3/7/2011
1
RPM Workshop 1:
BASIC RATEMAKING
Development of an Overall Indication
1
Development
of
an
Overall
Indication
Jennifer Jabben, FCAS, MAAA
Assistant Actuary
Allstate Insurance Company
Jennifer.Jabben@Allstate.com
March 20, 2011
New Orleans, LA
ANTITRUST NOTICE
• The Casualty Actuarial Society is committed to adhering strictly to the
letter and spirit of the antitrust laws. Seminars conducted under the
auspices of the CAS are designed solely to provide a forum for the
expression of various points of view on topics described in the programs or
agendas for such meetings.
• Under no circumstances shall CAS seminars be used as a means for
competing companies or firms to reach any understanding
–
expressed or
2
competing
companies
or
firms
to
reach
any
understanding
–
expressed
or
implied – that restricts competition or in any way impairs the ability of
members to exercise independent business judgment regarding matters
affecting competition.
• It is the responsibility of all seminar participants to be aware of antitrust
regulations, to prevent any written or verbal discussions that appear to
violate these laws, and to adhere in every respect to the CAS antitrust
compliance policy.
AGENDA
• BASIC RATEMAKING EQUATION
• UNDERLYING DATA MANIPULATION
• PROFIT AND CONTINGENCY PROVISIONS
•
EXAMPLE
3
•
EXAMPLE
3/7/2011
2
BASIC EQUATION
REQUIRED
PREMIUM
4
FUTURE LOSSES FUTURE EXPENSES
UW PROFIT &
CONTINGECNY
PROVISION
BASIC METHODS
LOSS RATIO
• Produces Indicated Rate Change
• Based on Premium
• Requires Existing Rates
PURE PREMIUM
• Produces Indicated Rates
• Based on Exposures
• Does Not Require Existing Rates
5
Note: The two methods produce identical results when identical data
and assumptions are used.
BASIC FORMULA:
REQUIRED
PREMIUM
(R)
UW PROFIT &
6
FUTURE LOSSES
(Includes Loss Adjustment Expense)
(L)
FUTURE EXPENSES
UW
PROFIT
&
CONTINGECNY
PROVISION
(Q)
VARIABLE
EXPENSES
(V)
FIXED
EXPENSES
(E
f
)
3/7/2011
3
BASIC FORMULA
R = L + V*R + E
F
+ Q*R
Solve for R:
R – V*R – Q*R = L + E
F
R*(1 – V – Q) = L + E
F
7
R = L + E
F
(1-V-Q)
Variable Permissible Loss Ratio = 1 – V – Q
– The percentage of each premium dollar that is intended to pay for the
projected loss and fixed expense components.
BASIC FORMULA:
Loss Ratio
Indicated Change = Loss Ratio + Fixed Expense Ratio
Variable Permissible Loss Ratio
8
(R
1
-R
0
) /R
0
= (L/R
0
+ E
F
/R
0
)
(1 –V –Q)
BASIC FORMULA:
Pure Premium
Indicated Rate = Pure Premium + Fixed Expense
Variable Permissible Loss Ratio
9
R
1
/X= (L/X + E
F
/X)
(1 –V –Q)
3/7/2011
4
DATA CATEGORIZATION
• CALENDAR YEAR
• POLICY YEAR
• ACCIDENT YEAR
10
CALENDAR YEAR
Premium and Loss transactions that occur during the
year.
– Advantages:
Dt i ilbl ikl
11
•
D
a
t
a
i
s ava
il
a
bl
e qu
i
c
kl
y
• FIXED AT YEAR END
– Consistent with Financial Statements
– Disadvantage:
• Premium and Loss Transactions DO NOT match.
– Loss data includes payments and changes to reserves for policies
whose premiums were earned in prior periods.
POLICY YEAR
Premium and Loss transactions on policies with effective dates
(new or renewal) during the year.
– Advantages
:
• Premium and Loss transactions DO
match.
12
–
data for ratemaking.
– Disadvantage:
• Data is not available until one term after the end of the policy year.
• Losses are NOT fixed at year end.
3/7/2011
5
ACCIDENT YEAR
Loss transactions for accidents occurring during the year, and
Premium transactions during the same 12 months.
– Advantages
:
• Represents a better match of premium and losses than Calendar
Year aggregation
13
Year
aggregation
.
– Transactions from accidents occurring in prior years do not distort the
data for ratemaking.
– Disadvantage:
• Data with slight time lag.
• Losses are NOT fixed at year end.
UNDERLYING
DATA MANIPULATION
HISTORICAL
DATA
LOSS EXPENSE PREMIUM
14
CAT/Large Loss
ADJUSTMENTS
LOSS
DEVELOPMENT
TREND
FIXED
VARIABLE
TREND
CURRENT
RATE LEVEL
TREND
TREND
Historical loss, premium and exposure data is
trended to reflect the level predicted to exist
during the pricing period.
to account for expected difference between the
15
–
to
account
for
expected
difference
between
the
historical period and the future period.
3/7/2011
6
TREND PERIOD
Experience Period
Exposure Period
16
Eff. Date
Eff. Date + 1 +
Policy term
Latest Year
of Data
Latest Year
-1
Latest Year
-2
Trend to Date =
Eff. Date + ½ +
½ Policy Term
CATASTROPHE/Large Loss
• Catastrophe losses are very volatile from year to year,
and should be removed from the underlying data
because of their large size and infrequency of
occurrence.
Recognition of exposure is appropriate and can be
17
–
Recognition
of
exposure
is
appropriate
and
can
be
incorporated using various methods.
• Long-Term Average, Catastrophe Simulation Modeling.
• Appropriate to give consideration to the impact of
other non-catastrophe large losses on underlying data
and analysis.
LOSS DEVELOPMENT
Adjustment made to underlying accident year
loss data to reflect an expected ultimate value.
– 2 reasons for Accident Year losses to develop
•
New Losses emerge after year
-
end (IBNR)
18
•
New
Losses
emerge
after
year
-
end
(IBNR)
• Development on known claims
3/7/2011
7
LOSS DEVELOPMENT FACTOR
(LDF) METHOD
ACCIDENT
YEAR
@ 12mo @ 24mo @ 36mo
2008 $1,000 $2,000 $2,500
ACCIDENT
YEAR
12-24 24-36
2008
200
125
Incurred Losses
Loss Development Factors
19
2009 $2,000 $3,000
2010 $2,500 X?
2008
2
.
00
1
.
25
2009 1.50
LDF 1.75 1.25
Estimated Ultimate 2010 AY Loss = $2,500 x 1.75 x 1.25 = $5,469
CURRENT RATE LEVEL
• Adjustment to reflect rate changes that are not
already included in the historical recorded
premium.
Common Techniques:
20
–
Common
Techniques:
• Extension of Exposures
• Parallelogram Method
PARALLELOGRAM METHOD
2009
2010 2011 2012
A
B
0%
Earned
100%
Earned
Rate Change = 10% on 1/1/2010
1.00 1.10
21
Area Percent of 2010 Rate Index
A .50 1.00
B .50 1.10
2010 1.00 1.05
2010 FCRL = (1.10/1.05) = 1.048
3/7/2011
8
PROFIT & CONTINGENCY
• UNDERWRITING PROFIT PROVISION
– Basic Selection = 5%
– More Complex Calculation
• Consideration of Investment Income
22
• CONTINGENCY
– Provision for expected differences, if any, between the
estimated costs and the average actual costs, that cannot be
eliminated by changes in the other components of the
ratemaking process.
? QUESTIONS ?
23