Fisher1

Question 1

experience rating relates

Answer 1

insured’s premium for current policy term to their own loss experience from prior policy terms

-insured’s actual experience is credibility weighted with expected losses to produce medication factor that is applied to manual premium to get modified premium

Question 2

if experience mod factor < 1

if experience mod factor > 1

Answer 2

• if experience mod factor < 1, it is a credit mod
• if experience mod factor > 1, it is a debit mod

Question 3

debit mod implies

Answer 3

risk has worse than average experience compared to other risks in the same class but this may be due to poor class fit or pure chance so debit mod shouldn’t be thought as a stigma

Question 4

experience rating is particularly well suited for

Answer 4

commercial lines since company management has a great deal of control over company practices

Question 5

experience rating helps distinguish

Answer 5

between risks within classification for differences such as: compensation, variation in plants & premises, operating processes, materials involved, management, employee morale, claims consciousness, relation to community

Question 6

in commercial lines, credibility for actual loss experience depends on

Answer 6

size of insured (measured by manual premium, expected loss, expected #claims, or exposures)

Question 7

credibility of individual risk experience increases when

Answer 7

there is greater variance between loss experience of risks within a classification

AKA experience rating is more powerful when classification plan does not sufficiently explain variance in loss experience between risks

Question 8

Advantages of experience rating

Answer 8

1. accounts for differences between risks in a class
2. accounts for variables that are difficult to quantify
3. further refinement of classification beyond manual rates

Question 9

Goals of experience rating

Answer 9

1. greater risk equity
2. safety incentive
3. enhance market competition

Question 10

greater risk equity

Answer 10

• main goal
• degree of charge based on past experience should be degree to which it is predictive of future losses
• ensures equity which means insureds are charged a premium that more closely relates to their loss potential and rates will not be unfairly discriminatory

Question 11

safety incentive

Answer 11

-by charging insureds higher premium for prior losses, insureds have a financial incentive for loss control

Question 12

enhance market competition

Answer 12

-more companies will be willing to sell insurance since experience rating helps guarantee an equal profit potential on all risks after application of experience mod

Question 13

goals 1&2 need to be balanced since

Answer 13

2nd in isolation would charge for all prior losses while 1st would only charge for non-random prior losses that are predictive of future loss potential

Question 14

3 types of credibility

Answer 14

1. classical: limited fluctuation credibility; determine full credibility standard using standard normal distribution based on given probability that observed experience will be within some % of true mean
2. Buhlmann: greatest accuracy or least squares credibility; involves analysis of variance
3. Bayesian: update prior hypotheses with new experience
   - experience rating uses Buhlmann credibility which means credibility is calculated using Z=E/(E+K)
   - individual risk experience is credibility weighted with experience of class containing risk

Question 15

-simplest type of experience rating plan

Answer 15

is one in which there is no subdivision of losses

-ISO commercial GL experience rating plan uses this version of experience mod formula

Question 16

under split plan

Answer 16

actual and expected losses are split into primary and excess components

• primary amount of each loss reflects claim frequency and receives the most weight in experience rating calculation
• excess amount of each loss reflects severity
• NCCI uses single-split plan for WC

Question 17

split plan works better when

Answer 17

parameter risk can be separated from process risk

-for WC: parameter risk=claim count uncertainty driven by many small med-only and TT claims & process risk=severity volatility driven by few but very influential Major PP, PT, and Fatal claims

Question 18

2 other credibility issues

Answer 18

1. maximum single loss (MSL): individual large losses can be capped to limit impact on experience mods since full loss amount isn’t likely credible
2. min and max mods: mod itself can be capped to limit extreme values
   - note that Z, MSL and min/max mods will all change with risk size with larger risks receiving more credibility and larger absolute values of caps

Question 19

there are several similar ways to test predictive accuracy of plan

Answer 19

• tests are usually performed for different risk size groups separately
  1. method 1: quintiles test
  2. method 2: efficiency tests

Question 20

quintiles test

Answer 20

• sort risks by their mods in increasing order
• group these sorted risks into 5 quintiles
• for each quintile, calculate manual and standard LRs using weighted averages
• under a plan performing ideally you would see: maximum dispersion in manual LRs (plan does good job of identifying risk differences) & flat standard LRs (shows plan corrects for risk differences ie shows appropriate amount of credibility has been given to actual loss experience)

Question 21

-if too much credibility to actual experience,

Answer 21

see risks with low mods getting too much credit for experience resulting in too big a reduction in their standard premium and as result having higher standard LRs & risks with high mods would get overly penalized resulting in their standard premiums being too high and thus having lower standard LRs

