UNIVERSITY OF WATERLOO
ACTUARIAL SCIENCE 462/862
TERM TEST #1
TUESDAY JANUARY 31, 2012
(2) 1. Based on the following information, calculate the company’s expected profit
provision (i.e. as a percent of premium):
•
Expected loss ratio = 60%
•
Expected loss adjustment expenses = 15% of expected losses
•
Operating expense ratio (OER) = 25% of premium
Solution:
•
Expected loss and loss adjustment ratio = 60% x 1.15 = 69%
•
Combined Ratio = Loss Ratio + OER + Profit
•
For equation to be in balance, combined ratio = 1
•
Therefore, Profit = 1 – Loss Ratio – OER = 1 – .69 – .25 = 6%
Alternative solution:
•
Assume OER include LAE ratio
•
Therefore, Profit = 1 – Loss Ratio – OER = 1 – .6 – .25 = 15%
{See lecture #1, slide 14
Æ
went through example in class}
(5) 2. A company has the following rating structure:
•
Policy premium = Base Rate x Territory Factor + Policy Fee
•
Base Rate = $1,000
•
Policy Fee = $50
•
Territory Factors:
•
Policies written:
•
On April 1, the Base Rate is changed to $1,100
Territory
Factor
11
.
0
21
.
5
# of Policies Written
Date Written
Territory 1
Territory 2
Jan 1, 2012
10
15
Jul 1, 2012
12
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Calculate the 2012 Earned Premium for this company.
b)
Calculate the 2012 on
‐
level factor that can be used for rate making.
Solution:
Picture not necessary but will find it helpful to draw it.
2012
2013
Jan
1J
u
l
y
1O
n
l
y
50% of policies written on July 1 are EARNED by end of year
Base rate increased April 1, 2012 to $1,100
a)
2012 Earned Premium:
•
Policies written on Jan 1, 2012 (fully earned by end of year)
o
Terr 1: 10 x ($1,000 x 1.0 + $50) = 10,500
o
Terr 2: 15 x ($1,000 x 1.5 + $50) = 23,250
•
Policies written on July 1, 2012 (only half earned by end of year, also base rate
is now $1,100)
o
Terr 1: ½ x 12 x ($1,100 x 1.0 + $50) = 6,900
o
Terr 2: ½ x 12 x ($1,100 x 1.5 + $50) = 10,200
•
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 Spring '11
 WsLennox
 1932, 1920, 1922, 1916, 1913, base rate

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