Ch 21: Assumptions 1

Question 1

Summary card

Answer 1

• Setting assumptions
• Mortality
• Investment return
• Expenses & expenses inflation
• Persistency
• Product risk
• Risk discount rate
• Profit criteria
• Consistency between assumptions

Question 2

Background on assumptions

What is the key reason assumptions are used for? (1)

What key risk does setting assumptions introduce? (1)

What kind of risks can be somewhat mitigated by appropriate matching of assets? (3)

Answer 2

• Assumptions used by insurers for variety of reasons, mostly assessng eventual cost of liabilities
• Setting assumptions => parameter risk: want to reduce this
• Not easy finding matched assets protecting from actual experience different to expected, can sometimes reduce following risks from investment matching:

1. Investment risk: relates return required meet current liabs for future payouts
2. Inflation risk: relates increase in inflation-linked liabs + liabs behaving approximately in line with inflation (eg expenses)
3. Marketing risk: ability to satisfy PHs in relation to any investment-linked/discretionary benefits.

Question 3

Methodology for setting assumptions

Answer 3

1. Investigate past experience; make past best estimate parameters; appropriate in context of historical conditions/then-circumstances
2. Consider future conditions (including commercial and economic environment ) during period for which assumptions will be used
3. Determine future best estimates assumptions, given expected future conditions
4. Extent of (a) relying past data vs (b) allowing for other factors, depends on data credibility/relevance + parameter’s predictability
5. Adjust best estimates with margin. Size of margin depends on:
   
   • purpose for which model is required
   • degree of risk associated with parameter

Question 4

Best estimate mortality:

Base rates

Answer 4

• Mort rates change over time and have 2 parts
• Base mortality:
  
  • the main demographic assumption for pricing => reflect future experience of lives taking out contracts
  • Adj rate from mort table
  • Restricted by regulation
• Exp future experience depends on:
  
  • Target mkt and Dbn channel
  • Level of underwriting and controls
  • Expected changes in experience since last investigation

Question 5

Best estimate mortality: base rates derivation (2)

Describe how to derive best estimate base mortality rates

Answer 5

1. Base rates usually uses adjusted rates from standard table
   
   • cheaper than own investigation
   • less errors eg inappropriate graduation
   • Larger samples sizes, esp at extreme ages
2. Adj based on own data (similar class of business)
   
   • data must be for relevant period and credible
     
     • conflict bet large # data and creation of heterogeneous groups
   • analysis divide data into relevant credible homogenous groups

Question 6

Best estimate mortality: base mortality derivation

What data sources can be used to det base rates

Answer 6

1. Data sources which can be used for adjustments
   
   • own past experience with that product,
   • own past experience with similar product(s),
   • reinsurance data
   • industry data i.e. standard tables
   • international data
   • national statistics

TRAINERS

Question 7

Best estimate mortality: base mortality derivation data sources

State advantages and disadvantages of these sources.

Industry wide investigations (3)

Population mortality statistics (2)

Reinsurer data (5)

Answer 7

• Industry wide investigations
  
  • useful for contracts where no standard table exists
  • good for showing trends, since trends in own data might be due to statistical variation
  • not 100% suitable since not based on insurer’s particular PHs
• Population mortality statistics
  
  • useful for showing trends if re-examined at regular intervals in past
  • not 100% suitable since not based on insurer’s particular PHs
• Reinsurer data
  
  • Adv
    
    • access to mortality experience of many direct writers
    • may be most relevant data available
  • Disadv
    
    • relates to large number of different companies
    • may have little/no suitable data
    • comes with a cost: cost of reinsurance

QUERIED/ QRCFD

Question 8

Best estimate mortality:
Mortality trends

Answer 8

• The mortality trend relates to how the rate of mortality changes over time.
• Estimating future mortality improvements is particular important:
  
  • for policies with longevity risk e.g. annuities
  • when rates are guaranteed rather than reviewable
• CHANGE DOG => factors that affect mortality

Question 9

Different approaches used to project mortality trends (3)

Answer 9

• Different approaches to project mortality trends over time:
  
  • expectations: uses expert opinion to specify range of future scenarios
    
    • can implicity include all relevant knowledge, incuding quantitative factors
    • subjective and subject to bias
  • extrapolation of historical trends
    
    • project historical mortality trends into the future
    • some subjectvity: choice of period to determine trends
  • explanatory projection techniques,
    
    • modelling bio-medical processes that cause death
    • only effective to extent process understood and mathematically model-able

