WHAT POLICY FEATURES DETERMINE LIFE INSURANCE LAPSE? AN ANALYSIS OF THE GERMAN MARKET

Transcription

1 WHAT POLICY FEATURES DETERMINE LIFE INSURANCE LAPSE? AN ANALYSIS OF THE GERMAN MARKET MARTIN ELING DIETER KIESENBAUER WORKING PAPERS ON RISK MANAGEMENT AND INSURANCE NO. 95 EDITED BY HATO SCHMEISER CHAIR FOR RISK MANAGEMENT AND INSURANCE NOVEMBER 2011

2 What Policy Features Determine Life Insurance Lapse? An Analysis of the German Market Martin Eling, Dieter Kiesenbauer * Abstract Considering the largest dataset ever used for this purpose (2.5 million contracts, 8.9 million policy years), we analyze the impact of product and policyholder characteristics on lapse in the German life insurance market. The sample period covers two periods of market turmoil that we incorporate in our generalized linear models. The results show that product characteristics such as product type or contract age and policyholder characteristics such as age or gender are important drivers for lapse rates. Our findings improve the understanding of lapse drivers and might be used by insurance managers and regulators for value and risk based management. 1 INTRODUCTION In this work, we analyze the impact of product and policyholder characteristics on lapse and surrender in the German life insurance industry using generalized linear models (GLMs). 1 A proper understanding of lapse drivers and the underlying dynamics is important for insurance managers and regulators. Lapse influences an insurer s liquidity and profitability (see Kuo et al., 2003; Prestele, 2006). Firstly, the insurer might suffer high losses from lapsed policies due to upfront investments for acquiring new business (Pinquet et al., 2011). Secondly, the insurer faces the loss of future profits from lapsed contracts. Thirdly, the insurer might face adverse selection with respect to mortality and morbidity. 2 Fourthly, the insurer might be exposed to a liquidity risk when forced to pay a surrender * Martin Eling is professor of insurance management and director at the Institute of Insurance Economics at the University of St. Gallen, Kirchlistrasse 2, 9010 St. Gallen, Switzerland (martin.eling@unisg.ch). Dieter Kiesenbauer is with the Institute of Insurance Science at the University of Ulm, Germany (dieter.kiesenbauer@uni ulm.de). 1 Lapse and surrender both refer to the termination of an insurance contract before maturity, but there is a slight difference between these two terms (see, e.g., Kuo et al., 2003; Gatzert et al., 2009). While lapse refers to the termination of policies without payout to policyholders, surrender usually indicates that a surrender value is paid out to the policyholder. In accordance with Renshaw and Haberman (1986) and Kuo et al. (2003), the term lapse is used throughout to refer to both surrender and lapse. This is consistent with standard measures of lapse as they typically include lapsed policies as well as surrendered ones. 2 For example, customers in poor health condition might be less likely to lapse a contract including death cover as they will hardly find comparable insurance cover at the same premium level. Analyzing long term care insurance, Pinquet et al.

3 value for many lapsed policies at the same time; otherwise a more conservative investment strategy might be used to ensure a sufficient liquidity at any time which reduces investment returns and hence affects the profitability adversely. The importance of lapse is especially discussed in the field of valuation and management of embedded options in life insurance contracts. Historically, the right to lapse a life insurance contract was not explicitly taken into account in the pricing process (Gatzert and Schmeiser, 2008). The possibility to lapse a contract, however, constitutes an implicit option present in life insurance contracts and its value can be quite substantial (see, e.g., Albizzati and Geman, 1994; Grosen and Jørgensen, 2000; Bacinello, 2003; Gatzert and Schmeiser, 2008). The decline of Equitable Life in the U.K. which was related to pension policies including guaranteed annuity options further intensified this discussion (see O Brien, 2006). In the 1990s, market annuity rates in the U.K. dropped significantly and fell below the guaranteed level making that option particular valuable for the customer. Therefore, insurers need to pay attention to all embedded options, including the policyholder s option to lapse a life insurance policy. Also regulators have identified lapse as one of the major risk components of life insurance companies which needs proper monitoring and management. For example, under the new European Union regulatory framework Solvency II lapse risk constitutes the largest sub module in terms of solvency capital requirement within the life underwriting risk module accounting for almost 40% of the capital requirement in this module (see EIOPA, 2011, p. 77/78). 3 The life underwriting risk itself accounts for almost 20% of the total capital requirements constituting the second most material component in terms of capital requirements behind market risk. The existing empirical literature on lapse can be distinguished based on the explanatory variables considered. The first set of literature uses environmental characteristics including macro economic indicators and company data. Initially, only the impact of interest rates and unemployment on lapse has been studied, referred to as interest rate and emergency fund hypotheses (see, e.g., Dar and Dodds, 1989; Outreville, 1990; Kuo et al., 2003). This work has been extended by Kim (2005a,b), Cox and Lin (2006), and Kiesenbauer (2011) considering additional economic indicators (such as gross domestic product and capital markets development) and company characteristics (including company size and legal form). The second set of literature uses single contract data to assess the impact of product and policyholder characteristics on lapse. So far, only a limited number of such analyses are available. Renshaw and Haberman (1986), Kagraoka (2005), Cerchiara et al. (2009), and (2011) find that policyholders lapsing contracts have better health histories compared to their peers continuing the contracts. 3 Under Solvency II the capital requirement for the lapse risk sub module is calculated as maximum of three stress scenarios which are broadly defined as follows (see CEIOPS, 2010, p , for details): (1) a long term decrease of lapse rates by 50%; (2) a long term increase of lapse rates by 50%; and (3) a mass lapse event of 30% of all policyholders.

