How can the margins added to assumptions be determined (includes CAPM)?
It’s all about the variance of the assumptions
- sensitivity test the assumptions to determine an appropriate margin
- determine the margin stochastically
- look at variance of assumption and assess margin analytically
What are the demographic assumptions and process of determining them
Mortality and morbidity, claim incidence, claim amount, lapse and renewal
- Collect data over base period
- Divide data into homogenous groups
- Calculate crude rates
- Graduate the crude rates
- Consider factors that have influenced the rates in the past and will continue into future
- Adjust factors and add margin for prudence
What factors that have influenced the rates in the past and will continue into future?
- Policyholder
- their education
- their lifestyle - Environment
- political
- economic downturn
- unemployment rates
- fertility/ageing population - Policy
- durations (survival, deferred, terms)
- policy coverage
- claims settlement delays
- distribution channels - Industry
- medical advancements > early detection, better treatments, higher costs
- changes in regulation or tax regimes
- competition environment
- shortage of medical staff
Real-world: discount rate
- shareholders need return for investing in insurance company
- shareholders need additional return based on risk taking on when insurer invests in specific project (pricing a new product)
To calculate 1 use CAPM
- assumes that if portfolio diversified enough, you are only exposed to risk of investing in the stock exchange not the risk of investing in a specific stock.
- E(Ri) = r + Bi (E(Rm)-r) can be used to determine the systematic risk
- Rm-r is the return required over and above the risk free rate for compensation of investing in the stock exchange
- Bi represents the riskiness of investing in this stock vs. the rest of the market, the higher this is the better the stock does when the market is performing well.
- Bi is cov(Ri,Rm)/var(Rm)
To calculate 2
- this is important because not all ‘projects’ are of equal risk
- projects become riskier: if high guarantees, lack of data, if there are options, if the design is complex and if there are big overhead costs
- this component is known as statistical risk, and can either add to 1 (if project is riskier than average) to take away from 1 (if project is less risky than average project)
- to determine
> compare with available market data
> determine stochastically by varying important parameter and seeing variance of rate of return
> determine deterministically through sensitivity testing of certain parameters that profits are most affected by
> determine analytically by looking at variances of parameters
Market consistent discount rate
- use swap rates or government bond yield curves to determine risk free rate
- the swap rates or yield curve used should vary according to the term
- risk discount rate reflect compensation required by the market
- margins are used in other assumptions (e.g. morbidity and expenses)
When it comes to economic assumptions, outline different approaches.
Risk discount rate:
- Risk-neutral: risk-free rate (gov bond yields/swap rates)
- Real-world calibration: CAPM + risk margin
Inflation rate
- Risk-neutral: inflation swaps
- Real-world calibration: historical inflation rates
Investment return
- Risk-neutral: risk-free rate (gov bond yields/swap rates)
- Real-world calibration: returns on assets now, predict future returns
Risk neutral vs. real-world
- if a real-world calibration you try and look at expected returns the assets will earn in the future
- if risk-neutral approach used, you assume all assets earn a risk free rate, to ensure that a consistent value for liabilities is calculated despite the actual assets invested in.
- real-world calibration is good for: valuations for internal purposes, for investment strategy
- risk-neutral approach is good for: valuations for solvency purposes (conservative approach), often required by regulators
- remember the risk premium ‘added’ to the risk free rate for growth assets, is not guaranteed. It may not pan out at all, but the assets is likely to earn at least the risk-free rate of return
Real-world: Investment return
- NB: depends on size of reserve, the delay between premium receipt and claim payment, guarantees given, duration of policy
- determine current returns assets are earning now
- consider the future asset mix and future corresponding returns
- the more assets and liabilities are matched, don’t need to rely on high investment returns to be able to meet future liabilities, so assumption matters less
- best estimate assumption reflected balance between returns expected in the future and current returns.
- if we expect positive cashflows in the future (i.e. income > outgo), then we need to buy assets in future, so incorporate reinvestment risk
- if we expect negative cashflows in the future (i.e. outgo > income), then we need to sell assets in future, so incorporate liquidity risk
- this rate should be net of any tax on returns
Real-world: Expense Inflation
- look at the mix of expenses that are sensitive to price inflation (rent, utilities) and those sensitive to salary inflation (salaries, benefits)
- determine historical inflation rates for each expense type over relevant period
- analyse trends/patterns in each expense type e.g. wage inflation > rent inflation
- compare with industry or peer inflation rates to make sure on track
- consider future changes: regulation, tax, technology upgrade, changes in business strategy or claims management upgrade
- calculate weighted average inflation rate to get best estimate assumption: 20% of expenses are salary-inflation related vs. 80% are price-inflation related
- consider the inflation rate could even increase between now and when the policy is issued too!
Commission and commission clawback
- commission depends on competitive rates in the market
- usually an amount if pre-agreed between broker and insurer
- legislation could be involved in calculation e.g. max limits
- forecast volumes of business under each distribution channel and the associated commission rate to get the commission payable
- commission can be expressed as: % of premium, % of sum assured or fixed amount
- the commission clawback depends on company’s own past experience and assumption may be different for different distribution channel
- should account for the fact that all commission that needs to be clawed back might not be
Tax
- depends on the tax rates within the region
- look at current tax regulations and try predict if any changes will be made.
- tax on premiums/ contributions: technically, insurer/sponsor not responsible for this tax but it should be incorporated into the premium/contribution rate
- tax on profits: don’t need to change any assumptions, just make sure that EPV net of taxes meets the required return.
- tax on investment income less expenses: investment return rates should be net of tax. Some rules may allow expenses to offset tax paid on investment income but only on straggered basis (i.e. over first 3-7 years)
Investment return investigation
Salary inflation investigation
Claims investigation
Mortality/morbidity investigation
Lapse rate investigation
New business investigation
