Valuations

Question 1

What is the process of conducting a valuation?

Answer 1

1. Determine the purpose of the valuation and users
2. Consider the previous valuation
3. Collect data
4. Set appropriate basis
5. Perform valuation calculations
6. Check against previous valuation

Question 2

Different types of claims

Answer 2

Attributional claims: Present a high frequency but lower severity
Large claims: Present a low frequency but high severity
Future latent claims: These are claims that have yet to emerge
CAT claims: claims that arise from catastrophic events, such as natural disasters

Question 3

What is stressed scenario for liquidity risk?

Answer 3

think actual cashflows

• premium collection delays
• increases in claim payments
• increases in expenses
• investment market performance is poor

Question 4

What is a stressed scenario for credit risk?

Answer 4

• increase in default probabilities
• recover rates drop
• there is high correlations between counterparties/asset classes

Question 5

What is a stressed scenario for underwriting risk?

Question 6

What are the principles of valuations?

Answer 6

Complete, Consistent (2) , Disclosed, Prudent, Assumption, Proportional.

1. Complete - liabilities include guarantees, options, expenses and obligated premiums.
2. Consistent - between valuations, passive approaches are less frequency but active align more with market-consistent.
3. Consistent - liabilities should be valued in a market-consistent way so align with assets.
4. Prudence - depending on purpose should allow for appropriate degree of prudence.
5. Assumptions - should be suitable, sufficiently prudent and consistent over time (usually economic disclosed but demographic can vary between entity)
6. Proportionality - simplifications to valuation techniques and approximations may be justified by the principle of proportionality.
7. Disclosed - the method and basis of valuation should be disclosed.

Question 7

What is the best estimate liability in different scenarios?

Answer 7

health insurer:
- outstanding claims reserve (IBNR + RBNA + ABNS or other)
- policy reserve (risk reserve + expense reserve)

retirement fund
- liability of active members
- liability of pensioner members
- liability of deferred members
- liability of members exiting the fund

Question 8

Why do we need to do valuations?

Answer 8

• to determine appropriate contribution rate required (social security scheme, DB fund)
• to assess appropriate level of contingency reserves
• to check health of the benefit arrangement (solvency level, funding level, long term financial position)
• determine source of surplus (DB funds, DC funds just due to operational issues)
• to analyse progress between valuations

Question 9

Funding choice considerations

Answer 9

Question 10

EAM

Answer 10

• if age at entry of new members = assumed age at entry, SCR is stable
• if age at entry of new members > assumed age at entry, deficit created.
• when recalculate using new age at entry, SCR will increase and AL will decrease.
• SCR increases because need to pay same benefits in shorter period of time.
• AL decreases, because SCR increases, so lower fund needed now to ensure benefits paid at retirement.

Question 11

AAM

Answer 11

• assumes there are no new members
• aims to produce stable contribution rate over active lifetime of member
• the cost of benefit accrual will increase with age, as members gets closer to retirement
• there is a surplus built up in the early years of membership (contributions outweighs accrued benefit), which is drawn on at the later years (accrued benefit outweighs contributions).
• the contribution rate is a weighted average of contribution rates of members of different ages and salaries.

Question 12

When is AAM preferred to PUM?

Answer 12

• AAM aims to produce stable contribution rate for members over their ‘active’ lifetime.
• AAM tends to build up surpluses in early years, which is drawn on in later years to keep contribution rates stable.
• PUM gives the ‘correct’ cost of the accrued benefits, but AAM overstates the cost in its contribution rate.
• AAM is preferred when the fund is seeking stability, as less likely to default payments to members.
• However, PUM might be better in terms of flexibility, and can avoid the opportunity costs that come with holding surpluses.

Question 13

AAM has a relationship to both PUM and EAM contribution rates.

Answer 13

• AAM = EAM when the age of all members at entry = assumed at age entry [start]
• AAM contribution rate is same at start when the existing age of individuals is the assumed entry age
• AAM contribution rate is higher when average age of individuals is the same assumed entry age
• although the average age is the same, the average contribution rate is not.
• AAM contribution rate is a weighted-average of contribution rates, of members of the same age and salary. As the later changes, so does the contribution rate.
• AAM = PUM when the control period = the number of years to retirement [end]
• AAM contribution rate is typically higher, due to surplus building up.
• PUM contribution rate is more reflective of cost of benefits accrued over time.

Question 14

What is a fully-funded system?

Answer 14

• system where liabilities are fully funded
• don’t rely on future members to pay for the benefits of current members
• each generation must set aside money to pay own benefits
• accumulated contributions and investment income should be enough to pay benefits at all times.
• if deficit arises, they should be amortised over a fixed period of time.
• all retirement funding methods are fully-funded provided: contributions actually paid, assumptions are borne in practice, or both are updated regularly.
• this is more prevalent in private pension world (rather than state) because is protects members against pension fund ending.
• this approach goes against the notion of intergenerational solidarity

Question 15

What is a mature fund/system?