Question 10

Best estimate mortality: mortality trends

State how each of the following might be taken into account when making projections of future mortality:

1. cohort effect
2. the combined effects of multiple factors
3. random effects

Answer 10

• 4 main cause: circ diseases, cancer, respiratory, infections
• Cohort effect
  
  • each year of birth cohort is modelled seperately,
  • allowing for specific mortality improvemebt rates by cohort
  • take into account smoking levels, alcohol consumption etc
• Multi-factor effects
  
  • Use multi-factor predictive modelling techniques (eg. generalised linear models),
  • Combine internal data with external factors affecting mortality,
  • Allowing for any correlations and interactions between them.
• Random effects
  
  • Use stochastic modelling (e.g. Lee-Carter or P-spline method)
  • Hard to calibrate as need understanding of drivers of mort

Question 11

Morbidity rates: Disability incidence and duration for IP

Describe how these rates may be determined (4)

What factors might affect the transition intensities (5)

Describe how rates are used (2)

Describe issues surrounding estimating these rates (3)

How might we control parameter uncertainty for these rates? (3)

Answer 11

• Benefits for IP can be modelled using a multi-state approach
  
  • ​​needs transition intensities (claim inception, recoveries, death)
  • calculated for homogenous groups
    
    • duration: revovery may differ vastly by duration in force
    • disability type: recovery may dif vastly by disability type
    • may seperate second/subsequent incidences: as more likely to claim in future
• Intensities influenced by
  
  • PH characteristics: identified at underwriting
  • prod design features: replace ratio/rehab benefits
  • economic morale: low => more likely claim
  • government welfare provision
  • tax: on premiums (discourage sales), relief on prems (enoucourage sales), way insurer is taxed, tax rates involved changing over time
• Intensities used to calc transitions probabilities
  
  • then construct projected numbers/proportions in each state at future ages.
  • can be used to calc claim inception rates/disability annuity values
• Issues surrounding estimating rates
  
  • Data limitations is the main issue
  • Published insurance incidence data has limited credibility
  • Worldwide stats may not be relevant
• Controlling parameter uncertainty
  
  • Assuming larger risk margins
  • Issuing products with reviewable premiums/charges
  • Reinsurance

Question 12

Morbidity rates: Incidence rate for CI

What factors influence claim distribution rates for CI (4)

What kind of factors complicate modelling/setting of assumptions (2)

Answer 12

• May be necessary to estimate significant number of distributions (40+) if each condition modelled seperately, plus allowance for future trends
• Other influences claim distribution (other than trends), include
  
  • advancement in medical science (cures=> more windfalls)
  • diagnosing conditions earlier (more claims)
  • simple/more readily available operations (more claims)
• influence new and existing business seperately
  
  • new business, can adjust premiums accordingly
  • existing business, can only adjust in force prems if revieawable
• Factors which complicate modelling/setting assumptions
  
  • using a disease-based and/or treatment-based claims definiton
    
    • These will need to be modelled separately=> est of rates => param risk
  • guaranteed and reviewable alternatives
    
    • lack of data limited past exp build up
    • product not around long enough

Question 13

Morbidity rates: Incidence and amount for LTCI

What key assumptions do we need to estimate for LTCI? (2)

What are important factors for LTCI contract assumptions? (5)

What issues arise when estimating necessary assumptions? (3)

Answer 13

• Estimate distribution of
  
  • Claim frequency
    
    • Medical advancements
    • Transition rates: improved health may reduce inception rates and rates for people moving to higher ben-levels
    • Mortality rate: improved health=> people needing benefits for longer
    • Data limited, no stats available
  • Claim amount
    
    • No control if indemnity unless cap
    • Costs: changing med care may => higher costs e.g. more expensive procedeurs
    • inflation: big problem if benefits are indemnity based
    • demand (for LTC) vs supply, usually demand is greater, leading to inflation heaveir than economic inflation

Question 14

Morbidity assumptions

Expand briefly on how size of benefit may impact morbidity assumptions (4)

Answer 14

• Impact of benefit size on assumptions
  
  • For IP, CI, and most LTCI, benefit amount fixed, so no assumption needed
  • But may be correlation between incidence rates and benefit size
  • Large policies, may want to alter assumptions,
    
    • to reflect better claims experience as PH rich
    • stricter level of underwriting
    • Use benefit amt as rating factor

Question 15

Investment return:

List 4 factors that affect the value assigned to the investment return assumption when pricing a life insurance contract.

