Chapter 17.18 Setting assumptions Flashcards
Outline a general process for setting assumptions (5)
- Investigate past experience; make past best estimate parameters; appropriate in context of historical conditions/then-circumstances
- Consider future conditions (including commercial and economic environment ) during period for which assumptions will be used
- Determine future best estimates assumptions, given expected future conditions
- Extent of (a) relying past data vs (b) allowing for other factors, depends on data credibility/relevance + parameter’s predictability
- Adjust best estimates with margin. Size of margin depends on:
purpose for which model is required
degree of risk associated with parameter
Different approaches used to project mortality trends (3)
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
to reduce the volatility in the mortality assumptions
Smooth the rates over time to avoid large fluctuations year by year [1]
Only change rates where there is a material reason to do so [½]
Increase the number of years data included in the investigation to improve the credibility [1]
but put more weight on recent years’ experience to ensure the experience is relevant. [½]
Reduce the number of cohorts [1]
to increase the exposed to risk [½]
and improve the credibility in each cohort [½]
Mortality BE consideration
the base mortality, ie the initial rate of mortality
the mortality trend, ie how the rate of mortality changes over time.
Homogeneous groups are likely to be derived by categorising according to:
age (not necessarily by year of age – at extremes of the age spectrum five-year groups
might be sensible)
gender
medically underwritten (normal life) vs medically underwritten (abnormal) vs not
medically underwritten
smoker vs non-smoker
distribution channel
possibly some form of broad grouping by occupation and/or geographical area.
if the mortality is under-estimated the company is at risk of a substantial loss
if the mortality is over-estimated the company is at risk of not selling the product.
Investment return
The two key factors which lead to sensitivity to the investment assumption are the size of the
reserves built up (relative to the cashflow, for example), and the investment guarantees given.
The larger the reserves, the greater the proportion of total cashflow (and profit) that arises from
investment income, and hence the greater will be the sensitivity to changes in the investment
return.
Market-consistent valuation for investment return
If a market-consistent approach is used then the expected investment return can be set as the
risk-free rate (regardless of the actual assets held). However, the investment return volatility
and correlation assumptions depend on the actual assets held.
The discount rate would also be set as the risk-free rate.
A margin is likely to be included in the other parameter values to allow for the risk in their
estimation.
Risk discount rate
The capital asset pricing model. The idea behind the CAPM is that a well-diversified portfolio of shares cancels out the risks of investing in individual shares and leaves only the unavoidable risks of investing in the stock exchange.
The following are among the features that can make a product design riskier, viewed as an
investment:
lack of historical data
high guarantees
policyholder options
overhead costs
complexity of design
untested market.
So one way to derive the risk discount rate would simply be to take the ‘risk-free’ rate (which we
can assess by looking at the yields on short-term government bonds) plus an allowance for the
riskiness of the product being sold.
Describe how a risk discount rate could be determined that reflects the expected level of
statistical risk, for a given new product, including the use of the following:
deterministic sensitivity analysis
stochastic simulation.
The following steps could be performed.
(1) Calculate some trial premiums for the product, based on best estimate assumptions of
future experience, and using the shareholders’ required return as the risk discount rate.
(2) Calculate the return on capital generated by these premiums, on the basis of a range of
different deterministic scenarios for the future experience. The scenarios used should
include adverse outcomes that have a feasible likelihood of occurring, for example with a
5% probability. (The actuary would need to devise these scenarios using his or her
judgement, based on historical experience, and on analysis of all the factors likely to
affect the experience in the future.) Should the return on capital obtained fall below
some required minimum level (such as the risk-free rate of return), then the premium
should be increased until this criterion is satisfied.
Alternatively, should the return on capital be consistently much in excess of the required
minimum level, then there may be justification in reducing the premium. (The company
would have to consider whether the product concerned represented a ‘lower than typical’
level of riskiness for the company in order to justify this – we have to keep in mind that
the overall required return reflects other factors than just statistical risk (eg the
availability of capital)).
Use these new premium levels in the next step.
