Chapter 19-Set assumptions

Question 1

1. Outline five key considerations in setting assumptions for actuarial work.

Answer 1

As in all actuarial work, when setting assumptions it is important to:
* consider the use to which the assumptions will be put
* take care over the choice of the assumptions that will have the most financial significance
* achieve consistency between the various assumptions
* consider any legislative or regulatory constraints
* consider the needs of the client.
* consider the market practice in the country

Question 2

2. Give four examples of where historical data can be useful in setting future assumptions.

Answer 2

Historical data can be helpful when choosing demographic assumptions. For example, historical levels of mortality in a country, industry or company may help with the choice of assumptions for the number of individuals who will survive to receive pensions, or for the extent to which contingent benefits will be payable. In many countries this data will have been analysed and used to produce a graduated decrement table. Past data can also be used to project future improvements in mortality.
Similarly, past data can be used when determining the probability of individuals leaving employment, becoming ill, retiring, being married or other significant life events.
In determining an assumption for future investment returns, past data on dividend yields on equities and on the total returns on relevant classes of investment may be useful. Where dividends are linked to an inflation index, past data on that index may be useful.
Past data on salary levels in a particular country, industry or company may be useful when making an assumption about future levels of salary growth. The history of an inflation index may also be useful in determining an assumption for future benefit growth that is linked either fully or partially to that inflation index.

Question 3

3. Give three examples of where current data can be useful in setting future assumptions.

Answer 3

The relationship between current yields for fixed-interest and indexlinked bonds may provide some indication of the market’s view of future levels of the inflation index to which the bonds are related.
Policy statements by governments or controlling banks may also be useful when making assumptions about economic factors.
A scheme sponsor may be able to provide information on planned future salary increases or likely future rates of withdrawal.

Question 4

4. In some instances, what will assumptions be defined by?

Answer 4

In some instances, assumptions may be defined in regulations or legislation.

Question 5

5. Explain why is it usually inappropriate to take an average rate from the past data and use this for projecting into the future.

Answer 5

It is unlikely to be sensible to take an average rate from past data and assume that it will be appropriate for projecting future experience. Past data does not provide the answer as to what will happen in the future, but simply provides information that can be considered when determining the most likely future experience.
The social and economic conditions are likely to have changed over any period of history. The actuary therefore needs to consider the conditions that will apply in the future period to which the projections will relate and how those conditions will lead to differences from the past data that is being used.

Question 6

6. When analysing past data, what must the relevance of that past data to future projections be balanced against?

Answer 6

The relevance of past data to future projections must also be balanced against the need for sufficient data for its analysis to be statistically credible. In making a judgement about future experience this conflict between credibility and relevance must be managed.

Question 7

7. List seven possible features of past data that the actuary may need to adjust for.

Answer 7

When using past data it is necessary to consider how to deal with:
* abnormal fluctuations
* changes in the experience with time
* random fluctuations
* changes in the way in which the data was recorded
* potential errors in the data
* changes in the mix of homogeneous groups within the past data
* changes in the mix of homogeneous groups to which the assumptions apply.

Question 8

8. Why is past economic data usually unsuitable for estimating future levels? Why is it not sensible to use economic data from a short time-frame? How might past data be amended to overcome these problems?

Answer 8

Economic data fluctuates with changes in economic and fiscal policy as well as with the general economic cycle. Past data for investment returns, salary levels and dividend yields in most countries fluctuate significantly over an extended time-frame. It could be thought that economic and fiscal changes mean that most past data are irrelevant and so only data that relate to a period after any recent significant change can be used. However, this would reduce the credibility of the data and increase the effect of any random fluctuation. It is necessary to use the earlier data and to try to strip out the fluctuations that relate to economic and fiscal conditions that differ from those that currently exist.

Question 9

9. What might past data for price inflation be used as an indicator for? What measure will give a better indicator of future price inflation?

Answer 9

Past levels of an index to measure price inflation usually fluctuate significantly and are often a useful indicator of the economic conditions that existed. They are therefore unlikely to be very useful in determining an assumption for future levels of inflation. Consequently, current index values may be a better guide to future levels of inflation.
For example, government projections and the ‘risk-free’ real returns indicated by the current yields on long-term index-linked bonds could be used.

