Quantifying the Impact of Non-Modeled Catastrophes

1. Quantifying the Impact of Non-Modeled Catastrophes Israel Krakowski Sara Drexler CAS Ratemaking Seminar March, 2003

2. Introduction • Methods to Estimate Catastrophe Provision from Historical Data • Balance credibility and responsiveness issues • Appropriate provision for individual states as well as Countrywide • We are only going to discuss non-hurricane and non-earthquake catastrophe estimates • In this session we will cover • A brief overview of existing methodologies • Several new methodologies developed internally at Allstate by Israel Krakowski

3. Agenda • Overview • Vocabulary • History of Methods • Description of New Methods • State Relativity Weighted with Countywide Complement • State Relativity Weighted with Regional Complement • Dual Capping Method • Summary/Discussion

4. Overview • Increasing cat losses per AIY over time • “One in 100 year” events for a particular state occur relatively frequently on a countrywide basis • In response, we are researching new methods to estimate future expected catastrophe losses • This presentation shows methods to develop catastrophe provision, not how to incorporate provision into the indication

5. Vocabulary • AIY – Amount of Insurance years 1AIY=$1,000 of dwelling coverage • Damage Ratios – Losses/AIY

6. History of Methods

7. Goals of New Methods • Develop an accurate, stable provision by state that results in an appropriate provision on a countrywide basis • Systematic approach to handle extreme events so a single outlying year does not drive the cat provision for a state • Appropriate application of credibility procedure • Provide result that is responsive to recent demographic and cat definition shifts • Method should be “sellable” to insurance departments and regional staff

8. Method to be Presented • State relativity weighted with countrywide • State relativity weighted with regional • Refinement of Dean et. al. paper • Several other methods are included with Forum paper and will not be discussed here

9. Data Considerations • Summary by state and calendar year of Allstate 1971-2000 catastrophe losses and AIY for HO, Renters, and Condo • Additional years have been added since the original research and are not included in this presentation • The nature of the analyses was constrained by the data available • From 1988 forward additional detail available: e.g. could have broken out catastrophes by peril

10. State Relativity Weighted with Countrywide Complement – General Outline • Develop State Damage Ratios • Calculate Countywide Damage Ratios • Calculate State Relativities • Cap State Relativities • Average Capped Relativities • Credibility Weight with CW Average of 1.000 • Balance Back to CW Average of 1.000 • Calculate Statewide Catastrophe Provision

11. Develop State Damage Ratios • Calculate Countrywide Damage Ratios • Calculate State Relativities • Cap State Relativities • Average Capped Relativities • Credibility Weight with CW Average of 1.000 • Balance Back to CW Average of 1.000 • Calculate Statewide Catastrophe Provision State Relativity Weighted with Countrywide Complement • Develop each state’s damage ratios for years 1981-2000 • State Damage Ratios – Losses/AIY • Only use years 1981 forward. Data for years 1971 through 1980 is sparse as evidenced by yearly variance

12. Develop State Damage Ratios • Calculate Countrywide Damage Ratios • Calculate State Relativities • Cap State Relativities • Average Capped Relativities • Credibility Weight with CW Average of 1.000 • Balance Back to CW Average of 1.000 • Calculate Statewide Catastrophe Provision State Relativity Weighted with Countrywide Complement • Each year’s Countrywide damage ratio is calculated as the weighted average of state damage ratios using latest year AIYs as weights • Countrywide catastrophe provision is the arithmetic average of recent years’ damage ratios • When breaking down the historical period into distinct segments the trend is flat for each period (Figure 1) • Using only most recent years allows us to be responsive to current level of catastrophe exposure • Can use a 10 year average or years since 1990 • One can tack on an additional load to be conservative

13. Figure 1 YearsLinear trend 1971-1978 0.006 1979-1989 0.000 1990-1999 -0.019 1990-2000 -0.010

14. Develop State Damage Ratios • Calculate Countrywide Damage Ratios • Calculate State Relativities • Cap State Relativities • Average Capped Relativities • Credibility Weight with CW Average of 1.000 • Balance Back to CW Average of 1.000 • Calculate Statewide Catastrophe Provision State Relativity Weighted with Countrywide Complement • Calculate state relativities as the ratio of state damage ratios to countrywide damage ratios • Relativities should be more stable than damage ratios • Trend should not be a problem so we can use more years of data than the Countrywide Catastrophe Provision (Exhibit 1)

15. Develop State Damage Ratios • Calculate Countrywide Damage Ratios • Calculate State Relativities • Cap State Relativities • Average Capped Relativities • Credibility Weight with CW Average of 1.000 • Balance Back to CW Average of 1.000 • Calculate Statewide Catastrophe Provision State Relativity Weighted with Countrywide Complement • Any relativity greater than the mean plus three standard deviations is capped to the next lowest relativity (not the cap number) • Benefit of capping process • Represents a systematic approach to dealing with extreme events • Cap is dynamic and is allowed to shift if exposure in a state is changing over time • Censoring at the cap would not have much impact and therefore would not result in increased stability • Drawbacks of capping process • A year with a lower relativity could result in a higher catastrophe provision than a slightly higher one • A higher than average single year could lead to a less stable average relativity if it is also used as the “next lowest relativity” in the capping process

