Chapter 20: Setting assumptions

Question 1

What is important to consider when setting assumptions?

Answer 1

When setting assumptions, it is important to:

• Consider the use to which the assumptions we be put
• Take over assumptions that will have the most financial significance
• Achieve consistency between various assumptions
• Consider legislative or regulatory constraints
• Consider needs of the client

Question 2

Demographic vs economic assumptions.

Answer 2

Demographic vs economic assumptions

• Demographic assumptions (e.g. mortality rates) relate to size and distribution of population
• Generally, affect the timing or number of the cashflows
• Economic assumptions (e.g. investment returns) relate to level of income or outgo
• Important to consider both demographic and economic assumptions
• Assumptions needed for a model of a pension scheme:
• Demographic assumptions:

 Rates of retirement in good health (early, normal, late)

 Rates of ill-health retirement

 Rates of withdrawal (other than death or retirement)

 New entrant rates

 Rates of mortality before and after retirement

 Proportion married

 Average age of spouses

 Spouses’ mortality

 Salary scale

• Economic factors:

 Investment return e.g. bond yields, equity returns

 Discount rate (for valuing liabilities)

 Price inflation

 Earnings inflation

 Pension increases

 Expenses

• Similar for long-term, short-term (general) and health insurance products and banking

Question 3

What information can be used to determine assumptions?

Answer 3

Historical data

• Likely to be primary source of data used in determining assumptions about future experience
• Can only use past data as a guide together with analysis of recent trends and current forecasts for future – past scenarios will not necessarily happen in future
• Can be helpful when choosing demographic assumptions
• E.g. historical levels of mortality in a country, industry or company may help with choice of assumptions for number of individuals who will survive to receive pensions
• Past data can also be used to help project future improvements in mortality
• Past data can be used when determining probability of individuals leaving employment, becoming ill, retiring, being married or significant life events
• Examples where past data form useful starting point for economic assumptions:

 Determining an assumption for future investment returns,

o past data on dividend yield on equities and

o past data on total returns on relevant classes of investment may be useful

 where dividends are linked to inflation index then past data on that index is useful

 past data on salary levels in particular country, industry or company useful when making assumption about future levels of salary growth

 history of an inflation index useful in determining assumption for future benefit growth that is linked either fully or partially to that inflation index

Current data and forecasts

• Current data may be used when determining assumptions
• Relationship between current yields for fixed-interest and index-linked bonds may provide indication of market’s view of future levels of inflation index to which the bonds are related
• Nominal yield = risk-free real yield (index-linked bond) + expected future inflation + inflation risk premium
• Policy statements by governments or controlling banks – useful when making assumption about economic factors
• Scheme sponsor may provide information on planned future salary increases or likely future rates of withdrawal
• Assumption may be defined in regulations or legislation

Question 4

What needs to be considered when determining the extent to which the information may be useful?

Answer 4

Relevance and credibility of past data

Fluctuations and changes over time

Data Recording

Heterogeneity

Standard tables

Question 5

What needs to be considered when determining the extent to which the information may be useful? - Relevance and credibility of past data

Answer 5

Relevance and credibility of past data

• Unlikely to be sensible to take average rate from past data and assume that it can be used to project future experience
• Past data does not provide the answer as to what will happen in future – just provide info that can be considered when determining most likely future experience
• Social and economic conditions likely to change over time
• Actuary needs to consider the conditions that will apply in future period and how those conditions will lead to difference from past data being used
• A change in benefits will also have effect on past data for a benefit scheme
• Relevance of past data to future projections must be balanced against need for sufficient data
• This is needed for its analysis to be statistically credible
• Manage conflict between credibility and relevance – when making judgement about future experience
• For demographic data – size of exposure to risk is NB in determining credibility of data
• Expected number of exits from particular decrement is also NB – varies depending on parameter being determined
• E.g. for actuary to place reliance on actual mortality statistics – past data set would have to be extremely large
• But actuary might be able to determine discontinuance rate from smaller set of data – because withdrawal rates from life, general or pensions contracts tend to be much higher than death rates
• When using past data, important to consider how to deal with:

 Abnormal fluctuations

 Changes in experience with time

 Random fluctuations

 Changes in way in which data was recorded

 Potential errors in data

 Changes in mix of homogeneous groups within past data

 Changes in mix of homogeneous groups to which assumption apply

Question 6

What needs to be considered when determining the extent to which the information may be useful? - Fluctuations and changes over time

Answer 6

Fluctuations and changes over time

Changes affecting economic data

• Economic data fluctuations = changes in economic and fiscal policy and general economic cycle
• Past data for investment returns, salary levels and dividend yields fluctuate over extended time-frame
• Could be thought that fiscal and economic changes mean that most past data are irrelevant and only data that relate to period after any recent change can be used
• But this would reduce credibility of data and increase effect of any random fluctuation
• Necessary to use earlier data and try strip out fluctuations that relate to economic and fiscal conditions that differ from those that exist currently