(1,3)

(2,1)

(4,3)

(3,3)

Answer 15

Significance of assumption on profitability depends on:
1. Level of reserves
* Larger reserves => + prop of inv inc in CF’s => + sens inv inc
2. Extent of investment guarantees given under the contract.
* This will affect asset mix
* more onerous the guarantee => more cautious assets selected => cautious investment return assumption
3. Intended investment mix for contract, current return and, where appropriate, likely future returns on this mix
* Analyze past and current yields
* Predict returns from future asset mix
* Asset mix derived from level of free assets to cover NUB, + => mismatch
4. Extent of any reinvestment risk, and extent to which reinvestment risk can be reduced by suitable asset choice
* overall best estimate investment assump will reflect expected balance btwn expected future and current investment yields
* if real cashfow positive in future => requires purchase of future assets. more this happens=>investment assump reflect expected future experience
* mismatching may mean need to buy/sell assets, so future investment yields still important

Question 16

Investment return: Market consistency

For a contract that is priced using a market-consistent approach, how do we set investment return assumption? (3)

Comment on this process specifically for stochastic modelling (2)

Comment on this process specifically for deterministic modelling (3)

Answer 16

• For market consistent approach
  expected investment return should be set as the risk-free rate
  irrespective of the actual underyling assets held
  this is true for both stochastic and deterministic models
• If stochastic modelling is used
  
  • need additional assumptions for investment return volatility and correlation assumptions
  • which are dependent on actual underlying assets
• If deterministic modelling is used
  
  • use risk-free rate appropriate to term of each cashflow
  • actual assets held are irrelevant
  • eg when pricing an annuity*

Question 17

Investment return:

Allowing for tax (5)

Allowance for future bonuses (3)

Answer 17

• Need to allow for tax on investment returns (if fund subject to tax)
  
  • apply appropriate tax rate to different components of tax return
    
    • eg income gain vs capital gains, or different asset classes’ tax
  • need to allow for assumptions re future tax rates
    
    • best to use current rates, allowing for imminent known changes
• Allowance for future bonuses
  
  • usually see higher premium rates on WP business than for conventional business,
  • assumption about future bonuses that intend to declare/included in premium rate,
  • either done by
    
    • convervative assumptions => reduced investment return assumpt
    • realistic assumptions, with explicit allowance for future bonuses in premium

Question 18

Expenses + commission:

What is the general principle when setting expense/commission assumptions? (1)

How might the expense assumptions be determined? (3)

Comment on the use of an expense model (1)

Comment on how fixed expenses should be catered for (1)

Give examples of marginal expenses which may arise (8)

Answer 18

• Expense and commission assumptions should reflect expected expenses to be incurred in processing/subsequently administering business
• Fixed expenses
  
  • Expense loadings should contain contribution for expenses not covered in marginal expense categories.
• Marginal expense examples
  
  • Initial acquisition (incl commission), initial medical underwritng, initial administration, renewal administration, sales channels’ renewal rewards, investment, withdrawal/PUP (usually allow for via suitable discontinuance terms), claim/maturity
• Assumptions would be determined by
  
  • analysing recent experience of existing business
  • Industry data
  • RE data
• Can be modelled:
  
  • an expense model used to project staff structure,overheads,buildings, systems
  • incl expected new business volumes and NUB mix
  • Tested for reasonability

Question 19

Expenses Analysis A311

Answer 19

All expenses of the organization must be identified and categorized as direct / indirect.

Direct expenses can be immediately allocated to a particular class of business.

Indirect expenses must be pragmatically apportioned between classes of business.

Not only must expenses be allocated to class but also to function, i.e. securing new business, maintaining existing business and terminating business.

Finally, an appropriate loading type must be determined, e.g. a fixed amount per contract / claim, a percentage of premium / sum assured / funds under management or a combination of these approaches.

