Chapter 20: Setting assumptions

Question 1

What factors to consider when setting assumptions (5)

Answer 1

• Use of the assumptions, e.g., setting pension scheme contribution rate, calculating scheme value in a takeover situation
• Financial significance of assumptions, e.g., investment returns, mortality
• Consistency with other assumptions, e.g., inflation and investment return should be consistent
• Legislative or regulatory assumptions, e.g., minimum levels of benefits must increase by
• Need of the client, e.g., consider company solvency and available capital when determining employer contribution rate

Question 2

Name two types of assumptions

Answer 2

Economic assumptions

• Investment returns
• Discount rate for valuing liabilities
• Earnings inflation
• Price inflation
• Pension increases
• Expenses

Demographic assumptions

• Rate of retirement in good/ ill health
• Rate of early retirement/withdrawal other than death
• New entrants
• Spouse mortality rate / Proportion of married members / Age of spouse
• Rate of mortality before and after retirement
• Salary scale

Question 3

For what can data be adjusted to make assumptions? (6)

Answer 3

• Changes in experience over time
• e.g., changes in mortality which mean members live longer -> receive pensions for longer
• e.g., economic data vary over time, such as inflation
• Changes in the way data is recorded over time
• e.g., changes in the way workers are classified between blue and white collar
• Potential errors in the data, through data checks
• Changes in the balance of any homogeneous groups
  underlying the data
• e.g., changes in salaries due to shifts in the workforce, such as more white-collar workers
• e.g., changes in asset mix due to ageing population
• Heterogeneity within the group the assumptions related to (data needs to be relevant to the group it applies to)
• Abnormal/ Random fluctuations in data

Question 4

What are the assumptions to value a defined benefit scheme? (11)

Answer 4

Think of cashflows of a DB scheme

+ Members and sponsors pay contributions to the scheme
Associated assumptions:
* Employee contribution rate
* Sponsor contribution rate

- Pensioners will receive benefits in the future based on the final salary
Associated assumptions:
* Salary inflation
* Mortality rates
* Ill-health retirement rates
* Ealy retirement rates
* Benefit escalation rates
* Early leaver rate

+ If the scheme is funded the scheme will generate investment income
Associated assumptions:
* Investment return

• Sponsor pays expenses associated with running the scheme
  Associated assumptions:
• Management expenses
• Investment management expenses

Question 5

What are the assumptions to price insurance products? (15)

Answer 5

The formula for pricing products:
PV(Premiums) = PV(Benefits) + PV(Expenses)

Benefits assumptions

• Cost of claims
• Frequency of claims
• Inflation (e.g., medical)

Expenses assumptions

• Initial expenses
• Ongoing expenses (regular communication, the salary of non-sales staff
• Claim expenses
• Expense inflation
• Commission

Demographic assumptions

• Mix and volume of new business
• Lapse rates
• Mortality rates
• Option take-up rate

General Assumptions

• Investment return
• Risk discount rate (if using cashflow projection to price the product)
• Tax rate

Question 6

Discuss the assumptions underlying a term assurance contract

• Investment returns (2)
• Mortality rates (2)
• Expense (4)
• Withdrawal rates (3)

Answer 6

Investment returns

• Low premiums and low reserves, so not generally very important
• Mort important for longer-term or single premium contracts

Mortality rates

• Very important
• Low mortality rates, but high sums assured. Underestimating mortality could lead to a loss being made

Expenses

• Important as a large part of the premium is used to cover these costs
• Initial expenses are likely to be higher than the regular premiums, so initial expense assumption is very important
• Expense inflation is important over a longer-term contract, especially if the premiums are guaranteed
• Claim expenses could be significant

Withdrawal rates

• Fairly important, especially early withdrawals that occur before the initial expenses are recovered
• Withdrawal benefits are less important at later durations as there is unlikely to be surrender benefit on this product, release of withdrawal reserves might generate a small profit
• Selective withdrawal as lapse rates increase, expect worse mortality

Question 7

Discuss the assumptions underlying an immediate annuity contract

• Investment returns (4)
• Mortality rates (3)
• Expense (3)
• Withdrawal rates (1)

Answer 7

Investment returns

• Very important
• Large, single premium that will be used to provide regular fixed benefits or remained of life
• Benefit payments are guaranteed, so investment returns are important
• Reinvestment risk if very long-term liabilities cannot be matched with assets of a suitable term

Mortality rates

• Important assumption
• Determine the duration of benefit payments
• Risk of overestimating mortality experience, assuming deaths occur early so fewer benefit payments

Expenses

• Fairly important
• Initial expenses are covered by a single premium
• Longer-term means expense inflation is important

Withdrawal rates
- Not typically covered by this product, so not important