4 Milhaud et al. (2010) cover the Scottish, Japanese, Italian, and Spanish life insurance markets. Using generalized linear models, these analyses indicate that factors such as policy duration, calendar year, policyholder age, or method of payment significantly influence lapse. Our study contributes to existing literature in four ways: Firstly, we consider the largest data set ever used for such purposes (2.5 million contracts, 8.9 million policy years). The data is obtained from a large German life insurer and includes seven different product categories including traditional and unit linked products. We are thus able to investigate whether different products exhibit different lapse behavior, in particular comparing traditional and unit linked products. The existence of such differences has not been studied empirically so far. Secondly, this is to our knowledge the first empirical study for the German life insurance market analyzing the impact of product and policyholder characteristics on lapse. 4 So far, only the relationship between surplus participation rates and lapse rates has been discussed by Cottin et al. (2007), Eling and Kiesenbauer (2011), and Kiesenbauer (2011) using market data. Thirdly, the analyzed time period from 2000 to 2010 is of particular interest since it incorporates two phases of crisis (the stock market plunge from 2001 to 2003 and the 2008 financial crisis) which can be integrated in the analysis. Finally, the available data address some of the shortcomings mentioned in previous studies. Having detailed information on the date of policy inception, exact policy durations can be calculated, i.e., not only in terms of calendar years (see Renshaw and Haberman, 1986). Furthermore, the data are already split into disjoint and homogeneous product categories such that grouping is not necessary (see Cerchiara et al., 2009). Moreover, we extend the existing literature by considering remaining policy duration, distribution channel and supplementary cover, which are all significant lapse drivers as we will show throughout our analysis. 5 Regarding the main results, we find that all considered product and policyholder characteristics have a statistically significant impact on the lapse rate development, but the magnitude of the effects varies. The largest variations are observed for calendar year, contract age, remaining policy duration, and premium payment (single vs. regular). The direction of impact is consistent with the existing literature (Renshaw and Haberman, 1986; Kagraoka, 2005; Cerchiara et al., 2009; Milhaud et al., 2010), except for product type which has only a limited effect on lapse rates. We extend the existing 4 Lapse is usually measured in terms of sum insured in the German market. Additionally, we consider lapse rates in terms of number of contracts and regular premiums as robustness measures (see Eling and Kiesenbauer, 2011). The modeling approach is the same as for the existing studies in this field, i.e., generalized linear models, which allows comparing our results with the existing ones. 5 The existing studies indicate further possibly relevant characteristics identifying different client segments based on socioeconomic information (e.g., policyholder income, area of residence, or tenant vs. homeowner). Due to strict regulation of data protection, insurers are only allowed to ask for information relevant for the risk assessment and pricing. Therefore, just like in all other existing studies such information is also not available in the German market. Also due to confidentiality reasons, actual lapse rates are not presented in this paper. Instead, similar to Cerchiara et al. (2009), we restrict to relative effects when presenting the results.

5 knowledge in that we show that the remaining policy duration, distribution channel, and supplementary cover are significant lapse drivers. Finally, we consider interactions between one fixed variable and all other characteristics in order to assess whether there exist differences for the different levels of product categories, distribution channels, supplementary cover, or premium payment. Again we find that the impact on lapse rates for all policy(holder) characteristics is very consistent across product categories. All these results are helpful for insurance managers and regulators, especially in the context of risk and value based management. The remainder of this paper is structured as follows: Section 2 provides an overview of the empirical literature regarding life insurance lapse. Section 3 describes the methodology and data. Section 4 presents and discusses the results of our analyses. We conclude with Section 5. 2 EMPIRICAL LITERATURE ON LIFE INSURANCE LAPSE The existing empirical literature studying lapse drivers can be subdivided into two classes depending on the characteristics considered as explanatory variables (see Figure 1). While the first set of literature focuses on environmental specifics (i.e., macro economic indicators or company characteristics), the second part focuses on product and policyholder features. Regarding the first stream much more research has been published since publicly available data can be used. The number of papers in the second stream is smaller and more recent since individual data on policies are needed, which are typically treated highly confidential. Considering the first stream of literature, the research on environmental root causes of life insurance lapse focused on the so called interest rate and emergency fund hypotheses for a long time. The interest rate hypothesis assumes that lapse rates are negatively related to internal rates of return, e.g., surplus participation, and positively related to external rates of return, e.g., market interest rates or stock returns (for details see Dar and Dodds, 1989; Kuo et al., 2003). The emergency fund hypothesis conjectures that personal financial distress forces policyholders to lapse their contracts in order to access the surrender value (see, e.g., Outreville, 1990). These two hypotheses have been studied empirically, e.g., by Dar and Dodds (1989), Outreville (1990), and Kuo et al. (2003) with focus on different life insurance markets and product types. It is hence not surprising that the results are not consistent, in particular as the variable specifications vary widely (see Kiesenbauer, 2011, for a more detailed discussion). These studies focus on information on interest rates or unemployment (as indicator for adverse economic conditions), but do not take into account other economic factors (e.g., stock returns, gross domestic product), company characteristics, or product and policyholder information.