Answer 15

• when the number of recipients relative to the number of contributors is constant
• when a fund/system just introduced, often a lot of contributors and few recipients
• as fund/system matures, the number of contributors and recipients increase
• if the projected population distribution assumed when the fund/system was set up, actually pans out, the number of contributions vs. recipients will be as expected, and so will the cost of benefit.
• often ageing populations can be an issue, causing cost of benefits > expected.
  > lower fertility: more pensioners vs. working class
  > higher longevity: pensions paid for longer than expected

Question 16

Just-in-time vs. Terminal funding

Answer 16

• sponsor contributes lump sum.
• lump sum funds: an entire scheme (JIT) vs. a series of payments (terminal funding)
• contribution trigger: external event e.g. insolvency (JIT) vs. member starting to receive a benefit (TF)
• duration of unfunded: benefit may be unfunded for many generations of members (JIT) vs. benefit unfunded until they start being paid, then fully funded (TF)
• ability to pay: sponsor is in financial hell to begin with so may not be able to pay this lump sum (JIT) vs. sponsor likely to pay as regular contributions received from employer (TF)

Question 17

Scaled premium approach

Answer 17

• partially funded method
• CR set so for each year in equilibrium period, contribution income +interest income on reserve of scheme will be adequate to meet benefit cost.
• needs to be appropriate enough assets to invest in (locally) to ensure interest income component is met.
• to avoid drawing on reserves post-equilibrium period, increase CR for new equilibrium period.
• important the fund at end of old period < fund at end of new period
• increase in CR doesn’t come with benefit improvement.
• period is usually 10,15, 20 years.
• the shorter the period, the lower the CR and the lower the accumulation of funds
• this approach is flexible, as it can adapt to changing conditions

Question 18

GAP vs. scaled premium

Answer 18

• investment strategy: for GAP matched position is very NB but scale premium, investment income + contributions used to meet cost of benefits
  > as a result scaled premium not exposed to market value risk but GAP is
  > GAP assets need to be marketable, so can sell quickly and maintain matched position
• the longer the equilibrium period, the more the CR rate would approach GAP CR.
• the GAP CR is more stable, but more opportunity cost to holding excess surpluses.
• GAP CR is less flexible, so cannot make changes if demographic projections don’t pan out.
• scaled premium CR might eventually exceed GAP CR over time.

Question 19

What are the assumptions of UPR?

Answer 19

• risk is uniform over the period (i.e. claim is 1/12 of premium for each month)
  > in reality, age and seasonality should be considered, in some months claims may be higher than others.
  > to solve, use weighted-average duration to run
• risk related premium will be sufficient to cover claims
  > experience may be far worse than expected in pricing/ product is a loss leader
  > business may make use of cross-subsidies so risk premium was never enough to begin with
  > to solve, hold URR

Question 20

Case estimates

Answer 20

• expert judgement used to determine the appropriate reserve
• can only be used once claim is already incurred and reported
• cannot be used to calculate policy reserves or IBNR
• not useful for CI as claim amount already known
• useful with PMI where intensity of treatment required unknown
• useful with LTC where length of time payment will be paid unknown
• use case estimation for large and unusual claims, use statistical techniques for rest of claims
• for PMI lots of large and unusual claims but LTC usually consistent except for extremely large sum insureds.

Question 21

Considered in case estimation

Answer 21

• the policyholder: medical history, age, gender
• the surgeon and hospital where it will be done
• the procedure being done
• the current levels of medical inflation
• the policy coverage

Question 22

How do you decide what statistical estimation technique to use?

Answer 22

• the accuracy of each reserving technique depends on how the available data corresponds to the assumptions of the method
• common to use different methods (blended methods) and compare the results of each method
• different methods will give different results due to
  > sensitivity to data anomalies
  > choice of claim cohort

Question 23

Comparison between different statistical estimation techniques

Answer 23

Question 24

What is AL definition?

Answer 24

AAM/EAM

• present value of total benefits based on projected final earnings for current active members in service in a retirement fund
• minus the value of the SCRCR multiplied by the present value of total projected earnings for all current active members throughout their expected future membership.

CUM/PUM

The present value of all benefits accrued at the valuation date, based on (current earnings - CUM/ future final salary - PUM) for members in service.

Question 25

What is SCR definition?

Answer 25

• present value of all benefits that will accrue to current active members in a retirement fund (after assumed entry age (EAM)/ after the valuation date (AAM), within the control period (PUM))
• by reference to service after that date and projected final earnings
• divided by the present value of total projected earnings for all current active members throughout their (expected future membership (AAM and EAM)/control period (PUM)).

CUM
- present value of all benefits of a retirement fund that will accrue in the control period following the valuation date
- by reference to service in that period and projected earnings at the end of that period
- plus the present value of all benefits accrued at the valuation date (that is the start of the control period) in respect of members in service
- multiplied by the projected percentage increase in earnings over the control period
- all divided by the present value of all members’ earnings in that control period.