the process of extracting hidden patterns from data that is used in a wide range of applications for research and fraud detection
What are the two most prominent actuarial activities?
1) ratemaking 2) estimating of unpaid liabilities and adequacy of loss reserves
What must an actuary consider when making rates?
Trends that may affect claim costs during the effective period of the rates. Must look at economic and regulatory factors.
What is a statutory annual statement?
A statement of opinion, by a qualified actuary as to whether the carried reserves make a reasonable provision for the liability.
What are some secondary tasks performed by actuaries?
-analyze reinsurance needs to determine how much risk the insurer should retain versus the cost of reinsurance. -estimate future cash flows so assets are available when claims are to be paid -assessing corporate risk by testing the adequacy of surplus under potential adverse situations (catastrophe, soft pricing) -providing financial and statistical information to regulators and applicable statistical agents. (With accounting and finance) -participate in corporate planning and budgeting
How do small insurers without actuaries determine rates?
Information from advisory organizations (actual rate or statistical data)
Why are actuarial consultants used?
-used by small insurers who don’t have their own actuaries. -can supplement staff actuary knowledge with socialized expertise and ease workload leaks. -regulatory authorities sometimes require insurers to provide a consulting actuary’s opinion verifying the accuracy and reasonableness of the staff actuaries’ work.
the process insurers use to calculate insurance rates, which are a premium component
What is the primary goal of ratemaking from the insured’s perspective and how does it complement underwriting’s primary goal (develop maintain profitable book of business)
Develop a rate structure that backed the insurer to compete effectively while earning a reasonable profit in its operations. The insurer’s rates must be competitive to meet underwriting goals.
What are the five ideal characteristics of rates?
-be stable -be responsive (can conflict with stability) -provide for contingencies -promote risk control -reflect differences in risk exposure.
Why should rates be stable?
-Changing rates is expensive -Drastic rate changes can cause dissatisfaction or regulatory/legislative action.
What does rates being responsive mean?
They must respond to changes in external conditions (losses and expenses)
Which contingencies should rates provide for?
Unexpected variations in losses and expenses.
How do ratemaking systems promote risk control?
Provide lower rates for policyholders who exercise sound risk control (burglar alarms, automatic sprinklers)
What would happen if rates didn’t take differences in exposure into consideration?
anti-selection: they would end up with only higher-risk insureds. People with high risk would gladly pay an average rate and people with lower risk would write with a carrier with a lower rate.
What are the three components to an insurance rate?
1) An amount needed to pay future claims and loss adjustment expenses (prospective loss costs) 2) An amount needed to pay future expenses, such as acquisition expenses, overhead and premium taxes (expense provision) 3) An amount for profit and contingencies (profit and contingency factor)
The rate per exposure unit for insurance coverage.
The price of the insurance coverage for a specified period.
A variable that approximates the loss potential of a type of insurance. (for property this is the value being insured, for product liability, sales)
The average amount of money an insurer must charge per exposure unit in order to be able to cover the total anticipated losses for that line of business. (sometimes includes legal costs)
The amount that is included in an insurance rate to cover the insurer’s expenses and that might include loss adjustment expense but that excludes investment expenses. It covers: -Acquisition expenses -General expenses -Premium taxes -Licenses and fees -Regulatory -Advisory organizations
Expense Provision (Underwriting Expenses)
Costs incurred by an insurer for operations, taxes, fees, and the acquisition of new policies.
The expense that an insurer incurs to investigate, defend, and settle claims according to the terms specified in the insurance policy. (ex. cost of in-house claims adjusters)
Loss Adjustment Expenses (LAE)
The expenses an insurer incurs to investigate, defend, and settle claims that are associated with a specific claim.
Allocated Loss Adjustment expenses (ALAE)
Loss adjustment expenses that cannot be readily associated with a specific claim.
Unallocated loss adjustment expenses (ULAE)
Income an insurer earns from premiums paid by policyholders minus incurred losses and underwriting expenses.
In the past insurer’s did not consider _____ results in rate calculations but now they are commonly included and may even be required in some states.
Investment returns have a much larger effect on _____ insurance rates than _____ insurance rates because claims for these exposures are often not paid until years after the loss occurs.
liability / property
What are the five areas of uncertainty which affect ratemaking?
1) Estimation of losses 2) Delays in data collection and use 3) Change in the cost of claims 4) Insurer’s projected expenses 5) Target level of profit and contingencies
The final paid amount for all losses in one accident year.
