Insurance is different from most products as it is a promise to do something in the future if certain events take place during a specified time period. Unlike a can of soup, a pair of shoes, or a car, the ultimate cost of an insurance policy is not known at the time of the sale

1. 1

2. 2

3. CHAPTER 1: INTRODUCTION
• In a free market society, an entity offering
a product for sale should try to set a price
at which the entity is willing to sell the
product and the consumer is willing to
purchase it.
Price = Cost + Profit
3

4. CHAPTER 1: INTRODUCTION
• Insurance is different from most products
as it is a promise to do something in the
future if certain events take place during a
specified time period.
• Unlike a can of soup, a pair of shoes, or a
car, the ultimate cost of an insurance
policy is not known at the time of the sale.
4

5. RATING MANUALS
• Premium= The price the insurance consumer
pays, is generally calculated based on a
given rate per unit of risk exposed.
• Insurance premium can vary significantly for
risks with different characteristics.
• RATING MANUALS the document that
contains the information necessary to
appropriately classify each risk and calculate
the premium associated with that risk.
5

6. RATING MANUALS
• The earliest rating manuals were very
basic.
• Over time, rating manuals have increased
in complexity.
• For some lines, the manuals are now
extremely complex and contain very
detailed information necessary to calculate
premium.
6

7. BASIC INSURANCE TERMS
• Exposure= basic unit of risk that underlies
the insurance premium.
• Homeowners insurance: one house
insured for one year (house-year)
• Workers compensation: Annual payroll.
• Automobile: vehicle-year or vehicle-
kilometer
7

8. BASIC INSURANCE TERMS
• Written exposures: the total exposures arising
from policies issued a calendar year or quarter.
• Earned exposures: the portion of the written
exposures for which coverage has already been
provided as of a certain point in time.
• Unearned exposures: the portion of the written
exposures for which coverage has not yet been
provided as of that point in time.
• In-force exposures: the number of insured units
that are exposed to loss at a given point in time.
8

9. BASIC INSURANCE TERMS
• Premium the amount the insured pays for insurance
coverage.
• Written premium: the total premium associated with
policies that were issued during a specified period.
• Earned premium: the portion of the written premium
for which coverage has already been provided as of a
certain point in time.
• Unearned premium: the portion of the written
premium for which coverage has yet to be provided as
of a certain point in time.
• In-force premium: is the full-term premium for policies
that are in effect at a given point in time.
9

10. BASIC INSURANCE TERMS
• Claim: demand to the insurer for
indemnification under the policy
• Claimant: individual making the demand
• date of loss=accident date=occurrence
date: The date of the event that caused
the loss.
• unreported claims=incurred but not
reported (IBNR) claims: Claims not
currently known by the insurer.
10

11. BASIC INSURANCE TERMS
• Loss: the amount of compensation paid or
payable to the claimant.
• Paid loss: amounts that have been paid to
claimants.
• case reserve: estimate of the amount of
money required to ultimately settle that
claim.
Reported Losses = Paid L + Case Reserve.
11

12. BASIC INSURANCE TERMS
• Ultimate loss: the amount of money required
to close and settle all claims for a defined
group of policies.
• incurred but not reported (IBNR) reserve:
The amount estimated to ultimately settle
these unreported claims
• incurred but not enough reported(IBNER)
reserve: development on known claims
Ultimate Losses = Reported Losses + IBNR
+ IBNER.
12

13. BASIC INSURANCE TERMS
• Loss Adjustment Expense (LAE):
expenses in the process of settling claims.
• Allocated loss adjustment expenses
(ALAE)
• Unallocated loss adjustment expenses
(ULAE)
LAE = ALAE + ULAE.
13

14. BASIC INSURANCE TERMS
• Underwriting Expenses:
1. Commissions and brokerage
2. Other acquisition
3. General
4. Taxes, licenses, and fees
14

