1. Agenda Background Model for purchase probability (often reffered to as conversion rate) Model for renewwal probability What is the link between price change, product mix and churn??

2. Bakgrunn Assume you have developed a new tariff model, using chapter 8,9 and 10 from the book Should you implement it «as is»? Compare new tariff with the gross tariff that exists today (gross tairff is the tariff used today adjusted for discounts and moderations) and analyze differences Evaluate consequences of the tariff used today and reconcile with the differences above: –How is the conversion rate today? –How is the renewal rate today?

3. Logistic regression – the probability that something is occuring Those with property, For example insurance Those without property, i.e., insurance Client age Product mix Geo- graphy Client age Product- mix Ge- ography Those having insurance are compared with those that do not have insurance If an explanatory variable is statistically significant it will be included in the model that predicts the probability that a client has an insurance product Name this probability p Then the modelled link between p and the explanatory variables is: This model can be used to score all customers since every customer is assigned a modelled p The idea is to prioritize those with high modelled p that do not possess the insurance product Variable 1 can for example be client age Estimated effect of variable 1

4. Purchase probability (conversion rate) villa insurance Model: Purchase probaility for villa insurance using logistic regression Database 1 (insurance data) : –Bank clients without insurance products –Insurance information is used Database 2 (bank data): –Bank clients without insurance products –Bank information is used Period: (1.5.2012-30.4.2014) Approximately 70 000 bank clients were offered villa insurance Approximately 31% accepted Model 1 is typically used for consequence analysis in connection with tariff development/assessment Model 2 is typically used by the sales department It is conceivable that a model 3 using both information sources could be developed. This was attempted but it did not outperform model 2. Model 1 and model 2 do both have 6 explanatory variables

5. Different events require separate treatment Sales to new customers Which factors drive the sales? What objects are easily sold? Which bank customers purchase villa insurance? Event Renewal What factors drive the renewal rate? How important is price change for the renewal rate? Is the churn wanted or not? Cross sales to existing customers What factors drive cross sales? Logistic regression Offer data Bank data and insurance data Respons: has purchased villa insurance (yes/no) Method and data Logistic regression Insurance data Respons: has renewed the policy (yes/no) Same as sales to new customers Is the company attractive for strategically important customers? Should the price be adjusted for specific groups? Follow up questions How does renewal vary with customer scoring? How does price sensitivity vary with customer scoring? Does the cross sales increase expected customer lifetime?

6. Purchase probability (conversion rate) villa insurance About the data Validation of model Explanatory variables in model Ranking of explanatory variables Interpretation of odds ratio for explanatory variables

7. Purchase probability villa insurance Model: purchase probability for villa insurance using logistic regression Database 1 (insurance data) : –Bank customers without property insurance products –Insurance data is used Database 2 (bankdata): –Bank customers without property insurance products –Bankdata is used Period: (1.5.2012-30.4.2014) Approximately 70 000 such customers were offered villa insurance Approximately 31% accepted Model 1 is typically used for consequence analysis in tariff development Model 2 is typically used for sales purposes A model 3 combining data from model 1 and 2 is conceivable. This was attempted but it did not outperform model 2 and was therefore discarded. Model 1 and model 2 do both have 6 explanatory variables

8. Validation of model 1(insurance data) The model was calibrated on 90% of the data (ca 63 000) The model was validated on the remaining 10% (ca 7 000) Modelled accept rate per decile Actual accept rate Mean actual accept rate

9. Explanatory variables model 1(insurancedata) Customer age Building age Building standard Use of the building Building size in square meters (proxy for insurable sum) Building type

10. Results model 1 insurancedata Wald is defined as (Estimate/sd(estimate))^2 Wald can be used to rank the importance of the explanatory variables Assume for example, as above, that all explanatory variables are statistically significant The variables customer age and building size have the highest Wald score In other words, The Wald criterion is ranking customer age and building size as the most important explanatory variables

11. Definition of odds ratio The odds ratio is the ratio of the odds of an event occuring in one group to the odds of it occuring in another group If the probabilities of the event in each of the grous are p1 (first group) and p2 (second group), then the odds ratio is: Where qx=1-px. An odds ratio of 1 indicates that the event is equally likely to occur in both groups An odds ratio greater than 1 indicates that the event is more likely to occur in the first group An odds ratio less than 1 indicates that the event is less likely to occur in the first group

12. Results model 1 insurance data The accept rate for young customers is higher than the accept rate for old customers The accept rate for semi- old is lower than the accept rate for old

13. Purchase probability villa insurance model 2 Validation of model Explanatory variables model Ranking of explanatory variables Interpretation of odds ratio for explanatory variables

14. Validation of model 2 (bankdata) The model was calibrated on 90% of the data (ca 56 000) The model was validated on the remaining 10% (ca 6 000) Modellert tilslag per decil Actual accept rate Average actual accept rate

15. Explanatory variables model 2 (bankdata) Number of products Has / has not house loan Has / has not a savings account and if yes what kind Has / has not active savings insurance Has / has not stake in mutual fund Occupational affinity(Academic, Nurse etc)

