Part 3

Question 1

1. What is basic equity principle

Answer 1

• Interests of unit holders not involved in the transaction should be unaffected by that transaction
• A unitholder’s return is the difference between the allocation and subsequent redemption price of a unit
• This should depend only on the earning of the backing assets less charges It should be unaffected by any other unit transactions during the period otherwise cross-subsidies between unit holders will occur

Question 2

internal unit linked fund

Answer 2

• Consists of a clearly identifiable set of assets, for e.g. equities, properties, fixed interest securities and deposits.
• The fund is divided into a number of equal units of consisting of identical subsets of the funds assets and liabilities
• Responsibility for unit pricing rests with the company subject to any relevant policy conditions
• Some companies may create more than necessary to cover the corresponding liabilities. The excess is known as Box management.

Question 3

Appropriation price

Answer 3

• Price at which the company will create a new unit
• It is the amount of money that should be put into the fund, per unit created, that preserves the interests of the existing unit holders
• The net asset value per existing unit must not alter as a result of creating a new unit
• An offer basis means that unit prices (both offer and bid) are derived from the appropriation price.

Question 4

Expropriation prices

Answer 4

• Price at which the company will cancel a unit, this is when the fund is contracting and some of the assets backing the unit funds need to be sold
• It is the amount of money that should be taken out of the unit fund, per unit cancelled, that preserves the interests of the continuing unitholders
• The net asset value per existing unit must not alter as a result of cancelling any existing unit
• This will be used to determine the bid price of the units
• The offer price is the amount a policyholder will have to pay when purchasing units
• 2 types of adjustments
  
  • Initial charge - this is the expropriation price plus charges
  • Rounding
• A bid basis means that unit prices (both offer and bid) are derived from the expropriation price

Question 5

How do you calculate the Appropriation price and Expropriation price

Answer 5

• Market value (offer price)
• Plus expense
• Less the value of current liabilities
• Plus any accrued income from fixed income securities and deposits, net of any outgo such as fund charges
• Less tax
• plus the value of any current assets, such as cash on deposit or investments sold but not yet settled
• less the value of any current liabilities, such as investments purchased but not yet settled or loans to the fund
• This gives the net asset value of the fund on an ‘offer basis’.
• Dividing by the number of units existing at the valuation date, ie before any new units are created, gives the appropriation price
• Rounding of the unit price based on stated rules
• This gives the value under offer basis. Dividing by the number of units existing at valuation date.
• The appropriation price is the unrounded bid price
• Initial charge is added to the appropriation price to give the offer price
• Initial charge may also be referred as bid/offer price
• It is normal to quote bid of offer price to a certain number of decimals
• The rounding could be done in the company’s favour by rounding the offer price up and the bid price down

Question 6

Things to consider during a mergers and acquisitions

Answer 6

Basic equity pricing basis Other Practicalilities

Question 7

Basic feature of a life insurance model

Answer 7

• Single policy tests - This Projects the expected cash and profit flows from a single policy from the date of issue.
• New business model - This projects all the expected cashflows arising from future sales of new business. It is useful for assessing future capital requirements for new business and overal return on capital achieved
• Existing business model - This is cash and profit flows projection from all exisiting business a company has in force at a particular time. This is used to evaluate the intrinsic value of the existing business and testing solvency
• Need to account for cash flow
• Capital requirement for either supervisory or solvency
• Allowance for interactions
  
  • Interactions between assets and liabilities
• Allowances for guarantees and options

Question 8

How to assess solvency

Answer 8

Measuring solvency

• Economic values
• Static vs dynamic testing
• The need for capital and the role of the estate
• How to determine the future solvency
  
  • Use a model to project its future assets and liabilities
  • Specify its future solvency objective e.g. does it wish to determine its solvency objective on a regulatory basis or economic basis
  • A regulatory basis would determine solvency for supervisory reporting purposes and would assess the company’s ability to meet the regulatory requirements in the future
  • An economic capital basis would determine solvency using best estimate or market consistent approach and would enable the company to understand its ability to withstand future adverse experience
  • In some jurisdictions, the approach may be equivalent or very close
  • The company should decide whether to use a deterministic or stochastic model
  • A deterministic model could be used with best estimate assumptions
    
