Application of survival analysis to policy surrenders

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Policy Surrender :Application of Survival Analysis Life Insurance Industry

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Business Intelligence


Our Understanding Key Challenges

Life Insurance industry witnessed drop of 6 percent in premium income in Apr-Feb, FY 12-13 compared to same period last year.

Policy surrenders worth Rs 70k Crores in FY12-13 with contribution of private sector at 30k Crores.

ULIPS contributed to nearly 97 percent of surrenders for private life insurers.

Most insurers have long terms persistency rates in single digits (61st month plus) compared to insurers world wide at nearly 80 percent.

Increased emphasis on customer due to mis-selling concerns.

Increased IRDA regulations along with slow growth and capital requirements have put pressure on margins.

Issues in Insurance Industry Degrowth in the industry High regulation - IRDA Stringent guidelines on expenditure

on distribution (Agents etc.) Market linked plans which were the

main stay have suffered as the stock market has been volatile

Competitive pressure for Growth among private insurers

High cost of customer acquisition from distribution channels

Loss of renewal premiums from existing policies due to lapsation

Overview of Life Insurance Industry


What is Survival Analysis?

Statistical Approach designed to study amount of time between entry of observation in the system and occurrence of event related to this observation.

The object of primary interest is the survival function, conventionally denoted S, which is defined as

where t is some time, T is a random variable denoting the time of death, and "Pr" stands for probability. That is, the survival function is the probability that the time of death is later than some specified time t.


Application to Life Insurance Industry

What is the probability of my customer to persist till x years?

Which customers are more likely to surrender after lock in period of x years?

Which customer segments are more likely to surrender?

How different factors affect survival timeframe of a customer?

In context of Life Insurance industry, survival analysis involves the modeling of time to event data where event can be one time event like surrendering a policy.

This will give the company an idea on when the risk of losing a customer is high/low and what causes this.

Quantitative Analysis


Need for Survival Analysis

Insurance is still considered a push through product with most people purchasing it for tax saving and investment considerations. Poor returns from a policy push customer towards surrendering insurance product for a better performing product.

Increasing penetration of online distribution channel and simplified mode of distribution have given customers choice to surrender insurance policy and move to a competing insurance provider.

Increased competition from Banks with portfolio of substitute products and easy of transacting pose a stiff challenge for Life Insurance firms competing for share of customer savings.

Slow growth in new business premiums, increased IRDA regulations and cost of customer acquisition makes it imperative to focus on customer longetivity and retain existing stream of premium income as much as possible.

Analysis of surrenders/ cancellations is necessary to understand factors and interplay between different factors affecting surrenders.


Benefits of Survival Analysis

Survival Analysis

Increased Premium Income

1. Customer Retention 2. Customer Life Time

Value Calculation 3. Efficient, well

targeted marketing campaign

1. Identification of high longevity, high margin prospects


Survival Methodology

There are 3 approaches for executing survival analysis.

Parametric Approach

• General Linear Model • Includes predictor

variables like Gender, Income, APE, Sum Assured.

• Analysis of factors affecting survival timeframe.

Semi- Parametric

• Cox Regression Model • Handles censored

cases well. • Allows one to include

predictor variables like Gender, Income, APE etc.

• Better Analysis of various factors affecting survival timeframe and interplay between these factors than GLM.

Non-Parametric

• Life Table Method • Kaplan- Meier Method • Examines distribution

of times b/w two events like Purchase of policy and Surrender, Last Partial With drawl and surrender.

• Covers censored cases like only partial with drawl but no surrender.

• Estimate conditional probabilities at each point when event occurs and takes product to estimate survival rate at each point.


Parametric Estimation – GLM Univariate Analysis

• In Insurance, the Gompertz model best suites the data and is used in most cases –

μx = e(α + β1Xi1+ β2Xi2 + … + ε)

• For estimating the force of mortality, the following equation can be used -

μx = e(α + β1Age+ β2Gender2 + β2*Time… + ε) Where µx (force of morality) = qx/1-qx where qx is distribution continuous function of time at surrender random variable.

Model

Details Data Assumptions • Provides regression analysis

and analysis of variance for one dependent variable by one or more factors and/or variables

• Investigate interactions between factors as well as the effects of individual factors

• Dependent variable is quantitative

• Predictor variables can be categorical or quantitative.

• Normal distribution of data sample

• Constant variances


Interpretation of Results

Model Unstandardized

Coefficients Standardized Coefficients t Sig.