-appear as downward trend in LRs as mods increase

Question 22

if too little credibility,

Answer 22

see risks with low mods getting too little credit for their experience resulting in too little reduction in their standard premium and as result having lower standard LRs & risks with high mods wouldn’t get penalized enough resulting in their standard premium being too low and have higher standard LRs

-appear as upward trend in LRs as mods increase

Question 23

efficiency tests

Answer 23

can only be used to compare 2+ plans

• sort risks by their mods in increasing order
• group these sorted risks into 5 quintiles
• for each quintile, calculate manual and standard LRs using weighted averages
• calculate efficiency test statistic
• lower test statistic indicates better plan performance

Question 24

schedule rating

Answer 24

is pricing mechanism that allows underwriters to subjectively adjust premium for individual risks based on risk characteristics that are not otherwise reflected in premium calculation

Question 25

schedule rating plans are filed with

Answer 25

set list of risk characteristics that will be considered by underwriters along with maximum credits and debits that will be allowed for each category and in total across all categories

Question 26

schedule rating adjustments are made by

Answer 26

risk characteristic and then summed to get total schedule credit or debit

• credit or debit is given in each category if the risk is either above average or below average related to other risks for that category
• ISO GCL plan categories: location, premises, equipment, classification, employees, cooperation
• credits and debits by risk characteristic are summed and then capped so max schedule debit of 25% and max schedule credit is -25%

Question 27

it is important for schedule credits and debits

Answer 27

to avoid reflecting any risk characteristics that are already fully reflected in experience rating

-partial exception would be if risk’s experience isn’t fully credible then some partial schedule credit would make sense on top of having risk characteristic partially reflected in experience mod

Question 28

three criteria for an effective credibility function in experience rating.

Answer 28

i. The credibility should be between zero and one (inclusive).

0 ≤ Z ≤ 1
ii. The credibility should not decrease as size increases.

d/dE (Z)≥ 0
iii. As the size of risk increases, the percentage charge for a loss of a given size decreases.

d/dE (Z/E) < 0

Question 29

relationship between the variance of the
hypothetical means and the credibility of individual risk experience.

Answer 29

As the VHM increases, the credibility of individual risk experience also increases.

Question 30

actuarial concept of individual rate equity as it applies to experience rating

Answer 30

Individual rate equity means charging risks a rate that is commensurate with their loss exposure.

Question 31

why splitting the formula into primary and excess components is preferable for
workers compensation risks.

Answer 31

Splitting losses into primary and excess components results in more accurate estimates of expected losses, because this would separate the parameter uncertainty related to the volume of claims in the primary layer, and the process risk related to the severity volatility in the excess layer.

This works well for Work Comp since it has many small Medical-Only claims, and fewer large and uncertain Lost-Time claims.

Question 32

why the excess component is capped

Answer 32

capping prevents large losses that are not predictive of future losses from having too big of an impact on the insured’s premium

Question 33

full credibility conflicts with one goal of experience rating.

Answer 33

Giving full credibility to loss experience conflicts with the goal of individual risk equity, which is to charge insureds for their true loss potential.

Giving full credibility to an insured’s loss experience would penalize the insured for having random losses that do not reflect their true expected loss.

Question 34

The main goal of experience rating is individual risk equity.

Answer 34

Experience rating recognizes that each risk has a different loss potential, so by modifying rates appropriately, the expected profit potential for each risk can be made equal. This ensures that equity is achieved and rates are not unfairly discriminatory.

Otherwise, risks with lower loss potential within the class would subsidize other higher loss potential risks.

Question 35

The average experience modification factor for the current plan is 1.05 and for the proposed Plan A is 0.99. The analyst says that proposed Plan A performs better because the average factor is less than 1.

Critique this statement.

Answer 35

While ideally the value of the average modification factor should remain close to 1 so as not to influence the overall premium level, this is not a major criteria in determining the best plan for experience rating.

Instead, a plan can be evaluated by looking at the dispersion of manual loss ratios across quintiles to see how well the plan identifies risk differences, and then looking at both the trend in standard loss ratios and the variance in standard loss ratios to see how well the plan corrects for these risk differences.

Question 36

Interpret each of the terms for

Mod = 1+Zp(Ap-Ep/E)+Ze(Ae-Ee/E)

Answer 36

Unity is the manual rate

The 2nd term is the charge if the actual primary losses are greater than expected.

The 3rd term is the charge if the actual excess losses are greater than expecte