RPM Workshop 1: BASIC RATEMAKING Overall Rate Level Considerations Mark Komiskey, FCAS, MAAA Assistant Actuary Allstate Insurance Company Mark.Komiskey@Allstate.com March 19, 2012 Philadelphia, PA

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AGENDA BASIC RATEMAKING EQUATION UNDERLYING DATA MANIPULATION PROFIT AND CONTINGENCY PROVISIONS EXAMPLE Goals for the Session: What is an indication? How do we calculate an indication?

BASIC EQUATION Required Premium should account for the costs associated with the transfer of risk: Losses, Expenses and Profit The Indication is the amount by which the current rates should increase or decrease in order to expect to earn our desired profit.

BASIC METHODS LOSS RATIO PURE PREMIUM Produces Indicated Rate Change Based on Loss Compared to Current Premium Requires Data on Existing Rates PURE PREMIUM Produces Indicated Rates Based on Loss per Exposure Does Not Require Data on Existing Rates Interactive Slide: Which method would you utilize? Scenario 1: A company is pricing a new line of business for which it has industry loss statistics.... {Pure Premium} Scenario 2: Exposure data is not available, or not accurate? {Loss Ratio} Scenario 3: Loss, Premium, and Exposure data are all accurate and available. {Either} Note: The two methods produce identical results when identical data and assumptions are used.

BASIC FORMULA: In order to derive the Basic Ratemaking Formulas, we will assign variables each of the components. Before moving on, I would like to discuss the Expense Component in detail. Please note that I have included Expenses associated with the Loss Adjustment Process in the Future Loss Component. Loss Adjustment Expense can be further classified into Allocated and Unallocated Loss Adjustment Expense ALAE = Expenses that can be directly connected to the processing of specific claims. {Independent Adjuster Fees, Legal Fees, Cost to Obtain Claim Information} ULAE = Expenses incurred in the claims processing that cannot be connected to any specific claims. {Salaries for Company Claims Personnel, Claim Office Expense} Note the Expense Category is divided into 2 categories. Variable Expenses: Those expenses that DO very directly with premium Commissions and Brokerage Expenses Taxes Fixed Expenses: Those which DO NOT vary with premium. General Expenses – day to day operations of company Other Acquisition – expenses incurred in acquiring and maintaining business, excluding commissions. Licenses and Fees – associated with conducting business in a state Interactive Slide: For the following types of expense, which category would apply? -Salaries of Home Office Employees {Fixed} -Advertising {Fixed} -Agent Compensation {Variable} -Ordering MVR Records {Fixed} -Premium Taxes {Variable}

BASIC FORMULA R = L + V*R + EF + Q*R Solve for R: R – V*R – Q*R = L + EF R*(1 – V – Q) = L + EF R = L + EF (1-V-Q) Variable Permissible Loss Ratio = 1 – V – Q The percentage of each premium dollar that is intended to pay for the projected loss and fixed expense components. We understand that the Required Premium must account for expected Losses, Expenses and Profit (with Variable expenses and Profit being a percentage of premium). Performing simple algebra – (click to bring the derivation onto the screen) we solve for the Required Premium. (click to bring in Var PLR) The denominator of this formula is referred to as the Variable Permissible Loss Ratio and represents the percentage of each premium dollar that is intended to pay for the projected loss and fixed expense components.

BASIC FORMULA: Loss Ratio Indicated Change = Loss Ratio + Fixed Expense Ratio Variable Permissible Loss Ratio R1 / R0 = (L/R0 + EF/R0) (1 – V – Q) As mentioned the Loss Ratio produces an indicated change, using the current premiums as the basis.

BASIC FORMULA: Pure Premium Indicated Rate = Pure Premium + Fixed Expense Variable Permissible Loss Ratio R1/X = (L/X + EF/X) (1 – V – Q) Pure Premium uses Exposures as the basis for determining the Indicated Rate. Using the PP formula you are able to determine the indicated rate change, by comparing the indicated Rate to the premium we would expect to get over the future policy period if we did nothing.

DATA CATEGORIZATION CALENDAR YEAR POLICY YEAR ACCIDENT YEAR Before we begin discussing the required adjustment to the underlying data for overall rate level indication analysis, we will spend a few minutes on data categorization. There are 3 main ways that Loss and Premium data is categorized.

