Chapter 20: Setting assumptions Flashcards
What is important to consider when setting assumptions?
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
Demographic vs economic assumptions.
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
What information can be used to determine assumptions?
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
What needs to be considered when determining the extent to which the information may be useful?
Relevance and credibility of past data
Fluctuations and changes over time
Data Recording
Heterogeneity
Standard tables
What needs to be considered when determining the extent to which the information may be useful? - Relevance and credibility of past data
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
What needs to be considered when determining the extent to which the information may be useful? - Fluctuations and changes over time
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
What needs to be considered when determining the extent to which the information may be useful? - Data Recording
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
What needs to be considered when determining the extent to which the information may be useful? - Heterogeneity
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
What needs to be considered when determining the extent to which the information may be useful? - Standard tables
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
What are some other factors that need to be considered when determining the assumptions?
The need for accuracy and prudence
Effect of assumptions on cash transactions
Implicit assumptions
What are some other factors that need to be considered when determining the assumptions? - The need for accuracy and prudence
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
What are some other factors that need to be considered when determining the assumptions? - Effect of assumptions on cash transactions
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
What are some other factors that need to be considered when determining the assumptions? - Implicit assumptions
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
Further factors for considerations when setting assumptions used in pricing a contract.
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
Further factors for considerations when setting assumptions used in pricing a contract - Margins
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
