A chief actuary is training junior underwriters on how portfolio composition impacts loss predictability. Match each portfolio scenario on the left with its corresponding statistical outcome or risk principle on the right, based on the Law of Large Numbers.
- Scaling a portfolio to include tens of thousands of similar, independent exposure units.Optimizes the Law of Large Numbers by minimizing variance between actual and expected aggregate losses.
- Utilizing historical loss data to determine exactly which specific policyholders will file claims next year.Represents a misapplication of statistical probability, as risk pooling cannot predict individual outcomes.
- Attempting to base actuarial rate pricing on a pool of only 25 large, highly variable corporate accounts.Yields poor loss predictability due to a statistically insignificant sample size and a lack of exposure homogeneity.
- Aggregating thousands of identically constructed properties that are all located on the same coastal barrier island.Compromises the effectiveness of risk pooling because the exposure units are not independent of a catastrophic peril.
Answer
Tens of thousands of independent units minimizes variance; predicting individual losses is a misapplication; 25 variable accounts yields poor predictability; and concentrated properties compromise risk pooling due to catastrophic dependence.
Each scenario correctly identifies a core tenet or limitation of the Law of Large Numbers. Proper application requires a massive pool of homogeneous, independent units to predict aggregate (not individual) losses.
Step-by-Step Solution
Key Concept
The Law of Large Numbers requires a massive pool of homogeneous, independent exposure units to accurately predict aggregate losses.