Dynamic Policyholder BehaviourMatthew Edwards

Chief / Senior Actuaries’ WorkshopWednesday 5 October

06 October 2016

Contents

06 October 2016 2

• Introduction

• Technique

• Examples

• Dynamic relationships

Introduction

06 October 2016

Regulation (Solvency II Delegated Acts)

06 October 2016 4

Article 26 – Policyholder behaviourWhen determining the likelihood that policyholders will exercise contractual options, including lapses and surrenders, insurance and reinsurance undertakings shall conduct an analysis of past policyholder behaviour and a prospective assessment of expected policyholder behaviour. That analysis shall take into account all of the following

a) how beneficial the exercise of the options was and will be to the policyholders under circumstances at the time of exercising the option;

b) the influence of past and future economic conditions;

c) the impact of past and future management actions;

d) any other circumstances that are likely to influence decisions by policyholders on whether to exercise the option.

The likelihood shall only be considered to be independent of the elements referred to in points (a) to (d) where there is empirical evidence to support such an assumption

Regulation (more)

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• Article 31 – allow for ‘dependency between two or more causes of uncertainty’

• Article 32 – take into account ‘all factors which may affect the likelihood that policy holders will exercise contractual options or realise the value of financial guarantees.’

• Article 34 – ‘insurance and reinsurance undertakings shall use a method to calculate the best estimate for cash flows which reflects such dependencies.’

Dynamic policyholder behaviour – does it exist?

6

Source: WTW research and annual reports

Financial crisis

Lapse rates for selection of leading life insurers

13 1 3

0% 50% 100%

Type of model used ParametricdistributionTime series

Expert judgement

6 1 3 2

0% 20% 40% 60% 80% 100%

Parametric distributionNormal

Logistic

Lognormal

Other

Willis Towers Watson Risk Calibration Survey 2016

10

1

Primary source of historical data

Internal External

1

3

5

1

Start year of historical data

Pre-1990 1990 - 20002000 - 2005 2006 - 2010

5

2

2

4

10

13

13

11

Separate risk factors to lapse up and down

Expenses stressed under lapse stress

Different stresses for the first and subsequent years

Lapses modelled dynamically under stressed market conditions

Yes No

Do you use the following when modelling lapses?

15 of 17 firms have separate risk factors for lapse and mass lapse

7

Other reasons to model behaviour better

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More granular assumption setting of lapse/surrender behaviour can improve• Accuracy of cash flows (unmodelled heterogeneity leads to drift over time)

• Accuracy of pricing assumptions (and minimisation of adverse selection risk)

• Understanding of policyholder behaviour

• Targetting of profitable customers (ie marketing)

Generally ties in with a more ‘customer-centric’ view

Contents

06 October 2016 9

• Introduction

• Technique

• Examples

• Dynamic relationships

EventModelFactors

What is a GLM?

Age

Duration

Benefit size

Lifestyle

Market level

GLM Probability of surrender

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GLMs — typical structure

1. What the maths means in practice (example):Probability of surrender in year =Base level for observed population ×Factor 1 (based on duration) ×Factor 2 (based on postcode group) ×Factor 3 (based on amount) ×Factor 4 (based on age) …

2. Each factor is a series of multiplicative coefficients3. All factors are considered simultaneously, allowing

for correlations in the data automatically4. The GLM finds the factor coefficients that will best fit the data5. Method allows for the nature of the random process involved, and provides information about the

(un)certainty of the result6. Robust and transparent — a standard technique for many years in GI, and over five years in life7. For surrender analyses, common to use a different mathematical form (logit transform)

Postcode Group

Multiplier

Group A 0.86

Group B 0.92

Group C 1.00

Group D 1.04

Group E 1.16

© 2016 Willis Towers Watson. All rights reserved. Proprietary and Confidential. For Willis Towers Watson and Willis Towers Watson client use only. 11

Contents

06 October 2016 12

• Introduction

• Technique

• Examples

• Dynamic relationships

Lifestyle (from postcode)

Moneyness of guarantee/option

Other policies

Factors typically found to be predictive Age

GenderPersonal data

Duration

Benefit amount

Options / riders?Policy data

Level of financial market

Bonus historyMarket data

Distribution

Company data

TIME PERIOD FACTOR

(EG CALENDAR YEAR)

13

0

5

10

15

20

0

0.5

1

1.5

2

2.5

3

3.5

Rescaled Predicted Values - Death_Bens

One-way

GLMresults

Effect of death benefit on surrender/lapse (in conjunction with effects of all other factors)

Larger death benefits make policies less likely to surrender, but this effect would not be seen with a normal analysis

14

Effect of Acorn Lifestyle groups on surrender/lapse

0

10

20

30

40

50

60

0.4

0.6

0.8

1

1.2

1.4

A B C D E

Rescaled Predicted Values - New Acorn_Group

15

Incorporating external data

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• We can incorporate external data and investigate its usefulness in creating a predictive model