Ratemaking is based estimating losses from______ ___________ __________ and adjusting those losses for _______ ____________.
Past coverage periods / future conditions
If loss reserve estimates are too low the rates will be too _____. If too high, the rates will be too _____.
Low / high
Demonstrate how inadequate reserving leads to inadequate rates. Ex. $30MM on total incurred losses for 3 year period and 300,000 car years (correct reserve) $28.5MM incurred losses (incorrect reserve)
Pure premium Correct: $30MM / 300k = $100 per car year. Incorrect: $28.5MM/ 300k= $95 per car year. For same exposure, insurer would be getting $5 less per car year.
What are the sources of delay in reflecting loss experience in rates?
-delay by insureds in reporting losses -time needed to analyze data and prepare rate filing -delay for rates being approved -time needed to implement rates -time period during which rates are in effect.
The period for which all pertinent statistics are collected and analyzed in the ratemaking process.
What can cause fluctuation in loss experience. (Frequency severity)
Economic inflation or deflation Legislative or regulatory changes such as modification in rules governing claim settlement can affect the number of losses.
Provide an example of why you would not use past expenses to determine projected expenses.
A new commission plan could be in force and past commission would t be a good estimate of costs for new policies.
Interest, dividends, and net capital gains received by an insurer from the insured’s financial assets, minus it’s investment expenses.
Which factors does the target level of profit and contingencies come from?
Overall desired rate of return, including likely returns from investment income versus underwriting profit. If trying to build business might accept a lower rate of return.
What are the three ratemaking methods?
-pure premium method -loss ratio method -judgment method
A method for calculating insurance rates using estimates of future losses and expenses, including a profit and contingencies factor. (Independent of current rates)
Pure premium method.
What are the four steps in the pure premium method?
1) calculate pure premium 2) estimate expenses per exposure unit based on the insurer’s past expenses. 3) determine profit and contingencies factor 4) add pure premium and expense provision and divide by one minus the profit and contingencies factor.
Incurred losses = $4MM Earned car-years = 100,000 Calculate pure premium
$4MM/100k = $40
Expenses = $1.7MM Earned car-years = 100,000 Calculate expenses per exposure unit
$1.7MM/100k = $17
Assuming a 5% profit and contingencies factor and previous values, calculate the rate per exposure unit. Pure premium: $40 Expenses per exposure unit: $17
= pure premium + expenses per exposure unit / 1 - profit & contingencies factor $40+$17 = $57 / 1-.05 = .95 =. $60
How are fixed expenses and variable expenses stated when ratemaking?
Fixed: dollar amount ($2.00 per car year) Variable (commissions, premium tax): percentage of rate (ex 12% of final premium)
Calculate the rate using the pure premium method: $40 premium $2.50 fixed expenses 12% variable expenses 5% profit and contingencies
$40 + $2.50 / 1 - 0.12 - .05 $42.50/.83. = $51
A method for determining insurance rates based on a comparison of actual and expected loss ratios.
Loss ratio method.
Which two ratios does the loss ratio method use?
Actual loss ratio: incurred losses / earned premium Expected loss ratio: 100% - expense provision
What is the loss ratio ratemaking equation?
Rate change = actual loss ratio - expected loss ratio / expected loss ratio
Actual loss ratio: 54% Expected loss ratio: 60% Calculate new rates
.54 - .60 / .60. -.06/.60 = - 0.10 10% decrease
Which methods are used to calculate rates for new types of insurance?
Pure premium or judgment
A method for determining insurance rates that relies heavily on the experience and knowledge of an actuary or an underwriter who makes little or no use of loss experience data.
Judgment ratemaking method
What are the steps involve in ratemaking?
- Collect data 2. Adjust data 3. Calculate overall indicted rate change 4. Determine territorial and class relativities. 5. Prepare rate filing and submit to regulatory authorities as required.
a factor that provides for differences in expected loss, individual company expenses, underwriting profit and contingencies; when multiplied with a loss cost, it produces a rate (used by companies that rely on loss cost filings made by advisory organizations)
loss cost multiplier
a method of collecting ratemaking data that estimates both earned premiums and incurred losses by formulas and accounting records
a method of collecting ratemaking data that analyzes all policies issued in a given twelve-month period and that links all losses premiums and expsure units to the policy to which they are related
a method of organizing ratemaking statistics that uses incurred losses for an accident year, which conssits of all losses related to claims arising from accidents that occur during the year, and estimates earned premiums by formulas from accounting records
What are the three categories of data needed for ratemaking?
