1. Retention & Conversion Modeling
2004 CAS Ratemaking Seminar
March 11-12, 2004
Robert J. Walling, FCAS, MAAA

2. Objectives Why do it? What characteristics matter?
How do you model it?
What applications are there?

3. Why Do Retention Modeling?
More complete picture of your customers and prospective customers
More complete picture of pricing impacts on policy retention, conversion and premium
Better specified pricing and financial models
Allows pricing to focus on program stability and profitable growth

4. Additional Benefits of Renewal & Conversion Analyses
Can help maximize profitability
Can be used for target marketing & profitable growth
Can enhance program stability
Facilitates consideration of market conditions in realistic customer responses

5. Rate Impacts: The Current Problem
What’s the impact of a +25% rate change?
Current Loss Ratio = Loss/Premium
Proposed Loss Ratio = Loss/(Premium*1.25)
= Loss/Premium*(1/1.25)
= Loss/Premium*80%
= 80% of Curr. Loss Ratio
The only answer is -20% on the Loss Ratio!

6. The Absurdity (If a little is good…)
What’s the impact of a 200% rate increase?
Ignoring inflation momentarily.
If Current Loss Ratio = Loss/Premium
Proposed Loss Ratio = Loss/(Premium*3)
= Loss/Premium*(1/3)
= Loss/Premium*33.3%
= 33% of Curr. Loss Ratio

7. More Absurdity (What Cycle?)
In 1999, PA Med Mal loss costs decreased 13.3%
Do you think the market would respond the same way to a 10% decrease today as it did in 1999?

8. Problem with the Current Pricing Analysis World
No change in response expected from policyholders:
Likelihood of Renewal
Satisfaction of Policyholder
Book Churning/Adverse Selection
Mix of Business Shift
Consideration of Marketing/Underwriting
Satisfaction of Agent
Competition
The objective of ratemaking is to determine a future premium level that will be adequate to cover future losses. Assuming that there is historical data available, the popular method is to analyze the historical experience, project it into the future, and use this future projection to determine an indicated premium level. If there is no data available, you need to then rely on competitive information or judgment to determine what the future level of losses are going to be.
In order to come up with a projected rate level, you need to project the future levels of several underlying components. These underlying components that need to be projected include claim severities and frequencies, expenses, investment income, and loss development emergence. When you go through this entire process, what you end up with is a point estimate of the indicated rate change, or one number that gets pegged as the indication. (+10.6%, -5%, whatever that number is).

9. Why Hasn’t Retention Modeling Been Done?
Sensitive to many factors
Tough parameterization issues
New business penalty poorly understood
More pressing product development and pricing needs
“New Territory” for many actuaries
If DFA and ratemaking really taste great together, why hasn’t DFA been more widely used for ratemaking? Well, we think that there are a couple of reasons why this has been the case…
First, many actuaries and many companies have established ratemaking techniques, and as with any established process, old habits can tend to be hard to break. With traditional techniques having been used for many years, when there is no real impetus for change, change comes slowly.
Also, many of the uses that you hear DFA being used for today lead you to believe that ratemaking is one of the least of its concerns. DFA is generally thought of in analyzing future surplus levels or future profits or losses. Reinsurers have made extensive use of DFA, and they have used it more in a high level evaluation of the financial status of a primary company, usually no real emphasis on pricing.
Lastly, because DFA is still really still growing up in terms of its development and application, many actuaries still see it as a black box and may not understand what is going on inside. It becomes a little difficult to apply something that we don’t understand, so the case of DFA and ratemaking.

10. The Flexible Shape of the Retention Demand Curve
Price (P)
100% 0%
Demand Curve
R = f(P)
Renewal Rate (R)
Let’s take a graphical look at what we are talking about here. Essentially, for a risk, we have the probability of renewal shown on the y axis, and we have this probability graphed as a function of the price. So it should be no surprise that as the price increases, the probability of renewal decreases, and vice versa.

11. Retention Curve Varies by Many Characteristics
If DFA and ratemaking really taste great together, why hasn’t DFA been more widely used for ratemaking? Well, we think that there are a couple of reasons why this has been the case…
First, many actuaries and many companies have established ratemaking techniques, and as with any established process, old habits can tend to be hard to break. With traditional techniques having been used for many years, when there is no real impetus for change, change comes slowly.
Also, many of the uses that you hear DFA being used for today lead you to believe that ratemaking is one of the least of its concerns. DFA is generally thought of in analyzing future surplus levels or future profits or losses. Reinsurers have made extensive use of DFA, and they have used it more in a high level evaluation of the financial status of a primary company, usually no real emphasis on pricing.
Lastly, because DFA is still really still growing up in terms of its development and application, many actuaries still see it as a black box and may not understand what is going on inside. It becomes a little difficult to apply something that we don’t understand, so the case of DFA and ratemaking.