    • Combined with scenario or sensitivity tests to assess the impact of adverse future experience
  • Alternatively, at least some of the variable maybe modelled stochastically in order to look at a range of outcomes, particularly adverse scenarios that might pose a threat to solvency
    
    • Investment returns on various asset classes and associated economic variables, such as inflation are likely to b modelled using stochastic simulations
• Depending on the nature of the company’s products and so the importance of mortality or longevity risk, morality may also be modelled stochastically
• The company should decide how many simulations to run
• The company would need to decide a risk tolerance e.g. probability of insolvency in 1 years time to be less than 0.5%
• The company should decide over how long a time horizon it wishes to project its future solvency
  
  • e.g. it could look over a fixed planning horizon e.g. 5 years or until all the existing business has runn off
• The company should decide whether and to what extent to include future new business in tis projection of future solvency
• Including only the existing in force business is more objective and may be sufficient to satisfy regulatory solvency requirements
• Including future new business requires subjective assumptions to be made about volumes and mix of future business
• But will provide a more realistic assessment of the company’s likely future solvency position given its business plans
• As a full projection of future solvency might require nested stochastic calculations, the company may adopt a simplified approach

Question 9

Product design factors

Answer 9

1. Financing
   
   1. Unless the company has substantial capital resources, it will want the benefits and charges to be designed so as to minimise its financing requirement.
   2. The absence of any surrender penalties may increase the reserving requirements.
   3. However this depends on the allocation rate for the single premium. lf the allocation rate is sufficiently low, the company may immediately cover its initial outgo.
   4. The reserving requirements may also be increased by any mis-matching between charge income and expense outgo.
   5. Capital requirements may be increased if there is more uncertainty around the future experience of this new product than there would be of an existing product.
   6. The company may then have insufficient capital resources to support any new business strain, especially if new business volumes are high if the new product is a success.
2. Onerousness of guarantees
   
   1. The insurance company needs to decide whether to guarantee any charges, eg the AMC.
   2. Guaranteeing charges will increase the capital requirements of the product.
3. Regulation
   
   1. The company should comply with any relevant regulatory requirements, eg maximum charge caps.
4. Consistency with other products
   
   1. The company should compare its intended charges for this product with those on its other products.
   2. Lower charges on the new product may lead to customers with existing policies being unhappy, and so may increase the persistency risk on the existing business.
5. Extent of cross subsidies
   
   1. As the allocation rate and annual management charge will deduct more from larger policies than smaller policies, there will be cross subsidies between policies of different sizes.
   2. Such cross-subsidies would put the company at risk of the business mix changing and it having more smaller policies and fewer large policies than it expected.
6. Distribution channel
7. Competitiveness
   
   1. The company should consider similar products offered by competitors and, in particular, their charge levels.
   2. A low annual management charge (AMC) may be particularly important as it is the easiest point of comparison between different companies.
   3. The company should also consider other elements of competition, eg fund past performance or the range of unit funds offered.
   4. lf the company compares favourably in some of these elements, it may be able to set higher charges than otherwise and still remain competitive.
8. Risk characteristics
   
   1. The company should consider how the charges for the product affect the risks of the product.
   2. The AMC applied as a percentage of the unit fund means the company faces the risk of poor investment performance reducing its charge income.
   3. When considering the matching between expenses and charges, the company should consider matching by both nature and timing.
   4. Anti-selection
   5. The AMC may be a good match to any investment expenses and may also provide a broad hedge against inflation of ongoing policy expenses.
   6. The policy fee could be a good match to ongoing expenses …
   7. … especially if the policy fee increases in line with an inflation index.
   8. The company may face persistency (withdrawal) risk as there are no surrender penalties … …
   9. although the extent of this depends on the balance between a low allocation rate (which reduces this risk) and a high AMC and policy fee (which increases it).
   10. The company should test sensitivity of profit to key items of experience, eg unit fund performance, persistency.
9. Admin systems (and other expertise)
   
   1. The company’s systems would need to be capable of administering the types of charges the company is proposing.
   2. This will depend on how similar the product is to the company’s current products.
10. Marketability
    
    1. The company will want its new product to launch successfully and so will want the charges to be marketable.
    2. The level of charges (lower charges improve marketability)
    3. The flexibility to vary charges (more guaranteed charges improve marketability)
    4. How easy the charges are to explain the balance between the different types of charges,
       
