Actuarial Notes

CAS Exam 5 Fall 2017, Question 15

Study guide: Exam 5

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

Accident Year Cumulative Reported Loss & ALAE ($000)
2014 5,615
2015 4,315
2016 2,745
Calendar Year Earned Premium ($000)
2014 10,800
2015 11,250
2016 12,375
Selected Reported Loss & ALAE Age to Age Factors 12-24 24-36 36-48
2.089 1.368 1.070
  • All policies are annual.
  • Exposures are written evenly throughout each calendar year.
  • Annual loss and ALAE trend = 5%.
  • Annual premium trend = 4%.
  • There has been one rate change in the past five years: +5%, effective July 1, 2015.
  • Fixed expense ratio = 15%.
  • Variable expense ratio = 25%.
  • Profit and contingencies provision = 5%.
  • ULAE provision = 6% of loss and ALAE.
  • Rates are to be in effect for one year.
  • There is no loss development beyond 48 months.

Part a (0.5 points)

Calculate the ultimate losses and ALAE for each accident year using the loss development technique.

Part b (0.75 points)

Calculate the ultimate losses and ALAE for each accident year using the Bornhuetter-Ferguson technique using an expected loss and ALAE ratio of 56%.

Part c (0.5 points)

Briefly justify an appropriate ultimate loss and ALAE selection from parts a. and b. above for accident years 2014 through 2016.

Part d (3 points)

Calculate the indicated rate change for policies effective July 1, 2017 using the ultimate loss and ALAE selections from part c. above, assuming full credibility.

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