C14 - Models Flashcards
Name three areas that may be modelled in connection with the financing of a scheme
Level and incidence of:
- Benefits
- Contributions
- Return on investments
Models can help the following areas of the decision making process for DB schemes
- 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
Four areas models may be used for DC schemes
- 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
Four areas models may be used for risk sharing schemes
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
Factors a model should allow for
- 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
Characteristics of a good model
- 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
Key requirements when both income and outcome are to be modelled
- Consistency between the model and assumptions used
- Allow for the level and incidence of possible cashflows
- Allow for any funding restrictions
Main difference between deterministic and stochastic models
Deterministic - each parameter is given a fixed value
Stochastic - parameters may be given a probability distribution of values
Stochastic modelling can be of significant help with the decision making process where:
- 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
Additional information required about parameters of a stochastic approach is adopted
Values relating to the:
- mean
- variance
- covariance
- skewness
Define:
- scenario testing
- sensitivity analysis
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
Emerging cashflow approach
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
Benefit event approach
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
Elements a full cashflow model needs to allow for
Projected level and incidence of payments to/from the scheme
Allowances when projecting the level of benefit outgo
- Inflationary growth in benefits
- Future accrual of Benefits
Allowances when projecting the incidence of cashflows
- Probability of exits eg deaths, withdrawals, divorce
- Probability of entrants eg new employees, meeting eligibility criteria
Significant features that would make a stochastic model useful in decision making process
- Incidence of Benefits/contributions
- Variance of level of benefits/contributions
- Covariances with asset proceeds
When are the present value and projection method are used
Present value (or discounted value) method - analysing occupational schemes
Projection methods
- anatomising unfounded or partially funded social security schemes
Social security vs occupational benefit projection
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
Information needed when carrying out projections for a social security scheme
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
Methods of projecting pension benefits expenditure in social security scheme
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
Demographic assumptions for a social security system
- Mortality improvements
- Future fertility
- Future migration
- Invalidity rates
- Age at Retirement
Financial assumptions for a social security system
- Economic activity rates
- Price Inflation
- Earnings Inflation
- Rate of pension increases
- Contribution Earnings limit increases
- Assumed rate of return on fund
How desire for stability and security affects model chosen
- 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)
