ASOP25.Credibility

Reading: Actuarial Standards Board of the American Academy of Actuaries, “Credibility Procedures”, December 2013.

Synopsis: This standard of practice covers key terminology and provides guidance on the development and selection of a credibility procedure. It also reminds actuaries of the necessary disclosures which should be made when working with credibility topics.

Study Tips

This is a short and straightforward reading that's probably only one question on the exam or crops up as a subpart of only a handful of questions. You also likely use the content a lot in your day-to-day work so should already be quite familiar with it. Read the wiki once and then skim it occasionally to keep it fresh.

Estimated study time: 1 Hour (not including subsequent review time)

BattleTable

Based on past exams, the main things you need to know (in rough order of importance) are:

• Three considerations when selecting or developing a credibility procedure.
• Knowing when the guidance applies and what disclosures an actuary should consider making.
• How to choose relevant experience, including how to handle the situation when your subject experience is contained within the proposed relevant experience.

Questions from the Fall 2019 exam are held out for practice purposes. (They are included in the CAS practice exam.)

reference	part (a)	part (b)	part (c)	part (d)
Currently no prior exam questions

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In Plain English!

The Actuarial Standard Board (ASB) issued Actuarial Standard of Practice No. 25 (ASOP 25) to provide actuaries with guidance when they are performing professional services related to selecting, developing or applying credibility procedures in their work.

Let's begin with a review of some key terminology used throughout the standard. Unlike ASOP 25, we'll introduce it in the order it's used.

Credibility

A measure of the predictive value in a given application that the actuary attaches to a particular set of data. Predictive value refers to the statistical value of the data set for its intended purpose - not how well the data can be used to predict future outcomes.

Subject Experience

A specific set of data drawn from the experience under consideration.

• For example, an actuary may have three accident years of data to use when building a model. They may divide it into two sets via a 70/30 train/test split. The training dataset would then be the subject experience.

Relevant Experience

Sets of data which include data other than the subject experience, that, in the actuary's judgment, are predictive of the parameter under study. Relevant experience may include subject experience as a subset.

Alice: "Let's look at a couple of examples I came up with for relevant experience."

1. An actuary pricing Homeowners water peril losses could use Condominium Owners water peril losses as a complement of credibility (relevant experience). Homeowners and Condomium Owners likely have very similar coverage terms for water peril losses so the Condominium Owners water peril losses are likely predictive of the Homeowners water peril losses.
2. An actuary pricing Renters insurance in a state may use Renters experience from neighboring states.
3. Rating California Private Passenger Automobile territories. Here, the subject experience is the insurer's own zip-code level experience. The relevant experience is the zip-code level experience published by the California Department of Insurance which is derived from statutory statistical reports from all insurers operating in that line of business.

Alice: "The subject experience for the first two examples is not contained within the relevant experience. However, in the third example the subject experience is contained within the relevant experience because all insurers report. More on this later."

Credibility Procedure

A process which involves either:

• The evaluation of subject experience for potential use in setting assumptions without reference to other data. Or,
• The identification of relevant experience and the selection and implementation of a method for blending the relevant experience with the subject experience. This includes improving the estimate of a parameter under study through combining relevant experience with subject experience.

Alice: "Check out the following two examples which I came up with to illustrate the concept of a credibility procedure for each of the bullet points above."

• Evaluating/choosing a suitable p value for use in a generalized linear model (GLM) so you can assess whether or not a variable should be included.
• Determining a suitable complement of credibility (relevant experience) and how much weight should be given to the subject experience vs the complement.

Full Credibility

The level at which the subject experience is assigned full predictive value. This is often based on a chosen confidence interval. The more precise you want to be, the greater your full credibility standard as you need more data to be more confident.

Alice: "Remember 1,082 claims for full credibility from Exam 5? That's based on a 90% chance of being within 5% of the true value for the parameter under consideration. That's what we're talking about here."

Risk Classification System

A system used to assign risks to groups (risk classes) based upon expected cost or benefit of the coverage or services provided.

Risk Characteristics

Measurable or observable factors or characteristics which are used to assign each risk to a risk class in a risk classification system.

Question: When does the guidance apply?

Solution:

The guidance applies when an actuary is:

• Required by law to evaluate credibility — for example, when filing a rate-level indication.
• Evaluating the credibility of subject experience or communicating that credibility has been evaluated in accordance with ASOP 25 — for instance, when calculating a full credibility standard for use in a one-way analysis.
• Blending subject experience with other relevant experience — such as when developing a rate-level indication using experience from neighboring states.
• Representing data as statistically or mathematically credible — for example, when advocating to include or exclude a variable from a generalized linear model (GLM).

Analysis of Issues and Recommended Practices

Selection or Development of a Credibility Procedure

You should use an appropriate credibility procedure when determining whether your subject experience is fully credible or how much credibility should be given to it when blending with relevant experience. Your choice of credibility procedure may be limited by applicable law and vary by practice area.

Question: Identify three considerations when selecting or developing a credibility procedure.

Solution:

1. Is it expected to produce Reasonable results?
2. Is it Appropriate for the intended use or purpose?
3. Is it Practical to implement when taking into consideration both the cost and benefit of using it?

Alice: "A great way to remember this is 1,082 gets a bad RAP. Is 1082 reasonable? — Probably not; it may need a severity modification. Is it appropriate? — Maybe for large risk classes but almost certainly not for individual risk rating. Is it practical? — Yes, but you can likely improve on it with minimal effort."

Credibility procedures should consider both the subject experience and relevant experience (the complement of credibility). The relevant experience is generally viewed as fully credible so you should make sure it actually is!

Key Consideration: Does older experience have the same predictive power as more recent experience? Alice: "This is a great question which leads nicely into Mahler.Credibility. Mahler uses baseball win records over time to demonstrate that (for baseball at least) older records are less predictive of future experience than recent experience."

Selection of Relevant Experience

It's important to use care and professional judgment when selecting and using relevant experience. The relevant experience should have similar characteristics to the subject experience — if it doesn't and cannot be adjusted to be similar then don't use it!

Question: Identify four characteristics that an actuary could consider when determining if relevant experience is suitably similar to subject experience.

Solution: Relevant and subject experience should have similar:

• Demographics,
• Coverages,
• Frequency,
• Severity

Question: What should I do if my subject experience is contained within my proposed relevant experience?

Solution: You should consider whether the subject experience is a material part of the relevant experience. Generally speaking, we want the subject experience to not be a material part of the relevant experience. If it is a material part then you should probably look for another set of relevant experience to avoid double counting / placing excessive weight on a portion of your book.

Alice: "I once worked for a company who wrote business in 44 U.S. states but had 52% of their business in California. It made no sense for them to use a countrywide complement of credibility because it made all of their indications for small states look like the rate need in California. Their solution was adjusting the relevant experience to be countrywide excluding California. Then, no other state made more than 10% of the complement which seemed more reasonable."

Question: What should I do if there is no relevant experience available?

Solution: This is where you must exercise your professional judgment. You need to take into account the available subject experience — if your subject experience is nearly fully credible then you likely don't need to worry as much about the relevant experience as you would if your subject experience had next to no credibility. Sometimes you're left with assuming no change/an indicated relativity of 1.000 is the only reasonable relevant experience you can use.

Professional Judgment and Credibility

Applying credibility procedures is not always a precise mathematical process. Sometimes it's acceptable to use your judgment to assign full, partial, or zero credibility to the subject experience without using a rigorous mathematical model.

Homogeneity of Data

Both the subject experience and relevant experience should be relatively homogeneous. Both types of experience may benefit from additional refinement to improve the homogeneity of the data and consequentially its predictive power. There is a trade off between homogeneity and the volume of data — increasing homogeneity often leads to less data being available.

Communications and Disclosures

Question: Briefly describe four types of disclosures an actuary may be required to make when working with credibility procedures.

Solution: An actuary should disclose the following (if applicable) when working with credibility procedures:

• The credibility procedures used and any material changes from prior credibility procedures.
• If any material assumption or method was prescribed by applicable law.
• If the actuary relies on other sources and disclaims responsibility for any material assumption or method selected by a party other than the actuary.
• If the actuary has materially deviated from the guidance of this ASOP.

Appendices

Alice: "ASOP 25 contains two appendices (background and comments). In our opinion you're definitely not going to be tested on the comments or the memo transmitted with the ASOP. However, Appendix 1 — Background and Current Practices — could conceivably be fair game even though it contains the following note: 'This appendix is provided for informational purposes and is not part of the standard of practice.'

The syllabus makes no mention about excluding appendices, so I recommend skimming this part of the wiki assuming you're not short on time."

Credibility is way of recognizing the need to properly balance concerns about stability and responsiveness. Too much credibility can lead to being overly responsive to change (little stability) while too little credibility provides needed stability but can result in being left behind because you're not responding to the signals.

Classical credibility procedures make an assumption about the form of the underlying probability distribution. Based on this distribution, a measure of volume is calculated so that the probability of the subject loss experience being within a specified percentage (r) of the expected value is equal to a specified parameter (p). The measure of volume is the full credibility standard. The classic example is 1,082 is being within 5% of the mean 90% of the time.

Limited Fluctuation Credibility assumes claims follow a normal distribution and assigns partial credibility based on the square root of the ratio of actual claims to the full credibility standard.

Empirical Credibility Procedures make no reference to an underlying distribution. Instead, they measure the statistical relationships of the subject experience to its mean and to comparable experience from prior experience periods.

Bayesian Credibility Procedures blend an a priori assumption about the underlying probability distribution with statistical information about the subject experience to produce a posterior distribution which reflects both. The a priori distribution may be based on relevant experience.

Bühlmann Credibility is an application of Bayesian credibility. Partial credibility is assigned via [math]\frac{n}{n+k}[/math] where n is the volume of subject experience and k is a parameter derived from the variances of the subject and relevant experience.

Credibility theory is being incorporated into generalized linear models and other statistical models. Credibility may be estimated based on the statistical significance of parameter estimates, model performance on a holdout (test) data set, or the consistency of these over time.

When performing credibility procedures in a ratemaking/pricing context, if the actuary assumes a frequency distribution, it's common to adjust the required sample size to reflect variation in claim size (or other factors).

Lastly, prospective experience rating formulas assign credibility to the actual experience of a single risk or group of risks. This subject experience may be subdivided into different components such as primary and excess losses. It's likely that each component should have its own, different, level of credibility.

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