FRM Part I · FRM Exam Part I · Insurance Companies and Pension Plans
An insurer writes premiums of $300 million and earns $240 million of them in the year. Incurred losses are $168 million. Underwriting expenses are $90 million, and these are measured against premiums written. What is the combined ratio using loss ratio on earned premiums and expense ratio on written premiums?
The combined ratio is 100%. The loss ratio is 70% (168 divided by earned premiums of 240) and the expense ratio is 30% (90 divided by written premiums of 300). Using earned premiums for expenses would wrongly give 107.5%, since the stated convention uses written premiums.
- A86.0%
- B100.0%Correct
- C107.5%
- D70.0%
Explanation
Loss ratio = 168/240 = 70%. Expense ratio = 90/300 = 30%. Sum = 100%. Using earned premiums for both would give 70% + 37.5% = 107.5%, which mixes in the wrong base for expenses. The 70% option omits expenses.
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