Chapter 21: Setting assumptions (1)

Question 1

Methodology for setting assumptions: (5)

Answer 1

1. Investigate the historical experience and make best estimates of the parameters from that experience.
2. Consider what the conditions (including the commercial and economic environment) will be like in the future period for which you are making your assumptions.
3. Determine what the best estimates of your assumptions will be, given expected future conditions.
4. The extent to which you would rely on experience data, and the extent to which you allow for other factors, including judgement, depends on the credibility and relevance of the data, and how predictable the parameter is.
5. The best estimates may need to be adjusted in order to include a margin for prudence.

Question 2

List assumptions needed: (6)

Answer 2

1. Mortality
2. Morbidity
3. Investment return
4. Expenses and commission
5. Expense inflation
6. Persitency (withdrawals)

Question 3

The expected future experience of the policyholders will depend crucially on three things:

Answer 3

1. the target market of the contract
2. the underwriting controls applied (or not applied)
3. the expected change in the experience since the time of the last historical investigation to the point in time at which the assumptions will on average apply.

Question 4

Approaches to determining future rates of mortality: (3)

Answer 4

1. Expectation approaches involve expert opinion and subjective judgment to specify a range of future scenarios.
2. Extrapolation approaches are based on projecting historical trends in mortality into the future.
3. Explanatory, or process-based projections attempt to model trends in mortality rates from a bio-medical perspective.

Question 5

Stochastic mortality projection methods and their use: (2)

Answer 5

1. Lee-Carter
2. P-spline

These models are used to project trends so that we can derive the values of q(x,y) for each age x and each year of birth y.

Question 6

Influences on transition intensities on IP products: (5)

Answer 6

1. policyholder characteristics identified in the underwriting stage
2. product design - e.g. replacement ratio and rehabilitation benefits
3. economic morale
4. government provision of welfare
5. tax

Question 7

What are the likely data limitations for IP:

Answer 7

1. published insurance parameters for incidence have limited credibility
2. worldwide statistics are plentiful, especially from the US, but may not be relevant.

Question 8

Influences on claim distributions for CI products include: (3)

Answer 8

1. advancement in medical science, which will impact cures.
2. earlier diagnosis
3. simpler and more readily available operations

Question 9

Modelling and setting assumptions for CI products is complicated by: (2)

Answer 9

1. use of disease-based and treatment-based definitions of claims, which may need to be modelled separately.
2. guaranteed and reviewable alternatives

Question 10

Data limitations on LTCI products: (2)

Answer 10

1. little data on claim frequency

2. an absence of insurance statistics

Question 11

For IP, CI and LTCI the larger policies tend to have better claim experience because: (2)

Answer 11

1. the policyholder will tend to be from higher socio-economic groups, and
2. there is a stricter level of underwriting imposed for larger sums insured.

Question 12

The value assigned to the investment parameter will be affected by: (4)

Answer 12

1. the significance of the assumption for the profitability of the contract, which will depend on the level of reserves built up and the investment guarantee given.
2. the extent of the investment guarantee given under the contract - this will affect the types of assets which the premiums from the contract will be invested.
3. the extent of any reinvestment risk and the extent to which this can be reduced by a suitable choice of assets.
4. the intended investment mix for the contract, the current return on the investments within that mix and, where appropriate, the likely future return.

Question 13

Expense assumptions: The actuary will want to reflect the incidence of the following marginal expenses: (8)

Answer 13

1. initial acquisition
2. initial medical underwriting
3. initial administration
4. renewal administration
5. renewal reward to sales channel
6. investment
7. withdrawal/ paid-up expenses
8. claim / maturity administration

Question 14

Factors that may be considered when setting the value of the inflation parameter: (4)

Answer 14

1. current rates of inflation, both for prices and earnings
2. expected future rates of inflation
3. the differential between the return on government fixed-interest securities and on government index-linked securities.
4. recent actual experience of life insurance company or industry.

Question 15

The risk to a life insurer from adverse future experience may be allowed for through: (3)

Answer 15

1. the risk element of the risk discount rate
2. using a stochastic approach
3. assessing what margins to apply to the expected values.

Question 16

Define the risk discount rate (in relation to investors)

Answer 16

The risk discount rate is expected rate of return investors will demand, and is equal to the risk-free rate plus a risk premium.

Question 17

Features that can make a product design riskier: (6)

Answer 17

1. lack of historical data
2. high guarantees
3. policyholder options
4. overhead costs
5. complexity of design
6. untested market

Question 18

The level of statistical risk could be assessed using one of the following methods: (4)

Answer 18

1. analytically, by considering the variance of the individual parameter values used.
2. by using sensitivity analyses with deterministically assessed variations in the parameter values.
3. by using stochastic models for some, or all, of the parameter values and simulation.
4. by comparison with any available market data.

Question 19

Example assumptions that should be consistent: (6)

Answer 19

1. Investment return and inflation
2. Tax (If the company is taxed on “I-E” type taxation”
3. New business and expenses
4. Investment return and bonus loading
5. Withdrawal rates and investment return
6. Other products

Question 20

Investment return assumptions will be set bearing in mind (List): (5)

Answer 20

1. the significance of reserves for the contract
2. the extent of investment guarantees
3. the importance of reinvestment
4. the intended asset mix for the contract

Question 21

Setting Mortality and Morbidity assumptions

Answer 21

1. An assumption is required for both the base and the mortality trend.
2. The actuary will consider the company’s recent experience of the contract, or related contracts.
3. This will allow appropriate adjustments to be made to standard tables. (Industry data and reinsurers’ data may be useful, especially if the company has little relevant data)
4. An allowance should also be made for expected changes in mortality rates over time using a combination of:
   - expectations approaches
   - extrapolations approaches
   - explanatory approaches

Question 22

Setting expenses and commission assumptions (2)

Answer 22

1. Expenses will be loaded for in accordance with the results of the most recent expense investigation.
2. In deciding on the split of expenses between “per policy” and “per unit premium”, some cross-subsidy might be necessary for competitive reasons.

Question 23

Setting expense inflation assumptions (2)

Answer 23

1. This will depend on expected future earnings inflation.

2. It must be consistent with the investment return assumptions.

Question 24

Setting persistency (withdrawals) assumptions: (3)

Answer 24

1. The assumption will take as a start point the most recent investigation for that contract or related contracts, or, in the absence of suitable data, industry statistics.
2. Some adjustment might be necessary.
3. The commercial and economic environment is important.

Question 25

Setting the basis - Margins

Answer 25

1. Margins will be necessary to guard against adverse future experience.
2. However competitive pressure forbids too much prudence in a pricing basis.
3. Risk may be allowed for through the risk discount rate, stochastic modelling or margins in the parameter assumptions.

Question 26

Market-consistent valuation:

Answer 26

1. the expected investment return can be set as the risk-free rate (regardless of the actual assets held).
2. However, the investment return volatility and correlation assumptions depend on the actual assets held.
3. A margin is likely to be included in the other parameter values to allow for the risk in their estimation.