Actuarial Notes

CAS Exam 5 Spring 2017, Question 13

Study guide: Exam 5

Given the following information for a book of business as of December 31, 2016:

Calendar Year Earned Premium ($000)
2015 3,910
2016 4,410

Rate Change History

Effective Date Average Rate Change
July 1, 2014 -2.0%
July 1, 2015 4.2%
July 1, 2016 3.6%

Reported Loss and ALAE ($000) Capped at $100,000 as of (months)

Accident Year 12 24 36
2014 1,116 1,448 1,610
2015 1,975 2,572
2016 2,145

Excess Loss and ALAE ($000) History — Trended Reported Loss and ALAE

Accident Year Unlimited Excess of $100,000
2009 3,538 718
2010 3,193 130
2011 1,990 234
2012 4,580 1,949
2013 2,369 120
  • All policies are annual.
  • Exposures are written evenly throughout each calendar year.
  • Annual premium trend = 2.8%.
  • Annual frequency trend = -2%.
  • Annual severity trend capped at $100,000 = 4%.
  • Fixed expense ratio = 4%.
  • Variable expense ratio = 22%.
  • Profit and contingencies provision = 6%.
  • ULAE provision = 6% of loss and ALAE.
  • Rates are to be in effect for one year.
  • There is no loss development beyond 36 months.
  • Assume full credibility.

Part a (0.75 points)

Calculate the ultimate loss and ALAE capped at $100,000 for accident years 2015 and 2016.

Part b (4.5 points)

Determine the indicated rate change effective July 1, 2017 using the results from part a. above.

Part c (0.25 points)

Briefly describe one reason the insurer might not take the full rate change determined in part b. above.

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Concepts tested

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