12. Renewal Behavior Characteristics
Renewal Pricing Change (% or $)
Competitive Position
Customer Rating Characteristics
Market Conditions
Inflation
U/W Cycle
Reinsurance Pricing
Market Capitalization

13. Renewal Behavior Characteristics
Traditional Rating Factors
Class - Multiple Policy
Territory - Limit
Limit - Account Size
Industry Group
Financial Underwriting Score (Credit, D&B)
Claims/MVR/Underwriting History
Age of Youngest Additional Driver
Satisfaction with Agent/Service
Number of Years Insured
Distribution Channel
What factors influence renewal ratios? Well first, all the factors that have been traditionally used for rating, things like age, credit, type of car driven etc. There are also some other factors that you may not have traditionally used for rating, but they become important in determining renewals. One of these factors in the change in premium. If a person’s rate goes up, they are more likely to go shopping. Likewise, if it goes down, they are less likely. What this type of analysis helps you to get at is at what point does a policyholder decide to shop? 5%? 10%? And at what point does an additional decrease in rates not really help retention rations anymore? 25%? 30%? We have guessed intuitively at this in the past, this analysis will help us get much closer to an actual insurance demand curve.
Also, to do this analysis effectively, you need some measures of the competitiveness of the market. This is a highly subjective measure, but it should not be ignored. You can use something like the difference between your price and the average price of your top three competitors. Or somehow scale your risks on a scale of 1 to 10 with one being very competitive and 10 meaning your rates are not competitive. However you decide to measure it, it does need to be measured.
Age of the youngest additional driver could be another. When people add youthful drivers, the sticker shock sometimes sends them shopping. How real is this?
How satisfied is the risk with the agent or with the service that they are getting? Again, this measure can be subjective, but there are surveys and other things that can help you get at this issue.
Number of years insured is another one, and the list can go on and on.
It is probably no surprise that these factors are identified as those that can affect renewals. However, the question is how do they interact with each other to predict the likelihood of a policyholder to renew?

14. Retention Modeling Database
Risk#
Age
Sex MS
Terr
Limit
Ren?
Comp
Score 1 25 M S 2 Y 3
500 64 F 6 17
525 4 36 5 44 N 21
600 7 55
625 8 70 9 29 10 40
656
To answer this question, you undertake a GLM analysis. This time you are not measuring frequency of accidents of pure premiums, you are predicting the probability of a policyholder renewing with you over the next policy term.
If you look at this example, essentially you are taking your traditional rating database, and adding items like those we determined earlier, as well as an indicator to tell you whether or not a policyholder renewed for the next policy term. This indicator as well as a scale measure of the competitiveness of each risk are shown here highlighted in red.

15. Multivariate Analysis Determines Renewal Probability
Risk#
Age
Sex MS
Terr
Limit
Comp
Score
P(Ren) 1 25 M S 2 3
500
.85 64 F 6
.86 17
525
.87 4 36
.80 5 44
.70 21
600
.92 7 55
625
.94 8 70 9 29 10 40
656
.91
Based on the expanded database, a GLM analysis gives you the true effect of each of the factors analyzed on credit. This analysis can then be used to come up with the probability that a specific risk will renew based on the characteristics of each particular risk. So now not only can we determine the proper rating structure based on our earlier discussions, but we can also now look at how likely a risk is to stay with us, or in other words, how long can we reasonably expect to make the potential profit on the risk.

16. Reviewing Renewal Differences

17. Competitive Position

18. Changing Market Conditions
Market conditions change over time in the historical data
Historical market conditions are not necessarily predictive of future market dynamics
How do you reflect future market conditions in a retention model?

19. Retention Modeling Database – Market Scenario Testing
Risk#
Age
Sex MS
Terr
Limit
Ren?
Market
Comp
Score 1 25 M S 2 Y 3
500 64 F 6 17
525 4 36 5 44 N 21
600 7 55
625 8 70 9 29 10 40
656
To answer this question, you undertake a GLM analysis. This time you are not measuring frequency of accidents of pure premiums, you are predicting the probability of a policyholder renewing with you over the next policy term.
If you look at this example, essentially you are taking your traditional rating database, and adding items like those we determined earlier, as well as an indicator to tell you whether or not a policyholder renewed for the next policy term. This indicator as well as a scale measure of the competitiveness of each risk are shown here highlighted in red.

20. Conversion Issues – Premium Quoted
Assumes the potential risk provides accurate information
Assumes only one quote is issued
Assumes the point of sale contact accurately retains all information
Often, records not kept for risks that don’t actually buy a policy

21. Conversion Issues – Current Premium
Assumes the insured knows actual current premium
Assumes insured knows actual current coverages
May be estimated by rate comparison engine

22. Conversion Issues – Solutions?
Look to an existing resource for conversion data
At least one Agency Management and Comparison Rating vendor can provide detailed, comprehensive conversion data with rating characteristics and competitive rank and/or competitor premiums along with “hit” statistics

23. What Applications Are There?
Retention/Conversion by class segment
Improved premium/policy/loss ratio impacts of rate changes
Lifetime Customer Value
Optimal Rate Changes/ Effective Rate Impact
Putting the puzzle together leads to some of the same applications as we talked about for the renewal and conversion analysis. Let me give a couple of examples of how this would work in practice.

24. Optimal Pricing Strategy
Risk Premium Model
Expenses
ProposedRates
Renewal/ Conversion Model
Optimization Algorithm
Most Loyal
Most Profitable
MOST VALUABLE

25. Parting Thoughts Where there is no vision, the people perish.
Proverbs 29:18
The data’s ready,
The technology’s ready,
ARE YOU READY???