Experience Rating (Fisher)

Question 1

Define experience rating

Answer 1

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

Insured’s actual loss experience is credibility weighted with expected losses to produce a modification factor that is applied to manual premium to get modified premiums.

Question 2

How do you interpret the modification factor

Answer 2

If mod < 1 = credit mod
If mod > 1 = debit mod

Debit mod implies risk has worse than average experience compared to other risks in same class.

It gives NO indication on good or bad risks, only indicate how compare to class.

Mod > 1 may be due to poor class fit or pure chance.

Question 3

List 4 differences that would be identified with experience rating

Answer 3

1. Compensation
2. Variation in pants and premises
3. Operating processes
4. Materials involved
5. Management
6. Employee morale
7. Claims consciousness
8. Relation to community

Question 4

Explain why experience rating is particularly well suited for Commercial Lines

Answer 4

Company management has great deal of control over company practices

Question 5

Discuss the relationship between credibility of individual risk experience and strength of classification plan

Answer 5

Credibility of individual risk experience increases with greater variance between loss experience of risks within classification.

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

When classification plan is very strong, experience rating will be less important

Experience rating only adds value when there is a lot of variance unexplained by rating variables (accounts for VHM within class)

Sophisticated class plan has more homogeneous classes (vs simple class plan) so experience rating has less impact

Question 6

List 3 advantages of experience rating

Answer 6

1. Accounts for differences between risks in class
2. Accounts for variables that are difficult to quantify
3. Further refinement of classification beyond manual rates (further tailored to loss potential)

Question 7

Describe 3 goals of experience rating

Answer 7

1. Greater risk equity (main goal)
   Degree of charge based on past experience should be degree to which it is predictive of future losses (not an attempt to charge back for past losses)
2. Safety incentive
   By charging insureds a higher premium for prior losses, insureds have a financial incentive for loss control.
   Need to be balanced with first objective since, in isolation, would charge for all prior losses, while first goal would only charge for non-random prior losses that are predictive of future loss potential.
3. Enhance market competition
   More companies will be willing to sell insurance since experience rating helps guarantee equal profit potential on all risks after application of experience mod.

Question 8

Describe the 3 types of credibility

Answer 8

1. Classical (aka limited fluctuation)
   Determine full cred standard using std normal distribution based on given prob that observed experience will be within some % of true mean
2. Buhlmann (aka greatest accuracy or least square)
   Involves analysis of variance
3. Bayesian
   Update prior hypotheses with new experience

Question 9

Experience rating uses which type of credibility?

Answer 9

Buhlmann

Credibility is the most important consideration in designing rating plan

Z = E / (E+K)
E = Expected Losses
K = EVPV / VHM

Question 10

Explain EVPV

Answer 10

Expected Value of Process Variance

Purely random variance resulting from loss process being stochastic.

If EVPV increases, K increases so Z decreases

Question 11

Explain VHM

Answer 11

Variance of Hypothetical Mean

Variation from expected experience due to risk being different than others in its class.

If VHM increases, K decreases so Z increases

Question 12

State 3 conditions Z should satisfy

Answer 12

1. included between 0 and 1
2. Derivative with respect to E positive
   (Z increases as E increases, ie red does not decrease as risk size increases)
3. Derivative of Z/E with respect to E negative
   (Z/E decreases as E increases, ie % charge for loss decreases as risk size increases)

If k is constant, all 3 conditions automatically satisfied and Z strictly smaller than 1

Question 13

Calculate Mod for no-split plan

Answer 13

No split = no subdivision of losses

Mod = (ZA + (1-Z)E)/E = 1 + Z(A-E)/E = (A+K)/(E+K)

ISO GL Experience rating plan uses this

Question 14

Explain split plan

Answer 14

Under split plan, actual and expected losses are split between primary and excess.