       1. eg the management charge and policy fee might appeal more than a low allocation rate.
11. Profitability
    
    1. ldeally the product needs to be priced so that the total premium income cover the whole business will be sufficient to cover all benefits and expenses, including the required share of overheads and development expenses, and make at least the required level of profit.
    2. The company will need to consider the assumptions it will use for pricing the product.
    3. Key assumptions include mortality, investment and expenses.
    4. The intended backing assets will need to be considered, as these are crucially important to annuity pricing.
    5. These are likely to bonds (fixed-interest or index-linked as appropriate), with a possible use of corporate bonds to gain higher yields.
    6. The company will want to ensure that the charges overall will be able to cover the expenses incurred, including commission, and to provide adequate profit.
    7. An adequate profit is one that meets the required rate of return of the capital providers, eg the shareholders if the company is proprietary.
    8. Different profit measures may be considered, eg net present value, internal rate of return, discounted payback period.
    9. The company will need to estimate future expense levels, which may be difficult as this is a new product.
    10. The company also needs to decide on the extent to which the product will contribute to general overheads of the company…
    11. … and the period over which it wishes to recoup the product development expenses.
    12. The pricing assumptions also include inflation, new business volume and new business mix. The assumed mix of business will be important in order to set risk factors and model points’
12. Sensitivity of profit
    
    1. The sensitivity of profit to variations in experience needs to be considered.
    2. This will not only include the sensitivity to changes in the mix of business (due to cross-subsidies), but to all other components eg mortality, investment return, expenses, inflation and new business volume.
    3. Appropriate sensitivity tests, involving all these factors, would need to be carried out.

Question 10

How to calculate the Free Surplus

Answer 10

Assets

• We will use the market value if available

Liabiliites

• To determine the liabilities, future unknown parameter values and cashflows are set so as to be consistent with market values, … .
• where a corresponding market exists. ln particular, assumed future investment returns are based on a risk-free rate of return, irrespective of the type of asset actually held, and the discount rates are also based on risk-free rates.
• However, adjustments may be made for an illiquidity premium and for the uncertainty associated with non-hedgeable risks (eg yio a risk margin).
• For without-profits immediate annuities, longevity and expenses are non-hedgeable basis elements.

Question 11

Main risk with options in a policy for insurance companies

Answer 11

The main risk is that the cost of the option is higher than expected… .. and so the loading applied to the original premium is insufficient… … and so the company makes a loss.

Question 12

How to calculate the Expropriation price

Answer 12

• Market value is calculated on a bid price
• Less expense that would be incurred in the sale
• Plus the value of any current assets, such as cash on deposit or investment sold but not yet settled
• Less the value of any current liabilities, such as assets investments purchased but not yet settled or loans to the fund
• Plus any accrued income, such as interest income from fixed interest securities and deposits net of any outgo
• Less any allowance for accrued tax
• This gives the net asset value of the fund on a bid basis
• During an outflow of money, if the fund was one off the company would switch back to offer
• Could use box management to avoid having to temporarily switch to a bid basis
• management box’ (ie create more units in the fund than are needed to meet policyholders’ liabilit¡es) to avoid having to temporarily switch to a bid basis 11) Divide by the number of units existing at the valuation date before any units are cancelled to get the expropriation price

Question 13

Basic features of a cashflow projection model for pricing term assurance

Answer 13

• The model needs to allow for all cashflows that may arise
• Which in this case are premiums, death benefits and expenses
• It also needs to allow for cashflows arising from the supervisory requirement to hold reserves and solvency capital
• It will be important to model the cost of capital, in this case as the initial expense and solvency capital requirement are likely to be much larger than the first premium
• The cashflows need to allow for any interactions, particularly where the assets and liabilities are being modelled together
• However, the investment returns is likley to be of little significance here, as term assurance contracts have low reserves
• However, the existence of selective withdrawals means that low persistency should be associated with high mortality rates
• The model should allow for the potential cashflows from any health options included in the contracts
• Such as options to increase the sum assured or increase the term of the contract
• It is unlikley that a stockastick model will be used in thise case