15. Underwriting Profit
• By writing insurance policies, the company is
assuming the risk that premium may not be
sufficient to pay claims and expenses.
• The company must support this risk by
maintaining capital, and this entitles it to a
reasonable expected return (profit) on that
capital.
• main sources of profit for insurance:
1. underwriting profit
2. investment income.
15

16. FUNDAMENTAL INSURANCE
EQUATION
Price = Cost + Profit.
• “price” is Premium.
• “cost” is the sum of the losses, claim-
related expenses, and other expenses
Premium= Losses + LAE + UW Expenses
+ UW Profit.
16

17. Ratemaking
• The goal of ratemaking is to assure that
the fundamental insurance equation is
appropriately balanced.
• The rates should be set so that the
premium is expected to cover all costs and
achieve the target underwriting profit.
1. Ratemaking is prospective.
2. Balance should be attained at the aggregate
and individual levels.
17

18. BASIC INSURANCE RATIOS
• Frequency: a measure of the rate at
which claims occur
18

19. BASIC INSURANCE RATIOS
• Severity: measure of the average cost of
claims
19

20. BASIC INSURANCE RATIOS
• Pure Premium (or Loss Cost):
• a measure of the average loss per
exposure
20

21. BASIC INSURANCE RATIOS
• Average Premium:
21

22. BASIC INSURANCE RATIOS
• Loss Ratio: a measure of the portion of
each premium dollar used to pay losses
22

23. BASIC INSURANCE RATIOS
• Loss Adjustment Expense Ratio:
LAE ratio compares the amount of claim-
related expense to total losses
23

24. BASIC INSURANCE RATIOS
• Underwriting Expense Ratio: a measure
of the portion of each premium dollar used
to pay for underwriting expenses
24

25. BASIC INSURANCE RATIOS
• Operating Expense Ratio: a measure of
the portion of each premium dollar used to
pay for loss adjustment and underwriting
expenses
25

26. BASIC INSURANCE RATIOS
• Combined Ratio: the combination of the
loss and expense ratios
26

27. BASIC INSURANCE RATIOS
• Retention Ratio: a measure of the rate at
which existing insureds renew their
policies upon expiration
27

28. BASIC INSURANCE RATIOS
• Close Ratio: hit ratio, quote-to-close ratio,
or conversion rate
• a measure of the rate at which prospective
insureds accept a new business quote
28

29. CHAPTER 2: RATING MANUALS
• Rating manual is the insurer’s documentation of
how to appropriately classify each risk and
calculate the applicable premium associated with
that risk.
• For most lines of business, the following
information is necessary to calculate the premium
for a given risk:
1. Rules
2. Rate pages (i.e., base rates, rating tables, and fees)
3. Rating algorithm
4. Underwriting guidelines
29

30. RATING MANUALS: RULES
• qualitative information that is needed to
understand and apply the quantitative rating
algorithms contained later in the manual
• The rules often begin with definitions related
to the risk being insured
• how to properly classify a risk before the
rating algorithm can be applied
• information about optional insurance
coverage, often referred to as endorsements
or riders
30

31. RATING MANUALS: RATE
PAGES
• For most lines of insurance, the rate varies
significantly based on the characteristics
associated with the risk.
• The rate pages generally contain the
numerical inputs (e.g., base rates, rating
tables, and fees) needed to calculate the
premium.
31

32. RATING MANUALS: RATE
PAGES
• Base rate: A base risk is a specific risk
profile pre-defined by the insurer.
• The base risk often represents a set of risk
characteristics that are most common,
though it can also be chosen based on
reasons more related to marketing
objectives.
• The base rate is the rate that is applicable
to the base risk
32

33. RATING MANUALS: RATE
PAGES
33

34. RATING MANUALS: RATING
ALGORITHMS
• The rating algorithm describes in detail how
to combine the various components in the
rules and rate pages to calculate the overall
premium
• the order in which rating variables should be
considered
• how the effect of rating variables is applied
(+,*,-,/)
• the existence of maximum and minimum
premiums
• specifics associated with any rounding
34