Question 20

Per policy expenses

Describe 3 methods of allowing for expenses that do not vary by policy size when setting premium rates or charges (3)

How do we incorporate commission in the expense assumption? (1)

How might tax be allowed for re the expense the assumption? (1)

Answer 20

• Do not vary by size of contract
• 3 methods to allow for per policy expenses:
  
  • Individual calculation of premium rates or charges
    
    • Calc prem normally and load explicity for pp expenses
    • Done for large and small polices
  • Policy fee addition to premium
    
    • charge a fee that covers pp expenses only
    • Prem loadings cover rest of the expenses
    • issue w/small policies - fee to - prem but + loadings to make up costs - fee
  • Sum assured differential
    
    • charge different premium rates according to SA band
• Commission rates
  
  • Aligned with market comm rates in which sales occur,
  • including extra pmts to distr channel eg. on achievement of certain high production targets.
• Expense treatment might be affected by tax regime. If “I-E” tax applies, can net expenses down for this (must be in line with investment income expense treatment)

Question 21

Expense inflation:

What will primarily affect the inflation assumption, and why? (2)

What 2 ‘periods’ for should be considered when setting the expense inflation assumption? (2)

List 5 factors that will considered when setting the expense inflation assumption for pricing (5)

Answer 21

• Key impact on inflation will likely be earnings inflation, as insurer’s expenses are mostly staff related
• Consider
  
  • inflation between pricing and sale
  • inflation from inception to termination
• 5 Factors affecting expense inflation
  
  • Current rates of inflation, both for prices and earnings
  • Expected future rates of inflation
  • Difference between fixed-interest government bond yields and index-linked government bond yields = exp inflation
  • (may be skewed by any risk premium implicit in price of government fixed interest bonds)
  • Recent actual inflation experience of life insurance company or industry
  • Investment assumption being used (be consistent)

Question 22

Persistency

Outline how to set the persistency assumption when pricing a product (7)

Answer 22

1. Pricing method being used: persistency assumptions needed if using cashflow method, not if using formula method
2. Withdrawal assumpt reflect expected future experience of contracts to be taken out (eg full withdrawal, partial, and paid-up)
3. Based on analysis of company’s recent experience, ideally of same contract, else of any similar contracts
4. If company doesn’t itself have adequate data, there may be indutry-wide experience it could use
5. Assess results to see if they have been affected by special factors, e.g. adverse economic situation
6. Adjust for differences in class of lives, e.g. benefit changes, distribution channel changes
7. Sensitivity test/add appropriate margins
   
   • withdrawal rates significantly impacted by economic state/commercial factors which are diffiicult to predict.
   • therefore important to sensitivity test/add margins

Question 23

Persistency:

What changes to benefits might lead to increased withdrawals? (6)

How might distribution channels impact withdrawals? (5)

Answer 23

Benefits

• Non-linked
  
  • Increase in discontinuance terms
  • Decrease in bonuse rates
• Unit-linked
  
  • Reduced fund performance
  • Increased charges
  • Removal/variation of guarantees/options

Distribution channel

• Who initiates the sale: lower withdrawal if client initiates
• Different sales practice: client pressurised for sale => higher rates
• Sales without gathering proper info: mis-selling
• Financial sophistication: varies by channel=> impacts rates
• Target markets: affected by dist channel, hence PH’s affluence + level of economic wealth

Question 24

Margins
How might we allow for risk in the use of parameters? (3)

What key factors infuence the margins to use? (3)

Answer 24

• Parameters discussed so far would only be best estimate parameters.
• We can allow for risk through:
  
  • the risk discount rate
    
    • only applicable to cashflow model
  • using stochastic approach
    
    • only applicable to cashflow model
    • using best estimate for non-stochastic assump,
    • use a risk free rate, modelling one/more assumption stochastically
    • Choose percentile to get act premium from dbn
  • including margins
    
    • eg RDR = Rf rate
    • eg inv ret = best est - margin
    • applicable to either cashflow/formula model
    • formula model needs judgement, as doesn’t help actuary determine extent of risk
• Size of margins depends on
  
  • degree of risk associated with each parameter used
  • financial significance of the risk from each parameter
  • purpose for assumptions
    
    • pricing => competitiveness (but also prevent losses)

Question 25

Profit requirements:

Explain what is meant by the term risk discount rate (5)

Answer 25

• RDR = req ret by SH for capital
• It’s made up of:
  
  • return they could get obtain from risk-free asset
  • plus risk premium to compensate for volatility of return
• demand higher returns for higher risk (default)
• market availability of capital should also be taken into account
  
  • Hard to raise offer > ret on capital by + RDR
• market’s view of risk discount rate is not necessarily most apt for any given product, as different products will have different levels of riskiness.

