CAS Data Analysis and Interpretation 3 — Questions and Answers
Question 1: A property insurer tests whether mean claim severity differs across three geographic territories using ANOVA. The F-statistic is large and the p-value is 0.002. The correct interpretation is:
- All three territory means are significantly different from each other
- At least one territory mean differs significantly from the others (Correct answer)
- The variance within each territory is significantly different
- Exactly two territories have equal means
Correct answer: At least one territory mean differs significantly from the others
A significant ANOVA F-test only indicates that at least one group mean differs; post-hoc tests are needed to identify which pairs differ.
Question 2: When applying the Bornhuetter-Ferguson (BF) method, the ultimate loss estimate blends:
- Reported losses and paid losses using equal weights
- A priori expected losses and development-method projected losses (Correct answer)
- IBNR reserves from two consecutive accident years
- Chain-ladder ultimates from paid and incurred triangles
Correct answer: A priori expected losses and development-method projected losses
The BF method weights the a priori expected ultimate with the chain-ladder projected unreported portion, providing stability for immature accident years.
Question 3: In logistic regression applied to binary claim outcomes (1=large loss, 0=small loss), the model output is best interpreted as:
- The expected dollar amount of the loss
- The log of the odds ratio of experiencing a large loss
- The probability that the loss exceeds a fixed threshold (Correct answer)
- The Z-score of the observation relative to the mean
Correct answer: The probability that the loss exceeds a fixed threshold
After applying the inverse logit transformation, logistic regression outputs the predicted probability that the response equals 1.
Question 4: A reserving actuary identifies that the paid loss development factors for the most recent accident year are significantly higher than historical averages. Before concluding that reserves are inadequate, the actuary should first investigate:
- Whether the company's surplus ratio has declined
- Changes in claims settlement practices or data processing that may explain the shift (Correct answer)
- Whether reinsurance recoveries have been properly netted
- Whether the calendar year diagonal totals are monotonically increasing
Correct answer: Changes in claims settlement practices or data processing that may explain the shift
Unusual development factors often stem from operational changes (e.g., accelerated settlements, data cleanup) rather than true reserve inadequacy.
Question 5: Which statistical test is most appropriate for assessing whether two independent samples of claim counts come from populations with the same distribution?
- Paired t-test
- Kolmogorov-Smirnov two-sample test (Correct answer)
- Chi-square goodness-of-fit test for one sample
- Durbin-Watson test
Correct answer: Kolmogorov-Smirnov two-sample test
The two-sample Kolmogorov-Smirnov test compares the empirical CDFs of two independent samples to test if they come from the same distribution.
Question 6: An actuary applies k-means clustering to policyholder telematics data. The optimal number of clusters k is typically chosen by:
- Setting k equal to the square root of the number of observations
- Examining the elbow in the plot of within-cluster sum of squares versus k (Correct answer)
- Using the Akaike Information Criterion from a GLM with k parameters
- Selecting the k that minimizes the Gini coefficient of cluster sizes
Correct answer: Examining the elbow in the plot of within-cluster sum of squares versus k
The elbow method identifies the k at which adding another cluster yields diminishing reduction in within-cluster sum of squares.
Question 7: Tail Value at Risk (TVaR) at the 99th percentile is preferred over Value at Risk (VaR) at the same percentile for capital modeling because TVaR:
- Is always lower than VaR, providing a more conservative estimate
- Captures the expected severity of losses beyond the VaR threshold (Correct answer)
- Can be computed without fitting a parametric distribution
- Is less sensitive to extreme outliers in the data
Correct answer: Captures the expected severity of losses beyond the VaR threshold
TVaR (also called CVaR) equals the expected loss given that the loss exceeds the VaR threshold, making it sensitive to tail severity rather than just the threshold level.
CAS Data Analysis and Interpretation 3
A property insurer tests whether mean claim severity differs across three geographic territories using ANOVA.
The F-statistic is large and the p-value is 0.002.
The correct interpretation is: