BAIC 5 - Risk Classification and Class Plans

Question 1

Three Purposes of Risk Classification

Answer 1

1. Protect the insurance system’s financial soundness
2. Be fair
3. Permit economic incentives to operate and thus encourage the widespread availability of coverage

Question 2

What does adverse selection have to do with protecting financial solutions?

Answer 2

1. Results from economic interaction of buyers and sellers - information mismatch between insurers and customers (**main threat to financial solvency in competitive markets)
2. If an insurer does not distinguish between good and bad risks, bad risks will purchase insurance from that insurer and good risks will seek lower prices elsewhere (or forego)
   - the relatively poor experience must result in higher prices or insolvency
   - as prices increase, remaining good risks will leave the insurer and prices begin to spiral upwards

Question 3

What is the relationship between actuarial equity and ensuring fairness?

Answer 3

Actuarial equity occurs when premiums do not intentionally redistribute or subsidize payments among classes

• Differences in prices between classes should reflect differences in expected costs
• Adverse selection occurs when prices do not reflect expected costs
• Reasonable risk classification systems designed to minimize adverse selection tend to produce prices that are valid and equitable (and not unfairly discriminatory)

Question 4

How to enhance competition and insurance availability

Answer 4

Any competitive market depends on sellers’ ability to seek out and address the needs of customers

• insurers have incentive to develop classification plans that identify risks and charge an adequate and competitive premium to attract the “best” customers and remain solvent
• the ability to identify and underwrite only the best risks is known as “skimming the cream”
• competition for lower cost risks is the most intense, but insurers must also target higher cost risks to increase market penetration
• class plans are refined until the cost exceeds the benefit

Question 5

Risk Classification Principles

Answer 5

In order to achieve the three purposes of risk classification, any sound risk classification system should:

1. Reflect expected cost differences
2. Distinguish among risks on the basis of relevant cost-related factors
3. Be applied objectively
4. Be practical and cost-effective
5. Be acceptable to the public

Question 6

Exposure Base vs. Rating Variable (differences)

Answer 6

1. The exposure base, which is a proxy for the actual exposure, must have a uniform, multiplicative relationship (proportional) with the expected losses
2. The difference between the exposure base and rating variables may seem somewhat arbitrary at times (The exposure base should accurately reflect a risk’s exposure to loss and the rating variables should determine the proper rate to charge)
3. In essence, the rate per base exposure is determined by the aggregate experience of the LOB and is refined further using the rating variables for the appropriate class

Question 7

Rating Variable Criteria

Answer 7

1. Actuarial (homogeneous, credible, predictive stability - responsive yet stable)
2. Operational (practical, unambiguous, mutually exclusive, exhaustive, expense, constancy, manipulation, measurable
3. Social (causal, controllable, affordable, socially acceptable, availability)
4. Legal (varies depending on LOB, constitutional, statutory and regulatory - federal and state - restrictions)

Question 8

Rating Variable Criteria Considerations

Answer 8

1. Some criteria conflict with each other (homogeneity and credibility must be balanced)
2. Replacement variables arise when the variables correlated to loss may not be the variables that cause loss (age-sex-marital status in personal auto correlates with loss and may act as a proxy for aggressiveness and carelessness)

Question 9

Purpose of Classification Plans

Answer 9

Rather than filing rates for every combination of risk characteristics, class plans often set a “Base Rate “ and use relativities/factors or additive charges that are applied to the Base Rate

• Relative differences between classes tend to change less frequently than the rates themselves
• Relativity analyses can be performed less often

Question 10

Purpose of the Rating Manual

Answer 10

Contains the Base Rates and the rating instructions to derive the rates for each combination of rating characteristics

Question 11

Three Models for Classification plans

Answer 11

1. Additive Model - rate is determined by the sum of the base rate and the costs associated with each appropriate rating variable. Ex: Rate = B + xi + yj + zk
2. Multiplicative Model - rate is determined by the product of the base rate and the factors associated with the relative costs of each appropriate rating variable. Ex: Rate = B * xi * yj * zk
3. Mixed model - the rate is determined by a mix of additive costs and multiplicative factors. Ex: Rate = B * (xi + yi) * zk + wj

Question 12

Classification Plan Remarks

Answer 12

1. In the examples, the lowest cost cell was used to select base classes, but alternative bases exist, such as for stability purposes, use the cell with the most exposures; or for marketing, use higher cost cells to produce “discounts”
2. There are usually infinitely many particular plans that are equivalent. For example: in an additive model, the base can be decreased by some amount and all the factors for a single rating variable can be increased to offset the change
3. Obviously, the loss costs will not always work out nicely so that the rating factors can be visibly determined. There may also be many factors divided into many tiers, resulting in thousand of classes
4. Multiplicative modes are more common than additive

Question 13

Classification Method - Univariate Analysis

Answer 13

Assuming the model is correct, we can find the average class relativities using a  univariate (one dimensional) analysis. We simply compare the relative difference between each tier and the base class for each individual variable
Ex: x1 = y1 = 1.0
x2 = sum(x2) / sum(x1)
y2 = su(y2)/ sum(y1)

Question 14

Univariate Analysis - Drawbacks

Answer 14

Univariate analyses are simple and intuitive, but

1) they do not account for correlation between variables (young drivers may in general drive older cars);
2) They do not consider interdependencies between factors (pure premium differential between men and women may differ by levels of age)

Question 15

Multivariate Analysis 3 methods

Answer 15

1. Minimum Bias - introduced by Bailey and Simon in the 1960s
2. GIA - General Iteration Algorithms extend the minimum bias procedure to a broader range of models and constraint-optimization problems
3. GLM

Question 16

Accounting for correlation - 3 step procedure (Minimum Bias and GIA)

Answer 16

1. Choose a rating model (additive, multiplicative, mixed) and variables
2. Select a bias function to optimize the model (minimize difference from observed loss costs)
3. Compare optimized models with goodness-of-fit tests to pick the best one

Question 17

Drawbacks of Minimum Bias and GIA procedures

Answer 17

1. Iterative (computationally intensive)
2. Have no systematic way to determine significance of variables
3. Produce no credible range for parameter estimates
4. Lack a statistical framework to assess quality of models

Question 18

Multivariate Method - GLM

Answer 18

1. Allows explicit assumptions to be made about the nature of the insurance data and its relationship with predictive models
2. Provides statistical diagnostics regarding significant variables and validating model assumptions
3. Can be used to easily determine and correct for correlations between variables
4. More technically efficient than iterative methods
   * *GLMS are now the industry standard. Other methodologies are being developed and studied. Predictive analytics is a complex and evolving area of actuarial practice