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Seven Years of Actuarial Work Overcoming the law of small numbers

Join Stephen L. Kolk, ACAS Vice President of Actuarial Services & Chief Actuary of Grange Insurance Group, as he shares insights and strategies for overcoming the challenges posed by the Law of Small Numbers in actuarial work. Discover the Ten Actuarial Commandments and learn how to grow, explore, and present data effectively in order to make informed decisions. Don't ignore the Law of Small Numbers - embrace it and ensure accuracy in your work.

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Seven Years of Actuarial Work Overcoming the law of small numbers

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  1. Seven Years of Actuarial WorkOvercoming the law of small numbers By Stephen L. Kolk, ACAS Vice President of Actuarial Services & Chief Actuary of Grange Insurance Group

  2. Three “R’s”

  3. Three “R’s” of Actuarial

  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 GROUPby Company

  8. GRANGE INSURANCE GROUPDWP by Major Product

  9. GRANGE INSURANCE GROUP DWP by State

  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

  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. Losses Adjustment Costs Expenses Total Costs Premium Combined Ratio Cost $60 10 30 $100 $100 100% What rate change is neededto cover a 15% trend change? 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?

  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. 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

  25. NEW TOOLS Improve Forecasting

  26. 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.

  27. 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.

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