6 Kim (2005a) provides the first empirical study considering a broader set of economic explanatory variables including, e.g., economic growth rates and seasonal effects. Moreover, the contract age since policy inception is considered as product characteristic. Kim (2005a) models aggregate lapse rates of a South Korean life insurer for four different product categories (endowment, annuity, protection plan, and education) using the logit and complementary log log model, respectively. The results indicate that policyholder lapse behavior indeed depends on additional exogenous factors beyond interest rates and unemployment rates. Using a similar set of explanatory variables to analyze single premium deferred annuities in the U.S., Kim (2005b) and Cox and Lin (2006) arrive at similar conclusions deploying a logit and tobit model, respectively. Additionally, Cox and Lin (2006) indicate that the Poisson and the negative binomial regression model are more appropriate to model lapse behavior, but these models require individual (i.e., single contract) data rather than aggregate lapse rate data. All these models, i.e., logit, complementary log log, tobit, Poisson, and negative binomial, belong to the same broad class of models, the so called generalized linear models. Kiesenbauer (2011) analyzes lapse rates in the German life insurance market using the same modeling approach as Kim (2005a). The author employs market data to study lapse behavior with respect to economic indicators and additional company characteristics such as company age, company size, or legal form. The analysis is based on publicly available market data and does not take into account any product or policyholder characteristics, except for the product split distinguishing endowment, annuity, term life, group, and unit linked business. The results support the above conclusion that other factors beyond interest rates and unemployment influence lapse behavior, including company characteristics. 6 Empirical literature analyzing life insurance lapse with respect to product and policyholder characteristics is rather limited. This is probably due to the fact that lapse data are treated highly confidential by most life insurers. Therefore, only aggregated lapse rate information is usually publicly available in most life insurance markets. An analysis of product and policyholder characteristics requires a more detailed data split which can only be provided by life insurers. The first empirical study of Renshaw and Haberman (1986) dates back to the mid 1980s, but only recently the topic attracts more attention. This is driven by accounting and regulatory changes which require an appropriate assessment of lapse. Table 1 provides an overview of the empirical literature comparing time period covered, sample size, products and policyholder characteristics considered, and modeling approaches. 6 Additionally, Kiesenbauer (2011) examines to which extent the interest rate and emergency fund hypotheses do hold for the German life insurance market. Both hypotheses do not hold for traditional, i.e., not unit linked, life insurance products, while they are supported when unit linked business is considered.

7 Renshaw and Haberman (1986) is the only work analyzing multiple companies based on a data set provided by the former Scottish Faculty of Actuaries. It is also the only work considering different product categories. All other existing studies focus on data of a single life insurer and consider only one product category. All existing empirical studies, which analyze the impact of product and policyholder characteristics on lapse behavior, use generalized linear models to assess the relevant contract features and policyholder characteristics. 7 Generalized linear models have been applied to a wide range of problems in actuarial science. Using these models in non life insurance pricing, in particular for motor insurance (see, e.g., Brockman and Wright, 1992; Ohlsson and Johansson, 2010), might be the most prominent example. Other fields include, e.g., survival modeling, multiple state models, and reserving (see, e.g., Renshaw and Haberman, 1996; Mosley, 2004). An exhaustive overview of the applications of generalized linear models in actuarial science can be found in Renshaw and Haberman (1996) or de Jong and Heller (2008). Generalized linear models are an extension of the widely used linear regression models and provide a particular rich class of models which are neither restricted to linear relationships nor to the usual normality assumption. The pioneering work in applying generalized linear models to life insurance lapse is Renshaw and Haberman (1986). According to Cerchiara et al. (2009), generalized linear models are especially powerful in investigating the relationship between the available explanatory variables and the observed response variable, i.e., lapse behavior in this case. GLMs allow assessing the direction and magnitude of the impact on the lapse behavior caused by the variability of single parameters, which is the main topic of this paper. Due to the different data samples and, in particular, the different explanatory variables, the results of the existing empirical studies analyzing product and policyholder characteristics are not directly comparable. The results are, however, consistent to the extent that all existing studies identify several significant explanatory variables and indicate their importance for lapse behavior. Renshaw and Haberman (1986) find an additional significant interaction between policy type and duration of policy meaning that the lapse rate not only depends on single factors but also on the combination of factors. All characteristics considered in Kagraoka (2005) are identified as significant including the change in unemployment rate being an economic indicator. Latter result supports the above mentioned emergency fund hypothesis. Such effects are captured only indirectly in the other studies using calendar year information. The study of Cerchiara et al. (2009) shows the importance of policy duration, calendar year, and product class. Milhaud et al. (2010) find the biggest surrender risks for policies including a fiscality constraint, i.e., surrender charges only apply for a certain part of the 7 Milhaud et al. (2010) consider additionally the CART model which does not belong to the class of generalized linear models.

8 contract duration. 8 As soon as the contract has reached the point when the policyholder can surrender without penalty, the lapse risk increases significantly. Other relevant risk factors include policyholder age or method of payment (i.e., regular vs. single premiums where regular premiums are further divided into monthly, bi monthly, quarterly, half yearly, and annual installments). 9 3 DATA AND METHODOLOGY 3.1 Data The German supervisor BaFin distinguishes three types of lapse rates: (1) early lapse representing the counseling and product quality; (2) late lapse assessing the insurer s service quality during the policy term; and (3) total lapse measuring portfolio growth, i.e., to which extent is lapsed business offset by new business written. The corresponding lapse rates are calculated in terms of sum insured. The early lapse rate is defined as ratio of all lapses without surrender value over new business written. The surrender value and thus this ratio strongly depend on the product design, e.g., term life insurance has a very limited surrender value for the entire contract duration. The late lapse rate is defined as ratio of all lapses with surrender value plus all policies made paid up (i.e., the customer stops or reduces premium payments but does not lapse the contract) over sum insured of the entire portfolio at the beginning of the calendar year. 10 Again this ratio depends on the product design. The total lapse rate is given by the aggregated sum insured of early and late lapses divided by the average volume of business in force during the calendar year (i.e., half of the portfolio sum insured at the beginning and at the end of the calendar year). Early, late, and total lapse rates in the German life insurance industry are displayed in Figure 2. These rates represent the entire market, as no further breakdown by product categories is available. The higher volatility of the early lapse rate fluctuating between 7 and 17% can be explained by the different denominator compared to late and total lapses. Sum insured is far less for new business compared to total business in force. The exceptional fluctuations for the early lapse rate in 8 This is a specific contract feature which does not exist in all insurance markets. In particular, surrender fees always apply in case of lapsing before maturity in the German life insurance market. 9 When discussing lapse, the existence of the secondary market for life insurance might affect customer behavior in certain product categories. Policies are purchased by life settlement providers, market makers, or auctioneers. Those contracts are placed in closed funds or trusts for life settlement securitization or kept in the buyer s own books (see Gatzert, 2010). Certain life insurance policies, which would be lapsed otherwise, are continued through the existence of a secondary market. Thus, lapse rates and surrender profits will decrease in markets with increasing relevance of the secondary market (see Gatzert et al., 2009). The importance the secondary market is still limited for the German life insurance market as it enters a state of stagnation (see Gatzert, 2010). Therefore, neglecting the secondary market for our analysis should have limited influence on the results. 10 This consideration is in contrast to Renshaw and Haberman (1986). Their definition of lapse only includes the premature termination of contracts (with or without paying a surrender value), but explicitly excludes conversion to a paid up amount or premium reduction.

