Insurance: Modelling the unpredictable

1. Insurance: Modelling the unpredictable Vicky Gardner February 2013

2. 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?

3. 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

4. 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.

5. 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

6. 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

7. 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

8. 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

9. Rating Factors – Age and Gender • 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

10. 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

11. Rating Factors - Smoking • Differences in premium for £300k term assurance, term of 15 years: • Smokers pay considerably more for term assurance • Differential increases with age

12. 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

13. 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

14. 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

15. 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”

16. 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

17. How Much Underwriting to do? • Which set of premiums should be charged to manage risk whilst also minimising underwriting cost and time?

18. 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

19. 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.

20. 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)

21. 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

22. 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?

23. Setting up Reserves • 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

24. 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

25. 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?

26. 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

27. Any Questions?