1. COTOR Training Session II GL Data: Long Tails, Volatility, Data Transforms September 11, 2006

2. COTOR Session II Presenters Doug Ryan MBA Actuaries, Inc. Phil Heckman Heckman Actuarial Consulting

3. Assumptions and Verification Behavior of mean, variance, distribution (sometimes) Verify by examining –Descriptive statistics –Regression diagnostics –Scatter plots –Residual plots

4. GL Data: Chain Ladder

8. What are they? Slope standard error R square: Percentage of variance explained by regression Intercept standard error Degrees of Freedom: # Observations - # Parameters

12. A Key Diagnostic: Standard Residual Standardize by subtracting mean (should be zero) and divide by standard deviation A z-score –Z = (x – mean)/sd

14. Two Factor Model One factor model: incremental loss =f(prior cumulative) –Compute separate function for each development age –Can use Excel regression functions Two factor model: incremental loss = f(accident period, development age) –Bornhuetter-Ferguson is an example –Nonlinear function, Use solver

15. GL Data: Two-Factor Model

20. GL Data: 3-Factor Model

24. GL Data: Log Chain Ladder

25. Why use logarithms? Descriptive statistics indicate data not normal A-priori belief that model is mutiplicative Residuals increase with value of dependent variable

29. GL Data: Log 2-Factor Model

30. Iterative Least Squares Start with all weights = 1 Estimate by minimizing weighted sum of squares Calculate new weights = 1/(1+ Old Weight*Squared Error) Reëstimate. Stop when weights stop changing.

40. GL Data: Summary