-losses, both paid and incurred (including loss adjustment expenses to be included in pure premium) -earned premium and/or exposure information -expenses, including a profit an contingencies factor
I using classes/territories, data must be identified for each ____ and _____.
class and territory.
The _____ ______ method is unsuitable for collecting ratemaking data for liability an workers comp insurance because the delay in the kids payment can be long and the loss reserves can be large relative to earned premiums.
Calendar-year method (the policy-year method or accident-year method should be used)
What are three ways to adjust premium and loss data?
-adjust premium to current rate level -adjust historic experience for future development -apply trending to losses and premium.
Rates during an experience period were written at different rate levels. How do actuaries adjust premiums to the current level?
Ideal: Calculate the premium for each policy in the experience period at the current rate level. (uneconomical) Alternative: Adjust historical premiums in total to current levels.
Provide an example of how historical premiums are adjusted to current levels. (on level premium adjustment)
Book of business has $100 of losses each year. (1) Developed Losses Year 1 Premium: $100 Year 2 Premium: $100 Year 3 Premium: $100 (2) Collected Premium Year 1: $200 Year 2: $160 Year 3: $128 (3) Collected Loss Ratio (1/2) Year 1 Loss Ratio: 50% Year 2 Loss Ratio: 63% Year 3 Loss Ratio: 78% (4) Rate Level Index (deviation of each years rates) Year 1 Rate Level Index: 1.00 Year 2 Rate Level Index: .80 Year 3 Rate Level Index .64 (5) On-Level Factor (rate level index for most recent term divided by rate level index for reach year) Year 1 On Level Factor: .64 Year 2 On Level Factor:: .80 Year 3 On Level Factor 1.00 (6) On-Level Premium 2x5 On Level Premium = $128 On Level Premium =$128 On-Level Premium = $128 (7) On-Level Loss Ratio 1 x 6 Year 1 Loss Ratio: 78% Year 2 Loss Ratio: 78% Year 3 Loss Ratio: 78%
A factor that is used to adjust historical premiums to the current rate level.
Quick way to perform on level premium adjustment.
On level factor is most recent rate level index (deviation from previous years rate) divided by rate level index from previous year. Ex. 2011 1.0 .64/1 = .64 2012 .80 .64/.80 = .80 2013 .64 / .64 = 1. On level premium is most recent years collected premium. The on level factor calculates the deviation from the most recent year’s rates.
How is future development of losses factored into rates?
Have to account for unpaid claims. have to estimate the value. Loss development factors are applied to current experience. This helps estimate the total cost to pay all claims within each year.
An actuarial means for adjusting losses to reflect future growth in claims due to both increase in the incurred amount for reported losses and IBNR losses.
Loss development factor.
The review of historic environmental changes and projecting such changes into the future.
Inflation of claim cost, the increasing safety if newer cars, or changes in legal liability are examples of ?
Changes in the environment which can be accounted for by trending.
What are some sources of trend adjustments?
-Consumer price index (CPI). -historical experience (own data or ISO/NCCI
A method of loss trending that assumes a fixed percentage increase or decrease for each time period. (Frequency and severity are looked at separately)
How do actuaries factor in changes that have affected payouts in recent years (ex. Change in legislation)
Must adjust past losses to what they would be under new guidelines.
Amount of homeowners insurance purchased changes with the value of the home. If home prices have risen what happens?
More premium might be collected on the same house. Must take increase in value into consideration
Why are territorial and class relativities and how are they calculated?
-variation of rates for certain class it territory from the base rate. -calculation; compare estimated loss ratio (or pure premium) for each territory/class to the statewide average loss ratio (or pure premium) (Must have sufficient exposures)
Which 7 items must be included in a rate filing?
1) Schedule of the proposed new rates 2) Statement about the percentage change in the statewide average rate 3) Explanation of the differences between the overall statewide change in rate and the percentage change of the rates for individual territories and/or rating classes (if any) 4) Data to support the proposed rate changes, including territorial and class relativities 5) Expense provision data 6) Target profit provision included in the rates, if applicable, and any supporting calculations. 7) Explanatory material to enable state insurance regulators to understand and evaluate the rate filing
Even though actuaries primarily prepare the rate filing, who handles most of the contact with regulators?
What are the four types of aggregations which attempt to match losses with premiums from the underlying coverage?
