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 & Chief Actuary of Grange Insurance Group
  • 2. Three “R’s” wRiting aRithmetic Reading
  • 3. Three “R’s” of Actuarial Reserves Reports Rates
  • 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. TEAMWORK • Coming together is a beginning • Keeping together is progress • Working together is success - Henry Ford
  • 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. 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 • 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. 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. 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. COMMANDMENT #1 KNOW THY DATA • 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 • 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. 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. 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. 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 • 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. 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. 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. 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. 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. 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 • 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. 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. • 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. 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. 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.