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# 10 Data Commandments to Overcome the Law of Small Numbers

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Presentation given in 2004 to the Casualty Actuaries of the Northwest by Stephen L Kolk, ACAS

Presentation given in 2004 to the Casualty Actuaries of the Northwest by Stephen L Kolk, ACAS

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• 1. 10 Data Commandments for Overcoming the Law of Small Numbers Lessons learned during Seven Years of Actuarial Work By Stephen L. Kolk, ACAS Vice President of Actuarial Services &amp; Chief Actuary of Grange Insurance Group
• 2. Three &#x201C;R&#x2019;s&#x201D; wRiting aRithmetic Reading
• 3. Three &#x201C;R&#x2019;s&#x201D; of Actuarial Reserves Reports Rates
• 4. Always advance, or else &#x2022; He who moves not forward, goes backward. &#x2013; Johann Wolfgang von Goethe &#x2022; If everything's under control, you're going too slow. &#x2013;Mario Andretti &#x2022; Even if you're on the right track, you'll get run over if you just sit there. &#x2013; Will Rodgers
• 5. TEAMWORK &#x2022; Coming together is a beginning &#x2022; Keeping together is progress &#x2022; Working together is success - Henry Ford
• 6. The LAW of LARGE NUMBERS &#x2022; The Law of Large Numbers states that regardless of the shape of the original distribution, the taking of averages results in a normal distribution. &#x2022; Insurance is an uncertain business, so we have to use averages &#x2022; The bigger the number of items in our average, the smaller the error. &#x2022; You need to average lots of items to be sure your average is indicative. &#x2022; This is why we looked and will continue to look at industry results&#x2026; &#x2022; This is also why we watch larger states more closely
• 7. GRANGE INSURANCE GROUP by Company 0 20,000,000 40,000,000 60,000,000 80,000,000 100,000,000 120,000,000 140,000,000 160,000,000 1997 1998 1999 2000 2001 2002 GIA RM
• 8. GRANGE INSURANCE GROUP DWP by Major Product 0 20,000,000 40,000,000 60,000,000 80,000,000 100,000,000 120,000,000 140,000,000 160,000,000 1997 1998 1999 2000 2001 2002 PP Auto Home Farm Comm Auto Other
• 9. GRANGE INSURANCE GROUP DWP by State 0 20,000,000 40,000,000 60,000,000 80,000,000 100,000,000 120,000,000 140,000,000 160,000,000 1997 1998 1999 2000 2001 2002 CA CO ID MT OR WA WY
• 10. The LAW of SMALL NUMBERS &#x2022; The Law of Small Numbers states that there are not enough small numbers to satisfy all the demands placed on them. - Richard Guy, statistician &#x2022; You can't tell by looking [at a few examples]. &#x2022; Superficial similarities spawn spurious statements. &#x2022; Capricious coincidences cause careless conjectures. &#x2022; Early exceptions eclipse eventual essentials. &#x2022; Initial irregularities inhibit incisive intuition
• 11. TEN ACTUARIAL COMMANDMENTS #10 &#x2013; Ignore the law of small numbers and truth will bite you. #9 &#x2013; Find credible data. How? Graph thy data #8 Skew is the rule #7 Prune thy data #6 Weed thy data
• 12. TEN ACTUARIAL COMMANDMENTS #5 Explore thy data&#x2026; #4 Show thy data! #3 Sort, shuffle and juggle thy data! #2 Grow thy data! #1 Know thy data!
• 13. COMMANDMENT #1 KNOW THY DATA &#x2022; To understand what has happened, find out what was counted and how.
• 14. Homeowners Pure Premium PUREPREMIUM ISO vs GIG companies 0 50 100 150 200 250 300 350 400 C a le n da r Q ua r te r En ding GIA RM ISO All GIG StatesHomeowners (excluding catastrophes) All Policy Forms Combined
• 15. COMMANDMENT #2 GROW THY DATA &#x2022; Master actuarial measurements by studying and using knowledge &#x2022; Master business results by refining databases and reports from them &#x2022; Keep basics a part of the many ways, old &amp; new, to capture and/or picture truth.