9 1999/2000 and 2004/05 were driven by announcements of the German federal government to enforce the tax treatment for certain life insurance policies from the beginning of 2000 and 2005, respectively. This led to a kind of closing sale significantly increasing the sales volumes in 1999 and 2004 and decreasing sales volumes in the following years. For the life insurance industry, premium volume and number of contracts belong to the key performance indicators and, hence, are in general more relevant than sum insured. Thus, it is not uncommon to calculate lapse rates in terms of lapsed regular premiums or lapsed number of contracts. Regular premiums, however, do not take into account single premium business. Number of contracts lacks completely any volume information, i.e., contracts with small and high premium are treated identically. The sum insured instead takes into account both single premium business and reflects contract size. 11 This explains the use of sum insured by the German supervisor. In this work, we measure lapse rates using sum insured according to the BaFin definitions (differentiating between early 12, late, and total lapse), but also consider regular premiums and number of contracts. This allows investigating whether significant differences exist. The data analyzed in this paper have been provided by a German life insurer 13 and cover the time period 2000 to 2010 including only contracts which have been newly issued during this time. The data set comprises seven different product types: term life insurance, endowment, (traditional) annuity, unit linked annuity, Riester pensions, (traditional) Rürup pensions, and unit linked Rürup pensions. While the first four products are common for many insurance markets, the latter three are specific to the German market. Riester and Rürup products constitute state aided private pension schemes. 14 Furthermore, as the unit linked business accounts for one third of all policies, we are able to assess whether there exist significant differences between these products and traditional business 11 The sum insured, however, varies widely for different life insurance products. For instance, the sum insured of term life insurance is usually much higher than for, e.g., disability insurance. 12 Contrary to the BaFin definition, we model the early lapse rate in terms of total business in force instead of using only new business. This changes the absolute lapse rate level, but should have only a limited impact on the relative effects. Using generalized linear models for the analyses (see Section 3.2) and focusing on new business neglects completely all early lapse events which do not occur within in the first year after policy inception which might bias the results heavily. 13 Lapse rate information is treated highly confidential by life insurance companies. Therefore, confidentiality needs to be maintained throughout the paper. We are thus not able to show absolute lapse rates. Instead we present effects relative to a reference level, i.e., how much smaller or higher is the lapse rate for a certain level (e.g., endowment) compared to a reference level (e.g., traditional annuity). This still allows to draw conclusions on the importance of the considered product and policy(holder) characteristics and the magnitude of the corresponding effects. Additionally, we cannot indicate the distribution mix of the company as it potentially allows identifying the company. 14 As the population in Germany and most developed countries is aging, the benefits of the social pension insurance are cut. Riester and Rürup pensions have been introduced in 2002 and 2005, respectively. Eligible beneficiaries for the Riester pension include employees being mandatory enrolled in the German statutory pension insurance, recipients of wage compensation benefits, and tenured civil servants. The detailed eligibility criteria, however, are complex (see, e.g., Börsch Supan et al., 2008). The Riester subsidization consists either of tax funded contributions (basis allowance plus children allowance) or an income tax refund. These subsidies depend on certain criteria and additional restrictions apply for such contracts (for details see Börsch Supan et al., 2008). Rürup pensions are subsidized private pensions especially targeting people that are not mandatory insured in the German statutory pension insurance (e.g., self employed people) and hence are not eligible for the Riester subsidies. Contributions are tax deductible and the accumulated capital needs to be repaid as a monthly, life long annuity (see, e.g., Corneo et al., 2010).

10 (endowment, annuity). Beyond the above outlined product split the following policy and policyholder information is available: Calendar year Strictly speaking, the calendar year constitutes an exogenous variable not being directly related to an insurance contract. The lapse behavior of customers, however, usually also depends on exogenous factors (see the above discussion on the emergency fund and interest rate hypotheses). The consideration of calendar year effects allows, for instance, to assess the existence of systematic deviations in lapse rates for certain years, e.g., in the stock market plunge from 2001 to 2003, driven by the enforced tax treatment starting in 2005, or during and following the 2008 financial crisis. Contract age Having the inception date of the policy, the contract age since inception is calculated in years. A contract age of t means that a policy is in its t th contract year. As the data set only includes polices written from 2000 onwards, the maximum observed contract age is eleven. This variable allows drawing conclusions on the counseling and service quality of the insurer, but also might reflect changes in customer needs. Remaining policy duration The termination date of the main insurance contract allows to calculate the remaining contract duration. It is measured in remaining years, i.e., a duration of t means that the contract will expire within the t th year from today. The customer can modify the contract term and, hence, the remaining contract duration changes accordingly. Policyholder age / sex The data include only information on age and sex of the person insured but not the policyholder. In all cases where the person insured is older than 18 years at policy inception, it seems likely that the person insured is actually the policyholder. Therefore, we restrict our analysis to those policies which only slightly reduces the extent of the data set. Distribution channel The data allow to identify both the distribution channel when the policy is issued as well as the currently responsible distribution channel. The considered life insurer uses a multi line distribution strategy as most German life insurers do. Due to confidentiality reasons, we only distinguish four distribution channels which are used by most life insurers in the German market, i.e., tied agents, brokers, banks, and other. For our analysis we focus on the current distribution channel since it might be more relevant than the original one for the lapse decision. 15 Supplementary insurance It is possible to combine a main insurance contract with additional covers. In the present data set supplementary covers include term life insurance, disability insurance, 15 All analyses have also been performed using the original distribution channel. As changes of the responsible distribution do not occur very often, the results do not change much. In particular, the observed effects and conclusions still hold when the original distribution channel is considered. Detailed results are available upon request.

