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(a) (1 point) State the two basic principles on which prospective experience rating plans are based. (b) (2 points) Propose an experience rating formula and explain how it takes into account these two basic principles. An insured company, WC Plumbing, reported a substantial operating loss in the latest year. Given that it experienced only three claims during the year, it is considering enrollment in a retrospective rating plan in an attempt to save on insurance costs. (c) (1 point) Recommend whether, from WC Plumbing's perspective, it would be a good candidate for retrospective rating and justify your recommendation.

You are conducting a ratemaking analysis for a portfolio of automobile insurance policies and are given the information in the following two tables: Calendar Year General and Other Acquisition Expenses Direct Earned Premiums 2008 108,000 691,000 2009 138,000 725,000 2010 115,000 770,000 2011 126,000 834,000 2012 130,000 866,000 Budgeted Direct Earned Premium at Current Rate Level 895,000 Budgeted Exposure Counts (vehicles) 1,150 Weighted Average Trended Pure Premium 476.00 ULAE as a Ratio to Claims 8.0% Commissions as a Percentage of Premium 12.0% Premium Taxes as a Percentage of Premium 2.0% Licenses as a Percentage of Premium 1.0% Profit and Contingencies Factor 3.0% (a) (2 points) Select a fixed and variable expense ratio as a percentage of direct earned premiums to be used for ratemaking purposes assuming that historically 30% of general and other acquisition expenses are considered to be fixed expenses. Justify your selection. (b) (2 points) Calculate the indicated rate and indicated rate change given the selected fixed expense ratio from (a). Recent rate changes and shifts in the mix of business can lead to distortions when using an approach based on a selected fixed expense percentage applied to a projected average premium for ratemaking. (c) (2 points) Explain how each of these situations can affect the level of fixed expenses in a ratemaking analysis and recommend a solution for each to avoid potential distortion

) Student Insurance Company writes four-month property policies for university students living in apartments. Policies are issued according to the university terms, which are Fall (September 1 to December 31), Spring (January 1 to April 30), and Summer (May 1 to August 31). Assume an annual frequency trend of 0% and an annual severity trend of 2.5%. Accident Period Reported Counts at Maturity Age in Months Exposures Ultimate 4 8 12 16 20 24 Severity Summer 2010 2,510 5,010 7,079 7,079 7,079 7,079 250,000 2,300 Fall 2010 1,401 4,221 10,287 10,287 10,287 10,287 350,000 2,320 Spring 2011 3,009 4,805 8,672 8,672 8,672 8,672 300,000 2,340 Summer 2011 2,622 5,240 7,614 7,614 7,614 7,614 262,500 2,360 Fall 2011 1,466 4,406 10,696 10,696 10,696 10,696 367,500 2,380 Spring 2012 3,137 5,030 9,293 9,293 9,293 315,000 2,400 Summer 2012 2,687 5,422 7,912 7,912 270,000 2,420 Fall 2012 1,504 4,527 11,339 378,000 2,440 Spring 2013 3,246 5,163 324,000 2,460 Summer 2013 2,761 277,500 2,480 Accident Period Age-to-Age Factors Maturity Age Interval in Months 4-8 8-12 12-16 16-20 20-24 Summer 2010 2.00 1.41 1.00 1.00 1.00 Fall 2010 3.01 2.44 1.00 1.00 1.00 Spring 2011 1.60 1.80 1.00 1.00 1.00 Summer 2011 2.00 1.45 1.00 1.00 1.00 Fall 2011 3.01 2.43 1.00 1.00 1.00 Spring 2012 1.60 1.85 1.00 1.00 Summer 2012 2.02 1.46 1.00 Fall 2012 3.01 2.50 Spring 2013 1.59 Project ultimate claims for Spring 2013 and Summer 2013 using a frequency-severity method given the information above, and justify all selections.

) Big Cat Insurance Company (BCI) is considering entering into a securitization agreement with respect to hurricane losses in a well-defined geographic region. One of its concerns with regard to such agreements is basis risk. (a) (1 point) Define basis risk and describe how it can occur in this context. BCI is considering four types of securitization: I. Indemnity-based securitization II. Index-based transaction III. Parametric indices IV. Notional portfolio (b) (2 points) State if there is basis risk for BCI with each of these securitization types. If there is no basis risk, explain why not, and if there is basis risk, explain how that securitization type creates basis risk. (c) (1 point) Indicate an action BCI can take to reduce basis risk for two of the securitization types that you identified as having basis risk.

Describe two situations for which the expected method would be a preferred approach for projecting ultimate claims. (b) (1 point) Define exposure base and leading indicator. (c) (1 point) Describe two desirable characteristics of exposures for actuarial work. You are given the following information about Motor Insurance Company (MI), which has been selling automobile insurance for five years: All policies are annual policies and are issued on January 1 of each year. At the 2012 cost level, the expected claim ratio is 75%. At the 2012 cost level, the pure premium is 220. The annual pure premium trend is 2.4%. MI has had no rate changes in the past five years. For 2008, the earned premium is 24,540,000 and earned vehicles are 87,600. Tort reform was instituted on January 1, 2009, resulting in a reduction in severity of 30%. MI introduced a 10% discount on January 1, 2010 that is applicable to 40% of its customers. (d) (3 points) Calculate the expected claims for 2008 using the expected method with the following approaches: (i) Expected claim ratio (ii) Pure premium

You are given the following information to calculate deductible factors: Claim Range Counts in Interval Claims 0-250 200 30,000 250-750 300 150,000 >750 100 150,000 Total 600 330,000 (a) (2 points) Calculate the indicated deductible factors for deductibles of 250 and 750 relative to a base of zero deductible. (b) (0.5 points) State two assumptions that you needed to make in using the information above to perform the calculation in part (a). (c) (1.5 points) Determine the range into which the deductible factor for a 500 deductible must fall in order to be consistent with the deductible factors calculated in part (a) and explain your reasoning