Ch 8: Asset shares Flashcards
Define asset share (4)
- Asset share is accumulation of premiums…
- …less deductions associated with the contract…
- …(plus, for with-profits policies, allocation of profits on without-profits business and surrender profits on with-profits business if applicable & appropriate)…
- …all accumulated at the actual rate of return earned on investments
How do we derive asset share formula from the asset share on an aggregate group of policies? (3)
- Consider cashflows for large group of n identical lives
- Aggregate asset share given by:
- n*(ASt + P - Et)*(1+it) - S*n*qx+t
- P = premium
- Et = Per policy expenses incurred at time t
- it = investment return earned year t to t+1
- S = death benefit assured
- qx+t = actual mortality rate year t to t+1
- For asset share of individual policy, then we divide this aggrgate by number of policies still in force at t+1 to obtain:
- ASt+1 = [n*(ASt + P - Et)*(1+it) - S*n*qx+t]/ n*(1- qx+t)
- Divide through by n, and we have our result
What is the formula for asset share of an individual policy?
ASt+1 = [(ASt + P - Et)*(1+it) - qx+t*S]/ (1- qx+t)
This can also be expressed as:
ASt+1 = [(ASt + P - Et)*(1+it) - qx+t*(S - ASt+1)
showing the costs of providing benefits in excess of the AS
Where:
- ASt = asset share at t years
- qx+t = mortality rate for year t to t +1
- P = premium received over year t to t+1
- Et = per-policy expenses incurred at time t
- S = death benefit sum insured
- it = investment return achieved in year t to t+1
Explain in words how an asset share may be calculated using a recursive formula (5)
- Asset share can be calculated recursively on year-to-year basis
- Initially, earned asset share is zero
- Each year cashflows, including premiums received and deductions made, e.g. to cover cost of benefits, are recorded
- Suitable rate of return on investments is used to accumulate asset share plus premiums less deductions (plus, for with-profits policies, allocation of any miscellaneous profits) to the year end to determine asset share
- Process is repeated for subsequent years
List 6 deductions that may be made in determining the individual asset share of a contract
Deductions include expenditure associated with contract(s) in particular,
- Expenses, including any commission
- Cost of benefits (in excess of asset share) i.e. both life cover and any guarantees or options granted
- Tax (if appropriate), including any reserves made for future tax liabilities
- Transfers of profit to shareholders, in case of proprietary company
- Cost of any capital necessary to support contracts in early years
- Contribution to free assets, eg to support smoothing and greater investment flexibility
Discuss key considerations for the cashflows that add to/increase the asset share calculation (money-in cashflows/inflows)
1,1
1,1
1,9
- Premiums - must be gross
- Profits - only applicable in the case of a with-profits contract
- Investment income
- Actual return not directly observed
- e.g on less marketable assets like property.
- may need to approximate e.g using indices
- With/without profits’ assets combined- decide allocation btwn
- Allocated return may be smoothed- over time and extent of smoothing subjective
- Data quality/detail not available, and even if data available
- Availables indices may not represent/reflect assets actually held
- Accurate calculations may only be done periodically
- Allowance for tax
- accrual of unrealised gains
- can be complex eg. through tax relief
- Allowance for expenses- actual investment returns must be reduce by investment expenses, some approximation may be needed
- Cost of capital- need to allow for where policies provided working capital, difficult to approximate
- Actual return not directly observed
Discuss key considerations for the cashflows that subtract from/reduce the asset share calculation (‘money-out cashflows/outflows) (7)
- Include commission
- Include expenses incurred- overheads, tax on policies, depending on how company pays tax)
- Cost of cover provided
- fixed benefits
- guarantees/options
- Tax on investment return - unrealised capital appreciation
- Profit to shareholders - compensate for
- capital provided to support new business
- smoothing payouts to with profit contracts
- Supporting capital cost - new business strain
- Undistributed profits
What typical developments do we expect for the progression of the asset share?
(consider early phases, then at muturity)
- In early phases, we usually expect a negative asset share
- This essentially means/is because policy has incurred expenses in excess of premiums/income
- Risks arise with a negative asset share
- Lapse risk, leading to company making losses and not recovering initial costs
- Subsequent movement of the AS will depend on
- Renewal expenses
- Investment income
- Cost of life cover
- At maturity
- Expect asset share > guaranteed sum insured
- With excess profits
- being distributed to shareholders or
- with profit policyholders
- retained
- for smoothing purposes
- grow the business
- to bolster solvency position
- use for future opportunities
State core uses of asset share (+-7)
- Setting surrender values
- Asset share will, over period of time, and allowing for smoothing, be upper limit on policy’s surrender value
- Company try ensure surrender val < ass share
- Setting with-profits bonus rates
- Compare assets to liabilities- indication of surplus available
- Deciding size of terminal bonus- sustainability of reversionary bonuses
Other uses:
- Monitor fairness across tranches of business/policies
- Asset share relative to benefit (where discretion available)
- Market value adjustment
- Asset share compared to smoothed benefit (under unitised business) gives indication of market value adjustment which may be needed
- Policy alterations
- Profit distrubution to shareholders
- Planning
- Project solvency position
- Monitor expected profitability on book of business + impact of actual experience <> expected