35. RATING MANUALS:
UNDERWRITING GUIDELINES
• Underwriting guidelines are a set of
company-specific criteria that can affect
decisions made prior to calculating a rate
1. Decisions to accept, decline, or refer risks
2. Company placement
3. Tier placement
4. Schedule rating credits/debits
35

36. 36

37. HOMEOWNERS RATING
MANUAL EXAMPLE
• Base Rates
• The exposure base for homeowners
insurance is a home insured for one year.
37

38. HOMEOWNERS RATING
MANUAL EXAMPLE
Rating and Underwriting Characteristics
• Amount of Insurance
the amount of coverage purchased to
cover damage to the dwelling and is the
maximum amount the insurer expects to
pay to repair or replace the home.
38

39. HOMEOWNERS RATING
MANUAL EXAMPLE
39

40. HOMEOWNERS RATING
MANUAL EXAMPLE
• Territory
• The location of the home is another major
determinant of homeowners insurance risk
40

41. HOMEOWNERS RATING
MANUAL EXAMPLE
• Protection Class and Construction Type
41

42. HOMEOWNERS RATING
MANUAL EXAMPLE
• Underwriting Tier
numerous underwriting characteristics that
are not explicitly shown in the rating
manual
42

43. HOMEOWNERS RATING
MANUAL EXAMPLE
• Deductible: The policyholder can choose
the deductible, the amount of each
covered loss the insured must pay.
43

44. HOMEOWNERS RATING
MANUAL EXAMPLE
• Miscellaneous Credits: discounts for new
homes, insureds who are claims-free in
the previous five years, and insureds with
multiple policies
44

45. HOMEOWNERS RATING
MANUAL EXAMPLE
• Additional Optional Coverages
45

46. HOMEOWNERS RATING
MANUAL EXAMPLE
• Expense Fee: an explicit expense fee in
the rating manual that is intended to cover
fixed expenses incurred in the acquisition
and servicing of insurance policies.
46

47. Homeowners Rating Algorithm
47

48. HOMEOWNERS RATING
MANUAL EXAMPLE
• It is common for companies to designate a
rounding procedure after each step.
• WGIC rounds to the penny after each step
and to the whole dollar at the final step.
48

49. Homeowners Rate Calculation
Example
• Amount of insurance = $215,000
• The insured lives in Territory 4.
• The home is frame construction located in Fire Protection Class 7.
• Based on the insured’s credit score, tenure with the company, and
prior loss history, the policy has been placed in Underwriting Tier C.
• The insured opts for a $1,000 deductible.
• The home falls under the definition of a new home as defined in
Wicked Good’s rating rules.
• The insured is eligible for the five-year claims-free discount.
• There is no corresponding auto or excess liability policy written with
WGIC.
• The policyholder opts to increase coverage for jewelry to $5,000 and
to increase liability/medical coverage limits to $300,000/$1,000.
49

50. HOMEOWNERS RATING
MANUAL EXAMPLE
50

51. HOMEOWNERS RATING
MANUAL EXAMPLE
• Solution:
• $501 = $500 x 1.04 x 1.10 x 1.15 x 1.00 x
0.85 x [1.0 - 0.20 - 0.10] x [1.0 - 0] + $35 +
$25 + $50.
51

52. HOMEOWNERS RATING
MANUAL EXAMPLE
• MEDICAL MALPRACTICE RATING
MANUAL EXAMPLE
• U.S. WORKERS COMPENSATION
RATING MANUAL EXAMPLE
52

53. CHAPTER 3: RATEMAKING
DATA
• INTERNAL DATA
• Policy Database
• Claims Database
• Accounting Information
• DATA AGGREGATION
• EXTERNAL DATA
• Statistical Plans
• Competitor Rate Filings/Manuals
53

