7. (10 points) Given the following information, calculate the 2010 accident year trended ultimate loss & ALAE to be used in a rate change analysis. - All policies are annual and written on January 1. - The rate change effective date is January 1, 2013 - The rate level is reviewed annually - Underwriting guidelines were revised on January 1, 2011, substantially changing the composition of the book of business - We have the following information: Accident Year Reported Loss & ALAE as of June 30, 2012 ($) 2010 9,000,000 2011 5,000,000 2012 500,000 - Use two-step trending with the following information: Calendar Year ending Sep 2009 Dec 2009 Mar 2010 Jun 2010 Sep 2010 Dec 2010 Mar 2011 Jun 2011 Sep 2011 Dec 2011 Mar 2012 Jun 2012 Reported Loss & ALAE Frequency Severity ($) Pure Premium ($) 0.058 20,355 1,181 0.059 20,125 1,187 0.062 20,500 1,271 0.063 21,575 1,359 0.063 21,388 1,347 0.065 19,903 1,294 0.078 19,567 1,526 0.078 19,238 1,501 0.079 19,538 1,543 0.082 20,063 1,645 0.081 20,050 1,624 0.082 19,950 1,636 1-step 2-step Frequency 16.0% 4.1% Severity -1.7% 2.5% - Use the following information to develop the trended losses to ultimate (note that the AY 2012 losses are given as of June 30, 2012): Selected Reported Loss & ALAE Age-to-Ultimate Factors Month 6 12 18 24 30 36 42 48 54 Factor 6.50 2.00 1.55 1.20 1.12 1.08 1.05 1.02 1.01 60 1.00 7. (10 points) Given the following information, calculate the 2010 accident year trended ultimate loss & ALAE to be used in a rate change analysis. - All policies are annual and written on January 1. - The rate change effective date is January 1, 2013 - The rate level is reviewed annually - Underwriting guidelines were revised on January 1, 2011, substantially changing the composition of the book of business - We have the following information: Accident Year Reported Loss & ALAE as of June 30, 2012 ($) 2010 9,000,000 2011 5,000,000 2012 500,000 - Use two-step trending with the following information: Calendar Year ending Sep 2009 Dec 2009 Mar 2010 Jun 2010 Sep 2010 Dec 2010 Mar 2011 Jun 2011 Sep 2011 Dec 2011 Mar 2012 Jun 2012 Reported Loss & ALAE Frequency Severity ($) Pure Premium ($) 0.058 20,355 1,181 0.059 20,125 1,187 0.062 20,500 1,271 0.063 21,575 1,359 0.063 21,388 1,347 0.065 19,903 1,294 0.078 19,567 1,526 0.078 19,238 1,501 0.079 19,538 1,543 0.082 20,063 1,645 0.081 20,050 1,624 0.082 19,950 1,636 1-step 2-step Frequency 16.0% 4.1% Severity -1.7% 2.5% - Use the following information to develop the trended losses to ultimate (note that the AY 2012 losses are given as of June 30, 2012): Selected Reported Loss & ALAE Age-to-Ultimate Factors Month 6 12 18 24 30 36 42 48 54 Factor 6.50 2.00 1.55 1.20 1.12 1.08 1.05 1.02 1.01 60 1.00
