Ch 8: Asset shares

Question 1

Summary Card

Answer 1

• Asset share definition
• Deductions
• Calculation
• Uses

Question 2

Define asset share (4)

Answer 2

1. Asset share is accumulation of premiums…
2. …less deductions associated with the contract…
3. …(plus, for with-profits policies, allocation of profits on without-profits business and surrender profits on with-profits business if applicable & appropriate)…
4. …all accumulated at the actual rate of return earned on investments

Question 3

How do we derive asset share formula from the asset share on an aggregate group of policies? (3)

Answer 3

1. Consider cashflows for large group of n identical lives
2. Aggregate asset share given by:
   
   • n*(AS_t + P - E_t)*(1+i_t) - S*n*q_x+t
   • P = premium
   • E_t = Per policy expenses incurred at time t
   • i_t = investment return earned year t to t+1
   • S = death benefit assured
   • q_x+t = actual mortality rate year t to t+1
3. For asset share of individual policy, then we divide this aggrgate by number of policies still in force at t+1 to obtain:
   
   • AS_t+1 = [n*(AS_t + P - E_t)*(1+i_t) - S*n*q_x+t]/ n*(1- q_x+t)
   • Divide through by n, and we have our result

Question 4

What is the formula for asset share of an individual policy?

Answer 4

AS_t+1 = [(AS_t + P - E_t)*(1+i_t) - q_x+t*S]/ (1- q_x+t)

This can also be expressed as:

AS_t+1 = [(AS_t + P - E_t)*(1+i_t) - q_x+t*(S - AS_t+1)

showing the costs of providing benefits in excess of the AS

Where:

• AS_t = asset share at t years
• q_x+t = mortality rate for year t to t +1
• P = premium received over year t to t+1
• E_t = per-policy expenses incurred at time t
• S = death benefit sum insured
• i_t = investment return achieved in year t to t+1

Question 5

Explain in words how an asset share may be calculated using a recursive formula (5)

Answer 5

1. Asset share can be calculated recursively on year-to-year basis
2. Initially, earned asset share is zero
3. Each year cashflows, including premiums received and deductions made, e.g. to cover cost of benefits, are recorded
4. Suitable rate of return on investments is used to accumulate asset share plus premiums less deductions (plus, for with-profits policies, allocation of any miscallaneous profits) to the year end to determine asset share
5. Process is repeated for subsequent years

Question 6

List 6 deductions that may be made in determining the individual asset share of a contract

Answer 6

Deductions include expenditure associated with contract(s) in particular,

1. Expenses, including any commission
2. Cost of benefits (in excess of asset share) i.e. both life cover and any guarantees or options granted
3. Tax (if appropriate), including any reserves made for future tax liabilities
4. Transfers of profit to shareholders, in case of proprietary company
5. Cost of any capital necessary to support contracts in early years
6. Contribution to free assets, eg to support smoothing and greater investment flexibility

Question 7

Discuss key considerations for the cashflows that add to/increase the asset share calculation (money-in cashflows/inflows)

1,1

1,1

1,9

Answer 7

1. Premiums - must be gross
2. Profits - only applicable in the case of a with-profits contract
3. Investment income
   
   1. Actual return not directly observed
      
      • e.g on less marketable assets like property.
      • may need to approximate e.g using indices
   2. With/without profits’ assets combined- decide allocation btwn
   3. Allocated return may be smoothed- over time and extent of smoothing subjective
   4. Data quality/detail not available, and even if data available
      
      1. Availables indices may not represent/reflect assets actually held
      2. Accurate calculations may only be done periodically
   5. Allowance for tax
      
      • accrual of unrealised gains
      • can be complex eg. through tax relief
   6. Allowance for expenses- actual investment returns must be reduce by investment expenses, some approximation may be needed
   7. Cost of capital- need to allow for where policies provided working capital, difficult to approximate

Question 8

Discuss key considerations for the cashflows that subtract from/reduce the asset share calculation (‘money-out cashflows/outflows) (7)

Answer 8

1. Include commission
2. Include expenses incurred- overheads, tax on policies, depending on how company pays tax)
3. Cost of cover provided
   
   • fixed benefits
   • guarantees/options
4. Tax on investment return - unrealised capital appreciation
5. Profit to shareholders - compensate for
   
   • capital provided to support new business
   • smoothing payouts to with profit contracts
6. Supporting capital cost - new business strain
7. Undistributed profits

Question 9

What typical developments do we expect for the progression of the asset share?

(consider early phases, then at muturity)

Answer 9

• 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

Question 10

State core uses of asset share (+-7)

Answer 10

1. 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
2. Setting with-profits bonus rates
   
   • Compare assets to liabilities- indication of surplus available
   • Deciding size of terminal bonus- sustainability of reversionary bonuses

Other uses:

1. Monitor fairness across tranches of business/policies
   
   • Asset share relative to benefit (where discretion available)
2. Market value adjustment
   
   • Asset share compared to smoothed benefit (under unitised business) gives indication of market value adjustment which may be needed
3. Policy alterations
4. Profit distrubution to shareholders
5. Planning
   
   • Project solvency position
   • Monitor expected profitability on book of business + impact of actual experience <> expected