54. CHAPTER 3: RATEMAKING
DATA
• DATA AGGREGATION
• When aggregating data for ratemaking
purposes, three general objectives apply:
1. Accurately match losses and premium for
the policy
2. Use the most recent data available
3. Minimize the cost of data collection and
retrieval
54

55. CHAPTER 3: RATEMAKING
DATA
• Calendar year aggregation
all premium and loss transactions that occur
during the twelvemonth calendar year without
regard to the date of policy issuance, the
accident date, or the report date of the claim
• Accident year aggregation
considers losses for accidents that have
occurred during a twelve-month period,
regardless of when the policy was issued or
the claim was reported
55

56. CHAPTER 3: RATEMAKING
DATA
• Policy year aggregation
considers all premium and loss transactions
on policies that were written during a twelve-
month period, regardless of when the claim
occurred or when it was reported, reserved,
or paid
• Report year aggregation
losses are aggregated according to when the
claim was reported, as opposed to when the
claim occurred.
56

57. CHAPTER 9: TRADITIONAL
RISK CLASSIFICATION
• The preceding chapters focused on making
sure the fundamental insurance equation is in
balance in the aggregate (i.e., the total
premium should cover the total costs and
allow for the target underwriting profit).
• In addition to focusing on the aggregate, it is
important for the actuary to be able to
develop a balanced indication for individual
risks or risk segments, too
57

58. CHAPTER 9: TRADITIONAL
RISK CLASSIFICATION
• The first stage of classification ratemaking
involves determining which risk criteria
effectively segment risks into groups with
similar expected loss experience.
• Once the insured population is subdivided
into appropriate levels for each rating
variable, the actuary calculates the
indicated rate differential relative to the
base level for each level being priced.
58

59. Adverse Selection
• The goal of classification ratemaking is to
determine a rate that is commensurate with
the individual risk.
• Consider the situation in which a company
(e.g., Simple Company) charges an average
rate for all risks when other competing
companies have implemented a rating
variable that varies rates to recognize the
differences in expected costs.
59

60. Adverse Selection
• In this case, Simple Company will attract and
retain the higher-risk insureds and lose the
lower-risk insureds to other competing
companies where lower rates are available.
• This results in a distributional shift toward
higher-risk insureds that makes Simple
Company’s previously “average” rate
inadequate and causes the company to be
unprofitable.
60

61. 61

62. 62

63. Favorable Selection
• when a company identifies a characteristic
that differentiates risk that other companies
are not using, the company has two options
for making use of this information:
1. Implement a new rating variable.
2. Use the characteristic for purposes
outside of ratemaking (e.g., for risk
selection, marketing, agency
management).
63

64. CRITERIA FOR EVALUATING
RATING VARIABLES
• Statistical
• Operational
• Social
• Legal
64

65. Statistical Criteria
• Statistical significance
• Homogeneity
• Credibility
65

66. Operational Criteria
• Objective
• Inexpensive to administer
• Verifiable
66

67. Social Criteria
• Affordability
• Causality
• Controllability
• Privacy concerns
67

68. TYPICAL RATING (OR
UNDERWRITING) VARIABLES
68

69. DETERMINATION OF INDICATED
RATE DIFFERENTIALS
• Pure Premium
• Loss Ratio
• Adjusted Pure Premium
69

70. CHAPTER 4: EXPOSURES
An exposure is the basic unit that measures
a policy’s exposure to loss.
CRITERIA FOR EXPOSURE BASES
•Proportional to Expected Loss
•Practical
•Historical Precedence
Personal Automobile: Car Year
Homeowners Earned: House Year
70

71. AGGREGATION OF EXPOSURES
In regards to aggregating exposures, there
are only two methods applicable:
calendar year and policy year.
• Written exposures
• Earned exposures
• Unearned exposures
• In-force exposures
71
EXPOSURES

