UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGNCollege of Business D E P A R T M E N T O F F I N A N C EFinance 431 Assignment 2Spring, 2008 Due: February 14, 2008The first four questions are based on the following cumulative loss payment information for an automobile insurer. Assume that no further development occurs after 96 months. The auto liability earned premiums for 2007 are $68,950,731. The expected loss ratio for 2007 is 78.0%. Use the average link factors to determine the age-to-ultimate factors. (If you are not using a spreadsheet program to do these calculations, round the link factors to three decimal places.) Cumulative Loss Payments for Auto Liability(000 omitted)Development Age (Months)Accident Year12 24 36 48 60 72 84 962000 13,25525,70631,66634,66336,13536,82737,18337,2172001 14,32127,55333,49636,52438,04138,82439,751 2002 15,63429,65535,85039,00340,72042,258 2003 17,21331,80338,13841,60744,304 2004 17,86232,40238,98642,643 2005 18,48533,12840,725 2006 18,71833,495 2007 21,753 1. Calculate the loss reserve for accident year 2007 using the expected loss ratio method.2. Calculate the loss reserve for accident year 2007 using the Bornhuetter-Ferguson method.3. Calculate the loss reserve for accident year 2007 using the Paid Loss Development method.4. Which of the values calculated above do you feel is the best estimate of theneeded loss reserves for accident year 2007? Why?5. Calculate the percent rate change that is indicated using the loss ratio method based on the following experience:Actual loss ratio 72.5%Expected loss ratio 78.0%6. Calculate the indicated gross premium using the pure premium method based on the following information:Loss frequency 4.5%Loss severity 7,680Fixed expenses 75Variable expenses (including profit) 16%7. The incurred losses for a given line of business were $68,950,000 in 2006 and the earned exposures were 59,000. The actuary is trending these losses for 3 years to use in a rate filing. If loss frequency is declining at a rate of 1.1% per year and loss severity is increasing at a rate of 3.8% per year, what is the trended pure premium?8. What is the primary risk to a personal lines insurer adopting multi-distribution channels for its products? Assume that the insurer is currently an independent agency insurer. Explain your choice.9. CNA writes a $100 million property insurance policy on a store. CNA purchases two reinsurance policies. One is a quota share policy that cedes 80% of each loss. The other is a per-risk excess reinsurance policy of $18 million excess of $2 million. (The quota share policy "inures to the benefit of" the per-risk excess policy.) A $32 million covered loss occurs. Indicate how much each of the insurers will pay:For the last question, you may use either the State Farm Car Policy we used in Finance 230 or the Personal Auto Policy included as Appendix B in the text. (Indicate which one you used in your answer.) Also, use the Homeowners 3 Special Form Policy in Appendix A of the text. You are the claims representative for an insurance company that has written both homeowners insurance and auto insurance for Bruce Handyman. Bruce is standing on a ladder in his driveway cleaning leaves out of the gutter. His wife, not realizing what Bruce is up to, backs the family car out of the garage and hits the ladder. Bruce tumbles to the ground, breaking his foot. He has to go to the hospital emergency room for this injury. Indicate whether the situation is a first or third party claim and whether or not it would be covered. If the claim would be covered, indicate whether the autopolicy or the homeowners policy would pay the claim.10. The medical bills for Bruce’s broken foot are $10,000. Bruce files a claim for his medical bills, but decides not to sue his wife, who already feels very badly about this accident.Fin 431 - Assignment 2 Answer Sheet Name_________________________(This sheet is for your answers only. Attach it to the front of your worksheets.)1.2.3.4.5.6.7.8.9. CNA __________________ Quota Share Reinsurer ________________Per-risk Excess Reinsurer