One time changes¶

One-time changes occur on a specific date or time. If predictions differ from targets, rates need adjustment.

Action:

Calculate direct effects.
Adjust premiums for rate changes.

Reasons¶

Rate Changes
Law Changes
- Implemented like a rate change or impact all policies (even in-force policies, whose premiums need recalculation).
- Changes to rates.
- Changes to coverages.
Court Rulings
- These are imposed by a court decision instead of a law.

Effects¶

Situation: A large rate increase occurs.

Direct Effects:
- The direct result is that premiums increase.
Indirect Effects:
- These cause a change in customer behavior.
- Result: Lower retention and close ratios.
- These are often difficult to quantify.
- More examples:
  - Workers' compensation: An increase in indemnity benefits leads to more claims being filed and longer periods out of work.
  - Rate decrease: Leads to an increase in retention and close ratios.
  - Workers' compensation: A decrease in benefits leads to fewer injured workers filing claims and injured workers returning to work sooner.

Calculating Direct Effects on Premiums¶

Both methods below yield the same output.

Re-rate Each Policy Directly
- Calculate (Total after) / (Total before) - 1.
Use In-Force Premium Distributions
- Calculate the distribution: Determine the original premiums for each class (e.g., by territory A and B, where the distribution might be 52.6% and 47.4% respectively).
- Calculate the percentage change in the multiplicative factors: (Final factor / Initial factor) - 1. For example, 1.0/1.0 - 1.0 = 0% and 0.85/0.90 - 1 = -5.56%. Do this for all changes.
- Then, perform a sum-product: Calculate the average percentage change weighted by the distribution of premiums. Use this to determine the multiplicative premium change.
- Now, weight this multiplicative effect (e.g., 7.11%) and any additive effect (e.g., 0%) by the proportion of multiplicative (e.g., 3800/4000) and additive (e.g., 200/4000) components of the original premium.

Calculating Direct Effects on Losses¶

Change in Coverage
- Coverage Increase:
  1. Losses might be capped at a lower coverage level (censored data), e.g., $500k versus an increased $1000k.
  2. A new type of coverage might not have historical data.
- Coverage Decrease:
  - We can restate historical data at new coverage levels.
- Ways to Calculate
- Restate Individual Claims:
  - Analogous to calculating premium levels at in-force policy levels. (e.g., Workers Compensation Indemnity Benefit Change).
- Representative Groups:
  - Use a weighted average of the impact on different segments.
- Simulate Losses Under New Coverage Levels:
  - This can be difficult due to parameter definition.
- Workers' Compensation Indemnity Benefit Change
- An example to calculate benefit change based on totals.
- SAWW (State Average Weekly Wage): The minimum or maximum benefit can be stated as a percentage of the SAWW (e.g., Min: 50% of SAWW ($1000) = $500; Max: 100% of SAWW = $1000).
- See also: Restate individual claims (analogous to calculating premium levels at in-force policy levels).
- Rate: Stated as "rate of 1/2 of their pre-injury wage." Here, 1/2 is the Compensation Rate.
- Situation:
  - Compensation rate changes from 1/2 to 2/3.
  - Minimum benefit remains 50% of SAWW (no change).
  - Maximum benefit changes from no limit to 100% of SAWW.
- Calculation using Max Benefit (avg wage, and avg wage/SAWW):
  - Which rows will receive the minimum benefit?
    - Old rate: If (Weekly wage / SAWW) is less than 50% / (1/2) = 100%. So, the first three rows with a ratio to SAWW < 100% will receive the minimum benefit as per the old rate.
    - New rate: Do the same for the new rate with 50% / (2/3) = 75%. So, the first two rows with a ratio to SAWW < 75% will receive a minimum benefit of $500 as per the new rate. This is natural, because if the weekly wage < SAWW, wages are lower and need to be provided for, and vice versa.
  - Which rows will receive the maximum benefit?
    - If the ratio (1) is more than 100% / (2/3) = 150%. Only records > 150% (the last one) will receive a maximum benefit of $1000.
  - The average weekly benefit is MIN[$1000, MAX($500, $900 x 2/3)].
- Direct Benefit change: New benefits / Old benefits - 1.

Adjust Premiums for Rate Change¶

We can on-level any premiums, but this is usually done for Earned Premiums.