72. 72
EXPOSURES

73. 73
EXPOSURES

74. 74
EXPOSURES

75. CHAPTER 5: PREMIUM
The goal of ratemaking is to determine rates
that will produce premium for a future policy
period.
PREMIUM AGGREGATION
In regards to premium aggregation, there are
only two methods applicable:
calendar year and policy year.
• Written premium
• Earned premium
• Unearned premium
• In-force premium
75

76. 76
PREMIUM

77. 77
PREMIUM

78. ADJUSTMENTS TO PREMIUM
In order for historical premium to be useful
in projecting future premium, it must first be
brought to current rate level.
The policies underlying the experience
period may have been written using rates
that are no longer in effect.
Extension of exposures & The parallelogram
method
78
PREMIUM

79. Simple Example
We assume that all policies have annual
terms and premium is calculated according
to the following rating algorithm:
Premium = Exposure × Rate per Exposure ×
Class Factor + Policy Fee
79
PREMIUM

80. Extension of Exposures
The extension of exposures method involves
rerating every policy to restate the historical
premium to the amount that would be
charged under the current rates.
January 1, 2011:
$7,370 (= 10 x $1,045 x 0.60 + $1,100)
The current base rate: 2012
$8,405 (= 10 x $1,045 x 0.70 + $1,090)
80
PREMIUM

81. Premium Development
In some cases, the actuary may not know
the ultimate amount of premium for the
experience period at the time the analysis is
being performed.
When this occurs, the actuary must estimate
how the premium will develop to ultimate.
1- when an actuary is using an incomplete
year of data.
2- when the line of business uses premium
audits.
81
PREMIUM

82. Premium Trend
• Inflationary pressure
• Distributional changes:
1- A rating characteristic: The amount of
insurance purchased (Homeowners).
2- Raising the deductible.
3- purchasing the entire portfolio of another
company.
82
PREMIUM

83. The following table shows data typically
used to estimate premium trend due to
distributional changes:
83
PREMIUM

84. The annual changes in average written
premium are used to determine the amount
the historical premium needs to be adjusted
to account for premium trend.
There are two methods for adjusting
historical data for premium trend: one-step
and two-step trending.
84
PREMIUM

85. One-Step Trending
1- The selected trend factor.
The basic one-step trending approach
involves the selection of a premium trend
based on the historical changes in average
premium.
For example, based on the data in previous
table, the actuary may make a trend selection
of 2%.
85
PREMIUM

86. 2- The length of time the trend should be
applied.
The trend period is typically measured as
the length of time from the average written
date of policies with premium earned during
the historical period to the average written
date for policies that will be in effect during
the time the rates will be in effect.
86
PREMIUM

87. Consider the case that the actuary uses
Calendar Year 2011 earned premium for the
analysis to estimate the rate need for annual
policies that are to be written during the
period of January 1, 2013 through December
31, 2013.
87
PREMIUM

88. The adjustment to Calendar Year 2011 earned
premium to account for premium trend on
annual policies is:
1.0508 (= (1.0 + 0.02)2.5).
Two-Step Trending
When the company expects the premium trend
to change over time. For example, when
homeowners insurer observes significant
increases in amount of insurance during the
experience period that are not expected to
continue into the future.
88
PREMIUM

89. LOSS DATA AGGREGATION
Assume these are the only claims reported
for the company and reserve levels are $0
prior to Calendar Year 2009.
89
CHAPTER 6 :LOSSES AND LAE

90. •The Calendar Year 2009 reported losses
are $10,000. This is the Calendar Year 2009
paid losses (i.e., the sum of the losses paid
in 2009 ($0)) plus the ending reserve at
December 31, 2009 ($10,000), minus the
beginning reserve in 2009 ($0).
•The Policy Year 2010 reported losses as of
December 31, 2011, are $0 since neither of
these policies was issued in 2010.
90
LOSSES AND LAE

