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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

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### 10 Data Commandments to Overcome the Law of Small Numbers

1. 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 & Chief Actuary of Grange Insurance Group
2. 2. Three “R’s” wRiting aRithmetic Reading
3. 3. Three “R’s” of Actuarial Reserves Reports Rates
4. 4. Always advance, or else • He who moves not forward, goes backward. – Johann Wolfgang von Goethe • If everything's under control, you're going too slow. –Mario Andretti • Even if you're on the right track, you'll get run over if you just sit there. – Will Rodgers
5. 5. TEAMWORK • Coming together is a beginning • Keeping together is progress • Working together is success - Henry Ford
6. 6. The LAW of LARGE NUMBERS • The Law of Large Numbers states that regardless of the shape of the original distribution, the taking of averages results in a normal distribution. • Insurance is an uncertain business, so we have to use averages • The bigger the number of items in our average, the smaller the error. • You need to average lots of items to be sure your average is indicative. • This is why we looked and will continue to look at industry results… • This is also why we watch larger states more closely
7. 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. 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. 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. 10. The LAW of SMALL NUMBERS • The Law of Small Numbers states that there are not enough small numbers to satisfy all the demands placed on them. - Richard Guy, statistician • You can't tell by looking [at a few examples]. • Superficial similarities spawn spurious statements. • Capricious coincidences cause careless conjectures. • Early exceptions eclipse eventual essentials. • Initial irregularities inhibit incisive intuition
11. 11. TEN ACTUARIAL COMMANDMENTS #10 – Ignore the law of small numbers and truth will bite you. #9 – Find credible data. How? Graph thy data #8 Skew is the rule #7 Prune thy data #6 Weed thy data
12. 12. TEN ACTUARIAL COMMANDMENTS #5 Explore thy data… #4 Show thy data! #3 Sort, shuffle and juggle thy data! #2 Grow thy data! #1 Know thy data!
13. 13. COMMANDMENT #1 KNOW THY DATA • To understand what has happened, find out what was counted and how.
14. 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. 15. COMMANDMENT #2 GROW THY DATA • Master actuarial measurements by studying and using knowledge • Master business results by refining databases and reports from them • Keep basics a part of the many ways, old & new, to capture and/or picture truth.
16. 16. COMMANDMENT #3 SORT, SHUFFLE AND JUGGLE THY DATA • 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. • So it takes actuarial work to make numbers remember the right things.
17. 17. COMMANDMENT #4 • SHOW THY DATA! • Depict stories whenever possible with graphs and pictures. The best way to say this is to paraphrase St. Francis of Assissi: “Use numbers only when absolutely necessary.” • In actuarial work there are a lot of absolutely necessary times for numbers.
18. 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. 19. COMMANDMENT #5 • EXPLORE THY DATA • To know, grow, and show data in a true manner, you have to understand the data. • How? Spend time with thy data. • DIG THY DATA! (pun intended)
20. 20. COMMANDMENT #6 • WEED THY DATA! • Flowers and fruits in thy data garden are grand. • But weeds creep in. • To keep data flowers and data fruit healthy… WEED THY DATA! • Use the “Yellow Book”… make sure your figures match official Annual Statements
21. 21. COMMANDMENT #7 PRUNE THY DATA • Give non-number people appropriate focus. Match displayed precision to the accuracy of the facts. • Don’t tell more than facts reveal. • Pruning corollary: DO SOME GRAFTING. • Get and use more credible data when you run out of truth.
22. 22. What is happening to Industry Homeowners’ 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. 23. COMMANDMENT #8 • SKEW IS THE RULE • My college statistical training was incomplete. There I only learned about the Normal Distribution. • On the actuarial job, there is no normal mountain of insurance data. • Therefore, know that skew is the rule or… be skewered!
24. 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. 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. 26. COMMANDMENT #9 • GRAPH THY DATA • This helps find the source of skewness • Graphs also show clouds of truth • Watch the clouds of truth to see which way the winds are blowing. • Are thy clouds of truth cumulonimbus, or cirrus, or ??? …With gratitude to Luke Howard, the Inventor of Clouds
27. 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. 28. COMMANDMENT #10 IGNORE THE LAW OF SMALL NUMBERS AND TRUTH WILL BITE YOU. • In other words, get out of thine own niche. Explore the insurance universe out yonder. • Use your actuarial eyes to bring truth into focus.
29. 29. COMMANDMENT #11 BONUS COMMANDMENT: USE HUMOR •Look for real-life surprises in the data •Share the surprise in story form to stir up laughter •Tell funny data stories to stay connected with people you work with
30. 30. THE GREATEST COMMANDMENT? WHAT STORIES DO YOU LIKE TO TELL? FIND CREDIBLE DATA TO LOVE • Use it to carve a path of truth that strikes a balance between stability and responsiveness. KEEP THE STORIES IN THE NUMBERS • RESULT: Putting actuarial stories back into the numbers. Do your part to keep insurance companies healthy.