(3) Repeat step (2), only this time modelling the variables stochastically. Calculate the
frequency (out of many simulations) with which the return on capital falls below the
required minimum rate. If this frequency is too high (say more than 5%), then the
premiums could be further raised until a 5% frequency is obtained. (Or premiums could
be reduced if the frequency is too low). Use these new premium levels in the next step.
(4) Calculate the return on capital obtained from any new level of premium produced from
steps (2) or (3), using best estimate experience assumptions. This new return on capital
can then be used as the new risk discount rate. This new risk discount rate now takes
account of the levels of statistical risk for the product.
The basis for a valuation will depend on whether the accounts are to be published or are
only for internal use.
Any published accounts may be subject to legislative constraints, in particular regarding:
whether a going-concern or break-up basis is to be used
whether the accounts have to be true and fair
whether assumptions should be best estimate or include margins.
going concern
assume insurer continues issuing new bussiness into future
break-up
assume new business cease immediately, or at some point in future e.g
…closed fund by company, or..
…transfer liabilities to another insurer, who will administer/procress claims until book runs down
Calculation of embedded value
Embedded value is the present value of shareholder profits in respect of the existing
business of a company, including the release of shareholder-owned net assets.
It can be calculated as the sum of:
The shareholder-owned share of net assets, where net assets are defined as the
excess of assets held over those required to meet liabilities.
The present value of future shareholder profits arising on existing business.
The value of the shareholder profits may be calculated as follows:
conventional without-profits business: the present value of future premiums plus
investment income less claims and expenses, plus the release of solvency reserves
unit-linked business: the present value of future charges (including surrender
penalties) less expenses and benefits in excess of the unit fund, plus investment
income earned on and the release of any non-unit reserves
with-profits business: the present value of future shareholder transfers, for example
as generated by bonus declarations
appraisal value
The appraisal value is the sum of the embedded value and the goodwill (ie the estimated
profits from future business). The appraisal value may be used when an insurance company is
to be sold.
Setting an embedded value basis
The expected future experience is usually taken as best estimate, unless more prudence is
needed for the particular purpose for which the accounts are required (eg published).
Risk can be allowed for by using a risk discount rate that is higher than the risk-free rate, or by
deducting a risk margin.
Discuss the risk to the company’s financial security that can be brought about by strengthening
the reserving basis.
The increase in capital strain per policy issued means that the company is more likely to become
insolvent on the supervisory basis. This assumes that volume of business and capital provision
remain unaltered.
If this were a significant threat, then the company would either have to reduce sales or increase
capital provision, either of which would have the effect of reducing future returns on capital.
Turning customers away would also send out very negative messages to the market, and may
deter intermediaries from recommending the company to customers in the future.
EV vs supervisory reserve assumption
The EV calculation will require experience assumptions (to project the business forward) as well
as reserving assumptions. [½]
The reserve values, including the required solvency capital, incorporated within the future profit
projections, should be calculated on a basis that is consistent with that used in practice, allowing
for any expected changes in conditions in the future that could affect the company’s reserving
basis. [1]
The experience assumptions used for the EV calculation will depend on the purpose for which the
EV calculation is needed. [½]
If the EV is required for internal purposes only, then the assumptions are likely to be the expected
values of the future experience, calculated realistically (ie without margins). [½]
The assumptions for an EV that are required for published accounts will reflect the purpose of
those accounts. For example, if they are required in order to present a true and fair view, they
will again be close to best estimates. [1]
If the EV is to be used as a basis for a sale price of the company, the basis could be prudent (on
behalf of the buyer) or optimistic (for the seller). [1]
The assumptions used for the supervisory reserves depend on the supervisory regime. [½]
For example, in some countries, reserves are set up on a relatively realistic basis, ie with relatively
small margins from the expected values, but there is a requirement for a substantial level of
solvency capital determined using risk-based capital techniques. [1]
In other countries, reserves are set up on a relatively prudent basis, ie with relatively large
margins, but with a relatively small solvency capital requirement. [½]
Whichever approach is adopted, the combination of reserves plus solvency margin should ensure
that the insurer holds enough assets to cover the liabilities on its existing business with a high
probability. [½]