• For instance, we can define a factor based on the difference between the declared fund yield of the insurer in each year and the guarantee attaching to the products

• This example relates to a block of savings business analysed over a 15-year period

• Later, we see how market returns in each year can be used

17

0%

-7%-8%

20%

28%27%26%

18%

-14%

16%

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

fondo-minimo

Log

of m

ultip

lier

0

500000

1000000

1500000

2000000

2500000

<=-0.64% -0.64% 0.86% 0.86% 1.28% 1.28% 1.64% 1.64% 1.86% 1.86% 2.64% 2.64% 3.5% 3.5% 4.57% 4.57% 7.01% >7.01%

Exp

osur

e (y

ears

)

Oneway relativities Approx 95% confidence interval Unsmoothed estimateP value = 0.0%Rank 2/4

Factor based on {yield – guarantee}

Excess of yield over guarantee level

Guarantee bites

Happy policyholders

Grumbly

???

Incorporating external data (2)

Predicting retirement age

Case study The following slides show some indicative results from a recent project investigating the

influence of factors on at-retirement policyholder behaviour Examples of factors found to be predictive: gender, age, policy type, policyholder wealth, time

since last payment to the policy, calendar year (and various others) The influence of financial markets (looked at in terms of equity markets and bond yields) was

borderline predictive Slides are shown with axes / values ‘blued out’

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19towerswatson.com

Age

Rescaled Predicted Values - 19 Age

-200

0

200

400

600

800

1,000

0%

1%

2%

3%

4%

5%

6%

7%

8%

46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

Model Prediction at Base levels

Model Prediction + 2 Standard Errors

Model Prediction - 2 Standard Errors

Comparison against market measures (1)

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• GLM results for calendar year compared against a range of plausible market measures

– First graph shows a straight comparison (so an interesting result would be market lines with similar or opposite trend to green GLM line)

– Second graph shows ‘GLM result / market index’ so an interesting result would be a generally horizontal line

• The relationships were also considered allowing for time lags (these showed no difference in predictiveness)

Comparison against market measures (2)

0

2

4

6

8

10

12

14

16

18

0

0.5

1

1.5

2

2.5

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

Exposure

Model Prediction at Base levels

ASX Index

FTSE All Share Financials Index

FTSE Actuaries 15y Gilt Yield

Merrill Lynch 15y+ Sterling AA Corporate TRRIndex

Merrill Lynch 15y+ Sterling AA Corporate PRRIndex

Calendar year

0

0.5

1

1.5

2

2.5

3

3.5

4

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

ASX Index

FTSE All Share Financials Index

FTSE Actuaries 15y Gilt Yield

Merrill Lynch 15y+ Sterling AACorporate TRR IndexMerrill Lynch 15y+ Sterling AACorporate PRR Index

Comparison against market measures (3)

Calendar year

Contents

06 October 2016 24

• Introduction

• Technique

• Examples

• Dynamic relationships

25

• An interaction (dependency) relates to how one risk factor varies according to the level of another (different from correlation)

• The ability to model interactions in GLMS can assist in understanding how policyholder behaviour varies with market movements

• The following graph uses the product guarantee * calendar year of exposureinteraction to show how the surrender rate seems to vary according to high or low guarantee levels

• We superimpose a graph of relevant bond yields

Dynamic policyholder behaviour

26

Surrender trends compared with investment market trends

0,0

0,5

1,0

1,5

2,0

2,5

2000 2001 2002 2003 2004 2005 2006 2007

Year

Valu

e of

yie

ld a

nd s

urre

nder

s re

lativ

e to

200

4

1.50-2.5%

4%

Market

Dynamic policyholder behaviour (2)

Calendar year

What does a dynamic policyholder behavior assumption look like?

06 October 2016 27

• From the previous case study / graph:– For low guarantees, market decreases lead to increased surrenders in a fairly linear

manner

– For high guarantees, market decreases seem to lead to decreased surrenders –presumably because policyholders value their guarantees more

• These relationships could reasonably give us the following dynamic adjustments to projected policyholder surrender rates to use in stochastic models:

– for high guarantee products, multiply rates by {yield / 3.6%}

– for low guarantee products, divide by 3 * {yield / 3.6%}

– sensible to add floors/caps to these algorithms (reduced effect beyond the limits)

What does a dynamic policyholder behavior assumption look like? (2)

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Triggers level of interest rates profit sharing rates compared to competitors level of equity index financial strength of an insurer

Usage in selected markets (Germany, Austria, France,

Italy) – common market approach for with-profit business

Cap for lapse increases

Floor for lapse decreases

2nd trigger -decrease

1st trigger -decrease

1st trigger - increase 2nd trigger - increase

∆ benchmark vs. technical interest rate

incr

ease

/dec

reas

e in

bas

e la

pse

assu

mpt

ions

06 October 2016 29

Expressions of individual views by members of the Institute and Faculty of Actuaries and its staff are encouraged.

The views expressed in this presentation are those of the presenter.

Questions Comments