Price inflation

• Past levels of index to measure price inflation fluctuate a lot and often useful indicator of economic conditions that existed
• Unlikely to be useful in determining assumption for future levels of inflation
• Current index values may be better guide to future levels of inflation
• E.g. government projections and risk-free real returns indicated by current yield on long-term index-linked bonds could be used
• Difference between yields on fixed-interest and index-linked bonds = estimate of inflation index

Use of real values

• Past data for price inflation useful in determining other economic assumptions – as conversion of past data into real terms will often remove much of fluctuation
• Actuaries often develop set of assumptions in real terms

Other economic adjustments

• Difficult to do other than subjectively
• Dividend levels could be adjusted to allow for changes in taxation
• But explicit adjustment may be spurious – as there may be changes to taxation of companies or individuals that have more significant effect

Demographic changes

• Demographic data will be affected by economic changes
• E.g. withdrawal and new entrant rates for benefit scheme are dependent on employee turnover – staff turnover lower in times of economic recession and high when economy is buoyant
• More early retirements after period of economic boom – because members’ finances will be healthy and may feel they can afford to retire early
• Similarly, withdrawal rates higher for life insurance business during economic recession – due to customers having to prioritise other outgo when finances are pressurised
• General insurance companies may find that customers switch from more expensive to less expensive cover options
• Explicit adjustment is difficult – so judgement and analysis of fluctuations and trends will be NB
• Mortality data is mainly affected by medical advances – past data considered with that in mind

One-off impacts

• Need to be considered to ensured that the assumptions are valid
• E.g. significant returns in one years on an asset could be because of government intervention
• High numbers of deaths could be due to an epidemic – meaning mortality experience for that year is unusually high
• Historical data relating to exceptional or one-off events should be disregarded in an analysis of trends
• Or data might be adjusted to more normal value for that period

Question 7

What needs to be considered when determining the extent to which the information may be useful? - Data Recording

Answer 7

Data recording

Changes in statistics recorded

• Statistics produced by state or data recorded by companies may chance over time
• Changes distort past data and could lead to inappropriate assumptions unless these changes are recognised

Errors in data recorded

• Data errors will cause distortions but may not be as easy to see as changes in way of recording data
• Management and verification of data recorded by companies has improved significantly as capability of computers improve
• Older data carries greater risk of data error – perhaps to extent that outweighs usefulness of having more data
• Actuary need to judge correct balance of relevance and credibility

Question 8

What needs to be considered when determining the extent to which the information may be useful? - Heterogeneity

Answer 8

Heterogeneity

Changes in the constituents of the population

• When adjusting past data, it is NB to recognise that past data may give false results due to changes in balance of homogeneous groups over time
• E.g. past levels of salary growth may reflect change in overall composition of workforce (replaced by mechanisation) rather than just changes in real salary levels for individuals

Splitting the population into homogeneous groups

• NB that past data used is relevant to group of individuals about whom assumptions are made
• Levels of salary growth and mortality usually differ by type of employment or social class
• Ideally past data split into homogeneous groups to reflect such differences
• Info needed to split data reliably is unlikely to be available and splitting data would result in significant reduction in credibility
• Thus, past data need to be adjusted in subjective manner to allow for differences in characteristics of individuals concerned

Example

• When considering company’s pension scheme – workforce may consist of manual labourers, clerical staff and management
• These groups likely to have different levels of mortality, staff turnover, salary growth, etc
• Even when company is large enough to derive reasonable credible data – if employees were split into homogeneous groups = size of each group would decrease and therefore credibility of data would be lower
• Particularly likely for management group – might only consist of few senior employees

Question 9

What needs to be considered when determining the extent to which the information may be useful? - Standard tables

Answer 9

Standard tables

• Past data has been analysed on national or industry level – in some countries
• Most common data for such analyses relates to mortality and morbidity
• Countries may analyse whole population’s experience based on censuses
• Disadvantage of census data - it includes all lives and not just the restricted population that effect insurance contract
• Also increased risk that data is out of date by the time it is published
• When using standard tables, same considerations are needed as when using company’s own past experience data:

 Whether data is relevant to the intended population at which product is marketed

 Whether adjustments need to be made to data to reflect continuation of past historical trends

Question 10

What are some other factors that need to be considered when determining the assumptions?