16. Results model 2 Bankdata Wald is defined as (Estimate/sd(estimate))^2 Wald can be used to rank the importance of the explanatory variables Wald can also be used to compare models Comparing the Wald levels of model 1 and model 2 it is noted that model 2 seems to have detected much stronger drivers for accept rate than model 1 Wald in model 2 is much larger than Wald in model 1 This was also indicated in the validation of model 2 where the range in accept rate between high and low deciles was considerably larger Range in accept rate model 1: 22%-45% Range in accept rate model 2: 9%-72%

17. Resultats model 1 Bankdata

18. Renewal rate villa insurance About the methodology About the data About the development of the portfolio Validation of model About the selection of time window Price sensitivity villa insurance Explanatory variables model Ranking of explanatory variables Interpretation of odds ratio for explanatory variables

19. Metodikk Renewal date Last active version before renewal version, named 1: Renewal version, named 2: Active version some time after renewal, named 3: Comparison of 1 and 2: The effect of tariff changes is measured The effect of index, change in discounts is measured Comparison of 3 and 2: The effect of exposure changes is measured (most relevant for motor insurance) Changes in deductible, change in coverage is measured Comparison of 3 and 1: The total effect of tariff change and exposure change is measured Due to 1,2 and 3 the total effect of the renewal may be decomposed into the effect of tariff changes and the effect of exposure changes Timeline

20. Renewal probability –Selection of time window for renewal: If the policy is active up to 60 days after the renewal date the policy is counted as renewed –4 years of data (all policies with tariff date from June 1, 2010) –Validation of model –Price sensitivity –Explanatory variables renewal model –Ranking of explanatory variables –Odds ratios explanatory variables

21. Fornyelsessannlighet villaforsikring Modell: Renewal probability for villa insurance using logistic regression Data: –Villas in the portfolio, active or historic, with tariff date > May 31, 2010 –Villas with good history (ca 71 000)

22. Validering av fornyelsesmodell Model calibrated on 90% of the data (appr 64 000) Model validated on the remaining 10% (ca 7 000) Persentile in renewal model Actual renewal rate Average actual renewal rate Renewal rate

23. Selection of time window The graph shows the total share not renewed in time after the renewal date for the 4 years period The graph shows that the share not renewed is highest in the renewal month and the month after The total share not renewed is 32% accumulated for the entire 4 years period Tid i måneder etter fornyelse Total share not renewed per month after renewal Not renewed Accumulated not renewed

24. Price sensitivity villa The graph shows renewal rate for different price changes for active and historic villa policies for the entire 4 years period The renewal rate is hardly changed when the price change is between -4% and 2% - reducing the premium does not reduce the churn in this case When the price change is between 2% and 14% the renewal rate is reduced with 0.5% per percent price increase When the price change is above 14% the renewal rate is reduced with 1% per percent price increase Persentil i fordeling av prisendring i fornyelsen Average renewal based on 4 years of data using 60 days window Estimated renewal rate based on the 4 year period

25. Results renewal model The customer age and price change in renewal are the most important variables Whether the customer has had a claim or not is not so important compared to the other variables

26. Results model 1 The renewal is increasing with increasing age The renewal is increasing with increasing building size The renewal is lowest for those with at least 5% price reduction (who are these?) The renewal is highest for those with price increase between 2% and 12% The renewal is higher for those that did not have claims (improvement potential in claims settlement department?)

27. Do main products like car and villa increase expected customer lifetime? How price sensitive is the customer? tid 1/5-2010 1/5-20111/5-20121/5-20131/5-2014 villa car Only villa Only car Both villa and car How many are in the portfolio here ? How many are remaining? And here? Price increase villa Price increase car Large Very large Significant Moderate Significant Moderate Negativ Moderate

28. The churn is declining with time and depending on product mix The churn is highest for those with villa and not car The churn is lowest for customers with villa and car The churn is highest the first year after the starting point and declining afterwards Are these results robust? Villa not car Car not villa Both villa and car Yearly churn for different product mix Churn

29. Hypothesis: the churn is highest the first year Observe those who are in the portfolio one year later, i.e., 1/5-2011. How many are still in the portfolio after 1,2 og 3 years? The churn is highest for those with villa and no car The churn is lowest for customers with villa and car The churn is highest the first year and declining aftwerwards Villa not car Car not villa Both villa and car Yearly churn for different product mix Churn

30. Resultats from 3 starting points Starting point: 1/5 2010 Starting point: 1/5 2011 Starting point: 1/5 2012 Churn villa not carcar not villa both villa and car

31. Summary churn, product mix and price change In periods with severe price increases the churn is higher This result is reconcilable with the results from the renewal rate model. This indicates a quite strong link between churn and price change. Those with villa and no car have the highest churn, those with car and no villa have medium churn and those with villa and car have the lowest churn. Independent of product mix the churn measured in time after starting point seems to be declining. (the churn 1 year after the starting point is highest, 2 years after a little lower etc) The difference in churn between the product mix groups is falling as a function of time after the starting point The results indicate that customers with both villa and car are less price sensitive than customers with only one main product