Question

1. (10 points) Assume a company has the following information about expenses Written Premium Earned Premium Commissions and Brokerage Expenses incurred Other Acquisition Expenses Incurred General Expenses Taxes, Licenses & Fees Incurred 2016 2017 2018 Expense Ratio Expense Ratio ($000s) 6,100 5,920 12.0% 13.0% 945 12.8% 12.7% 760 5.0% 5.5% 325 2.1% 2.2% 130 Questions: a. (5 points) Use the three-year average to calculate a total expense ratio, for use in ratemak- ing, assuming all expenses are variable. b. (5 points) Calculate the variable permissible loss ratio using the expense ratio calculated in part a.

Answer 1

a)

	2016 Expense Ratio	2017 Expense Ratio	2018 Expense Ratio
Written premium Earned premium Commissions and Brokerage expenses incurred Other acquisition expenses incurred General expenses Taxes, licenses & Fees incurred	12.0 % 12.8 % 5.0 % 2.1 %	13.0 % 12.7 % 5.5 % 2.2 %	6,100 5920 15.5 % 12.5 % 5.32 % 2.1 %

Total expense ratio =  
total fundcost total fundasset

Total expense ratio for the year 2016 = 31.9 %

Total expense ratio for the year 2017 = 33. 4 %

Total expense ratio for the year 2018 = $\frac{2160}{6100}$ x 100 = 35.4%

Total expense ratio for three years = 33.5 %

b) Variable Permissible Loss Ratio (VPLR) = 1 - % of Variable Expense

= 100-33.5 % = 66.5