11 accident insurance, and surviving dependents insurance. As these supplementary covers can be arbitrarily combined, the number of possible combinations is high. In order to reduce complexity, we only model whether a policy includes any supplementary cover or not, but do not distinguish between the number and/or type of supplementary cover(s). 16 It is possible that some of the other policy(holder) characteristics vary for main cover and supplementary cover (e.g., policyholder age/sex or policy duration). We always focus on the main insurance contract to determine the value of the corresponding characteristic. A contract with supplementary cover is counted as single contract since usually only the entire contract can be lapsed. For premiums and sum insured, we always consider the total amount including all additional covers. Premium payment We distinguish between single premium business and contracts with regular premium payments. The data do not distinguish between different regular premium installments, e.g., monthly, quarterly, or semi annually (see Milhaud et al., 2010). Most customers pay their premiums monthly or annually in the German life insurance market. Changes in the underlying policy(holder) characteristics for a single contract as well as premium exemptions or reductions are identified comparing year end values for the entire portfolio from one year to the next. For simplicity reasons, we assume that contract modifications always take place at the anniversary of the contract. It might be interesting to investigate seasonal effects (see Kagraoka, 2005). This requires, however, monthly or quarterly data which tremendously increases the cost of data provision. Some characteristics change during the life time of an insurance contract, e.g., policyholder age, contract age, or remaining policyholder duration. Therefore, the data need to be prepared for the analysis as follows. Each contract is split into all possible combinations of considered product and policy(holder) characteristics. We denote such a combination of characteristics as model point. A sample model point is: endowment (product type), 2005 (calendar year), 5 (contract age), 35 (remaining policy duration), 25 (policyholder age), broker (distribution channel), no (supplementary cover), male (policyholder sex), and regular (premium payment). For each model point, the exposure of all contracts in the portfolio needs to be determined, i.e., the time (measured in years on a daily basis) all contracts belong to the corresponding model point. Finally, we determine the number of early and late lapse events for each model point. Each lapsed contract is counted as lapse in the model point which represents the product and policy(holder) characteristics at the lapse date. 16 Some combinations of main insurance and supplementary cover are only available in a limited number of cases. Having a reasonable number of observations for each characteristic is a prerequisite to run the generalized linear model; otherwise the results might be strongly biased.

12 The data set considered covers 2.5 million contracts and almost 8.9 million contract years. It, hence, represents the broadest study in terms of sample size compared to all existing analyses (see Table 1). Number of contracts, contract years, and early/late lapse events are displayed for all product categories in Table 2. The contract years and early/late lapse events are further broken down by calender years. As only new business written from 2000 onwards is considered, the number of contract years is strongly increasing during the first years and stabilizing at later years. Riester and Rürup pensions have been introduced in 2002 and 2005, respectively. Therefore, these products did not exist in previous years. Term life insurance accounts only for about 5% of the entire portfolio. The split between early and late lapse is different for term life. As this product does not accumulate major savings, most lapse events are classified as early lapse even if the lapsed contract has been in force for several years. 3.2 Methodology We use generalized linear models (GLMs) to analyze lapse rates depending on the considered product and policy(holder) characteristics. This class of models has been introduced by Nelder and Wedderburn (1972) as extension to linear regression models weakening the restrictive assumptions of those models (i.e., normally distributed errors, constant variance, and additivity of explanatory variables). As GLMs have been widely applied in actuarial science (see, e.g., Renshaw and Haberman, 1996), we only provide a short summary of relevant aspects for our analysis. McCullagh and Nelder (1989) discuss theory and application of GLMs in detail. -1 The generalized linear model is defined as E(Y) = g ( X), where Y represents the vector of dependent variables, E(.) refers to the expected value, and X denotes the matrix of observed values of the considered characteristics. Y is called the random component of the GLM. Its elements Y u are assumed to be independent having a distribution which belongs to the exponential family (e.g., Normal, Binomial, or Poisson). The linear predictor X is called systematic component where denotes the regression coefficients. The relationship between random and systematic component is given through the monotonic and differentiable link function g. In our case, the random component Yu models the number of lapses for the model point u of the considered product and policy(holder) characteristics. The possible values for each product and policy(holder) characteristic are referred to as i i 0,, n 1 Var v and are displayed in Table 3. Var Var determines the considered characteristic and n Var represents the total number of values for each characteristic.

