Transcript Insurance: Modelling the unpredictable

INSURANCE: MODELLING THE
UNPREDICTABLE
1
Vicky Gardner
February 2013
AGENDA
What is an actuary?
 What is insurance?
 Types of life insurance
 Pricing: How do we group people together to
charge an appropriate premium?
 Underwriting: How do we further differentiate
the prices for higher-risk individuals?
 Reserving: How do we make sure we have enough
capital to pay claims?

2
WHAT IS AN ACTUARY?
“Actuaries are experts in risk management. They
use their mathematical skills to help measure the
probability and risk of future events. This
information is useful to many industries, including
healthcare, pensions, insurance, banking and
investments, where a single decision can have a
major financial impact.”
Source: UK Actuarial Profession
3
WHAT DO ACTUARIES DO?

Consultancies - offering advice on issues such as:




Investment - involved in:




acquisitions and mergers,
financing capital projects,
occupational pension schemes.
research and on the pricing and management of investments,
mitigating the risk of investments,
using their understanding of insurance or pension liabilities to
manage the corresponding assets.
Insurance
Investigate and analyse a huge range of numerical
information,
 to create and price polices,
 to ensure they have the money to cover claims.


Pensions


designing and advising on company pension schemes,
placing a value on accumulated pension commitments.
4
WHAT IS INSURANCE?


The transfer of risk from one party to another, in
exchange for payment
Covers “insurable risks”:
Premium charged is high enough to cover risk cost and
expenses
 Nature of loss is financial and can be quantified
 Risk should be random to avoid anti-selection


For Life Insurance, the policyholder must have an
“insurable interest” on the person they are insuring
usually this means would be disadvantaged financially if
the insured party died
 the law says that you have an unlimited insurable interest
in yourself, your spouse or your civil partner. In practice,
this extends to live-in partners


Involves pooling of risk
5
TYPES OF LIFE INSURANCE

Term assurance – pays on death only in term
Level or decreasing
 With or without Critical Illness

Whole of Life – pays on death
 Income Protection – pays a monthly benefit when
cannot work due to illness/disability
 Pure Endowment – pays only on survival to end
of term
 Endowment Assurance – pays on death in term
or survival at end of term

6
HOW DOES IT WORK?


Customer pays a regular premium to insurer
Premium calculated to cover:








On insured event (death, diagnosis of critical illness,
signed off work due to illness etc), insurer will pay a
lump sum/monthly benefit to policy owner/beneficiary
Payment only made if claim found to be valid



Average cost of payout + margin for adverse experience
Future expenses
Commission to brokers
Profit
Reinsurance costs
Tax
It meets the definition
No material missing/incorrect information on the original
application
Policy may or may not terminate at that point
7
HOW DO WE PREDICT FUTURE CLAIMS?


Pool the risk into homogenous groups that represent
similar risks
Model the expected total payout over that group




Divide the cost equally between the members of the
group


Total Premium per person = £500
Groups split by:





e.g. risk of death = 5%
Total people = 100 with sum assured of £10,000 each
Total payout = 100 * 5% & £10k = £50,000
Age
Smoker Status
(Sex)
Occupation
Premiums adjusted further by underwriting
8
RATING FACTORS – AGE AND GENDER

Differences in premium for £200k term
assurance, term of 10 years:
Age
Male
Female
20
£7.77
£6.05
30
£9.55
£7.46
40
£15.06
£11.99
50
£32.37
£26.03
60
£85.73
£68.42
Males used to pay around 25% more for term
assurance (identical since “G-Day”)
 Premiums increase sharply at the older ages

9
LIFE EXPECTANCY BY GENDER
Until 21st December 2012, term assurance
premiums for females were lower than for males
 European Court of Justice (ECJ) ruled this illegal
– gender can no longer be used in EU
 Statistics show differences do exist
 ECJ argue that the differences are due to socioeconomic and lifestyle factors
 Other evidence suggests other reasons:

More active hearts in females
 Testosterone increases risky behaviour, cholesterol


A few countries where difference is reversed:

Zimbabwe, Lesotho, Swaziland, Afghanistan
10
RATING FACTORS - SMOKING

Differences in premium for £300k term
assurance, term of 15 years:
Age
Non-smoker
Smoker
30
£13.32
£20.19
40
£23.12
£42.61
50
£51.94
£119.06
60
£163.27
£343.95
Smokers pay considerably more for term
assurance
 Differential increases with age

11
LIFE EXPECTANCY BY COUNTRY

Country of residence has a large impact on life
expectancy:
Disease prevalence
 Medical facilities
 Lifestyle
 Types of work


Estimates of different countries’ life expectancies:






Monaco – 89.7
Japan – 83.9
UK – 80.2
USA – 78.5
Nigeria – 52.0
South Africa – 49.4
12
LIFE EXPECTANCY BY REGION - UK
Within countries, large differences exist
 Lowest male life expectancies:

Inverclyde – 73.0
 Glasgow – 71.6
 Blackpool – 73.6


Highest:
Kensington & Chelsea – 85.1
 Westminster – 83.8
 East Dorset – 82.0

Source: Office of National Statistics - 2009
13
IMPACT OF REGION ON ANNUITY
PAYMENTS
Some annuity providers use postcode as a rating
factor
 Example: Age 65, £200k pension pot, healthy
non-smoker. Best monthly payments:

Chelsea: £571.89 (L&G)
 Glasgow: £587.83 (L&G)
 2.8% increase in benefit due to living in a “less
healthy” region


Postcode is a proxy to:
Occupation
 Lifestyle
 Income

14
ADD MORE RATING FACTORS?
The more rating factors, the more accurate the
pricing – the “homogenous pools” become smaller
 Similar to motor insurance
 Need data to add more factors – more sparse for
life insurance since fewer claims and often
inappropriate to use data from overseas
 Already difficult to sell life insurance – more
questions put people off
 Need to be consistent with what other insurers
are rating by to avoid “anti-selection”

15
UNDERWRITING


Around 60% of applicants for life insurance will get the
headline premium shown on the initial quote (based on
basic information only)
Before a policy is taken out, the applicant must undergo
underwriting. Consists of:
Medical questions, including family history
Lifestyle questions e.g. alcohol consumption, dangerous
activities
 Financial questions – is sum assured reasonable compared
with salary?



Some applicants will then:
have a rating applied e.g. premium is increased by 50%
have an exclusion applied e.g. won’t pay out if cancer
diagnosed (will still usually pay out on death)
 be declined (temporarily or permanently)



Need to balance the cost of underwriting with the better
risk classification it allows
16
HOW MUCH UNDERWRITING TO DO?

Which set of premiums should be charged to manage risk
whilst also minimising underwriting cost and time?
Person
Pure Risk
Cost
Premium
Set A
Premium
Set B
Premium
Set C
A
£8
£8
£11.25
£47.14
B
£10
£10
£11.25
£47.14
C
£12
£12
£11.25
£47.14
D
£15
£15
£11.25
£47.14
E
£60
£60
£67.50
£47.14
F
£75
£75
£67.50
£47.14
G
£150
£150
£150
£47.14
Total
£330
£330
£330
£330
17
HOW MUCH UNDERWRITING TO DO?

If we choose not to price every applicant for their individual
risk characteristics, we are then subject to business mix
risk
Person
Quantity
Pure Risk Premium
Cost
Set A
Premium
Set B
Premium
Set C
A
1
£8
£8
£11.25
£47.14
B
1
£10
£10
£11.25
£47.14
C
5
£12
£12
£11.25
£47.14
D
30
£15
£15
£11.25
£47.14
E
10
£60
£60
£67.50
£47.14
F
5
£75
£75
£67.50
£47.14
G
7
£150
£150
£150
£47.14
Total
32
£2,553
£2,553
£2,479
£2,781
18
SENTINEL EFFECT
The sentinel effect in underwriting refers to the
tendency for unhealthy individuals to apply for
insurance coverage where testing is not
performed
 This is ok as long as it is priced for
 The risk comes when other insurers do test for
the condition so we get a disproportionate share
of higher-risk individuals.