Question 14

What are the key considerations duirng a mergers and acquistions for unit price

Answer 14

• Basic equity
  
  • When calculating the unit prices at the merger date, the company should ensure that each unit linked policyholder has the same value of units afterwards as they did immediately prior to the merger
  • Since it wont be possible to keep all the unit prices the same, this means that the number of units must be adjusted accordingly
  • The company will need to decide on the starting price for the new funds, which could either carry on from the existing price for one of the funds or could be an arbitrary new figure, say 100p
  • The number of decimal places to record for both the unit price and number of units will affect how accurately the policy values can be kept the same as before the merger
  • To demonstrate that policyholders havent been adversely affected on teh day of the merger, the company is likely to send out a unit statement to each policyholder. This would show their holdings as at merger date, in terms of both the old funds and the new funds, so the before and after positions can be reconciled
• Pricing basis
  
  • The pricing basis to use each fund will need to be decided. For each new fund, the cmpany should look at the past pattern of the unit transaction on the previous funds and derive the overall position of the new fund, ie whether it is expanding or contracting. If its is expanding, then an offer basis will be used, other wise a bid basis will be sued
  • For some policyholders, the merfer will mean a change of basis for at least soem of their funds, so the cmpany needs to decide how
• Other aspect of the calculation
  
  • It is possible to calculate either the bid or offer price first and then derive the other one from it. If the two sets of funds used different methods, then the cmopany will need to decide which one to go with, which might depend on which of the company’s unit pricing systems will be used
  • Round rules will also need to be decided
  • The calculation of unit pricies might have happened at different times of day in the two previous companies, e.g one at none and one at 5pm. if so, the merfed company will need to decide what time to use, which might depend on which system are to be used in the new set up.
  • The valuaton of certain types of asset, eg property, might have been updated more frequently in one company than in the other. This needs to be brought into line in the new company and might involve obtainining current valueations for all the property holdings
  • All aspects of the calculation should be consistent with all sales and marketing literature and other documentation issued by thhe company, so this should all be reviewed and updated as necessary
• Practicalities
  
  • If the two companies use different unit pricing systems then the merged company will need to decide which one to carry on using the merger. This decision should be based on an analysis of the pros and cons of each system, taking into account ease of use, speed, flexibility, compatibility with other investment and policyholders systems
  • If any unit pricing is carried out externally, the copany will need to discuss whether its better for this to continue for all the new funds or whether it should now all be carried out internally

Question 15

How to model the bonus distrbution in the model

Answer 15

• Program the dividend formula so that it will calculate the correc annual dividend per policy
• It must be dynamic, the projected dividend varying with the projected actual interest, expense and mortality experience, for each homogenous grouping
• The valuation basis for these elements will need to be included so that the model can calculate the difference between actual and expected
• It will be sensible to inlude, as a parameter in the model, the proportion of the surplus emerging each year which is distrinuted to policyholders

Question 16

How to use stochastic model to determine the charges for the guarantee

Answer 16

• A representative selection of model points would be chosen
• Seperate model points would be used for each fund
• And possibility different premium size and for different ages and gender
• The unit fund would be projected, net of all charges, allowing for deaths and withdrawals
• These charges would inlucde the charges applied to the exisiting contract (eg fund management charges, policy fees etc) as well as the reduced allocation rate to be charged for the new guarantee
• The model would be run with different alloation rates for each model point to find the optimal solution in terms of both marketability and profitability
• A suitable probability distribution for the unit growth rate variable would be chosen
• This distribution may be the same for the two funds, but it would have different parameters (eg volatility) to reflect differences in teh behaviour of the backing assets
• If a risk neutral (or market consistent) calibration were being used, the parameters of this distribution would be chosen to replicate the market prices of actual financial instrucments as closely as possible
• It is most important that the model could reproduce ten-year put options on both European and North American equities as this is the financial instrument that the guarantee resemble more closely
• The expected return woudl be the risk free rate, regardless of which fund was being considered. The volatility will be different
• If a real world calibration were being used, the parameters of the unit growth rate distribution would be chosen to accord with realistic long term expectations of future investment returns on portfolios of either European or North American equities as approrpriate
• A determinisitic assumption would be used to model mortality
• Withdrawals might be modelled stochastically such that the level of withdrawals is related to the fund performance eg withdrawals could be low late in the policy term if the matrurity guarantee is likely to bite
• However, a stochastic model of withdrawal rates might be considered too complex or sjubjective, and so a deterministic assumption could be used supported by scenario testing
• The unit fund value at maturity would be simulated a large number of times using the stochastic unit growth rates
• The excess of the guaranteed value over the unit fund at maturity, where positive, is the simulated guarantee cost for each simulation
• The guarantee is (insert)
• So the stochastic model could be used to generate a distribution of guarantee
  
