Ch 21: Assumptions 1

Question 1

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 1

• Assumptions used by insurers for variety of reasons, mostly assessng eventual cost of liabilities (pricing, reserving and ongoing profitability measurement)
• Setting assumptions may => 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 liabilities for future payouts
2. Inflation risk: relates increase in inflation-linked liabilities + liabilities behaving approximately in line with inflation (eg expenses)
3. Marketing risk: ability to satisfy policyholders in relation to any investment-linked/discretionary benefits.

Question 2

Best estimate mortality:

List 2 seperate parts of moratlity to be considered when setting best estimate mortality assumptions (2)

Answer 2

1. Base mortality: initial rate of mortality, the main demographic assumption for pricing/evaluating life insurance contracts
2. Mortality trend: how mortality rate changes over time

Question 3

Outline a general process for setting assumptions (5)

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
   • sensitivity of results for a given parameter

Question 4

Best estimate mortality: base mortality derivation

Describe how to derive best estimate base mortality rates, in terms of

rates reflecting future experience (3)

Answer 4

1. Rates should reflect expected future experience of lives to be insured by contract being priced, in terms of
   
   • target market: affected by distribution channel
   • underwriting controls:
   • expected experience change: since last historical investigation, to point assumptions will apply on average (usually 10 - 15 yrs)
2. The company will usually use standard mortality tables and adjust them for expected future experience

Question 5

Best estimate mortality: base mortality derivation

Describe how to derive best estimate base mortality rates, in terms of

what rates are actually based on + adjustments (7)

Answer 5

1. Base rates usually uses adjusted rates from standard table
   
   • saves resources
   • protects against errors eg inappropriate graduation
   • sufficient data: analysis own experience=> derive adjustments
   • data must be over _enough years (_adequate volume), but also few enough years (prevent excessive heterogeneity from trends over time)
   • analysis divide data into relevant homogenous groups
   • further adjustments if different experience expected from that which analysed data relate (target market, underwriting , distribution method)
     *

Question 6

Best estimate mortality: base mortality derivation

Describe how to derive best estimate base mortality rates, in terms of

data sources (6)

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

Question 7

Best estimate mortality: base mortality derivation data sources

In using data for adjustments when deriving best estimate base mortality rates, list some pros/cons related to the following data sources which may be used:

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
  
  • Ads
    
    • access to mortality experience of many direct writers
    • may be most relevant data available
  • Disads
    
    • relates to large number of different companies
    • may have little/no suitable data
    • comes with a cost: cost of reinsurance

Question 8

Best estimate mortality: mortality trends

What do we meant by ‘mortality trend’? (1)

State 2 circumstances where the estimation of future mortality improvements is particularly important (2)

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

Question 9

Describe how we might consider expected changes in mortality over time

Different approaches used to project mortality trends (3)

Considerations to the product (2)

Answer 9

• Different approaches to project mortality trends over time:
  
  • expectations: uses expert opinion + subjective judgement 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
• Considerations should also be given to the product e.g.
  
  • important for contracts paying significant death benefit
  • important for annuities where increased longevity is a risk
  • not important for single premium savings contracts

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

• Cohort effect
  
  • each year of birth cohort is modelled seperately, allowing for specific mortality improvemebt rates by cohort (as well as by age and sex)
  • • Multi-factor effects
  • Use multi-factor predictive modelling techniques (eg. generalised linear models), accounting for personal attributes along 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)

Question 11

Morbidity assumptions

What factors/kind of rates should we consider when setting morbidity assumptions (4)

Answer 11

• Key factors/assumptions

1. Disability incidence rate and duration for IP
2. Incidence rate for CI
3. Incidence and amount for LTCI
4. Impact of benefit size on assumptions

Question 12

Morbidity assumptions

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

Answer 12

• Impact of benefit size on assumptions
  
  • For IP, CI, and most LTCI, benefit amount fixed, so no assumption needed for this
  • But may be correlation between incidence rates and benefit size
  • Only for very large policies, may insurer want to alter assumptions, to relfect better claims experience from
    
    • PH belonging to higher socio-economic class
    • stricter level of underwriting

Question 13

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 13

• 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 14

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 14

• 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
  
  • may need to model seperately model claims defitions which are disease-based and/or treatment-based (eg coronary artery bypass, major organ transplant, heart valve replace)
  • guaranteed and reviewable alternatives
  • lack of data, only cancers/heart attacks will provide enough data…otherwise hasn’t really been around long enough

Question 15

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 15

• Estimate distribution of
  
  • claim frequency
  • claim amount (if funding for care)
• Important influences for LTCI assumptions
  
  • 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
    • Costs: changing med care may => higher costs e.g. more expensive procedeurs
  • Economic factors
    
    • inflation: big problem if benefits are indemnity based
    • demand (for LTC) vs supply, usually demand is greater, leading to inflation heaveir than economic inflation
• Issues arising when estimating necssary assumptions
  
  • Data limitations
  • Little data on claim frequency to base estimates of future transition rates
  • Absence of insurance statististics (industry data)

Question 16

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 16

1. Significance of assumption. This depends on:
   
   • level of reserves (larger reserves => more important)
   • extent of investment guarantees
   • can be significant assumption, even if not much investment risk eg single premium conventional term ass (due to reserve size)
2. Extent of investment guarantees given under the contract. This will affect asset mix
   