CALENDAR YEAR Premium and Loss transactions that occur during the year. Advantages: Data is available quickly FIXED AT YEAR END Consistent with Financial Statements Disadvantage: Premium and Loss Transactions DO NOT match. Loss data includes payments and changes to reserves for policies whose premiums were earned in prior periods. While the Calendar Year method does have logistical advantages, the distortion of the Loss data would suggest there may be a more appropriate categorization method for ratemaking purposes.

POLICY YEAR Premium and Loss transactions on policies with effective dates (new or renewal) during the year. Advantages: Premium and Loss transactions DO match. Transactions from policies effective in prior years do not distort the data for ratemaking. Disadvantage: Data is not available until one term after the end of the policy year. Losses are NOT fixed at year end. The Policy Year view, addresses our concern with the matching of loss and premium data; however, the delay in data availability proves to be problematic.

ACCIDENT YEAR Advantages: Disadvantage: Loss transactions for accidents occurring during the year, and Premium transactions during the same 12 months. Advantages: Represents a better match of premium and losses than Calendar Year aggregation. Transactions from accidents occurring in prior years do not distort the data for ratemaking. Disadvantage: Data with slight time lag. Losses are NOT fixed at year end. the Accident Year method is used in much of the Ratemaking Process, as it provides a better match of premium and losses with only a slight delay in data availability. <<INSERT DATA CATEGORIZATION EXERCISE HERE>>13

UNDERLYING DATA MANIPULATION This diagram illustrates the various adjustments made to historical data in order to appropriately estimate future levels of the components discussed earlier. You will notice that a TREND adjustment is made to each of the Loss, Expense and Premium components; we will discuss this adjustment first.

TREND Historical loss, premium and exposure data is trended to reflect the level predicted to exist during the pricing period. to account for expected difference between the historical period and the future period. The actuary evaluates, and then adjusts for, how changes over time affect such items as claim costs (severitiy), claim frequencies, expenses, exposures, and premiums. An appropriate level of actuarial judgement should be employed in selection of the applied trend. -may use data generated by the book of business, or by a different book of business w/ similar influences (CW data), might also use Industry Insurance data, and Non-insurance data (Cons Price Index, Med. Cost Index) -consideration given to: credibility of data and expected future changes not yet observable in the historical trend data. -statistical models that may be used to derive trend information from historical data: Regression (linear or exponential), time series, econometric, forecasting. {Interactive Slide} Specific to Loss Trends What are some reasons we would expect changes in frequency levels? -Distributional Shifts to segments with higher frequency levels (age, deductible, territory) -Changes in traffic conditions due to changes in population density -Changes in claiming behavior What are some reasons we would expect changes in severity levels? -change in costs of materials, parts, medical services. -Distributional Shifts (vehicle type, value of home, deductibles/limits) -Legal and Judicial Environment -propensity to sue, jury awards, etc. Distributional shifts are the main driver of the trend applied to premium and exposure data. While Variable expenses are proportional to premium, and therefore change for the same reasons premiums do, Fixed Expenses should be trended to account for inflation and/or changes in salaries, marketing expenses, etc. ( use the Compensation Cost Index for wages/benefits or the Consumer Price Index for remaining components).

TREND PERIOD Experience Period Exposure Period Latest Year - 2 Latest Year of Data Trend from the mid-point of the experience period to the midpoint of the exposure period. We determine the Trend Period using the assumption that losses occur and premiums/exposures are written and earned uniformly over time. The indication evaluates the adequacy of rates for all policies written during a period of time, generally 1 year. Trend to Date = Eff. Date + ½ + ½ Policy Term Eff. Date + 1 + Policy term Eff. Date

CATASTROPHE/Large Loss Catastrophe losses are very volatile from year to year, and should be removed from the underlying data because of their large size and infrequency of occurrence. Recognition of exposure is appropriate and can be incorporated using various methods. Long-Term Average, Catastrophe Simulation Modeling. Appropriate to give consideration to the impact of other non-catastrophe large losses on underlying data and analysis. In addition to Trend, there are 2 other adjustments made to historical loss data. The first is adjusting for Catastrophe/Large Loss data. - read description on slide -

LOSS DEVELOPMENT Adjustment made to underlying accident year loss data to reflect an expected ultimate value. 2 reasons for Accident Year losses to develop New Losses emerge after year-end (IBNR) Development on known claims The second adjustment is Loss Development. As mentioned earlier, one deficiency of the Accident Year data is that losses are not known at year end. There may be losses on claims that have been incurred, but were not reported before year end and there can also be changes in the incurred loss amounts on known claims. Loss Development adjustments are made to reflect expected ultimate loss amount. Loss Development is a frequent topic in actuarial literature, which discusses dozens of techniques and variations of them. -There are various assumptions underlying each technique, the appropriateness of those assumptions influences the accuracy of the method. Therefore, the best method depends on the situation at hand. For purposes of illustration I will outline a frequently used, simple Link Ratio method. {go to next slide}