91. ADJUSTMENTS TO LOSSES
Losses need to be projected to the cost level
expected when the rates will be in effect.
This is typically done using historical losses
with a series of adjustments.
1- Removing extraordinary events (e.g.,
individual shock losses and catastrophe
losses).
91
LOSSES AND LAE

92. One approach is to exclude these losses in
their entirety or, more typically, may just
exclude the portion above some
predetermined threshold.
Another one is to examine the size of loss
distribution and set the threshold at a given
percentile, such as the 99th percentile
2- Developing immature losses to reflect
their ultimate settlement value.
92
LOSSES AND LAE

93. Loss Development
The process of adjusting immature losses to
an estimated ultimate value is known as loss
development.
The chain ladder method is based upon
the assumption that aggregate losses will
move from unpaid to paid in a pattern that is
generally consistent over time.
93
LOSSES AND LAE

94. The method can be performed separately on:
1- Claim counts
2- Losses
The analysis can be done on various
definitions of:
1- Claims: reported, open and closed.
2- Losses: paid and reported
Generally, the analysis should be undertaken
on a body of homogeneous claims.
94
LOSSES AND LAE

95. A-
The boxed value is the reported losses for
accidents occurring in 2004 at 27 months of
maturity (i.e., the losses paid and case
reserves held as of March 31, 2006 for
accidents occurring in 2004).
95
LOSSES AND LAE

96. B-
The boxed value shows that losses for
Accident Year 2004 increased (or
developed) 47% (= 1.47 – 1.0)
from age 15 months to age 27 months.
96
LOSSES AND LAE

97. C- The next step is to calculate age-to-
ultimate development factors for each
maturity.
For example:
The age to- ultimate development factor for
losses at age 51 months is the product of
the selected age-to-age development factors
for 51-63 months and 63-75 months (1.02 x
1.00).
97
LOSSES AND LAE

98. D- These age-to-ultimate development
factors are then applied to the reported
losses at the most recent period of
development.
98
LOSSES AND LAE

99. 3-Adjusting the losses for underlying trends
expected to occur between the historical
experience period and the period for which
the rates will be in effect.
•Inflation
•Increasing medical costs
•Advancements in safety technology
•Social influences
•Distributional changes
99
LOSSES AND LAE

100. Loss Trend
•Linear and exponential regression models are
the most common methods used to measure
the trend in the data.
•Similar to premium trends, the actuary must
calculate the applicable loss trend period.
•This is the period of time from the average loss
occurrence date of each experience period to
the average loss occurrence date for the period
in which the rates will be in effect.
100
LOSSES AND LAE

101. LOSS ADJUSTMENT EXPENSES
•Allocated loss adjustment expenses (ALAE)
•Unallocated loss adjustment expenses
(ULAE)
For ratemaking purposes, ALAE are often
included with losses, and ULAE are
considered as the factor that is applied to
reported loss plus ALAE to incorporate them.
101
LOSSES AND LAE

102. 102
LOSSES AND LAE

103. CHAPTER 7: OTHER EXPENSES
AND PROFIT
UNDERWRITING EXPENSE CATEGORIES
Underwriting expenses (or operational and
administrative expenses) are incurred in the
acquisition and servicing of policies. these expenses
are classified into the following four categories:
 Commissions and brokerage
 Other acquisition
 Taxes, licenses, and fees
 General
103

104. UNDERWRITING EXPENSE
CATEGORIES
• Commissions and brokerage are
percentage of written premium paid to
agents or brokers as compensation for
generating business.
• Commission rates may vary between new
and renewal business.
• Contingent commissions vary the
commission based on the quality or
amount of business written.
104

105. UNDERWRITING EXPENSE
CATEGORIES
• Other acquisition costs are expenses
paid to acquire business other than
commissions and brokerage expenses like
costs for media advertisements, mailings
to prospective insureds, and salaries of
sales employees
105

106. UNDERWRITING EXPENSE
CATEGORIES
• Taxes, licenses, and fees include all taxes
and miscellaneous fees due from the
insurer like premium taxes and licensing
fees.
106