Question 26

Profit requirements:

Deciding on a risk discount rate

Outline how CAPM can be used to give guidance on the RDR to use (5)

Answer 26

• CAPM
  
  1. Assumes
     
     1. Perfect market (well-diversifed portfolio available to diversify risk, leaving unavoidable inv risk only)
     2. Perfect information
     3. investors want risk free return (suitable proxy for Rf asset) + risk premium (measure risk)

4. Ei = rf + (Em-rf)Bi
5. Bi = Cov(Ri,Rm)/Var(Rm)
6. (Ei-rf) = risk premium prop to (Em-rf)= mkt risk prem
7. Bi measure of riskiness of asset:
   
   • Bi>1=> mkt price + => asset val +/- > mkt avg
   • Measure of systematic risk (cannot be diversified away)
   • No reward for specific risk

Question 27

Profit requirements:

Deciding on a risk discount rate

Why can’t we simply use CAPM? (2)

What might affect the riskiness of products/projects undertaken by insurer? (6)

Answer 27

• Can’t simply use CAPM as
  
  • assumptions may not hold
  • not all projects company undertakes are equally risky (some products have more innovative features, eg)
• 6 things that might affect riskiness of products/project life company undertakes
  
  • Lack of historical data
  • High guarantees
  • Policyholder options
  • Overhead costs
  • Complexity of design
  • Untested market
• RDR = rf + allowance for riskiness of products
  
  • Difficult to assess this risk => use stat methods

Question 28

Profit requirements:

Deciding on a risk discount rate using statistical methods

How might we use a statistical approach to asses the insurer’s risks and allow for them in the RDR? (4)

Answer 28

• Can assess these risks (and allow for them) by
  
  • analytically, by considering variances of individual parameter values used i.e VaR[Return]
  • sensitivity analysis : assess change in assump => change in profit
  • using stochastic models: stoch params are NB ones=> est var of return
  • comparison with any available market data

Question 29

Profit requirements:

How do we bring together the 2 approaches for deciding on the RDR? (CAPM and statistical) (7)

Answer 29

• Bringing CAPM and statistial meths for RDR estimation together
  
  1. Ei= true level of return for risk of comp
  2. Less risky => req lower RDR than Ei and v.v.
• also consider that
  
  1. risk reduces as profit emerges, but fundamental risk profile remains the same
  2. RDR must be more than risk free; risk free changes, so does RDR
  3. Margin between risk free and RDR must attempt to reflect all risk sources on product
  4. RDR on different products=> reflect relative risks of products
  5. RoC on whole company must meet required rate of return from capital providers
  6. RDR is number used as profit criterion in profit testing to ensure RoC is suff

Question 30

Profit requirements: profit criteria (1) and market consistent valuation (3)

Answer 30

• Profit criteria must be decided on that has to be met by pricing premiums/charges, given assumptions used…remembering that this too is actually an assumption which affects the overall outcome
• Market consistent valuation
  • Alternative approach to using RDR is to use market consistent valuation
  • Effectively uses risk free rate for discount rates, generally modelled as term dependant
  • Would then include margins in other parameters (expenses, mortality, persistency) to allow for risk in their estimation

Question 31

Consistency between assumptions is of vital importance.What do we mean by consistency? (3)

Answer 31

• By consistency, we mean
  
  • considering assumptions in totality, not just isolation
  • realistic allowing for how variables behave together, if where correlated
  • sometimes relationships between 2 parameters more important than absolute value

Question 32

Consistency between assumptions: examples

Give some examples of aspects where consistency is important between parameters used (6)

Answer 32

• Investment return and inflation
  
  • long term relationship btwn expense inflation & returns on diff asset classes must be valid
  • sometimes, no need to allow for future investment conditions if no reinvestment risk exists
• Tax
  
  • if company taxed on “i-E”, investment income and expense assumptions must reflect this
  • profits from profit testin should be measured net of tax
• Investment return and bonus loading
  
  • consistent in situations where bonus must be loaded for specifically
• Withdrawal rates and investment return
  
  • lapse rates affected by general economic climate, which feeds into investment return
  • lapse also affected by: bonus levels, discontin terms, renewl comm
• Consistency with other products
  
  • basis be consistent with other related products.
  • inconcistency could lead to similar products being sold at different prices, affecting consumer buying/discontinuance
    
    • lapse and re-entry
    • bad publicity/marketing risk
    • profits will be at increased risk from changes in new bus mix
• New business and expenses
  
  • Loadings for expenses: such that given anticipated sales volumes over expected lifetime give total loadings which recoupe develop costs + pay fair share towards company overheads
  • Profit contribution: if new bus assumptions don’t turn out to have been optimistic, product shold make additional profit contribution
  • Assumption should reflect competitive position: or product in market