Question 10

10. Give an example of when past price inflation data can be useful for setting assumptions.

Answer 10

Past data for price inflation can be very useful in determining other economic assumptions, as conversion of past economic data into real terms will often remove much of the fluctuation.

Question 11

11. Give an example of a fiscal change that should be allowed for when using historical dividend levels to set assumptions for future dividend levels. Explain a potential problem that arises if an explicit adjustment is made.

Answer 11

Dividend levels could be adjusted to allow for changes in taxation applying to those dividends. However, an explicit adjustment may be spurious, as there may be changes to the taxation of companies or individuals that have a more significant effect.

Question 12

12. What significant factor should be borne in mind when projecting mortality experience into the future? How does this affect the analysis?

Answer 12

Much of the demographic data will also be affected by economic changes. Again, explicit adjustment is difficult and so judgement and analysis of fluctuations and trends will be important.
Mortality data is mainly affected by medical advances. Past data should be considered with this in mind. This is likely to result in significant emphasis being placed on the most recent data with consideration of past trends and their underlying reasons being important in determining the extent of future change.

Question 13

13. Why is it important to split data into homogeneous groups? In practice, how is historical data used?

Answer 13

It is important that the past data used is relevant to the group of individuals about whom assumptions are to be made. Levels of salary growth and mortality, for example, usually differ by type of employment or social class. Ideally the past data would be split into homogeneous groups to reflect such differences. In practice the information necessary to split the data reliably is unlikely to be available, and splitting the data would result in a significant reduction in credibility. Therefore, past data will usually need to be adjusted in a subjective manner to allow for differences in the characteristics of the individuals concerned.
In adjusting past data it is important to recognise that the past data may give false results due to changes in the balance of homogeneous groups over time. For example, past levels of salary growth may reflect a change in the overall composition of a workforce (for example production line workers being replaced by mechanisation) rather than just the changes in real salary levels for individuals.

Question 14

14. What particular care needs to be taken when accessing older data produced either by the State or by companies?

Answer 14

Over time, statistics produced by the State or data recorded by companies may change. Such changes distort the past data and could lead to inappropriate assumptions unless these changes are recognised.
Data errors will also cause distortions but may not be as easy to recognise as changes in the ways of recording the data. Generally, the management and verification of data recorded by companies has improved significantly as the capability of computers has improved. Older data may carry a greater risk of data error, perhaps to an extent that outweighs the usefulness of having more data.

Question 15

15. Give two examples of one-off impacts that might invalidate the use of past data.

Answer 15

For example, significant returns in one year on a specific asset could be because of government intervention. High numbers of deaths could be due to an epidemic meaning that mortality experience for that year is unusually high.

Question 16

16. Describe standard tables based on population data and one of their disadvantages.

Answer 16

In some countries past data has been analysed on a national or industry level. The most common data for such analyses relates to mortality and morbidity. Countries may analyse the whole population’s experience based on censuses. One disadvantage of census data is that it includes all lives, and not just the restricted population that buy insurance contracts. Thus, census data generally includes lower socio-economic groups that distort the experience of lives effecting insurance contracts.

Question 17

17. What considerations should be taken into account when using standard tables?

Answer 17

When using standard tables, the same considerations are needed as when using the company’s own past experience data:
* whether the data is relevant to the intended population at which the product is marketed
* whether adjustments need to be made to the data to reflect continuation of past historical trends.

Question 18

18. Describe three factors to consider when deciding on the need for accuracy in setting assumptions.

Answer 18

When considering the assumptions to use to project future experience, the actuary needs to consider the purpose for which the assumptions are to be used and the significance of each assumption in the overall result. This helps assess the degree of accuracy required and hence the extent to which it is necessary to try to remove distortions from data. It also helps judge whether the assumption should reflect the best estimate of the future experience or whether it is appropriate to reflect any uncertainty about future experience by an overstatement or an understatement within the assumption.
Where assumptions are used to place a capital value on future cashflows, it is usually unnecessary to make a judgement about the accuracy of each assumption. Instead it is necessary to determine that the overall value resulting from the combination of assumptions is appropriate. However, where the individual cashflows are important, it
may be necessary for the accuracy of each assumption to be assessed.
Consideration of the potential financial significance of errors in the assumptions also helps assess the degree of accuracy required, the extent of margins necessary or the level of risk being taken.

