CAS Exam 9 Spring 2015, Question 20
Study guide: Exam 9
Below is information about a large property and casualty insurer that writes Homeowners' and Workers' Compensation business.
- The insurer expects to write $1 billion of business over the next year, equally split between its Homeowners' and Workers' Compensation lines of business.
- The expected loss ratio is the same for both products.
- Each product is expected to earn $25 million in underwriting income over the course of the year.
- $500 million of surplus is held between these two products.
- The average duration between occurrence and payment of a claim is one year for Homeowners' and three years for Workers' Compensation.
- There is no investment income.
Part a (1 point)
Using two allocation methods, calculate the return on equity for each line of business. Assume a steady state environment.
Part b (1 point)
For each allocation method above, briefly explain how the above return on equity figures would change if the Workers' Compensation line of business has been growing at a faster pace than the Homeowners' line of business for the past several years.
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