Session 7, Analyzing Annuity Policyholder Behavior Using Predictive Modeling and Cluster Analysis. Moderator: Mark William Birdsall, FSA, MAAA, FCA

Transcription

1 Session 7, Analyzing Annuity Policyholder Behavior Using Predictive Modeling and Cluster Analysis Moderator: Mark William Birdsall, FSA, MAAA, FCA Presenter: Mark William Birdsall, FSA, MAAA, FCA Marianne C. Purushotham, FSA, MAAA

2 2016 Valuation Actuary Symposium Analyzing Annuity Policyholder Behavior Using Predictive Modeling and Cluster Analysis Marianne Purushotham FSA, MAAA Mark Birdsall FSA, MAAA

3 Session overview Assumption-Setting Analysis for Material Assumptions Predictive modeling techniques to support dynamic assumption development Cluster analysis to support assumption development for products without credible historical data Example Application: Applying experience for VAs with GLWBs experience in setting assumptions for FIAs with GLIBs Next Steps 2

4 Assumption Setting Analysis for Material Assumptions 3

5 Assumption-Setting Analysis for Material Assumptions In a Principle-Based Approach (PBA) environment, the bar has been raised for assumption-setting VM-31 documentation requirements are more thorough than the analogous requirements for asset adequacy analysis Document sources of assumptions as well as the assumptions themselves Set an objective standard for determining which assumptions are material Example: Use sensitivity testing results 4

6 Assumption-Setting Analysis for Material Assumptions Need to align experience studies more closely with assumptions being supported Composite industry experience must be unraveled to ensure relevance to the assumptions being set Policyholder behavior assumptions calibrated to company and/or industry experience-identify key drivers of experience Consider interactions of interdependent assumptions in dynamic functions An objective methodology is needed to develop margins Development of actual to expected ratios Consider credibility of company experience 5

7 Over to you Marianne.. 6

8 Predictive Modeling Techniques to Support Dynamic Assumption Setting 7

9 Variable and Fixed Indexed Annuities with GLWBs: Material Assumptions 1. Full Surrenders 2. GLWB Utilization 8

10 Ongoing Research Goals Explore potential predictive analytics applications that may aid in the development or validation of dynamic assumptions for modeling purposes Explore best practices in modifying information from products with credible historical experience to those with similar designs but limited historical data (ex. full surrender or utilization assumption for FIA product with GLIB) Explore approaches to incorporate information from predictive modeling exercises into dynamic assumption forms Industry peer review group providing input 9

11 Predictive Modeling Exercise Data Sources Training set is used to build the model LIMRA/SOA VA GLB Utilization Experience Reports 2012 experience data Both policy and product design factors as potential predictors Validation set is used to test the model LIMRA/SOA VA GLB Utilization Experience Reports 2013 experience data 10

12 Predictive Modeling Exercise Key Findings VA with GLWB Full Surrender Rates By Duration and Utilization Status (Data Exploration Process) Utilization: defined as taking regular withdrawals at the level of % of maximum. VA Contracts with GLWB Rates of Full Surrender by Benefit Utilization Status Status B: Irregular Partial Withdrawals Status C: Regular Withdrawals Utilizing Benefit Status A: No Withdrawals All surrender charge structures. 11

13 Predictive Modeling Exercise Key Findings Overall Model Fit Statistics Models Tested Logistic Regression Decision Tree GLM (Poisson) Benefit Utilization Status A 77% 70% 72% Benefit Utilization Status B 75% 68% 69% Benefit Utilization Status C 80% 73% 81% 12

14 Predictive Modeling Exercise Key Findings Model Validation Statistics Model Fit/% Observations Predicted Correctly Logistic Regression Status A Status B Status C Decision Tree GLM (Poisson) Logistic Regression Decision Tree GLM (Poisson) Logistic Regression Decision Tree GLM (Poisson) 77/74% 70/68% 72/69% 75/72% 68/70% 69/73% 80/76% 73/75% 81/77% Model Selection Logistic Regression Logistic Regression No Model 13

15 Predictive Modeling Exercise Key Findings Key Factors Affecting Full Surrender Utilization Status Policy Duration Market Attained Age of Policyholder Distribution Channel Surrender Charge Level In-the-Moneyness Range Policy Size 14

16 Cluster analysis to support assumption development 15

17 Cluster Analysis Common in marketing applications Identifies sub-segments of a population that naturally group Marketing Goal = develop more customized sales and marketing approaches for different/similar groups 16

18 Cluster Analysis Methods Agglomerative Hierarchical Start: Each record in the full population = single cluster Process: Combine clusters that are close by defined distance measure Iterate: Until entire population is a single cluster Select optimal cluster structure for data and purpose Euclidean Distance Clustering Start: User designates a maximum number of clusters and a seed Process: Every record in the full population is assigned to the nearest cluster based on distance to the seed Original seeds are replaced by means of the current clusters Iterate: Until the means in the cluster group no longer change Select optimal cluster structure for data and purpose 17