Answer 10

The need for accuracy and prudence

Effect of assumptions on cash transactions

Implicit assumptions

Question 11

What are some other factors that need to be considered when determining the assumptions? - The need for accuracy and prudence

Answer 11

The need for accuracy and prudence

Purpose of the valuation

• When considering assumptions to use to project future experience:

 actuary needs to consider purpose for which the assumptions are to be used

 and the significance of each assumption in overall result

• This helps assess degree of accuracy required and hence extent to which it is necessary to try remove distortions from data
• Helps judge whether assumption should reflect best estimate of future experience or,
• if it is appropriate to reflect any uncertainty about future experience by overstatement or an understatement with assumption
• the degree of prudence incorporated in set of assumptions always depends on objectives of client for whom the model is being built

Accuracy of assumptions

• where assumptions are used to place capital value on future cashflows – usually unnecessary to make judgement about accuracy of each assumption
• Instead, necessary to determine that overall value resulting from combination of assumptions is appropriate
• But where individual cashflows are NB – may be necessary for accuracy of each assumption to be assessed

Significance of errors

• Consideration of potential financial significance of errors in assumptions also helps assess degree of accuracy required, the extent of margins necessary or level of risk being taken
• Will inevitably be some deviation from actual experience compared with assumptions made
• Actuary needs to be aware of which assumptions have material effect on result and communicate this info to decision-makers

Question 12

What are some other factors that need to be considered when determining the assumptions? - Effect of assumptions on cash transactions

Answer 12

Effect of assumptions on cash transactions

• Sometimes necessary to determine sum of money that will be one-off payment from one party to another – which cannot be corrected by adjustment to future payments
• E.g. when acting as expert witness to determine fair compensation settlement between two parties, it is important that assumptions used are the actuary’s best estimates of future experience
• Under- or over-statement will give one party a direct financial advantage at the expense of another

Question 13

What are some other factors that need to be considered when determining the assumptions? - Implicit assumptions

Answer 13

Implicit assumptions

• Necessary to be aware of implicit assumptions within a model and consider the effects
• E.g. the funding method for an occupational pension scheme may assume that:

 New members continue to join or new policies continue to be written and therefore the age/sex distribution of a population will be maintained

 No new entrants will join or no new policies will be written and so existing population should be treated as closed group

• In an insurance context, the assumption as to whether or not the insurance company is open or closed to new business is also critical
• Because it will affect the contribution that each policy must make to the fixed overhead of the business
• May also affect the nature and term of the investment held

Question 14

Further factors for considerations when setting assumptions used in pricing a contract.

Answer 14

Assumptions used in pricing contracts

• Further factors for consideration:

 the extent to which margins against adverse future experience are required

 the risk discount rate to be used

 the profit criterion to apply

Question 15

Further factors for considerations when setting assumptions used in pricing a contract - Margins

Answer 15

Margins

• The assumptions will be estimates of expected values for the parameters
• Where cashflow model is being used to price a product, the risk to provider from adverse future experience could be allowed for by:

 adjusting the risk element of risk discount rate

 using a stochastic discount rate

 applying margins to expected values

• by including a margin or margins somewhere in the basis, the risk from adverse future experience is reduced

Profit margins

• In pricing a product, a profit requirement will have to be incorporated
• Because it is reasonable to suppose that owners of provider decide where to invest by comparing the returns offered by different projects, relative to risks that are run
• For a proprietary life insurance company, owners are shareholders
• Shareholders want to make a profit on investment in a life insurance company
• Thus, basis for pricing contracts should include a profit margin

Question 16

Further factors for considerations when setting assumptions used in pricing a contract - Risk discount rates

Answer 16

Risk discount rate

• Rate that is used to discount the pricing cashflows may be set as sum of:

 expected rate of return which could either be

          o	the risk-free rate of return typically used for statutory or fund valuations where a risk-free or prudent view is required or,

          o	 the shareholders’ required rate of return – likely more market-based and include and allowance for investment risk

PLUS

 A risk margin – reflects inherent risk within cashflows of product that is being priced

• Not all products are equally risky
• Provider should view itself as investor – as in the long run profits emerging from company are profits emerging from the products that it sells
• Change in mix of business e.g. away from old and safe contracts towards new and innovative contracts would change the market’s evaluation of the provider’s risks
• Following features can increase the risks in product design:

	Lack of historical data
	High guarantees
	Policyholder options
	Overhead costs
	Complexity of design
	Untested market

• Difficult to assess these risks and to say what effect they should have on the risk discount rate

Question 17

Further factors for considerations when setting assumptions used in pricing a contract - Profit criterion

Answer 17

Profit criterion

• Often a single figure that tries to summarise the relative efficiency of contracts
• May be possible to determine which contracts make most efficient use of company’s capital
• This can be done by applying a profit criterion to different contracts and ranking the results in order
• Methods of quantifying profitability include:

 Net present values
 Internal rate of return
 Discounted payback period

• E.g. possible profit criterion for an insurer is the NPV of profits
• Emerging from each of its product lines is a predetermined proportion of the distribution costs
• i.e. NPV cashflows/ distribution costs = must be the same for all product lines