107. UNDERWRITING EXPENSE
CATEGORIES
• General expenses include all remaining
expenses associated with insurance
operations and any other miscellaneous
costs, excluding investment income
expenses.
• general expense category includes
overhead associated with the insurer’s
home office and salaries of certain
employees.
107

108. UNDERWRITING EXPENSE
CATEGORIES
• Underwriting expense are further divided into
two groups: fixed expenses and variable
expenses.
Fixed expenses like overhead costs are
assumed to be the same for each risk,
regardless of the size of the premium.
Variable expenses vary directly with premium
and the expense is a constant percentage of
the premium. Premium taxes and
commissions are two examples of variable
expenses.
108

109. Methods for calculating expense
provision
• Three different procedures used to derive
expense provisions for ratemaking:
 All Variable Expense Method
 Premium-based Projection Method
 Exposure/Policy-based Projection Method
109

110. All Variable Expense Method
• This method treats all expenses as variable.
• It assumes that expense ratios during the projected period will be
consistent with the historical expense ratios.
• This approach used when pricing insurance products for which the total
underwriting expenses are dominated by variable expenses like many
commercial lines products.
110

111. Deriving Expense Ratio
111
 To derive the expense ratio, the historical calendar year expenses are divided
by either calendar year written or earned premium during that same historical
period.
 Written premium is used when expenses are incurred at the inception of the
policy.
 Earned premium is used when expenses are incurred throughout the policy.
 The choice to use countrywide or state data varies by type of expense.
 If the expenses are usually assumed to be uniform across all locations, the
countrywide figures will be used to calculate these ratios.
 when the expenses vary by state and sometimes by territory within a state, the
expense is typically based on state data.

112. Potential Distortions Using this
Approach
• The expense provision in the rates varies
directly with the size of the premium.
• This approach understates the premium need
for risks with a relatively small policy premium
and overstates the premium need for risks with
relatively large policy premium.
• This method undercharges the risks with
premium less than the average and overcharges
the risks with premium more than the average.
112

113. PREMIUM-BASED PROJECTION
METHOD
• The expense ratios are calculated for each year as well as
the arithmetic average of the three years.
• The selected expense ratio is then divided into fixed and
variable ratios.
• The fixed and variable expense ratios are summed across
the different expense categories to determine total fixed
and variable expense provisions.
113

114. Potential Distortions Using this Approach
114
• Fixed expense ratio will be distorted if the historical and
projected premium levels are materially different. There are a
few circumstances that can cause such a difference:
 Recent rate changes can impact the historical expense ratios
and lead to an excessive or inadequate overall rate indication.
 Significant differences in average premium between the
historical period and the projected period can lead to an
excessive or inadequate overall rate level indication.
 This method can create inequitable rates for regional or
nationwide carriers if countrywide expense ratios are applied
to state projected premium to determine the expected fixed
expenses.

115. EXPOSURE/POLICY-BASED PROJECTION
METHOD
115
• Variable expenses are treated the same way as the Premium-
based Projection Method,
• Historical fixed expenses are divided by historical exposures
or policy count rather than premium.
• When fixed expenses are constant for each exposure,
expenses are divided by exposures. if fixed expenses
constant for each policy, then historical expenses are divided
by the number of policies.

116. Data used for Exposure/Policy–Based
procedure for each expense category
116

117. TRENDING EXPENSES
• While there is an expectation that expenses change
over time due to inflationary pressures and other
factors, they should be trended.
• The variable expenses will automatically change as
the premium changes, so there is no need to trend
the variable expense ratio.
• Fixed expenses are assumed to be a constant dollar
amount. There is an expectation that the average
fixed expenses will increase over time due to
inflationary pressures.
117