13 PT PP Let ˆ ˆ ˆ T x u x,, x represent the vector of observed values for model point u. Modeling all characteristics categorically, we consider the vector i i 0,, n 1 Var x which is defined as Var x Var i 1 0 if v else Var i xˆ Var The value Var v 0 is referred to as reference level of the corresponding characteristic. In order to have a common reference level for all analyses, we use the value that has the largest exposure and represents at least one early and one late lapse event. 17 For instance, no Riester pension has been terminated early in calendar year 2009 or As those empty cells bias the results, they are not taken into account. 18 In order to reduce the number of regression coefficients to be estimated, the reference levels of all characteristics are combined with the intercept of the linear predictor. The linear predictor can thus be written as follows: X 0 CA CA 1 1 DC 1 x x PT 1 DC 1 x PT 1 x CA CA DC 3 x PT 6 DC 3 x PT 6 x PD PD 1 1 SC 1 x CY 1 SC 1 x CY 1 PS 1 PD 46 x PS 1 x CY 10 PD 46 x CY 10 x PP PP 1 1 x PA PA 1 1 PA 48 x PS 48 According to Cerchiara et al. (2009), the logit link g(x) = log(x/(1 x)) along with binomial error terms is the typical approach for modeling lapse (or retention or new business conversion) rates. The resulting modeling results are, however, not easily interpretable. The Poisson model with g(x) = log(x) which is favored by Kagraoka (2005) provides a reasonable approximation, if (1) the response variable is close to zero (being usually the case for lapse rates) and (2) the model output is used qualitatively rather than quantitatively, i.e., the focus is rather on the identification of relevant lapse drivers and not on predicting future lapse rates accurately (which fits our research focus as outlined in Section 2). 19 As each model point defines a specific combination of the product and policy(holder) characteristics considered, each contract has a unique path through a certain subset of all possible model points. The time each contract belongs to a certain model point u is used to define the exposure (time) e u. Latter is the sum of the time that each contract belongs to the model point u (in years, possibly zero) taking into account all contracts in the portfolio. Introducing additionally the lapse rate lr u, we can rewrite the GLM as E(Y u ) = e u lr u = exp( X). This yields 17 The reference level for the distribution channel is chosen arbitrarily in order to maintain confidentiality. 18 Removing data might also bias the results. As the considered data set is very large and only a negligible amount of data is removed, we assume this effect to be very limited. 19 The binomial model (mentioned by Cerchiara et al., 2009) and the negative binomial model (mentioned by Kagraoka, 2005) have also been analyzed. These modeling approaches require count data instead of exposure data. Compared with the Poisson model on count data, the parameter estimates of the Binomial model are almost identical, while those of the negative binomial model are different to a certain extent but still yield qualitatively identical conclusions. Detailed results are available upon request.

14 lr u PT PT PT PT PP PP x x x exp( 0 ) exp exp 1 1 e u Adj.factor for product type Adj.factor for Baselevel premium payment i.e., the lapse rate depends on a multiplicative structure. The base level, which corresponds to the lapse rate of the joint reference level for all considered characteristics, is adjusted for each product and policy(holder) characteristic if it differs from the reference level. Note that for each model point Var and each characteristic x 0 for at most one i 1,, n 1. i Var The above discussion focuses strictly speaking on the consideration of number of contracts. The same line of argument can, however, be applied for lapsed regular premiums and lapsed sum insured assuming that each single Euro can be lapsed or not. Thus, the same modeling approach is used, except that the exposure is measured in Euros instead of years. The exposure of regular premiums and sum insured for the model point of a single contract is determined as product of timely exposure (in years) multiplied by yearly premium and total sum insured, respectively. So far, only single effects of the explanatory variables have been considered (e.g., product category or calendar year), but not the combination of different variables, e.g., effects of calendar year 2008 for Riester pensions. These so called interactions allow to take into account not only changes within one explanatory characteristic, but also combinations of two or more characteristics (see, e.g., Renshaw and Haberman, 1986; Cerchiara et al., 2009). We focus on interactions between only two factors as interactions increase the model complexity and, hence, increase the run time of the corresponding GLM analyses tremendously. 20 The same reference levels are considered for the generalized linear model including interactions as for the model without interactions. 4 RESULTS We present the results of two model specifications in the following. The results of the generalized linear model (GLM) without interactions are discussed in Section 4.1. The results including interactions between product category, supplementary cover, premium payment, and distribution channel, respectively, with all other characteristics (as described in Section 3.2) can be found in Section GLM without interactions 20 For each interaction of two factors, the number of additional variables is calculated as product of the number of levels for each considered characteristic less one. For instance, the consideration of interactions between product category and distribution channel introduces 18=(7 1) (4 1) additional regression coefficients to be estimated.

15 Table 4 displays the results of the GLM estimations without interactions for total lapse considering three different measures for lapse rates, i.e., number of contracts, regular premium volume, and sum insured. The resulting lapse rate levels differ for the different measures. The effects of the considered product and policy(holder) characteristics relative to the reference level are, however, very consistent as shown in Table 4. Most of the considered variables are consistently significant at the 1% level and the coefficient estimates are close to each other. The parameter estimates represent the natural logarithm of the multiplicative effect relative to the reference level. For instance, a value of 0.15 for endowment (using number of contracts to measure exposure) means that the lapse rate for endowment policies is exp(0.15) = 1.16 times the lapse rate of annuities representing the reference level; in other words, the lapse rate for endowments is 16% higher than the lapse rate of traditional annuities. In Table 4 we focus on total lapse, but similar results do hold for early and late lapse. These results are available upon request. In the following, we discuss the results of each characteristic in detail. Due to the above observation, we focus on the consideration of number of contracts. The results are visualized using a similar format compared to Cerchiara et al. (2009). The solid, dashed, and dotted line represent the estimated regression coefficients for total (as displayed in Table 4), late, and early lapse, respectively (left axis). The estimate for the reference level is set to zero as it is included in the intercept term (see Section 3.2). The columns represent the exposure in million years as volume measure for the different levels of the characteristic (right axis). The GLM does only provide results for such classes for which at least one lapse event is present. Classes which do not contain any lapse event need to be removed from the analysis. The exposure for the analysis of early lapse (light gray boxes) is hence usually less than the exposure for late and total lapse (additional dark gray boxes). We use the same scale for both axes in all figures to facilitate the comparability of the magnitude of the effects across different characteristics. Whenever possible, our results are compared to the results of the existing studies. Product type The total lapse rate does not vary much across product categories (see Figure 3). Compared to the lapse rate of traditional annuities, which constitutes the reference level, the lapse rates of the other products are between exp( 0.37) = 0.69 for traditional Rürup pensions and exp(0.15) = 1.16 for endowments, i.e., from 31% less to 16% higher. Endowments experience the highest lapse rate followed by Riester pensions. While this result might be expected for Riester pensions (due to the complicated product introduction and the recent discussion regarding high acquisition and administration cost of those products), it is rather surprising for endowments. Latter effect might be explained by the restriction to new business written since 2000 (neglecting the large portfolio of policies in force for a long time and hence less prone to lapse). This indicates, however,