19 K-Means Euclidean Distance Clustering Max Number of Clusters k= 3-10 Distance Measure = Euclidean Distance Select Optimal Number of Clusters k=3-10 Describe Clusters Key Characteristics 18

20 Selecting Optimal Number of Clusters Degree of differentiation provided CCC (Cluster Convergence Criterion) Approximate Overall Expected R-squared Pseudo F Statistic Relative size/materiality of clusters Balance with additional complexity of greater number of clusters 19

21 Selecting Optimal Number of Clusters Cluster Analysis Statistics Number of Clusters Pseudo F Statistic CCC Approximate Overall Expected R 2 3 2,572, ,853, ,963, ,558, ,562, ,930,625 1, ,058,380 1, ,657,

22 Selecting Optimal Number of Clusters Relative Size/Materiality Cluster Cluster Size 1 12, , , , , , ,072 Total Population 1,951,840 21

23 Cluster Characteristics *indicates PM key characteristic Cluster Utilization Status Policy Duration Market Attained Age Distribution Channel Surrender Charge Level ITM Range Policy (AV) Size* Policy Costs Cluster Full Surrender Rate to Overall Population Level 1 High More NQ Bank/NBD More 150%+ More large AVs Extremes 2.9% 2 High Older More NQ Ind/Bank/N BD More 150%+ Extremes 2.3% 3 Career/Ind More no SC 4 High More under 60 5 Low More under 60 More under 100% Bank/NBD Higher SC More under 100% NBD Higher SC More under 100% 6 High Older NBD More No SC More 150%+ More small AVs * * * * * * * * 2.5% 2.3% 3.5% Extremes 2.3% 22

24 Over to you Mark.. 23

25 Including VAs with GLWBs Experience to Set FIAs with GLIBs Assumptions Example: VAs with GLWBs have developed a substantial amount of experience, both before and after GLWB utilization Customer clusters with respect to full surrender experience have been identified A substantial amount of FIAs with GLIBs have been sold, but the number of contract holders utilizing GLIBs is still relatively small Develop customer clusters with respect to full surrender experience 24

26 Including VAs with GLWBs Experience to Set FIAs with GLIBs Assumptions Compare the customer clusters for VAs with GLWBs with the customer clusters for FIAs with GLIBs Stratify the VAs with GLWBs experience by customer cluster Stratify the FIAs with GLIBs experience by customer cluster 25

27 Including VAs with GLWBs Experience to Set FIAs with GLIBs Assumptions For similar customer clusters between the two product types, compare experience for the three contract statuses (pre-utilization with no withdrawals, preutilization with withdrawals, and post-utilization) Test hypotheses about the relative level of surrenders by customer cluster for FIAs with GLIBs versus VAs with GLWBs Post-utilization full surrenders may be consistently low so they do not vary significantly by customer cluster or product type For FIAs with GLIBs, the contract status with respect to preutilization with withdrawals may be small enough to combine with the other pre-utilization experience 26

28 Including VAs with GLWBs Experience to Set FIAs with GLIBs Assumptions For similar customer clusters between VAs with GLWBs and FIAs with GLIBs, combine the experience data and develop dynamic full surrender functions from key predictors, including customer cluster, product type, and adding measures of benefit prominence, such as: Number of other riders on the contract besides GLWB/GLIB The rider charge for the GLWB/GLIB rider as a percentage of the total contract charges The ratio of the current account value to the sum of the premiums paid less prior withdrawals 27

29 Including VAs with GLWBs Experience to Set FIAs with GLIBs Assumptions Calibrate the dynamic functions against the experience for each product type and customer cluster Optimize model fit for each product type and customer cluster by testing different model types For dissimilar FIAs with GLIBs customer clusters, use the stratified experience for FIAs with GLIBs plus other factors learned from the other cluster experience to set the dynamic functions, including a margin for greater uncertainty 28

30 Refining Experience Studies with Company-Level Feedback In predictive modeling using industry data, the company code may be one of the significant predictors The data aggregators (statistical agents for PBR) don t have as much detailed data as the companies submitting the data, sometimes based on historical precedent regarding the submitted fields in a data call Industry-level analysis can provide a roadmap for companies to follow to a point, but companies can follow up to unpack the information embodied in the company code and improve the predictive model using data only available to them If companies report the results of this analysis to the data aggregators, additional insights for modeling at the industry level may become possible and industry experience studies made more useful. 29

31 Next Steps Develop customer clusters for FIAs with GLIBs with respect to full surrender experience Stratify the VAs with GLWBs and FIAs with GLIBs experience by customer clusters Test hypotheses about the relative level of surrenders by customer cluster and contract status For FIAs with GLIBs customer clusters similar to VAs with GLWBs customer clusters, develop dynamic full surrender functions using combined data 30

32 Next Steps For dissimilar FIAs with GLIBs customer clusters, use the stratified experience for FIAs with GLIBs plus other factors learned from the other cluster experience to set the dynamic functions, including a margin for greater uncertainty Build dynamic functions for VAs with GLWBs utilization Implementation of dynamic functions in cash flow projection models for VAs with GLWBs and FIAs with GLIBs 31