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Trends

  • Account for price level changes across years. Answer the question: "What if the exact same policies were written in the year the future rates would be effective in?" and "What if the exact same losses were claimed in the effective year?"
  • Trend Periods
    • EP/WP: Avg Earned Date. MP for the CY and PY. Say for
      • CY Avg Earned Date = \(7/1/20\) (assuming not the first year1)
      • PY Avg Earned Date = \(7/1/20 + \dfrac{1}{2}(\text{Policy Period})\)
      • CY/PY Avg Writ Date = CY Avg Earned Date \(-\dfrac{1}{2}(\text{Policy Period})\)
    • Claims: Avg Accident Dates
      • AY/CY Avg Accident Date = \(7/1/20\)
      • If rates are effective in the year \(2022\) then the policies can be written between \(1/1/2022\) and \(12/31/2022\). And the accidents for those policies will be covered between \(1/1/2022\) to \(12/31/2023\). So the MP is \(1/1/2023\).
        • So effectively MP of the PY + \(\dfrac{1}{2}(\text{Policy Period})\)
    • One good mantra of finding the average aggregation date is to find the average of average.
      • If the company started writing policies in 2011, then the first policy that is considered in CY 2011 EP would be on Jan 1, 2011. The average date for which would be July 1, 2011 (assuming annual policy), or April 1, 2011 (3) (assuming semi-annual policies). The average dates would be uniformly distributed between the dates from July 1, 2011 (6) to Dec 31, 2011 (12) or April 1, 2011 (3) to Dec 31, 2011 (12). Taking the average of these average dates, we would land on Sep 30, 2011 (\(\dfrac{6+12}{2}=9\)) or Aug 15, 2011 (\(\dfrac{3+12}{2} = 7.5\))
      • If the company was writing policies before 2011, then the first policy that is considered in CY 2011 EP would be ~~on Jan 1, 2010~~ (not considered because its average date is July 1, 2010 (not in 2011! It should be in 2011! (I am using too many nested brackets!!! CRAZY!))), on July 1, 2010. The average date for which would be on Jan 1, 2011 (which is indeed in 2011!). So, if we take all the average dates, we will find them uniformly everyday throughout the year 2011. So the average accident date would be the average of these average dates, i.e. from Jan 1,2011 to Dec 31, 2011, which is essentially July 1, 2011.
      • I feel that might be a satisfactory explanation for average dates. %% # Trends

Trends represent changes in the mix of business (MoB), inflation, and socio-economic factors. These affect Premiums, Losses, Exposures, or Expenses over time.

Note: Trends are not applied to the number of policies written, which also changes over time. The reason is that we want the MoB, inflation, and socio-economic conditions of the data to match those of the policy period being priced. The goal is to ensure the insurer hits their Target profit. We are not concerned about how many policies the insurer writes in the future, but rather, forecast the expected average costs and average premiums.

Trends reflect changes that occur gradually over time:

  • Gas Prices
    • Gas prices increasing may cause people to drive less, thus reducing the frequency of accidents.
  • Medical Care Costs
    • An increase in the cost of medical care can increase the claim severity of liability coverage.
    • The insurer's rates become more and more inadequate over time if the policies are priced based on some older (lower) level of severity.
  • Higher Deductibles
    • Customers switching to higher deductibles will lead to a reduction in claims, and so they would be asked to pay less pure premiums.
    • Fewer claims would cross the deductible threshold, so claim frequency reduces.
    • There is lesser severity per claim as each claim is being deducted by a higher amount.
  • Labor and Material Costs
    • Linked to the labor and material costs, which may change over time.
    • Since coverage for homeowners insurance is measured in terms of replacement cost, the cost of rebuilding the house increases due to the increase in material and labor costs.
    • Average premiums increase. But since coverage is also increased, there will be an increase in the pure premium.
  • Payroll (Exposures)
    • When exposures are inflation sensitive, e.g., payroll in Workers' Compensation.
    • Employers increase payroll to keep up with inflation. So the indemnity claim severity will increase as workers are paid a portion of their wages when they are out of work.
    • Frequency per unit dollar of income reduces because the expected worker injury counts have nothing to do with increased payroll or inflation.
    • We have to take a call based on the combined impact.

ASOP 13

Read through 1-4, but 3 is most relevant for trending.

  • Sect. 2.6 ASOP 13 applies to any type of data
    • Not just Prem/losses... Coverage, payroll, expenses.
  • Sect. 3.1 How to present?
    • Depending on the intended purpose, you may have to calculate a single point or a range of possible trends.
  • Sect. 3.2 Data
    • Based on insurance / non-insurance data?
    • Credibility concerns?
    • Relationship between data? (premium link with inflation).
    • Distortions in data? (Seasonality).
  • Sect. 3.3 Relevant economic and social influences
    • Court decisions. Are courts being more generous to plaintiffs? If so, losses can go up.
  • Sect. 3.4 Methodology
    • Consider current best practices.
    • Consider past methods used (no need to use them, just try them out).
    • We need the best information (estimate) and to make the best business decision. Don't try to reverse engineer a trend rate to get a target rate changes.

Source

  • Insurer's data
    • Past trends would indicate future trends.
  • Industry data
    • More stable. But may be less relevant.
  • Economic data
    • Inflation. CPI (medical care).
  • Use one of them or a weighting of a combination.

Distortions

  • One-time changes
    • Rate changes can cause change in average premiums. Can distort the trend for premiums.
  • Catastrophic or shock losses
    • Usually remove the record.
  • Seasonality
    • Annualize data in order to remove seasonality.

Concepts

  • Trends are based on difference in AVERAGE / pure premiums, not TOTAL premiums
    • Even if the number of policies written increases, the average/pure premium won't change.
    • The same set of policies in the past (if written in the future) since it's the same set of policies it will be the same in number.
  • Granularity of data
    • Use state-level data for trends if we are looking at rate changes in a state. But if state-level data is volatile (small volume of data), consider using country-wide data.
    • Homeowners, look at trends by peril. Fire-related vs. water-related. Then there is more homogeneity in the data. But not at the cost of statistical significance (volume of data).
  • Balance stability with responsiveness
    • Be conservative: it was a fluke and the change will not continue forward in the future. Select the historically stable rate.
    • Be Fully responsive: the change is highly indicative of the rates in the future. Hence select the new rate.
    • Be Judgemental: Somewhere in between.

Premium data

  • Earned Premium
    • When forecasting Loss Ratios. EP is in the denominator of LR.
  • Written Premium
    • Is a leading indicator of EP.
  • Premium developments from audit #explore

Loss data

  • Trend frequency and severity separately
    • Re-combine freq/severity to PP trend.
  • CY data
    • For short tailed LOB.
    • Assumes that book is not significantly growing.

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  1. If its the first year, then there will be imbalance in the year and the premium will be earned in a triangular fashion in the CY, which will lead to the average earned date not be the MP but something that has to be geometrically determined. ↩

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