16 that customer lapse behavior for endowments might be changing in the future. The results regarding traditional and unit linked products are mixed. While unit linked annuities have a lower lapse rate, unit linked Rürup pensions experience higher lapse rates compared to their traditional counterparts. Compared to annuities, Rürup pensions experienced so far reduced lapse rates. Rürup pensions are designed for self employed people and are state aided. As those customers might be better financially educated and the federal subsidies might be lost in case of lapse, this might explain the lower lapse rates. The potential loss of federal subsidies, however, has no observable impact on Riester policies. The significantly lower early lapse rate for Riester policies is due to the different treatment of acquisition costs in these policies. They have to be equally distributed over the first five years of the contract term. Therefore, a surrender value is built up much earlier such that a lapse in the first contract years is counted as late lapse instead of early lapse, i.e., it is a reclassification of lapse which has only a minor impact on the overall lapse rate level. This effect is reversed for term life insurance. These products provide almost pure risk cover and have only a very limited savings component. Therefore, most of these policies do not possess a surrender value when they are lapsed. Most lapses are, hence, classified as early lapse. Product types or groups are also considered by Renshaw and Haberman (1986), Cerchiara et al. (2009), and Milhaud et al. (2010). The results of Renshaw and Haberman (1986) indicate that term life insurance has higher lapse rates than endowment policies and unit linked products suffer the most lapses. These results are different to our results, which might be credited to the differences in the underlying products, i.e., life insurance in the U.K. and Germany might not be directly comparable. In particular, the guarantee levels of unit linked products might have changed. While these policies possessed initially almost no guarantee (Renshaw and Haberman (1986) use data from 1976), today these products usually include a variety of guarantees, e.g., investment guarantees at contract maturity (see, e.g., Gatzert et al., 2011). Cerchiara et al. (2009) categorize the analyzed portfolio consisting exclusively of savings policies into reasonably homogeneous product groups, but not providing further details on the exact methodology. They find that the product group has a strong effect varying from 56% to +421% relative to the reference product group. Four product groups of endowment policies are distinguished by Milhaud et al. (2010) based on profit participation (with vs. without) and premium payment (single vs. regular). As there are no and only two lapse events for non profit policies with regular and single premiums, respectively, the regression result seem not to be representative and reliable for these groups. When comparing with profit policies, single premium business is lapsed less often than regular premium business. Calendar year The development of lapse rates with respect to calendar year is displayed in Figure 5(a). The total lapse rate was 66% lower in 2000 compared to Lapse rates have been steadily

17 increasing from 2000 to 2004 in the years of and following the stock market plunge. They remained stable from 2004 to 2007, but increased strongly in 2008 and 2009 (+22% and +20% compared to the previous year), the year of and following the 2008 financial crisis. Lapse rates begin to deteriorate again in 2010 reaching almost the 2008 level. Therefore, increasing lapse rates might be a consequence of economic crises which is in line with the emergency fund hypothesis and which is argued by German life insurers (see, e.g., Lier, 2010). While the development of the late lapse rate is almost identical compared to total lapse, the development of the early lapse rate is different. Developing similar until 2007, the early lapse rate constantly falls from 2007 to This might also be related to the different treatment of acquisition cost as discussed above. Due to court rulings, this cost has to be distributed over the first contract years instead of deducting it completely from the first premium(s). This yields (higher) surrender values from the contract beginning such that lapsed policies are classified more often as late lapse which is also in line with the fact that the late lapse rate increases more strongly than the total lapse rate. Additionally, new business volume (of regular premium business) has decreased following the 2008 financial crisis and thus early lapse volume might have been further reduced. Cerchiara et al. (2009) is the only study also considering calendar year effects from 1991 to In general, lapse rates have been constantly falling until the end of the 1990s. In the following years, the lapse rate has been increasing reaching the maximum in This result is consistent with our findings. The lapse rate increase in the Italian data, however, is not constant since it is disrupted with two peaks in 2000 and The authors, however, do not provide any explanation for these exceptional developments. Contract age The differentiation of early and late lapse might seem odd when contract age is considered. The difference between both lapse rates is the (non )existence of a surrender value. As discussed in Section 3.1, this is not necessarily related to the contract age and depends on product design and regulation. Therefore, it still makes sense to consider these lapse types separately for contract age. Total and late lapse rates are highest for young policies and are afterwards steadily decreasing with contract age (see Figure 5(b)). Most policyholders realize quickly whether they really need a purchased policy and have been advised appropriately by the salesperson. If the customer, for instance, cannot afford the regular premium payments, the customer might lapse the contract within the first years after policy inception. If a product really fits the policyholder s need, it is less likely that the policy will be lapsed. Life insurance savings might then only be used in case of personal financial distress according to the emergency fund hypothesis (see, e.g., Dar and Dodds, 1989; Kuo et al., 2003). The development of the early lapse rate is slightly different, as it first decreases and

18 increases again. This is driven by term life insurance policies. 21 As those products are almost pure risk insurance, no surrender value is built up. Any lapse independent of contract age is, hence, classified as early lapse. Moreover, term life insurance is often used to backup mortgages. As soon as the mortgage is repaid, the insurance coverage might not be required anymore explaining the lapse rate increase with increasing contract age. Contract age is considered as explanatory variable in all existing empirical studies (see Renshaw and Haberman, 1986; Kagraoka, 2005; Cerchiara et al., 2009; Milhaud et al., 2010). The results are very consistent with our findings as the general development is similar. The lapse rate is highest for the first contract years and then gradually decreases. Remaining policy duration The relationship between remaining policy duration and lapse rates is displayed in Figure 5(c). Apart from policies with a very short remaining duration, lapse rates increase with increasing remaining duration. This effect is in line with the above observation regarding contract age. Policies having a long remaining duration have usually been issued in the last year(s), while policies with shorter remaining durations are already in force for a longer time period. The different behavior of policies with a remaining duration of less than five years is driven by early lapse events which are related to term life insurance. As mentioned above, these policies do not build any material surrender value and, hence, might be terminated premature when the insurance coverage is not needed anymore. Remaining policy duration has not been considered as explanatory factor in existing studies. Policyholder age When considering the relationship between age of the policyholder and lapse rates in Figure 5(d), the magnitude of the age effect is limited as the corresponding curves are relatively flat. Three age groups can be distinguished: policyholders until age 25, policyholders between 26 and 40, and policyholders older than 40. Policyholders in the middle group have an almost constant lapse rate at the level of the reference age The lapse rate for the youngest policyholders is significantly below, but steadily increasing. Such policies might be initially sponsored by the policyholder s parents. When the family circumstances change (e.g., marriage or birth of children) the needs might change and the insurance premiums are not affordable any longer. Lapse rates for the oldest age group are steadily increasing until age 60, before decreasing again. For products with a savings component, a possible explanation for this effect is that especially people older than 50 might have difficulties to find a new job in case of unemployment. According to the 21 When the same analysis is performed excluding term life insurance, the early lapse rate decreases quickly to zero within the first four contract years. Results are available upon request. 22 As the estimates of the corresponding regression coefficients are close to zero, the corresponding variables are not statistically significant different from zero.