16. Develop State Damage Ratios • Calculate Countrywide Damage Ratios • Calculate State Relativities • Cap State Relativities • Average Capped Relativities • Credibility Weight with CW Average of 1.000 • Balance Back to CW Average of 1.000 • Calculate Statewide Catastrophe Provision State Relativity Weighted with Countrywide Complement • Calculate arithmetic average of 1981-2000 capped relativities • No benefit of weighting relativities has been shown since relationship of variability to exposure level is unclear • Arithmetic average relativity does not differ significantly from an AIY weighted average

17. Develop State Damage Ratios • Calculate Countrywide Damage Ratios • Calculate State Relativities • Cap State Relativities • Average Capped Relativities • Credibility Weight with CW Average of 1.000 • Balance Back to CW Average of 1.000 • Calculate Statewide Catastrophe Provision State Relativity Weighted with Countrywide Complement • Uses Buhlmann credibility factor: n/(n+k) • n = number of years of relativities in average • We use number of years rather than exposures because exposures not independent, especially past a certain threshold where exposure concentration increases • k = average process variance/variance of hypothetical means • The process variance and variance of hypothetical means are calculated using all available years of capped relativities across all states • Complement of credibility of 1.000 is not appropriate when there is a wide spread of average relativities (Exhibit 2)

18. Develop State Damage Ratios • Calculate Countrywide Damage Ratios • Calculate State Relativities • Cap State Relativities • Average Capped Relativities • Credibility Weight with CW Average of 1.000 • Balance Back to CW Average of 1.000 • Calculate Statewide Catastrophe Provision State Relativity Weighted with Countrywide Complement • The unbalanced state relativities result in a countrywide relativity of less than 1.000. Relativities are adjusted: • Determined countrywide expected losses based on the countrywide selected catastrophe factor • Sum the pre-balanced expected losses across all states • Distribute the difference between 1 and 2 in proportion to each state’s standard deviation measured in latest year expected losses. • Using this approach has several benefits: • Results in an appropriate provision countrywide • It compensates for high (low) relativity states being underestimated (overestimated) by the use of a 1.000 complement of credibility • Resulting cat load is a function of each state’s size and variability • Exhibit 3 Shows numerical example

19. Develop State Damage Ratios • Calculate Countrywide Damage Ratios • Calculate State Relativities • Cap State Relativities • Average Capped Relativities • Credibility Weight with CW Average of 1.000 • Balance Back to CW Average of 1.000 • Calculate Statewide Catastrophe Provision State Relativity Weighted with Countrywide Complement • Statewide catastrophe provision is calculated by multiplying capped, credibility weighted, balanced relativity by the countrywide catastrophe provision • Benefits of method: • Allows use of long term data to determine relativity while using more responsive data for countrywide provision • Adjustments to data are determined objectively with each state’s characteristics used to determine both capping and balancing • Drawbacks of method: • Complement of credibility is suspect • Despite the fact that any state has the potential to have capped losses, the capping/balancing process could be controversial

20. State Relativity Weighted with Regional Complement • Regions are developed by combining several contiguous states with similar damage ratios and using correlations to determine close calls • Region-wide damage ratios are also calculated by weighting with latest year’s AIYs • Method credibility weights each state with its own region rather than countrywide

21. State Relativity Weighted with Regional Complement • For regional methods credibility weight differs from countrywide in the expected process variance • Took weighting of state’s own sample process variance with average of all states in region’s process variance • Took weighting of maximum sample process variance for all states with average of all state’s sample process variance • Also adjusted VHP to eliminate negative values • As with previous method • State relativities are balanced to Regions which are themselves balanced to provide an adequate countrywide provision • We are using relativities which allows us to use all available valid years without concern for trend in damage ratios • Exhibit 4 shows example

22. State Relativity Weighted with Regional Complement • Benefits • Complement of credibility is more appropriate than countrywide • We are able to consider the individual state variability (in our estimation of the process variance) in the credibility weight. • No need for capping since adjustments to credibility procedure neutralizes the impact of extreme events • Drawbacks • Regions are not optimal because they are developed around political boundaries when they theoretically should be developed around geographic boundaries • States may argue if extremely high cat state is included in their region

23. Dual Capping Method • Method originally proposed by Dean et al • Rank catastrophe loss ratios over all available years (17 in Dean paper) • Censor losses above and below • Divide net excess losses by all years EP to get load • This is added to each individual year’s capped ratios • Problems • Historical premium inadequacies can distort • Historical catastrophe loss ratios are trended or not • Trending is problematic • Not trending is inconsistent with non catastrophe methodology and distorts which year will be capped • 17 years is not enough

24. Dual Capping Method • Proposed modification • Rather than go back in time to get more points use a region for the latest 10 years. If region has, e.g., 7 states, there are 70 points • Rank all the damage ratios, rather than loss ratios, and double censor as before • Benefits • No premium adequacy problem • No trending problem • Contains more points • Drawbacks • Some states don’t fit in group well and will be overly capped • Looks too much like smoothing losses between states • Exhibit 5 shows example

25. Summary • We’ve reviewed several methods to develop non-modeled catastrophe provisions • All of these methods attempt to balance the need for stable long term averages while being responsive to more recent catastrophe exposure distributions • What are your thoughts on the models presented or other alternatives? Use the following criteria to evaluate: • Accuracy • Stability • Sellability