• 16. COMMANDMENT #3 SORT, SHUFFLE AND JUGGLE THY DATA &#x2022; What numbers do best is forget things. As soon as you write them down, they forget both where they have been and where they are going. &#x2022; So it takes actuarial work to make numbers remember the right things.
• 17. COMMANDMENT #4 &#x2022; SHOW THY DATA! &#x2022; Depict stories whenever possible with graphs and pictures. The best way to say this is to paraphrase St. Francis of Assissi: &#x201C;Use numbers only when absolutely necessary.&#x201D; &#x2022; In actuarial work there are a lot of absolutely necessary times for numbers.
• 18. What rate change is needed to cover a 15% trend change? Losses Adjustment Costs Expenses Total Costs Premium Combined Ratio Cost \$60 10 30 \$100 \$100 100% Trend Change +15% +15% New Cost \$69.00 11.50 30.00 \$110.50 \$100 110.5% Required Rate Change = \$110.50 / \$100 = +10.5%
• 19. COMMANDMENT #5 &#x2022; EXPLORE THY DATA &#x2022; To know, grow, and show data in a true manner, you have to understand the data. &#x2022; How? Spend time with thy data. &#x2022; DIG THY DATA! (pun intended)
• 20. COMMANDMENT #6 &#x2022; WEED THY DATA! &#x2022; Flowers and fruits in thy data garden are grand. &#x2022; But weeds creep in. &#x2022; To keep data flowers and data fruit healthy&#x2026; WEED THY DATA! &#x2022; Use the &#x201C;Yellow Book&#x201D;&#x2026; make sure your figures match official Annual Statements
• 21. COMMANDMENT #7 PRUNE THY DATA &#x2022; Give non-number people appropriate focus. Match displayed precision to the accuracy of the facts. &#x2022; Don&#x2019;t tell more than facts reveal. &#x2022; Pruning corollary: DO SOME GRAFTING. &#x2022; Get and use more credible data when you run out of truth.
• 22. What is happening to Industry Homeowners&#x2019; Rates? Conning Average Homeowner Premium Change versus Homeowner Loss Costs -2% 0% 2% 4% 6% 8% 10% 1996 1997 1998 1999 2000 2001 Mar'02 June'02 AnnualChangeinPercent CPI - Total Housing Costs CPI - Household Furnishings CPI - Medical Costs CPI - Hospital and related services Conning Avg Homeowners' Ins. Prem.
• 23. COMMANDMENT #8 &#x2022; SKEW IS THE RULE &#x2022; My college statistical training was incomplete. There I only learned about the Normal Distribution. &#x2022; On the actuarial job, there is no normal mountain of insurance data. &#x2022; Therefore, know that skew is the rule or&#x2026; be skewered!
• 24. GIA Farmowners vs Industry 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 110% 120% 1997 1998 1999 2000 2001 08/03 Year AdjustedLossRatio
• 25. RM Farmowners vs Industry 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 110% 120% 130% 1997 1998 1999 2000 2001 08/03 Year AdjustedLossRatio
• 26. COMMANDMENT #9 &#x2022; GRAPH THY DATA &#x2022; This helps find the source of skewness &#x2022; Graphs also show clouds of truth &#x2022; Watch the clouds of truth to see which way the winds are blowing. &#x2022; Are thy clouds of truth cumulonimbus, or cirrus, or ??? &#x2026;With gratitude to Luke Howard, the Inventor of Clouds
• 27. NEW TOOLS Improve Forecasting Frequency Chart Policies .000 .006 .012 .017 .023 0 289.7 579.5 869.2 1159 158,000 160,250 162,500 164,750 167,000 50,000 Trials 49,826 Displayed Forecast: GIG12/31/04PIF
• 28. COMMANDMENT #10 IGNORE THE LAW OF SMALL NUMBERS AND TRUTH WILL BITE YOU. &#x2022; In other words, get out of thine own niche. Explore the insurance universe out yonder. &#x2022; Use your actuarial eyes to bring truth into focus.
• 29. COMMANDMENT #11 BONUS COMMANDMENT: USE HUMOR &#x2022;Look for real-life surprises in the data &#x2022;Share the surprise in story form to stir up laughter &#x2022;Tell funny data stories to stay connected with people you work with
• 30. THE GREATEST COMMANDMENT? WHAT STORIES DO YOU LIKE TO TELL? FIND CREDIBLE DATA TO LOVE &#x2022; Use it to carve a path of truth that strikes a balance between stability and responsiveness. KEEP THE STORIES IN THE NUMBERS &#x2022; RESULT: Putting actuarial stories back into the numbers. Do your part to keep insurance companies healthy.