Extension of Exposures
- Re-rate all historical policies at an individual policy level with the new rates to get on-level full-term premiums, then recalculate Earned Premium (EP) and % earned using those rates.
- Advantage: Most accurate method.
- Disadvantage:
  - Requires detailed historical policy-level data (though nowadays this method is quite common as data is often available).
  - Requires significant computing power for large datasets.
  - Needs assumptions for new rating variables with no historical data.
  - Difficult to incorporate changes in schedule rating guidelines for commercial lines.
- Method: Simply calculate the premiums with the new rates.
- Parallelogram Method
- Advantage: Quick to calculate.
- Disadvantage:
  - Assumes policies are written evenly throughout the year. This can be partially addressed by using smaller time periods (like quarterly).
  - Inappropriate for class ratemaking. The direct effects of a rate change are calculated at an aggregate level. So, if classes A and B have direct effects of 0% and 20% respectively, but the aggregate increased by 10%, the parallelogram method would apply a 10% direct effect to both A and B. This can be addressed by on-leveling premiums at the class level using class-level rate impacts and performing the method for each class.
  - See also: Disadvantage #2 (class ratemaking) when done at a book of business level.
- Method:
  - Gather effective dates and amounts of all rate changes.
  - Group policies into rate level groups (RLG). RLGs are the triangular, parallelogram, or square portions in the policy diagram where each shape has the same rate level.
  - Calculate the portion of the time period's earned exposure for each RLG. Just take a fraction of the shape's area over the year.
  - Calculate the Cumulative Rate Level Index (CRLI) for each RLG. Assign the oldest RLG a rate level of 1 (so, CRLI = 1); subsequent ones can be calculated by applying the rate changes to the previous CRLI. For example, CRLI(A) = 1 and CRLI(B) = CRLI(A) x (rate change for B = 1.1) = 1 x 1.1 = 1.1.
  - Calculate the Weighted Average CRLI (WA.CRLI) for each time period. Areas in the diagram are the weights. For example, Area A = 0.5 x (6 months / 12 months) = 0.125 is the weight for RLG A, and Area B = 1 - Area A = 0.875 is the weight for RLG B. So, for this time period, the WA.CRLI = 0.125 x (1) + 0.875 x (1.1) = 1.0875. The average rate level for CY2011 would be 1.0875.
  - Calculate the On-Level Factor (OLF) for each time period: Current CRLI / WA.CRLI. Say the latest CRLI calculated = 1.078. For CY2011, OLF = 1.078 / 1.0875 = 0.9913.
  - Multiply OLF by the earned premium for the appropriate time period to obtain On-Level Earned Premium (OLEP). Say, the CY2011 EP = $50,000. Then the CY2011 OLEP = $50,000 x 0.9913 = $49,563.
  - Interpretation: If historical policies had all been written with the current rates, we estimate CY2011 EP would have been $49,563 instead of $50,000.
- Notes (B.3.6):
  - The slant of the rate change line depends on the policy term (6-month policies will have less slope than 1-year policies).
  - We can ignore rate changes before the start of the time period we are considering for calculation. For example, if there was a rate change before CY2011 that has already affected all policies earning in 2011, we can just set the rate at the beginning of 2011 as CRLI = 1. This is because in the final step for calculating OLFs, we would anyway be canceling out the previous rate changes in the numerator and denominator.
  - Law changes are represented by vertical lines, as they affect all in-force policies.
  - For policy years, the time periods would now look like parallelograms; nothing else changes.
  - Calendar quarters are just thinner time periods.
  - Drawing diagrams can be helpful.
  - Common Student Mistake: Don't calculate an OLF for each historical RLG. Do calculate a single average rate level from the historical period and obtain a single OLF for that period.
- See also: Parallelogram Method (assumption of uniformity doesn't hold, so use shorter time periods), Parallelogram Method for losses, and Method (same as Parallelogram Method with the exception of using actual exposures instead of area).
- Use Actual Writings Distribution and Group Data by Rate Level
- Advantage: More appropriate than the parallelogram method when actual writings are not uniform.
- Disadvantage: Same as Disadvantage #2 (class ratemaking) when done at a book of business level.
- Method: Same as Parallelogram Method with one exception: instead of taking area (as a result of the uniformity assumption), consider the actual exposures (e.g., 10% in the first 2 months, 50% in the following 6, and 40% in the rest).
- More...
- On-Level Written Premium (OLWP) with Law Change B.3.8
- Parallelogram Method for losses.

Adjust Losses for Coverage Changes¶

NCCI estimates benefit changes. We assume that benefit changes impact all losses from all policies.

Parallelogram Method
- The assumption of uniformity doesn't hold well, so use shorter time periods.
Ways in which Benefit can Affect:
- Slant lines: Losses on policies written after a certain date.
- Vertical lines: All new losses occurring after a certain date.