BAIC 4 - Loss and Premium Adjustments

Question 1

Use of Multiplicative Factors

Answer 1

1. Compensate for any incompleteness in our data (immature losses)
2. Restate past data to reflect any expected changes between the past and the future

Question 2

The two categories of data that actuaries adjust

Answer 2

1. Losses and Claims

2. Premium and Exposures

Question 3

Loss Adjustments Categories

Answer 3

1. Loss Development Factors - Losses may change over their lifetime, so immature losses are developed to an ultimate basis
2. Trend - Ultimate losses are projected into the future. Projections can be made for claim cost, claim frequency, etc.
3. Unallocated Loss Adjustment Expense (ULAE) - An allowance is added for unallocated loss expenses usually in the form of a multiplicative factor

Question 4

Reasons to develop losses

Answer 4

1. Claim values change over time - loss payment estimates are made when the claim is reported. Estimates can be incorrect or new information can lead to revised estimates
2. Claims Incurred but not reported (IBNR) - Not all claims are reported immediately so there is a lag between when an accident occurs and when a claim is filed (for whatever reason)

Question 5

Actual Loss Development Triangle

Answer 5

Consists of several years of data and is an aggregate of many claims

Question 6

Link Ratio

Answer 6

Measure of Growth (or shrinkage) of losses from one period to the next.
For example, a 27:15 link ratio measures the change in losses from the 15-month evaluation point to the 27-month evaluation point

Question 7

Loss Development Factor

Answer 7

Described in terms of what time they represent development from and to
For example: An LDF for “15 to Ultimate” is a measure of how much losses are expected to increase from the 15-month age to the ultimate age. It is the product of the applicable link ratios

Question 8

Tail Factor

Answer 8

The final link ratio, used for Ult:63 and will be provided

Question 9

Trend Factor Consideration

Answer 9

1. Internal vs. External Data - Internal data comes from a company’s own insurance experience; External Data comes from other sources like Federal Reserve data or the Boeckh construction price index (used for property insurance)
2. Exponential Trend vs. Econometric Analysis
3. Current Cost Factors vs. Trended Cost Factors - CCFs bring historical experience to the “current” level; TCFs bring “current” experience to the prospective level

Question 10

Trend Adjustment Factor

Answer 10

(1 + trend) ^ trend period

trend = average annual percent change (annual trend)

Question 11

Trend Period Calculation Terms

Answer 11

1. Filing Effective Date - Date when the revised rates go into effect
2. Filing Expiration Date = Date when the revised rates are superseded by another filings (often 0.5, 1, or 2 years after the original Filing Effective Date)
3. Average Prospective Policy Effective Date - Midpoint of a policy written on the Average Prospective Policy Effective Date
4. “Trend From” Date - Average loss date in the experience period
5. “Trend To” Date - Same as Average Prospective Loss Date
6. Trend Period - Difference between the trend from and trend to dates

Question 12

Methods to calculate link ratios

Answer 12

1. Arithmetic Mean (we use this)
2. Mean of the last 5 factors
3. “Best 3 of 5”

Question 13

Trend Period Example

1. What is the average loss date for Accident Year ending 6/30/2003?
2. What is the average loss date for Policy Year ending 6/30/2003?

Answer 13

1. 1/1/2003

2. 7/1/2002

Question 14

Overlap Fallacy

Answer 14

The argument that applying both trend factors and loss development factors leads to excessive rates

• Loss development brings immature past losses to their ultimate value at the historical cost level.
• Trend restates ultimate past losses at future cost levels

Question 15

Categories of Premium Adjustments

Answer 15

1. Restating at Current Rate level - Past premiums are recalculated at the current rate level using the most recent rates
2. Trend - Premiums may depend upon an exposure base that increases predictably (e.g. insured property value; gross sales). Expected increase in exposure must be taken into account when projecting future premiums
3. Changes in Mix of Business - Ex: Consumer attitudes may shift (choosing deductibles of $1000 instead of $500)

Question 16

Methods to adjust premiums to current level

Answer 16

1. Extension of Exposures (Premium at Present Rate) - Recalculate premiums for each individual policy using the current rates
2. On-leveling (Parallelogram Method) - Estimate premiums for blocks of policies based on past rate level changes and when they came into effect

Question 17

Extension of Exposures (PPR) Advantages and Disadvantages

Answer 17

Advantages - Accurate, Easy to understand and explain

Disadvantages - Resource-intensive, Requires extensive detail on policies

Question 18

On-leveling Advantages and Disadvantages

Answer 18

Advantages - Not resource-intensive, easy to calculate
Disadvantages - Potential for error due to faulty assumptions, difficult to explain to others
**the (simple) on-leveling method assumes that policies are written uniformly throughout the year

Question 19

On-level factor

Answer 19

Current Rate Level / Average Rate Level

Question 20

Using Adjustment Data in Ratemaking

Answer 20

Earned Premium * On-level Factor = Adjusted Premium