Actuarial Notes

CAS Exam 5 Fall 2014, Question 8

Study guide: Exam 5

A company is reviewing the rate level adequacy in State X. Given the following information for a book of business:

  • All policies are annual.
  • Rate change history:
    • -5% effective April 1, 2012, mandated by law to apply to all policies in force with no impact on losses.
    • 10% effective January 1, 2013.
  • New rates will be in effect for 12 months beginning on April 1, 2015.
  • Selected annual underlying loss trend = 2%.
  • Selected annual premium trend = 0%.
  • Loss adjustment expense provision = 4% of loss.
  • Projected expense ratios:
    • Fixed = 5%.
    • Variable = 27%.
  • Underwriting profit and contingencies provision = 8%.
  • Ultimate losses are estimated using the reported development technique.
  • Credibility of the indicated rate change = 0.6.
  • State X's earned premium is 5% of the total earned premium countrywide.
  • State X is part of Region A, and accounts for 50% of the total earned premium for that region.
  • Potential complements of credibility include:
    • Countrywide rate indication = 10%.
    • Total Region A rate indication = 8%.
    • Major competitor rate indication for State X = 4%.
    • Annual inflation trend for State X = 3%.
Calendar Year Ending Earned Premium ($000)
December 31, 2012 9,500
December 31, 2013 9,800
Accident Year as of December 31, 2013 Reported Losses ($000)
2012 4,800
2013 4,100

Age-to-Age Reported Loss Development Factors

Accident Year 12-24 months 24-36 months 36-48 months 48-60 months 60-72 months
2008 1.37 1.15 1.06 1.02 1.00
2009 1.35 1.15 1.05 1.02
2010 1.32 1.12 1.07
2011 1.28 1.09
2012 1.25

Part a (1 point)

Recommend a complement of credibility from the list above. Briefly explain the recommendation, including a brief discussion of each potential complement not selected.

Part b (3.25 points)

Calculate the indicated rate change using the complement of credibility recommended in part a. above. Briefly justify selection of age-to-age reported loss development factors.

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Concepts tested

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