Question 19

19. Discuss the assumptions to use when acting as expert witness to determine a fair compensation settlement between two parties.

Answer 19

For example, when acting as expert witness to determine a fair compensation settlement between two parties, it is important that the assumptions used are the actuary’s best estimate of the future experience. Under- or over-statement will give one party a direct financial advantage at the expense of the other. Consequently each party will have a preference for which side of ‘best estimate’ they would like to see each assumption.

Question 20

20. Give two examples of implicit assumptions within a model, in relation to the funding of an occupational pension scheme.

Answer 20

It is necessary to be aware of implicit assumptions within a model, and consider the effects of these. For example, 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 the existing population should be treated as a closed group.

Question 21

21. State three ways of allowing for risk in the assumptions.

Answer 21

The assumptions will be estimates of the expected values for the parameters. Where a cashflow model is being used to price a product, the risk to the provider from adverse future experience could be allowed for by:
* adjusting the risk element of the risk discount rate
* using a stochastic discount rate
* applying margins to the expected values.

Question 22

22. In pricing a contract, what is another assumption that will have to be made in order to determine whether the contract is a good investment?

Answer 22

In pricing a product, a profit requirement will need to be incorporated. This is because it is reasonable to suppose that the owners of the provider decide where to invest by comparing the returns offered by different projects, relative to the risks that are run.

Question 23

23. What factors make a contract design riskier? (High financing requirements)

Answer 23

Not all products are equally risky. The provider should view itself as an investor like any other when it considers the risks of a new product, as in the long run the profits emerging from the company are the profits emerging from the products that it sells.
The following features can increase the risks in a product design:
* lack of historical data, hence the need for greater margins
* high guarantees, which increase the provisions
* policyholder options, which increase uncertainty involved
* high overhead costs
* high initial expenses
* high initial commission
* complexity of design
* without-profit designs with non-reviewable premiums
* regular premium design
* untested market.

Question 24

24. Describe the term ‘profit criterion’.

Answer 24

A profit criterion is often a single figure that tries to summarise the relative efficiency of contracts. By applying a profit criterion to different contracts and then ranking the results in order, it may be possible to determine which contracts makes most efficient use of a company’s capital.
The methods of quantifying profitability include:
* net present value is the expected present value of the future cashflows under a contract, discounted at the risk discount rate
* internal rate of return is the discount rate that would give a NPV of 0
* discounted payback period is the earliest policy duration at which the accumulated
value of profits is 0.
For example, a possible profit criterion for an insurer is that the net present value of profits emerging from each of its product lines is a pre-determined proportion of the distribution costs. Such a criterion reduces the bias towards products with high commission rewards in the distribution system.

Question 25

25. Discuss the advantages and disadvantages of these profit criteria.

Answer 25

Net present value
The main advantage of NPV is that, given a choice between two different sets of cashflows, economic theory dictates that the investor should choose that with the higher net present value.
However this assumes:
* a perfectly free and efficient capital market
* that the NPV is calculated using a discount rate, which correctly reflects the inherent riskiness of the product.
It is not a very simple measure to present to non-technical people.
By itself it tells us very little - it would need to be expressed in terms of a ratio for it to be more meaningful. For example, NPV as a percentage of:
* expected present value of premiums
* distribution costs/ initial commission.

Internal rate of return
It is a simple measure.
It is compatible with shareholders saying that they want a return of at least x%.
It is easily comparable with other forms of investment (eg other products, projects).
However, it might not be unique.
It might not exist.
It is difficult to relate to other measures (eg premium income).

Discounted payback period
It is a useful means of comparing products if capital is a particular problem.
It is easy to explain as a ‘break-even’ point.
The discounted payback period ignores cashflows subsequent to the discounted payback period itself.
The discounted payback period approach will often not agree with the net present value as a means of deciding between two different sets of cashflows.