   • more onerous the gaurantee => more cautious assets selected => reflected cautious investment return assumption
3. Intended investment mix for contract, current return and, where appropriate, likely future returns on these assets
   
   • consider likely asset mix
   • investigate returns on assets
   • predict future returns bearing impact of future changes to economic environment
4. Extent of any reinvestment risk, and extent to which reinvestment risk can be reduced by suitable asset choice: the less important reinvestment risk the less account needs to be taken of future investment yields
   
   • overall best estimate investment ass 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 ass reflect expected future experience
   • even if negative real future cashflows=> mismatching may mean need to buy/sell assets, so future investment yields still important

Question 17

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 17

• 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 udnerlying 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 18

Investment return:

Allowing for tax (5)

Allowance for future bonuses (3)

Answer 18

• Need to allow for appropriate allowance 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, by making some assumption about future bonuses that intend to declare/included in premium rate, either done by
    
    • convervative assumptions, reduced investment return
    • realistic assumptions, with explicit allowance for future bonuses in premium

Question 19

Non-marginal 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 19

• Expense and commission assumptions should reflect expected expenses to be incurred in processing/subsequently administering business
• Assumptions would be determined by
  
  • analysing recent experience for type of business concerned..
  • …dividing expenses by function, as appropriate, and possibley whether expected to be proportinal to premium/benefit, or an amt per contract
  • if insufficient own data? use similar other product. else industry data, else reinsurance data
• In practice, an expense model may constructed/used to project staff structure/associated overheads.
  
  • Output taken in conjunction with expected new business volumes to give suitable per policy/per premium costs.
• Fixed expenses
  
  • Expense loadings should contain contribution for expenses not covered in marginal expense categories, but distinction between fixed/marginal sometimes blurry.
• 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

Question 20

What is a key risk when setting per policy expenses? (1)

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

• A key risk when setting per policy expenses relates to how to incorporate expenses that do not vary by size of contract
• 3 methods to allow for this risk:
  
  • Invididual calculation of premium rates or charges
    
    • normally only for very large cases as small cases would be very uncompetitive
    • • Policy fee addition to premium
    • (or deduction from regular benefit payments) for non-linked contracts or charges that match per policy expenses for unit-linked contracts
    • • Sum assured differential i.e. for non-linked contracts,
    • charge different premium rates according to which band benefit falls into and for unit-linked contracts apply different charges )(e.g. allocation rates) according to which band premium payable falls into.
• Commission rates => likely aligned with market company intends selling product in, including extra pmts to distr channel eg. on achievement of certain high production targets.
• Expense treatement 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 setting assumption, and point from which new policies will be sold
  • inflation during term of policy
• 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 (may be skewed by any risk premium implicit in price of government fixed interest bonds)
  • Recent actual 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. 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

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:
  
  • through the risk element of the risk discount rate
    
    • only applicable to cashflow model
  • using stochastic approach
    
    • only applicable to cashflow model
    • using best estimate for non-stochastic assumptins, using a risk free rate, modelling one/more assumption stochastically
  • assessing margins to apply to expected values
    
    • and using a risk free rate to discount
    • applicable to either cashflow/formula model
    • formula model needs judgement, as doesn’t help actuary determine extent of risk
• Use 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

• return on capital demanded by providers of that capital. It’s made up of:
  
  • return they could get obtain from risk-free asset
  • plus risk premium to compensate for volatility of return
• can be determined by quantifying risk premium appropriate for company e.g. using CAPM
• market availability of capital should also be taken into account
• 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

What methods can be used to determined RDR? (2)

Answer 26

• To determine RDR, can use
  
  • CAPM
  • Statistical methods

Question 27

Profit requirements:

Deciding on a risk discount rate

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

Answer 27

• CAPM
  
  1. Assumes
     
     1. Perfect market (well-diversifed portfolio available to diversify risk)
     2. Perfect information
     3. investors want risk free return + risk premium
  2. Choose suitable proxy to represent risk free asset
     
     1. eg gov issued: short term deposits, bonds, long dated infl-linked bonds
  3. Estimate average risk premium which well-diversified portfolio has yileded over the risk free rate over a period of time
  4. Risk premium in proportion to Beta=> use to estimate Beta
  5. From Beta we can estimate expected return for company as
     
     1. Exp Return = risk free + Beta*(Exp Market Return - risk free rate)
  6. Doesn’t allow for specific risk of company, only market risk

Question 28

Profit requirements:

Deciding on a risk discount rate using statistical methods

Why can’t we simply use CAPM? (2)

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

Answer 28

• 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

Question 29

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 29

• Can assess these risks (and allow for them) by
  
  • analytically, by considering variances of individual parameter values used i.e VaR[Return]
  • sensitivity analysis
  • using stochastic models
  • comparison with any available market data

Question 30

Profit requirements:

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

Answer 30

• Bringing CAPM and statistial meths for RDR estimation together
  
  1. If we consider CAPM to give overall true expected return required, then less risky than average products will have RDR < CAPM return, and vice versa
• 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

Question 31

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

Answer 31

• 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 32

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

Answer 32

• 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 33

Consistency between assumptions: examples

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

Answer 33

• 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…who’s basis may even form a starting point for the new prod
  • inconcistency could lead to too 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