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

An insurer has 10,000 policyholders, half high-risk with expected annual claim cost of 1,200 and half low-risk with 400. It charges a single premium equal to the pooled expected cost. Low-risk customers whose maximum willingness to pay is 700 all leave. What is the new break-even premium per remaining policyholder, and what is the original pooled premium?

The original pooled premium is 800, the average of 1,200 and 400 with equal weights. Because low-risk customers will pay at most 700, they leave, and the remaining pool is all high-risk, so the break-even premium rises to 1,200 per policyholder. This is adverse selection.

  1. AOriginal 800; new 1,200Correct
  2. BOriginal 800; new 800
  3. COriginal 1,200; new 1,200
  4. DOriginal 400; new 1,200

Explanation

Original pooled premium = 0.5×1,200 + 0.5×400 = 800. Since 800 exceeds the low-risk willingness to pay of 700, they leave. Only high-risk remain, so break-even rises to 1,200. Keeping 800 would leave the insurer losing 400 per policy.

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