118. TRENDING EXPENSES
• Some companies use internal expense data to
select an appropriate trend.
• Similar to the premium and loss trend the
historical change in average expenses are
examined to select an expense trend.
• Many companies use government indices
(e.g., Consumer Price Index, Employment
Cost Index, etc.) and knowledge of anticipated
changes in internal company practices to
estimate an appropriate trend.
118

119. TRENDING EXPENSES
• The selected fixed expense ratio will be
trended from the average date that expenses
were incurred in the historical expense period
to the average date that expenses will be
incurred in the period that the rates are
assumed to be in effect.
• After expenses are trended, the expense
ratio or average dollar amount of expense is
often called the projected (or trended) fixed
expense provision.
119

120. REINSURANCE COSTS
• In proportional reinsurance, reinsurance costs may not
need to be explicitly considered in ratemaking
• analysis.
• In non-proportional reinsurance, the projected losses
are reduced for any expected non-proportional
reinsurance recoveries.
• The cost of purchasing the reinsurance is typically
done by reducing the total premium by the amount
ceded to the reinsurer.
• Alternatively, the net cost of the non-proportional
reinsurance (i.e., the cost of the reinsurance minus the
expected recoveries) may be included as an expense
item in the overall rate level indication.
120

121. UNDERWRITING PROFIT PROVISION
Total Profit =
Investment Income + Underwriting Profit
121

122. Investment Income
• There are two major sources of investment income:
 investment income on capital
 investment income earned on policyholder-supplied
funds.
• Capital funds (equity on the balance sheet or
policyholder surplus) belong to the owners of the
insurance company.
• Insurers hold and invest money coming from two types
of policyholder-supplied funds:
 unearned premium reserves and
 loss reserves.
122

123. Underwriting Profit
• Underwriting profit is the sum of the profits
generated from the individual policies.
• the underwriting profit is defined as
follows:
UW Profit =
Premium - Losses - LAE – UW Expenses
123

124. PERMISSIBLE LOSS RATIOS
• There are two kinds of permissible loss ratio:
Variable Permissible Loss Ratio (VPLR)
Total Permissible Loss Ratio (PLR)
• VPLR = 1.0 - Variable Expense % - Target Profit % = 1.0 - V- QT
• PLR = 1.0 - Total Expense % - Target Profit % = 1.0 - F-V- QT
124

125. CHAPTER 8: OVERALL
INDICATION
• This chapter will demonstrate how to
combine the various estimated components
to ascertain whether the current rates are
appropriate.
• There are two basic approaches for
determining an overall rate level need:
1. Pure premium method
2. Loss ratio method
125

126. PURE PREMIUM METHOD
• The pure premium method is generally the simpler and
more direct of the two ratemaking formulae as it
determines an indicated average rate, not an indicated
change to the current average rate.
• The pure premium indication formula is:
126

127. LOSS RATIO METHOD
127
• The loss ratio method is the more widely used of
the two rate level indication approaches.

128. Equivalency of Methods
128
• Since both formulae can be derived from
the fundamental insurance equation, it
should be understood that the two
approaches are mathematically equivalent.

129. Comparison of Approaches
• There are two major differences between
the two approaches:
 difference in the underlying loss measure used.
 difference in the output of the two formulae.
129

130. Difference in the loss measure used
• The loss ratio indication formula relies on the loss
ratio and the pure premium indication formula relies
on the pure premium statistic.
• The loss ratio indication formula requires premium at
current rate level and the pure premium indication
formula requires clearly defined exposures.
• The pure premium approach is preferable if premium
is not available or if it is very difficult to accurately
calculate premium at current rate level. the loss ratio
method is preferable if exposure data is not available
or if the product being priced does not have clearly
defined exposures.
130

131. Difference in the output of the two formulae
• The result of the loss ratio indication formula is an
indicated change to the currently charged rates.
• The result of the pure premium formula is an
indicated rate. Because of this difference, the
pure premium method must be used with a new
line of business for which there are no current
rates to adjust.
131

132. BASIC INSURANCE RATIOS
132
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