1Premium
MATH 3640
2Exposure Trend
• Rate changes are not the only thing that can change the average premium level
• Average premium level can change over time due to inflation in lines of
business with exposure bases that are inflation-sensitive.
– Example: WC (payroll), GL (receipts)
• For lines of business with inflation-sensitive exposure bases, it is typical to
project exposures (and thus premium) to future inflationary levels
• These trends are calculated using either internal company data (e.g. WC payroll
data) or an industry/government indices (e.g. average wage index)
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3Premium Trend
• Average premium level can change over time due to changes in the
characteristics of the policies written.
• Referred to as distributional changes and the resulting change in the average
premium level is referred to as premium trend
• Examples of premium trend
– Rating characteristic can cause the average premium to change
– Moving all existing insureds to a higher deductible
– Company may purchase the entire portfolio of another company
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4• How to measure premium trend?
– Do not use changes in total premium because a company that is growing
(or shrinking) will have increasing (or decreasing) total premium even if
the distribution of types of policies remains constant.
– Determine whether to use EP or WP for premium trend
• WP reflects shifts in the distribution more quickly than earned premium
• WP is a leading indicator of trends that will eventually emerge in EP, so
trends observed in WP are appropriate to apply to historical EP
• Quarterly average WP (as opposed to annual average WP) to make the
statistic as responsive as possible
– Average WP must be adjusted for the current rate level. Otherwise you
will see an abrupt change in the average WP on the effective date of the
rate change.
• Two methods for adjusting historical data for premium trend
– One-step trending
– Two-step trending
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5One-Step Trending
• Two ways to determine the trend period
– Length of time from the average written date in the experience period to
the average written date in the projected period (typically used)
– Length of time from the average date of the premium earned in the
experience period to the average date of premium earned in the
projected period
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6One-Step Trending
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• Example 1: Annual Policies, Adjusting CY2023 EP for premium trend
– Average written date for CY 2023 = 1/1/2023
• Underlying data includes policies written from 1/1/2022 to 12/31/2023
– Average written date for PY 2025 = 6/30/2025
• Policies written from 1/1/2025 to 12/31/2025
– Trend length is from 1/1/2023 to 6/30/2025 (2.5 years)
– Apply the following trend to CY 2023 EP: (1 + premium trend)^2.5
CY 2023 PY 2025
1/1/2022 1/1/2023 1/1/2024 1/1/2025 1/1/2026
7One-Step Trending
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• Example 1: Annual Policies, Adjusting CY2023 EP for premium trend
• Also can be determined based on the average date of premium earned in the
experience period to the average date of premium earned in the projected
period
– Average earned date for CY 2023 = 6/30/2023
– Average earned date for PY 2025 = 12/31/2025
– Trend length is from 6/30/2023 to 12/31/2025 (2.5 years)
– Apply the following trend to CY 2023 EP: (1 + premium trend)^2.5
CY 2023 PY 2025
1/1/2022 1/1/2023 1/1/2024 1/1/2025 1/1/2026
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• Example 2: Semi-annual Policies, Adjusting CY2023 EP for premium trend
CY 2023 PY 2025
• Average written date for CY 2023 = 4/1/2023
• Underlying data includes policies written from 6/30/2022 to 12/31/2023
• Average written date for PY 2025 = 6/30/2025
• Trend length is from 4/1/2023 to 6/30/2025 (2.25 years)
1/1/2022 1/1/2023 1/1/2024 1/1/2025 1/1/2026
9One-Step Trending
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• Example 3: Annual Policies, Adjusting PY2023 EP for premium trend
PY 2023 PY 2025
• Average written date for PY 2023 = 6/30/2023
• Average written date for PY 2025 = 6/30/2025
• Trend length is from 6/30/2023 to 6/30/2025 (2 years)
1/1/2022 1/1/2023 1/1/2024 1/1/2025 1/1/2026
• Example 4: Ann Pols, Prop Rate in Affect for 2 yrs Adj PY EP for prem trend
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One-Step Trending
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CY 2023 PY 2025 - 2026
• Average written date for CY 2023 = 1/1/2023
• Average written date for PY 2025-2026 = 1/1/2026
• Trend length is from 1/1/2023 to 1/1/2026 (3 years)
• What about EP to EP?