19 emergency fund hypothesis (see Outreville, 1990), those persons might access their life insurance savings as emergency funds. Other customers in the late 50 s might choose to retire early and use their life insurance savings to bridge the gap until the payments from the social pension scheme start. The following decline might be driven by two effects. First, the likelihood of immediate access to life insurance savings (due to unemployment or early retirement) decreases with age. Second, single premium business might increase in this age group (i.e., paying a lump sum into a deferred annuity to receive later a life long annuity). As this business experiences less lapse (see below), it might yield reduced lapse rates. The policyholder age is also considered as explanatory factor in all existing empirical studies (see Renshaw and Haberman, 1986; Kagraoka, 2005; Cerchiara et al., 2009; Milhaud et al., 2010). However, the modeling approach differs. Cerchiara et al. (2009) is the only work considering the current policyholder age as we do, while all other studies focus on the underwriting age of the policyholder, i.e., age of the policyholder at policy inception. We decided to use the current policyholder age as it reflects the current policyholder status and, hence, seems to be more relevant for the lapse decisions. All other studies use age buckets combining up to 40 years instead of considering effects for each age. Moreover, the considered range of age values differs across studies. Therefore, our results are not directly comparable to the existing findings. The results of the existing studies are consistent as all find decreasing lapse rates with increasing policyholder age (group). Distribution channel Most German life insurance companies use different distribution channels including tied agents, brokers, and banks, among others, but have one main distribution channel. The insurer providing the data follows a similar strategy. 23 As displayed in Figure 6(a), early, late, and total lapse rate are close to each other for the different distribution channels considered. Compared to the tied agent channel, the lapse rate in the bank channel is 25% higher, while it is 6% less for brokers. Existing literature on the coexistence of different distribution channels discusses two main hypothesis: the product quality hypothesis and the market imperfection hypothesis (Trigo Gamarra, 2008). The product quality hypothesis conjectures that the service quality, among others, differs between distribution channels. Trigo Gamarra (2008) and Eckardt and Räthke Döppner (2010) find evidence of an increased service level among independent agents (i.e., brokers) for the German market. Our results thus support the existing literature studying the product quality hypothesis in Germany. Although the product quality hypothesis has only been studied for dependent and independent agents, it might also apply to the bank channel. Bank agents might focus on the fulfillment of short term sales targets, while tied agents should focus to maintain a long term customer relationship. This increases the risk of miscounseling and, hence, lowers service quality in 23 Due to confidentiality reasons, we cannot unveil the concrete distribution mix, in particular the weight of the different channels. This information might allow reconciling the underlying company.

20 the bank channel providing a possible explanation for the higher lapse rate. Other distribution channels include, e.g., branches or direct. Distribution channels have not been considered as explanatory factor in existing studies. Supplementary cover Contracts including supplementary cover(s), e.g., disability insurance, exhibit higher lapse rates than contracts without those additional covers. The effect is displayed in Figure 6(b) and amounts to +16% for total lapse, +18% for late lapse, and +7% for early lapse. On the one hand, this result might be surprising since one might expect that policies with additional covers experience less lapse, as it gets more expensive (if possible at all) to obtain identical insurance coverage for the additional covers, e.g., by purchasing stand alone disability insurance at a higher entry age. On the other hand, the premium for policies including additional cover is higher than for stand alone policies. In case of financial distress, it is more likely that a policyholder is forced to lapse such a product bundle. Additionally, Pinquet et al. (2011) believe that customers insufficient knowledge of insurance products can cause lapse. Product bundles including insurance covers which are not necessary might be more often sold to customers being not that familiar with insurance matters. Due to the usually higher premium of such contracts, those are more likely to be lapsed afterwards when the customer discovers that the product bundle does not fit the policyholder s needs. Finally, the product bundle might include unnecessary or duplicate insurance coverage. As supplementary covers often cannot be lapsed separately, the customer might decide to lapse the entire contract. Existence of supplementary insurance covers has not been considered as explanatory factor in existing studies. Policyholder sex The total lapse rate for female is 9% less than for male (see Figure 6(c)). The early lapse rate is 17% lower, while the late lapse rate is only 6% lower. This might be explained with a higher risk aversion of female in financial matters (see, e.g., Halek and Eisenhauer, 2001). Females might be less willing to purchase insurance products they do not completely understand or if they are not sure whether they can fulfill long term premium payments. This finding of a reduced lapse rate for females is in line with Kagraoka (2005) who argues that housewives only purchase life insurance if the household income is sufficiently large. Kagraoka (2005) finds that the lapse rate of female policyholders is 13% less than for male customers (based on the Poisson model; for the negative binomial model the effect is 11%). Due to data availability, only Kagraoka (2005) analyzed the impact of gender on lapse rate, although all studies discuss the relevance of this factor.