19
SENTINEL EFFECT EXAMPLE

1000 people want insurance





Insurer X and Y both charge £14 (=£10*90% + £50*10%)
If both insurers don’t ask about condition A, there is no bias in
the insurers chosen so all insurers end up with 10% of their
customers having condition A, matching what they priced for
Now Insurer X asks about condition A:



charges £10 for those who have it
charges £50 for those who have it
The 900 people without the condition go to insurer X.



100 of these have medical condition A and have risk cost of £50
900 of these have no medical condition and have risk cost of £10
Profit margin remains the same
Volumes increased
The 100 people with the condition go to insurer Y.



Profit margin falls
Volumes fall
Premiums must increase (which makes the price differential between
X and Y even worse)
20
ANTI-SELECTIVE BEHAVIOUR
People who know they are a greater risk but the
insurer does not – information asymmetry
 For example, the applicant has a medical
condition not covered by the underwriting
questions (cannot ask for genetic test results)
 Also occurs later on in the policy. A customer in
good health is more likely to lapse than a
customer is poor health.

End up with a higher mortality rate than priced for
as more weighted towards the unhealthy people
 These customers also more likely to take out options
to increase sum assured

21
SETTING UP RESERVES
In the UK, most life insurance policies are paid
for by level monthly premiums
 For example, a 30 year old taking out a 20-year
policy may pay £12 per month.

At the start of that term, the risk that customer
represents is much lower than £12
 At the end of that term, the customer is almost 50
and the risk that customer represents is much higher
than £12
 So early premiums cross-subsidise later premiums

We need to hold back some of the premiums in
reserve to cover expected future claims
 How do we calculate how much to hold back?

22
SETTING UP RESERVES
Year
1
2
3
4
5
6
7
Premium
£100
£100
£100
£100
£100
£100
£100
Average Claim Cost
£30
£35
£50
£70
£90
£115
£135
Profit (no reserves)
£70
£65
£50
£30
£10
-£15
-£35
Reserve Set-Up
£0
£0
-£10
-£30
-£10
+£15
+£35
Total Reserve at
end of year
£0
£0
£10
£40
£50
£35
£0
Profit (with
reserves)
£70
£65
£40
£0
£0
£0
£0


Total
£175
£175
If we took the profit as it is made, we would make a loss in later years
and not have enough capital to pay claims
So we need to set aside reserves to cover future claims and delay the
release of profits
23
SETTING UP RESERVES
Not quite as simple as this!
 Also need to allow for:









Expenses and expense inflation
Commission paid to distributors
Tax
Interest earned on reserves
Lapses
Regulatory solvency requirements
Reinsurer payments and share of claims
Need to consider what would happen if claims
were higher than expected – must be able to
withstand a 1 in 200 shock

e.g. Swine flu epidemic, terror attack
24
HOW DO WE MODEL SHOCKS?


We don’t just set aside reserves for our best guess of
future claims. We need to hold more than this to
allow for future adverse experience
Stress testing
e.g. 10% increase in mortality rates
 e.g. 20% increase in expenses


Scenario testing
e.g. 10% increase in lapses AND 10% increase in mortality
 to allow for parameters being correlated (especially in a
recession)



Stochastic modelling
How prudent does the regulator want our reserves to
be?
25
SUMMARY
Life insurance is a long-term business and
modelling the full lifetime of the business is
crucial
 Uncertainty needs to be allowed for as much as
possible but

Need to remain competitive
 Cannot wait till end of policy to release profit
(unhappy shareholders)


Actuaries play a critical part in:
Pricing the risk appropriately
 Ensuring enough capital is put aside to meet claims

26
Any Questions?
27