• Trend length is from 6/30/2023 to 6/30/2026 (3 years)
1/1/2022 1/1/2023 1/1/2024 1/1/2025 1/1/2026 1/1/2027 1/1/2028
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Practice
Calculate the premium trend period for the following scenarios:
• Scenario #1:
– Premium trended from CY2023
– Annual policies
– Proposed Effective Date: 1/1/2025
– Rates will be in effect for 2 years
• Scenario #2:
– Premium trended from CY2023
– Semi-annual policies
– Proposed Effective Date: 1/1/2025
– Rates will be in effect for 2 years
• Scenario #3:
– Premium trended from PY2023
– Semi-annual policies
– Proposed Effective Date: 4/1/2029
– Rates will be in effect for 2.5 years
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Practice - Answers
Calculate the premium trend period for the following scenarios:
• Scenario #1: WP to WP: 1/1/23 to 1/1/26 (3 years) or EP to EP: 6/30/23 to 6/30/26
– Premium trended from CY2023
– Annual policies
– Proposed Effective Date: 1/1/2025
– Rates will be in effect for 2 years
• Scenario #2: WP to WP: 4/1/23 to 1/1/26 (2.75 years) or EP to EP: 6/30/23 to 4/1/26
– Premium trended from CY2023
– Semi-annual policies
– Proposed Effective Date: 1/1/2025
– Rates will be in effect for 2 years
• Scenario #3 : WP to WP: 6/30/23 to 6/30/30 (7 years) or EP to EP: 10/1/23 to 10/1/30
– Premium trended from PY2023
– Semi-annual policies
– Proposed Effective Date: 4/1/2029
– Rates will be in effect for 2.5 years
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• Difficult to apply this approach when the changes in average premium vary
significantly year-by-year and/or when historical changes in average premium
are significantly different than the changes that are expected in the future.
– Example: Company moving all their insureds to a higher deductible at
renewal on 1/1/2019, the shift would be completed by 12/31/2019 and
not continue into the future. In this situation – use two-step trending
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• Used when the company expects premium trend to change over time
• If the trend during the historical period has been significantly different from
what is expected to occur in the future, it makes sense to adjust the historical
data to current levels accordingly, but to apply a different trend into the
forecast period to reflect what is expected to occur in the future.
• Example: Insurer observes significant increases in amount of insurance
purchased during the experience period that are not expected to continue into
the future
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Two-Step Trending
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• Two Steps in ‘Two-Step Trending’
– Current Trend Step
– Projected Trend Step
• Actuary must adjust the historical premium to the average premium level of the
most recent point in the trend data (current trend step)
• Current Premium Trend Factor = Latest Avg. WP @ Curr Rate Lvl
Hist. Avg. EP @ Curr Rate Lvl
• Factor adjusts historical CY earned premium to the average written
date of the latest quarter available
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Two-Step Trending
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• Average CY 2023 EP = $740
• Average CY 4Q2023 WP = $753
• Current Premium Trend Factor = $753/$740 = 1.0176
• Latest average written premium is 4Q2023 and the average written date is
11/15/2023
o Average written date for 4Q2023 WP is 11/15/2023. This is different from
the average written date of 4Q2023 EP.
o 11/15/2023 will be the start date for the ‘projected trend step’
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Example – Current Trend Step
• Another option when the historical average premium is volatile is to select a
premium trend for the ‘current trend step’.
