AS462_Term_Test_1_solutions

AS462_Term_Test_1_solutions - UNIVERSITY OF WATERLOO...

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Unformatted text preview: UNIVERSITY OF WATERLOO ACTUARIAL SCIENCE 862 TERM TEST #1 TUESDAY FEBRUARY 8, 2011 (2) 1. Given the following information, calculate the combined ratio. 2010 Earned Premium $350,000 2010 Incurred Losses $210,000 Loss Adjustment Expense Ratio 0.15 Underwriting Expense Ratio 0.23 Solution: Combined Ratio = Loss Ratio + Operating Expense Ratio (OER) Incurred Losses 210,000 = = .60 Earned Premium 350,000 LAE OER = U/W Expense Ratio + Earned Premium 0.15 210,000 = 0.23 + 0.09 = 0.32 = 0.23 + 350,000 Loss Ratio = CR = .60 + .32 = 0.92 (2) 2. The following activity occurred on five policies. Assume the exposure base is earnedcar years. Policy 1 2 3 4 5 Effective Date July 1, 2009 November 1, 2009 January 1, 2010 March 1, 2010 July 1, 2010 Original Expiration Date June 30, 2010 October 31, 2010 December 31, 2010 February 28, 2011 June 30, 2011 Mid Term Cancelation Date n/a May 31, 2010 n/a June 30, 2010 n/a Calculate: a) 2010 calendar year written exposure b) 2010 calendar year earned exposure c) 2009 policy year written exposure d) In force exposure as at June 1, 2010 Solution: 2009 2010 2011 1 2 3 4 5 {diagram not necessary but students will find it helpful solving the question if they draw it} a) 2010 calendar year written exposure o Policies 3, 4 & 5 were written in 2010 total = 3 o Policies 2 & 4 cancelled in 2010 total cancellation = 5/12 for policy 2 & 8/12 for policy 4 = 1.083 o Total written = written cancelled = 3 1.083 = 1.917 b) 2010 calendar year earned exposure o Policy 1: 6/12 o Policy 2: 5/12 o Policy 3: 12/12 o Policy 4: 4/12 o Policy 5: 6/12 o Total = 2.75 c) 2009 policy year written exposure o Policy 1: 12/12 o Policy 2: 7/12 o Total = 1.583 d) In force exposure as at June 1, 2010 o Policies in force = 1, 3, 4 total = 3 (2) 3. Based on the following information, calculate the 2009 Earned Premium at prospective levels using 2 step trending. Calendar Year 2009 2010 Earned Exposures 500 550 Written Exposures 540 600 OnLevel Earned Premium 275,000 315,000 OnLevel Written Premium 295,000 345,000 All policies are annual Proposed effective date of new rates is January 1, 2012 Rates are expected to be in effect for 1 year Projected premium trend is 4% per annum Solution: 1 2 3 4 2009 Average EP @ CRL (275,000/500) Most recent average WP @ CRL (345,000/600) Current Trend Factor: [ (2) / (1) ] Future trend period: Midpoint of latest data point = July 1, 2010 Average written date in = July 1, 2012 Trend period (years): CY 2009 EP at prospective level: 275,000 x 1.0455 x 1.04^2.00 = 550.00 575.00 1.0455 2.00 5 310,960.00 (3) 4. Using the Loss Ratio Method, calculate the indicated class relativities. Credibility is determined by the formula Z = Premium at Current Rate Level 750,250 540,225 475,800 624,400 2,390,675 Reported Loss & ALAE 615,200 375,500 341,600 501,200 1,833,500 n , where n = # of claims. 445 Current Relativity 1.00 0.95 1.07 1.16 Class 1 2 3 4 Total Number of Claims 540 295 265 395 1,495 Class 1 is to remain the base class The complement of credibility is no change (i.e. the current relativity) Solution: (1) Premium at Current Rate Level 750,250 540,225 475,800 624,400 2,390,675 (2) Reported Loss & ALAE 615,200 375,500 341,600 501,200 1,833,500 (3) (4) (5) Number of Claims 540 295 265 395 1,495 (6) Class 1 2 3 4 Total Loss Ratio 82.0% 69.5% 71.8% 80.3% 76.7% Indicated Change 6.9% 9.4% 6.4% 4.7% Credibility 1.00 0.81 0.77 0.94 (7) Credibility Weighted Indicated Change 6.9% 7.6% 4.9% 4.4% (8) Current Relativity 1.00 0.95 1.07 1.16 (9) Credibility Weighted Indicated Relativity 1.0692 0.8775 1.0173 1.2109 (10) CWI Relativity @ Base Class 1.0000 0.8208 0.9514 1.1326 Calculations: (3) = (2) / (1) (4) = (3)class / (3)total (6) = squareroot[(5) / 445] (max= 1) (7) = (4) x (6) (9) = (8) x [1 + (7)] (10) = (9)class / (9) class1 (3) 5. Briefly explain the 3 statistical criteria that should be considered when selecting rating variables. Solution: Statistical significance: the expected cost estimates should vary for the different levels of the rating variable, the estimated differences should be within an acceptable level of statistical confidence, and the estimated differences should be relatively stable from one year to the Homogeneity: the groups should be defined such that the risk potential is homogeneous within groups and heterogeneous between groups Credibility: the number of risks in each group should either be large enough or stable enough or both for the actuary to be able to accurately estimate the costs (i.e. credibility) (1) 6. a) What assumption does the parallelogram method make for determining premium at current rate levels? b) What calculation could be done to make the parallelogram method more accurate when this assumption does not hold? Solution: a) Method assumes policies are written evenly throughout the year b) could calculate the actual distribution of writings and use these to determine more accurate weightings to calculate the historical average rate level ...
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This note was uploaded on 10/30/2011 for the course ACTSC 462 taught by Professor Wslennox during the Winter '11 term at Waterloo.

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