1) policy-year method 2) calendar year method 3) accident-year method 4) report-year method
This method of aggregating data uses earned premium, exposure units, and incurred loss associated with a group of policies issued during a specific 12 month period. It is the only method that exactly matches losses, premiums and exposure units to a specific group of insureds. (most reinsurance contracts are on this basis.)
What are the two disadvantages to the policy-year ratemaking data collection?
-takes longer to gather data -additional expense to gather data by policy year (other methods the data is a. Byproduct of accounting operations) the The cost is starting to decrease with automated record keeping.
How are delays in data collected overcome in the policy-year method?
Estimating the ultimate values of data for which final values are not yet available. (Reduces the apples-to-apples advantage)
This method of aggregating data involves aggregating data from accounting records to estimate earned premiums and incurred losses.
the total premium on all policies written (put into effect) during a particular period
the portion of written premiums that corresponds to coverage that has not yet been provided
reserves set aside for future expected claim payments but not associated with any specific claim; includes a provision for incurred but not reported (IBNR) claims, future development of known claims (beyond the carried case reserves), and potential reopening of claims that have been settled
How are earned premiums calculated from written premium and unearned premium reserves (under the calendar-year method?
Earned premium = written premium for year + (unearned premium at beginning - unearned premium at end of year)
How are incurred losses under the calendar-year method?
Incurred Losses = Losses paid during the year + (loss reserves at the end of the year - Loss reserves at the beginning of the year)
Why does the incurred loss formula sometimes result in inaccuracies?
The estimated incurred losses for a given year might be distorted by changes in reserves for losses that occurred in previous years. (more common with liability claims)
How difficult is it to obtain calendar-year data?
Very easy. The data is already formatted for reporting their income on financial statements.
Why can calendar-year data alone not be used in the pure premium ratemaking method? What else has to be included?
It doesn’t contain exposure unit data. Exposure unit information can be collected separately.
Why is the calendar-year method the least accurate?
Calendar year losses can arise due to changes in reserves for losses that occurred in previous years so they may not reflect current experience alone. Losses are frequently not available at the desired level of detail (bulk reserves not calculated at class or territorial level)
EP Jan 1- Dec 31 Incurred losses are all losses occuring during this period
Accident-year method Detail: This method uses the earned premium for the calendar period being reviewed, but calculates incurred losses for the given period using all losses and claims arising from insured events occurring during that period. The claims can be open or closes; if they arose from an insured event that occurred during the specified period, they are included in incurred losses for that period.
What is the biggest positive of the accident-year method
They are not affected by changes in reserves for events that occurred in other periods.(correct the largest source of error in the calendar-year method)
Comment on the following attributes of the accident-year method: 1) speed of calculation 2) accuracy 3) economy
1) speed of calculation: quick - faster than policy year 2) accuracy: almost as accurate as policy year method 3) economy: almost as cost effective as the calendar-year method…. need separate tabulation of loss data
The NAIC Statement Schedule that shows detailed historical information on paid and reserved losses and LAE. Useful when using the accident-year method.
coverage that is triggered by a claim alleging bodily injury or property damage that is made during the policy period, even if the claim arises from an event that happened before policy inception
A method similar to the accident-year method. Claims are aggregated by when the claim was reported rather than when it occurred. Good for medical malpractice, general liability which use claims-made coverage. Least common.
Report year method.
Why is the experience period for wind coverage usually 20 years or more?
A catastrophe would otherwise cause a large swing in rates.
Which three factors are considered in determining the appropriate experience period?
1) legal requirements 2) vary ability of losses over time 3) the credibility of ratemaking data.
What is used fur property insurance severity claim trending?
External composite index (construction cost index and CPI)
Why is sekar are tending of claim severity and claim frequency common in liability insurance?
Different factors affect each. -inflation or deflation affects severity -legislative, regulatory, it other external changes, such as a modification of rules governing claim settlement affect frequency.
Why is trending of losses and premiums necessary in some lines, such as fire insurance.
Severity trending determined effect of inflation. Rates must be “tended” to account for increase in property values.
Why is there a special problem with trending workers comp insurance?
A court decision can change the benefits unexpectedly. When trending wc severity, rates and losses must be adjusted with a “law amendment factor”
On what type of policy is trending applied to the risk control portion of the rate and why?
Equipment breakdown insurable. Rc is large portion of the rate.
The minimum amount of coverage for which a policy can be written; usually found in liability lines. • The minimum amount of insurance for which manual rates are available.
In liability insurance, why are only basic limit losses used in calculating incurred losses?
Prevents the calculation from being affected by occasional large losses.