  • If a risk neutral calibration were being used, the charges would be set as the average of the discounted value of the guarantee cost
• This discounting would be performed at a the risk free interest rate
• If a real world calibration were being used, the charges would be accumulated in each simulation in a similar way to the prjoection of the unit fund (althought the charges could be inveseted in different assets requireng a different set of parameters)
• The charges would then be set so that their accumulated value exceeded the guarantee cost in a large number of simulations say 90%
• Sensitivity tests could then be performed on these charges eg sensitivity of the charges to the choice of probability distribution or its parameterisation could be investigated
• Charges for all product variations would be extrapolated from the model points

Question 17

Describe how a model may be used to determine whether the current investment strategy remains appropriate for the company.

Answer 17

• The model would start with the business in force
• This may be on a policy by policy basis or using model points. [1]
• It would also start with the current asset split, i.e. based on the current investment strategy. [1]
• Free assets will be included. [2]
• The company also needs to incorporate future new business for the plan period. [2]
• The new business is likely to be modelled using a series of model points… [1]
  
  • … that are representative of the expected future mix of new business. [1]
• The liabilities and the assets would then both be projected forward in order to determine the asset and liability cashflows [2]
  
  • … on assumptions that represent best estimate expected future experience, [1]
  • …although the company will want also to consider the effect of variations from these. [1]
• It may need to consider any additional business plan expenses over and above those anticipated through expense allowances [1]
• Or alternatively it may be able to reduce per policy expense assumptions to reflect the significant expected future new business growth. [1]
• The company would need to allow for the taxation basis within its projections [1]
• The appropriate period over which to assess investment strategy should be determined (e.g. the business plan period)… [1]
  
  • … and the frequency of determining the asset/liability position in the projection should be decided upon (e.g. annually) [1]
• For the assets, stochastic investment models can be incorporated [2]
  
  • …in order to project future investment income and changes in capital values. [1]
• Inflation rate models can also be used to project future expenses on the liabilities side. [1]
• Dynamic assumptions should be used within the liability valuation basis which take into account the simulated investment conditions. [1]
• The simulation exercise will also need to incorporate differing levels and mix of new business to assess. [1]
• These are likely to be done using deterministic rather than stochastic approaches. [1]
• The company will also need to incorporate a projection of the solvency capital requirements on the regulatory solvency basis. [2]
• The assets, liabilities and capital requirements will be valued taking into account the regulatory requirements… [1]
  
  • … e.g. admissibility requirements [1]
• The item of interest will be the excess of the value of the assets over the value of the liabilities
• This will need to be sufficient to cover comfortably the level of solvency capital required by the company. [1]
• What is “comfortable” may depend on the level of cover provided in other companies [1]
• The company’s solvency risk appetite would also need to be considered. [1]
• The stochastic model will produce a statistical distribution of the amounts available each year to cover the level of solvency capital required. [1]
• From this, the probability of potential future insolvency can be estimated based on the current investment strategy. [1]
• The simulations could also be used to determine the level of free assets that the company needs in order to support the current investment strategy… [1]
• … and keep the probability of insolvency below an acceptably low figure. [1]
• The probability of future insolvency will then be assessed against shareholders’ risk appetite. [1]
• If it fails to meet shareholder requirements, then the company will have to consider making the investment strategy more conservative. [1]
• The effect of the investment strategy on future shareholder earnings and dividends should also be considered. [1]
• In particular, the current investment strategy might meet probability of insolvency requirements but it might not maximise shareholder income [1]
• Alternative investment strategies should therefore be modelled in the same way… [1]
  
  • … in order to maximise shareholder income whilst keeping the risk of insolvency sufficiently low [1]
• The company may also be interested in the relative liquidity of assets… [1]
• … so that it can finance additional new business strain from high volumes