Actuarial Notes

CAS Exam 5 Spring 2019, Question 7

Study guide: Exam 5

Given the following data as of December 31, 2018:

Accident Year Reported Loss and ALAE ($000s) Calendar Year Earned Premium ($000s)
2016 2,000 2016 4,600
2017 1,750 2017 5,100
2018 800 2018 5,800
Development Age to Ultimate Selected Cumulative Development Factors
36 1.46
24 2.08
12 4.90
65% Expected loss and ALAE ratio
4% Annual loss and ALAE trend
3% Annual premium trend
6% Fixed expense ratio
26% Variable expense ratio
5% Profit and contingencies provision
8% ULAE provision as a % of loss and ALAE
0.7 Credibility of historical experience
+8% Complement of credibility taken from a competitor rate change filing

Rate change history:

  • -2% Rate change effective January 1, 2016

  • +3% Rate change effective July 1, 2018

  • All policies are annual.

  • Exposures are written evenly throughout each calendar year.

  • New rates will be in effect for one year starting January 1, 2020.

Part a (0.5 points)

Calculate the ultimate loss and ALAE for each accident year using the reported Bornhuetter-Ferguson technique.

Part b (3.5 points)

Calculate the credibility-weighted indicated rate change using the latest three accident years.

Part c (0.75 points)

Briefly describe a disadvantage of using a competitor rate change filing as the complement of credibility and justify a more suitable alternative.

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Concepts tested

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