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INSURANCE: MODELLING THE UNPREDICTABLE

Vicky Gardner

February 2013

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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?

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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

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WHAT DO ACTUARIES DO? Consultancies - offering advice on issues such as:

acquisitions and mergers, financing capital projects, occupational pension schemes.

Investment - involved in: 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.

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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

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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

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HOW DOES IT WORK? Customer pays a regular premium to insurer Premium calculated to cover:

Average cost of payout + margin for adverse experience Future expenses Commission to brokers Profit Reinsurance costs Tax

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 It meets the definition No material missing/incorrect information on the original

application Policy may or may not terminate at that point

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HOW DO WE PREDICT FUTURE CLAIMS? Pool the risk into homogenous groups that represent

similar risks Model the expected total payout over that group

e.g. risk of death = 5% Total people = 100 with sum assured of £10,000 each Total payout = 100 * 5% & £10k = £50,000

Divide the cost equally between the members of the group Total Premium per person = £500

Groups split by: Age Smoker Status (Sex) Occupation

Premiums adjusted further by underwriting

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RATING FACTORS – AGE AND GENDER

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

Differences in premium for £200k term assurance, term of 10 years:

Males used to pay around 25% more for term assurance (identical since “G-Day”)

Premiums increase sharply at the older ages

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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 socio-

economic 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

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RATING FACTORS - SMOKING

Age Non-smoker Smoker

30 £13.32 £20.19

40 £23.12 £42.61

50 £51.94 £119.06

60 £163.27 £343.95

Differences in premium for £300k term assurance, term of 15 years:

Smokers pay considerably more for term assurance

Differential increases with age

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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

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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

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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

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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”

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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

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HOW MUCH UNDERWRITING TO DO?

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

Which set of premiums should be charged to manage risk whilst also minimising underwriting cost and time?

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HOW MUCH UNDERWRITING TO DO?

Person Quantity Pure Risk Cost

Premium 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

If we choose not to price every applicant for their individual risk characteristics, we are then subject to business mix risk

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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.

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SENTINEL EFFECT EXAMPLE 1000 people want insurance

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

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. 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)

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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

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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?

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SETTING UP RESERVESYear 1 2 3 4 5 6 7 Total

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 £175

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 £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

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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

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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?

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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

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Any Questions?