β S.E. Β Constant 3.645 6.765 0.539 0.612

Age -0.505 0.512 -0.518 -0.986 0.135

Gender 1.765 2.927 0.096 0.603 0.354

Age and Gender are predominating factors effecting the hazard rate which also means that survival rate differs across gender

No. Time Gender Age Status mu qx px 1 1 1 43 0 0.85928 0.461706 0.538294 2 1 1 43 0 0.128766 0.110027 0.889973 3 1 0 47 0 0.068429 0.06721 0.93279 4 1 1 67 1 0.425892 0.289871 0.710129 5 1 0 35 0 0.078491 0.073546 0.926454

Where qx is the probability of policy surrender for the customer and px is the probability of survival


Semi-Parametric Estimation - Cox Regression Analysis

Details Data Assumptions • Models time-to-event data in

the presence of censored cases

• Provides estimated coefficients for each of the covariates, giving the impact of each covariate

• Quantitative time variable • Categorical or continuous

status variable • Categorical or continuous

Independent variables

• Independent observations

• Constant hazard ratio across time

• Model equation depends on the distribution of the dependent variable. For e.g. A

parametric regression model based on the exponential distribution is,

Log[hi(t)] = α + β1Xi1+ β2Xi2 + … + ε

• For example, if we are looking to predict the time left for policy surrender of a customer,

the equation will be,

Log[hi(t)] = α + β1Age+ β2Premium + β3Income + β4Gender + … + ε

Where t is number of years before policy surrender



Variable β SE Wald D.F. Significance Exp(β)

Age 0.982 0.914 1.154 1 0.052 2.670

Gender 0.563 0.345 2.663 1 0.113 1.756

Premium 0.115 0.056 4.217 1 0.543 1.122

Age and Gender are predominating factors effecting the hazard rate which also means that survival rate differs across gender


Non-Parametric Estimation – Life Table Method

• One of the oldest methods for analyzing survival data • Kind of an “enhanced‟ frequency distribution table • The distribution of survival times is divided into a certain number of intervals • It shows a hypothetical group of individual beginning with a certain age and

traces the history of the entire group year by year until all have surrendered their policy

Details Data Assumptions • Subdivides the period of observation

into smaller time intervals • For each interval, all people who have

been observed at least that long are used to calculate the probability of a terminal event occurring in that interval

• The probabilities estimated from each of the intervals are then used to estimate the overall probability of the event occurring at different time points

• Quantitative time variable

• Dichotomous/Categorical status variables

• Categorical factor variables

• Probabilities for the event of interest is stable with respect to absolute time

• No systematic differences between censored and uncensored cases


Survival analysis is carried out using life table method for a data set using gender as a discriminating factor -


Interval Start

Hazard Time

Number entering this

Interval

Number withdrawn during this

Interval

Number exposed to risk

Number terminal

events

Proportion

terminating

Proportion surviving

Cum. Proportio

n surviving

at end

SE of cum.

surviving

0 50 0 42 0 0 1 1 0 1.0+ 50 20 22.8 5 0.3128 0.6872 0.6872 0.0592

SURVIVAL ANALYSIS TIME FOR MALE

Interval Start

Hazard Time

Number entering this

Interval

Number withdrawn during this

Interval

Number exposed to risk

Number terminal

events

Proportion terminatin

g

Proportion

surviving

Cum. Proportio

n surviving

at end

SE of cum.

surviving

0 20 0 20 0 0 1 1 0 1.0+ 20 13 5.5 2 0.4128 0.5872 0.5872 0.2631

SURVIVAL ANALYSIS TIME FOR FEMALE

The above results indicated that the proportion of surviving for males is greater than that for females


• “Estimating Survival Probabilities for pensioners of Life Insurance Corporation of India”, Hemal Pandya, Journal on Banking, Financial Services and Insurance Research, 2011

• “A new approach to analyzing persistency of Insurance Policy”, Loi Soh Loi, Wu Tuan and Robert Lian Keng Heong, Nanyang Technological University, Singapore

• “Customer duration in non-life insurance industry”, Erik Gustafsson, Mathematical Statistics Stockholm University, 2009

• “Application of Survival Analysis Methods to Long Term Care Insurance”, Rudolph Czado, Sonderforschungsbereich 386, Paper 268 (2002)

• “Survival methods for analysis of customer lifetime in Insurance“, Ana Maria Perez Marin, University of Barcelona, 2005

References


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Lokesh is working as General Partner in Spice New Investment fund. In this current role, Lokesh is responsible for identifying startup companies in Education domain and help them transform their ideas into big enterprises. Prior to that Lokesh was heading Spice Labs as its CEO. Ajay spearheads analytics division at Bharti Airtel since 2 years with responsibility for customer insights, Cross Sell up sell and other key analytics initiatives. Prior to this he was responsible creating analytics competency and successfully applied analytics in direct marketing initiatives and multiple business functions across the organization with Max Life Insurance. Before Max Life Insurance, he has worked with firms like GE in setting up analytics team for its Insurance clients and IBM and PWC on similar initiatives.

Dinesh has 12 years of strong experience in data driven analytical consulting, modeling and statistical analysis. He has held senior positions in companies like Cequity, ICICI, GE Capital, Inductis at senior positions in analytics capacity. Throughout his career has provided analytical leadership, tactical solutions and measurable delivery of financial opportunities through advanced data mining/predictive analytics solutions for various business verticals like Retail, Insurance, FMCG, Automobile, Travel & Hospitality, Telecom, Mutual Funds etc.

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Application of survival analysis to policy surrenders