C14 - Models

Question 1

Name three areas that may be modelled in connection with the financing of a scheme

Answer 1

Level and incidence of:

• Benefits
• Contributions
• Return on investments

Question 2

Models can help the following areas of the decision making process for DB schemes

Answer 2

• Choice of benefit design
• Choice of the method of financing to be used
• Choice of assets to be held
• Ongoing monitoring of the financing position

Question 3

Four areas models may be used for DC schemes

Answer 3

• Target an appropriate level of benefits
• Determine an appropriate pattern of contributions
• Illustrate variability of retirement outcomes
• Assist in risk and investment profiling of the arrangement

Question 4

Four areas models may be used for risk sharing schemes

Answer 4

To determine:

• benefits payable
• level of over/under funding relative to target benefit
• amount of discretionary awards
• whether adjustments need to be made to benefits payable

Question 5

Factors a model should allow for

Answer 5

• All features of the benefits
• Contribution amounts and timings
• Assets held and investment returns received
• General economic and fiscal environment
• Funding restriction/guarantees that may be in place

Question 6

Characteristics of a good model

Answer 6

• Theoretical grounding in relation to the scenario being used to project
• Practical
• Results should be capable of interpretation, verification and communication
• Acceptable expenses
• Appropriate parameters
• Results not unduly sensitive to fluctuations with time
• Allows for individual features of the scheme to the extent they are statistically significant and significant to the decision making process

Question 7

Key requirements when both income and outcome are to be modelled

Answer 7

• Consistency between the model and assumptions used
• Allow for the level and incidence of possible cashflows
• Allow for any funding restrictions

Question 8

Main difference between deterministic and stochastic models

Answer 8

Deterministic - each parameter is given a fixed value

Stochastic - parameters may be given a probability distribution of values

Question 9

Stochastic modelling can be of significant help with the decision making process where:

Answer 9

• Incidence or variance of income relative to benefits or contributions is significant to the decision making process
• Guarantee is offered which is not/cannot be matched by assets
• Value needs to be placed on benefits, especially those with optionality
• Significance of the decision is high, as they provide more info and have a lower risk of model error

Question 10

Additional information required about parameters of a stochastic approach is adopted

Answer 10

Values relating to the:

• mean
• variance
• covariance
• skewness

Question 11

Define:

• scenario testing

- sensitivity analysis

Answer 11

Scenario testing involves changing assumptions in combination

Sensitivity analysis involves changing assumptions in isolation

Both may be used with a deterministic model in a range of assumptions as an alternative approach to stochastic modelling

Question 12

Emerging cashflow approach

Answer 12

PV of Projected benefit out go in year t = sum of B(k,t)v^t from 1 to N(t)

B(k,t) is the benefit paid to kth beneficiary
N(t) is total number of beneficiaries
V is the discount rate

Question 13

Benefit event approach

Answer 13

PV of Projected benefit outgo
= sum from 1 to N of Ba(x)

B is the level annual pension payable to a closed group of N individuals currently aged x

Question 14

Elements a full cashflow model needs to allow for

Answer 14

Projected level and incidence of payments to/from the scheme

Question 15

Allowances when projecting the level of benefit outgo

Answer 15

• Inflationary growth in benefits

- Future accrual of Benefits

Question 16

Allowances when projecting the incidence of cashflows

Answer 16

• Probability of exits eg deaths, withdrawals, divorce

- Probability of entrants eg new employees, meeting eligibility criteria

Question 17

Significant features that would make a stochastic model useful in decision making process

Answer 17

• Incidence of Benefits/contributions
• Variance of level of benefits/contributions
• Covariances with asset proceeds

Question 18

When are the present value and projection method are used

Answer 18

Present value (or discounted value) method
- analysing occupational schemes

Projection methods
- anatomising unfounded or partially funded social security schemes

Question 19

Social security vs occupational benefit projection

Answer 19

Projections of social security benefits are:

• more likely to be based on population effects and data rather than scheme membership
• unlikely individual data will be available or projections made at individual level
• funding position or assets may not be relevant
• projections usually assume open membership and allow for new entrants
• no fixed idea of ‘member’ as membership will vast with employment etc moving back and forth

Question 20

Information needed when carrying out projections for a social security scheme

Answer 20

Projections involve combining demographic projections with estimates of:

• proportions of population who are contributors or beneficiaries of the scheme
• contributory salary of contributory members
• amounts of pension payable to different categories of beneficiary

Question 21

Methods of projecting pension benefits expenditure in social security scheme

Answer 21

Factor method
P(x,t)=l(x,t)k(x,t)a(x,t)
P(x,t) expenditure at start of t for those aged x
l(x,t) population aged x at t
k(x,t) population aged x receiving pension at t
a(x,t) average amount of pension for those aged x at t

Survival method
Calculate pension awards in each future year, project them forward recursively by looking at previous years expenditure, adjusting for survival and future pension increases

Question 22

Demographic assumptions for a social security system

Answer 22

• Mortality improvements
• Future fertility
• Future migration
• Invalidity rates
• Age at Retirement

Question 23

Financial assumptions for a social security system

Answer 23

• Economic activity rates
• Price Inflation
• Earnings Inflation
• Rate of pension increases
• Contribution Earnings limit increases
• Assumed rate of return on fund

Question 24

How desire for stability and security affects model chosen

Answer 24

• Stability important, model may be desirable that targets a given contribution rate but allows a volatile funding level (ie prospective benefits funding method)
• Security important, model may be desirable for hat targets a given funding level but allows volatile contributions (ie accrued benefits funding method)