LOSS DEVELOPMENT FACTOR (LDF) METHOD Incurred Losses Loss Development Factors ACCIDENT YEAR @ 12mo @ 24mo @ 36mo 2008 $1,000 $2,000 $2,500 2009 $3,000 2010 X? ACCIDENT YEAR 12-24 24-36 2008 2.00 1.25 2009 1.50 The LDF method assumes the ultimate losses are proportional to the current losses, and uses multiplicative factors to develop losses to ultimate. Walk through example. Loss Development methods can be applied to either paid loss or incurred loss data. -Incurred losses are subject to lower loss development, implying greater stability of development patters. Incurred Losses are prone to distortion if reserving practices change. -Paid Losses aren’t subject to reserve distortion, but for some longer-tailed covereages where losses are paid slowly, a significant amount of loss development is implied and potential inaccuracy in ultimate estimates if development patterns change. LDF 1.75 1.25 Estimated Ultimate 2010 AY Loss = $2,500 x 1.75 x 1.25 = $5,469

CURRENT RATE LEVEL Adjustment to reflect rate changes that are not already included in the historical recorded premium. Common Techniques: Extension of Exposures Parallelogram Method Having already discussed the adjustments to Loss and Expense data, we need to cover one additional adjustment which is made to premium. In order to determine the expected future premium in the exposure period, we must adjust historical recorded premium data to reflect any rate changes not already included. 2 common techniques: Extension of Exposure Method: Re-reates each individual policy using the current set of rates. While this is the most accurate means of adjusting the premiums, it requires extensive detail and mechanization. Parallelogram Method Uses geometric relationships to calculate the average rate level for each year as compared to the current rate level, and derives Factors to adjust historical years to the current rate level, assuming the premium is written evenly throughout the year and there is no change in exposure level over time. This method does not require specific policy information.

PARALLELOGRAM METHOD A B Area Percent of 2010 Rate Index A .50 1.00 B Rate Change = 10% on 1/1/2010 100% Earned A 1.00 1.10 B 0% Earned 2009 2010 2011 2012 Area Percent of 2010 Rate Index A .50 1.00 B 1.10 2010 1.05 Using a simple example, I will outline the parallelogram method. Using a rectangle for each year, the horizontal axis represents time and the vertical axis represents the proportion of policy premium that has been earned at any given point in time. Assume a rate change was implemented on January, 2010, and that we are pricing annual policies (so the rate earns over a 12 month period) The recorded premium data would be ½ on the old rates and ½ on the new rates. We want to adjust the premium data to be on the new rate level. Since there is no rate activity in the experience period prior to 1/1/2010, we set the Rate Index for Area A to 1.00 the Rate Index for Area B reflects the change and is 1.10. To determine the Rate Index for 2010, we determine a weighted average rate indexes in effect for the year. In this example it is easy to see that half is in section A and half is in section B, however if date of the rate change was not 1/1 you would just find the area of A and B as a proportion of the total. Now the current Rate Index is 1.10, so the factor to bring 2010 premiums to the current level is (1.10/1.05) = 1.048. <<Parallelogram Exercise>> 2010 FCRL = (1.10/1.05) = 1.048

PROFIT & CONTINGENCY UNDERWRITING PROFIT PROVISION CONTINGENCY Basic Selection = 5% More Complex Calculation Consideration of Investment Income CONTINGENCY Provision for expected differences, if any, between the estimated costs and the average actual costs, that cannot be eliminated by changes in the other components of the ratemaking process. Before working through a comprehensive example of the Indication, it is important to reference the final component which is the acknowledgement of a target profit provision. Detailed methodologies associated with the determination of the UW Profit Provision can be fairly complex, and are outside of the scope of this presentation. In general, the UW Profit Provision can be a basic selection, say 5%, or a more complex calculation that incorporates expected investment income. When appropriate a contingency provision is included, this acknowledges the potential for differences in estimated and actual costs that cannot be controlled for through the ratemaking process.

? QUESTIONS ? At this point we have covered the basic steps used in the Development of an Overall Rate Level Indication, before we move onto an interactive example does anyone have any questions?