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FRM Part I · FRM Exam Part I · Insurance Companies and Pension Plans

An insurer has 10,000 identical one-year policies. Each has an independent 2% claim probability and a fixed claim amount of 50,000. What is the standard deviation of the total claims as a percentage of the expected total claims, and what does it show about pooling?

The standard deviation is about 7% of expected claims. Expected claims are 200 and the variance is 10,000 x 0.02 x 0.98 = 196, giving a standard deviation of 14 claims, or 14/200 = 7%. Relative risk falls with the square root of pool size, though it is not eliminated.

  1. AApproximately 7.1%, showing relative risk falls as the pool growsCorrect
  2. BApproximately 14.0%, showing relative risk is independent of pool size
  3. CApproximately 1.4%, showing relative risk is eliminated
  4. DApproximately 0.7%, showing relative risk rises with pool size

Explanation

Per-policy claim count is Bernoulli with p = 0.02. Number of claims has mean 200 and variance 10,000 x 0.02 x 0.98 = 196, so standard deviation is 14 claims. Relative to the mean this is 14/200 = 7%, about 7.1% when rounded loosely. Relative risk scales as 1/sqrt(n), so it falls as the pool grows but is not eliminated.

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