Actuarial Notes

CAS Exam 6C Fall 2019, Question 14

Study guide: Exam 6C

The following information is available for a federally regulated property and casualty insurance company as at December 31, 2018. The company writes only personal property insurance. All amounts are in thousands of dollars ($000s).

From Annual Return page 80.10 – Commissions:

A. Deferred Commissions at Beginning of Year B. Unearned Commissions at Beginning of Year C. Direct (commissions in respect of premiums written) D. Reinsurance assumed E. Reinsurance Ceded F. Net G. Deferred Commissions end of year H. Unearned Commissions end of year I. Net Commissions attributable to the period
? 2,200 18,000 0 ? ? ? 2,500 17,100

Other financial information from page 80.10:

Item Amount
J. Gross contingent commissions 500
K. Ceded contingent commissions 250
L. Gross other non-deferrable commissions 300
M. Ceded other non-deferrable commissions 100
N. Ceded commission income 600

Other information:

Item Value
O. Direct unearned premium 120,000
P. Assumed unearned premium 0
Q. Ceded unearned premium 6,000
R. Expected reinsurance premium 5,000
S. Selected undiscounted loss ratio (excl. ULAE) 88.00%
T. Selected ULAE ratio 5.00%
U. Discount rate 3.50%
V. Margin for adverse deviations (MfAD) for claims development 7.00%
W. MfAD for recovery from reinsurance ceded 2.00%
X. MfAD for investment return rates 0.75%
Y. Maintenance expense ratio (% gross premium) 3.50%
Z. Contingent commission rate (% gross premium) 0.00%

Note: Candidates may use the letters A to Z in the formulas in their solutions.

The cumulative accident year payment pattern is as follows:

Age (Months) % Cumulative Paid
12 60%
24 90%
36 100%

Part a (1.25 points)

Calculate the total net commissions as they appear on the Annual Return page 80.10.

Part b (3.5 points)

Calculate the premium deficiency, if any.

No current syllabus covers this question; it is kept for the record.

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