Term Test 1_solutions

# Term Test 1_solutions - ACTUARIALSCIENCE462/862 TERMTEST#1...

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UNIVERSITY OF WATERLOO ACTUARIAL SCIENCE 462/862 TERM TEST #1 TUESDAY JANUARY 31, 2012 (2) 1. Based on the following information, calculate the company’s expected profit provision (i.e. as a percent of premium): Expected loss ratio = 60% Expected loss adjustment expenses = 15% of expected losses Operating expense ratio (OER) = 25% of premium Solution: Expected loss and loss adjustment ratio = 60% x 1.15 = 69% Combined Ratio = Loss Ratio + OER + Profit For equation to be in balance, combined ratio = 1 Therefore, Profit = 1 – Loss Ratio – OER = 1 – .69 – .25 = 6% Alternative solution: Assume OER include LAE ratio Therefore, Profit = 1 – Loss Ratio – OER = 1 – .6 – .25 = 15% {See lecture #1, slide 14 Æ went through example in class} (5) 2. A company has the following rating structure: Policy premium = Base Rate x Territory Factor + Policy Fee Base Rate = \$1,000 Policy Fee = \$50 Territory Factors: Policies written: On April 1, the Base Rate is changed to \$1,100 Territory Factor 1 1.0 2 1.5 # of Policies Written Date Written Territory 1 Territory 2 Jan 1, 2012 10 15 Jul 1, 2012 12 12

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a) Calculate the 2012 Earned Premium for this company. b) Calculate the 2012 on level factor that can be used for rate making. Solution: Picture not necessary but will find it helpful to draw it. 2012 2013 Jan 1 July 1 Only 50% of policies written on July 1 are EARNED by end of year Base rate increased April 1, 2012 to \$1,100 a) 2012 Earned Premium: Policies written on Jan 1, 2012 (fully earned by end of year) o Terr 1: 10 x (\$1,000 x 1.0 + \$50) = 10,500 o Terr 2: 15 x (\$1,000 x 1.5 + \$50) = 23,250 Policies written on July 1, 2012 (only half earned by end of year, also base rate is now \$1,100) o Terr 1: ½ x 12 x (\$1,100 x 1.0 + \$50) = 6,900 o Terr 2: ½ x 12 x (\$1,100 x 1.5 + \$50) = 10,200
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