CY 2023 EP average written date is 1/1/2023 and we are trending to 11/15/2023
(0.875 years)
If we choose a 2% premium trend for the ‘current trend step’, we would adjust
2023 CY EP by (1.02)^0.875
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• Apply a separate adjustment to project premium into the future policy premium
(projected trend step)
– Average written date from end of step 1 = 11/15/2023
– Average written date for PY 2025 = 6/30/2025
– Trend length is from 11/15/2023 to 6/30/2025 (1.625 years)
CY 2023 Projected EP @ Current Rate Level
= CY 2023 EP @ Current Rate Level x Current Trend Factor x Projected Trend Factor
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CY 2023 PY 2025
Two-Step Trending
1/1/2022 1/1/2023 1/1/2024 1/1/2025 1/1/2026
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Example
Given the following information use two-step trending to calculate earned premium
(@ CRL) at prospective levels:
– Annual policies and uniform writings throughout the year
– Projected premium trend = 10%
– Proposed effective date for the next rate change is 1/1/2027
• Rates will be in effect for 3 years
CY
Earned
Premium*
Written
Premium*
Earned
Exposures
Written
Exposures
2008 1,000,000 1,100,000 1,000 1,050
2009 1,250,000 1,500,000 1,300 1,400
2010 1,500,000 1,650,000 1,450 1,505
* At current rate level
Current Premium Trend Factor = Latest Avg. WP @ Curr Rate Lvl
Hist. Avg. EP @ Curr Rate Lvl
CY 2021 = = 1.096346
CY 2021 = 1.096346
CY 2022 = 1.140199
CY 2023 = 1.059801
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Example
Given the following information use two-step trending to calculate earned premium
(@ CRL) at prospective levels:
– Annual policies and uniform writings throughout the year
– Projected premium trend = 10%
– Proposed effective date for the next rate change is 1/1/2027
• Rates will be in effect for 3 years
Current Premium Trend Factors
CY 2021 = 1.096346
CY 2022 = 1.140199
CY 2023 = 1.059801
PY 2014 PY 2015 PY 2016CY 2010CY 23 PY 2027 PY 2028 PY 20295 yr Trend Period
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Example
Given the following information use two-step trending to calculate earned premium
(@ CRL) at prospective levels:
– Annual policies and uniform writings throughout the year
– Projected premium trend = 10%
– Proposed effective date for the next rate change is 1/1/2027
• Rates will be in effect for 3 years 5 yr projected trend period
CY
Earned
Premium*
Written
Premium*
Earned
Exposures
Written
Exposures
2008 1,000,000 1,100,000 1,000 1,050
2009 1,250,000 1,500,000 1,300 1,400
2010 1,500,000 1,650,000 1,450 1,505
* At current rate level
CY 2021 = 1.096346
CY 2022 = 1.140199
CY 2023 = 1.059801
* 1,000,000 = 1,096,346
* 1,250,000 = 1,425,249
* 1,500,000 = 1,589,702
* (1.10)^5 = 6,621,284
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Practice
Given the following information use two-step trending to calculate earned premium
(@ CRL) at prospective levels:
– Semi-Annual policies and uniform writings throughout the year
– Projected premium trend = 10%
– Proposed effective date for the next rate change is 4/1/2026
• Rates will be in effect for 2.5 years
CY OLEP Avg OLEP Avg OLWP
2003 3,500,000 3,500 3,750
2004 3,990,000 3,800 3,650
2005 4,290,000 3,900 4,000
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Practice - Answer
Given the following information use two-step trending to calculate earned premium
(@ CRL) at prospective levels:
– Semi-Annual policies and uniform writings throughout the year
– Projected premium trend = 10%
– Proposed effective date for the next rate change is 4/1/2026
• Rates will be in effect for 2.5 years 6/30/23 to 6/30/27 (4 years)
CY OLEP Avg OLEP Avg OLWP
2003 3,500,000 3,500 3,750
2004 3,990,000 3,800 3,650
2005 4,290,000 3,900 4,000
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CY 2021 = (4,000 / 3,500)
CY 2022 = (4,000 / 3,800)
CY 2023 = (4,000 / 3,900)
* 3,500,000 = 4,000,000
* 3,990,000 = 4,200,000
* 4,290,000 = 4,400,000
* (1.10)^4 = 18,447,660
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