Primary amount reflects claim frequency and receives most weight in experience rating calculation

Excess amount reflects severity

Works better when parameter risk (cc uncertainty driven by many small med-only and TT claims for WC) can be separated from process risk (severity volatile driven by few but very influential major PP, PT and F claims)

Question 15

Calculate Mod under Split Plan

Answer 15

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

Zp = E/(E+Kp)
Ze = E/(E+Ke)

Question 16

NCCI formula for Experience rating

Answer 16

Mod = (Ap + (1-W)Ee + B + wAe)/(E+B)

W is excess loss weighting factor
B is Ballast value

Question 17

Describe 2 other credibility issues in experience rating (ie adjustments)

Answer 17

1. Max single loss (MSL)
   Individual large losses can be capped to limit impact on experience mods (since full amount is not likely credible)
   Prevents a single random event from exerting too much influence on calculation of mod
2. Min & Max mods
   Mod itself can be capped to limit extreme values
   Ensures that experience rating adjustment is not too extreme

Z, MSL and Min/Max mods will all change with risk size (larger risks receiving more credibility and larger absolute value of caps)

Question 18

List 2 things an effective rating plan should do

Answer 18

1. Identify risk differences among similar risks
   Distinct & upward trend in manual LR
2. Adjust for them
   Std LR less dispersed and no trend

If trend in LR:
Rating plan does not enhance equity (risks with highest mods pay more P than equitable)
Rating plan does not enhance market competition (risks with higher past loss experience generate lower LR and higher profits so more desirable than risks with good past experience)

Question 19

Explain 2 methods to test Experience Rating Plan

Answer 19

1. Quintiles Test (visual)
   a. Rank risks by mod size
   b. Collapse into 5 quintiles
   c. Calculate manual LR and Std LR for each quintile
   If P not available, replace manual LR with actual losses/expected lossess and std LR by actual losses/modified expected losses
   d. Check for trends in MLR and SLR
2. Efficiency Test
   Can only be used to compare 2 or more plan
   a. Rank risks by mod size
   b. Collapse into 5 quintiles
   c. Calculate MLR and SLR for each quintile
   d. Efficiency Test Statistic = Var of SLRs / Var of MLRs
   Lower test statistic indicated better plan performance (better at adjusting premium and risks of differing experience more equally desirable)

Question 20

How do you interpret result of quintiles test

Answer 20

Ideally, you want:
1. max dispersion in MLR (show plan does a good job at identifying risk differences)
2. Flat Std LR (most important! Shows plan corrects for risk differences, ie appropriate amount of red is given to actual loss experience

Too much cred = downward trend in LR as mod increases

Too little cred = upward trend in LR as mod increases

Question 21

How do you calculate population variance?

Answer 21

Sum of (Xi - Xbar)^2 / n

Question 22

Describe the purpose of Schedule Rating

Answer 22

Pricing mechanism that allows underwriters to subjectively adjust premium for individual risks based on risk characteristics that are not otherwise reflected in premium calculation (nor in experience rating).

Used for commercial lines and WC risks.

Question 23

Discuss the potential overlap between schedule rating and experience rating

Answer 23

If a particular risk characteristic is already expected to be captured in experience, it should not be also captured in schedule rating.

A partial exception exists if risk’s experience is not fully credible (ex: very small employer). Then, may still appropriate to apply schedule credit/debit on top of having risk characteristic partially reflect in experience mod.

Question 24

Recommend a modification to experience plan when upward trend in Std LRs

Answer 24

1. Increase K (increase credibility)
2. Split plan between primary and excess losses s.t. distribution is less skewed = better predictive accuracy

Question 25

Define off-balance factor

Answer 25

Measure of weighted mod factor

Question 26

If one does not believe in Experience mod, list 2 additional informations that can be requested to confirm adequacy.

Answer 26

1. Detail of actual losses to determine whether it was pure chance or if it is very predictive of future.
2. Recent changes to risk that could impact losses. For example, if risk just implemented a new return to work program, the future losses would be expected to be lower than what experience suggests.

Question 27

In the Mod formula for split plan, interpret each term

Answer 27

Unity is manual rate

2nd is charge if actual primary losses are greater than expected

3rd is charge if actual excess losses are greater than expected

Question 28

List 2 reasons why overall experience mod (entire portfolio) might be below 1.0

Answer 28

1. Manual rates may be too high relative to expected costs, pushing down off-balance
2. Risks large enough for experience rating tend to have better loss experience than risks too small to qualify for experience rating
3. Overall mod for industry might be below 1, so insurer is just following industry

Question 29

Argue that in a competitive insurance market, rates will not be unfairly discriminatory.

Answer 29

Forces of supply and demand will push rates down for overpriced risks.

All risks will now pay rates commensurate for their exposure to loss so rates are not unfairly discriminatory.