110
Briefly describe two non-pricing solutions that can address inadequate rates.
• Expense reductions such as:
◦ The company can lower expenses such as reducing advertising or laying off employees.
• Loss cost reductions (exceeding premium reductions) such as:
◦ The company could offer incentives to educate insureds about safety features or
courses and attempt to decrease losses.
◦ The company could reduce coverage without reducing rates.
◦ The company could implement better safety incentives for insureds to control losses.
• Increase investment income by adopting a more aggressive investment strategy.
• Reduce underwriting profit target by accepting the lower profit provision.
• Shifting to more profitable business. Examples:
◦ Focus on marketing to groups that are appropriately priced.
◦ Change underwriting guidelines to write more profitable business.
111
Briefly describe the issue with including shock losses in an actuarial analysis.
You overstate the rate indication after years with shock losses and understate the rate indication
after years with no shock losses.
112
Briefly describe two diagnostics used to test generalized linear models.
• Standard errors: Narrow standard errors around estimates suggest that a variable in the
model is statistically significant. Wide standard errors, often around an estimate of 1,
suggest that the factor is detecting mostly noise, and the variable should be eliminated
from the model.
• Deviance tests (such as Chi-Squared or F tests): These tests are used to compare models
with different variables in them. In particular, they are often used to assess whether it is
justified to add additional variables to a model.
• Consistency over time: Estimating parameters on data sets for consecutive time periods
allows you see whether the estimates tend to be stable over time. If the results are more
stable over time, they tend to be more reliable for future predictions.
• Validation using a holdout sample: You can split a data set into a modeling data set and a
holdout sample. You then build the model using the modeling data set, and use it to predict
values in the holdout data set. If there are significant differences between the predictions
and the actual values in the holdout data, then the model may be over or under fitting the
original modeling data set, and would thus be less predictive in general.
113
Briefly describe the effect of a small first party deductible on fixed expenses.
A first party deductible usually reduces the expenses associated with processing and
investigating small nuisance claims, since these claims would no longer be the responsibility of the insurer if they are below the deductible.
114
Describe the effect of a large deductible on fixed expenses.
If the insurer pays all losses first and then seeks reimbursement from the insured for losses
below the deductible, there will be an extra cost for the insurer to bill and process these
amounts. These costs include creation of the bills, monitoring deductible payments, and
pursuing collecting the deductible amounts through collection agencies or lawsuits.
115
Explain the difficulties in selecting a tail factor for the claims development technique. Describe twoapproaches that can be used.
There is generally little relevant data that can be used in the tail. Plus, due to the age, claims trends,
benefits levels, and policy limits may have changed, so this must be considered in the selection. The tail selection is very important because the selection affects all accident years reserve needs, thus has a disproportionate leverage on the total reserve need.
Common methods for selecting a tail factor include: any 2 of:
• Doing a special study that contains more years of data.
• Using an industry benchmark tail factor.
• Fitting a curve (e.g., exponential decay) to the LDFs and extrapolating the tail factor.
• Use reported-to-paid ratios at the latest paid development period.
• Judgment (e.g., arbitrarily picking a value like 1.05).
116
A new CEO of an insurance company that only writes homeowners insurance decides to layoff all ratemaking actuaries in the company, and to calculate rate indications based on the latest calendar year combined ratio with a target combined ratio of 95%. Explain the short-term and long-term impact of this change on each component of the fundamental insurance equation.
In the short-term, UW Expenses would be lower due to not paying the actuarial salaries. There would be no immediate impact to premiums, losses, or LAE. UW profit would go up due to lower UW expenses with all else unchanged.
In the long-term, UW expenses would still be lower, but presumably losses and LAE would go up due to adverse selection. Premiums would rise in response to the higher combined ratios, but they would lag behind the higher losses and LAE. As a result, UW profit would decrease.