Why doesn’t a single large fire loss affect ratemaking calculations in the state in which it occurred?
Balance is spread over the rates of all states.
• A type of computer program that estimates losses from future potential catastrophic events. • A computer program that uses scientific theory and past experience to predict future losses.
• The level of confidence an actuary has in a projected losses; increases as the number of exposure units increases. • Expressed as a percentage from 0 (can’t happen) to 100 (must happen), and is the measure of confidence that data reflect actual experience.
• The factor applied in ratemaking to adjust for the predictive value of loss data and used to minimize the variations in the rates that result from purely chance variations in losses. • Expressed as a probability from 0 (can’t happen) to 1 (must happen), and is the measure of assurance that past results will indicate future results.
What happens when an advisory organization deems rates not credible?
Ex. Auto insurance. For some classes and territories, rates are calculated as a weighted average of the indicated rate for the territory or class and the statewide average rate.
a factor applied to the rates for basic limits to arrive at an appropriate rate for higher limits
Increased Limit Factor
an amount over and above the expected loss component of the premium to compensate the insurer for taking the risk that losses may be higher than expected
Why are the increased limit factors large for lines such as auto liability and general liability?
1) additional coverage purchased can be much higher than the basic limit 2) higher limits can require a portion of the coverage to be reinsured (cost of reinsurance in rate) 3) large losses occur less frequently and take longer to settle so variability of losses is greater and credibility is lower. 3)
A loss reserve that represents the estimated loss value of each individual claim.
What are the three components of bulk (sometimes called IBNR reserves?)
1) IBNR reserves 2) reserves for loss that have been reported but have inadequate reserves 3) reserves for claims that were closed but are reopened.
Which parties analyze loss reserves and why?
-management: find cost of doing business -insurers auditors: determine if financial statements accurate indicate its financial condition and performance. -rating agencies: determine company’s rating -regulators: assure claims will be paid.
a person who uses mathematical methods to analyze loss data and develop insurance rates
What are the effects of overestimated loss reserves?
financial strength ratings can be lowered, statutory limits on premiums that can be written can be reduced, insurer could be dissolved/insolvent
List three common methods to estimate ultimate losses.
1) Expected loss ratio method 2) Loss development method 3) Bornhuetter-Ferguson method
This method of estimating ultimate losses uses a prior estimate of ultimate losses rather than current experience. It is often used when current experience is limited or of little predictive value.
Expected loss ratio method
This method of estimating ultimate losses assumes that future changes in the loss will occur in a similar manner as in the past. Assumes that experience to date is an indicator of what future payments will be.
Loss development method.
This method of estimating ultimate losses uses parts of loss development and expected loss ratio methods. It accepts experience to date and assumes that future results are independent of current experience.
Phil wants to estimate how many homers David Ortiz will hit. We look at his record and see that he hit 20 homers in 2012. 1/4 of the way through the 2013 season he has hit 15 home runs. Based on the Expected loss ratio method of calculation how many homers will he hit in 2013?
- Uses only previous experience.
Phil wants to estimate how many homers David Ortiz will hit. We look at his record and see that he hit 20 homers in 2012. 1/4 of the way through the 2013 season he has hit 7 home runs. Based on the Loss development method how many homers will he hit in 2013?
- Uses only current experience.
Phil wants to estimate how many homers David Ortiz will hit. We look at his record and see that he hit 20 homers in 2012. 1/4 of the way through the 2013 season he has hit 7 home runs. Based on the Bornhuetter-Ferguson method how many homers will he hit in 2013?
- Uses current experience only for current 1/4 and previous experience for the remainder.
Besides projecting losses, the loss development method is also used for …..
Projecting allocated loss adjustment expenses, claim counts and premiums
What are the four steps in the loss development method?
1) Compile the experience into a loss development triangle. 2) Calculate the age-to-age development factors 3) Select the development factors to be used. 4) Apply factors to experience to make projections
A table showing values for a specific group of claims at different points in time.
loss development triangle.
What are the limitations of the loss development method?
It assumes that future experience will develop the same way it has in the past. Changes in business practices or external conditions can effect usefulness. Large one-time events such as catastrophes disrupt the historical pattern of development.
What else does the actuarial department do besides mathematical models and statistical techniques?0
Insurance operations, accounting, insurance law, and financial analysis.
What do actuaries at advisory organizations do?
Collect loss and premium data from many insurers to use in calculating expected loss costs. They also maintain contact with regulators to make rate filing easier.
Comparison of Aggregation Methods