Ch 8: Asset shares

Question 1

Define asset share (3)

Answer 1

1. Asset share is accumulation of premiumsrolled up with interest…
2. …less expenses and claims
3. Similar to gross premium retro reserve but uses actual exp rather than basis

Question 2

Components of Asset share
MONEY IN

1,1,7

Answer 2

1. Premiums - must be gross
2. Profits - only applicable in the case of a with-profits contract
3. Investment income
   
   1. Actual return observed
   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- allow for unrealised capital gains
   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 3

Components of Asset share
MONEY OUT

7

Answer 3

1. Include commission- nett of tax
2. Include expenses incurred nett of tax
3. Cost of benefits in excess of asset share
4. Tax on investment return + Tax reserves setup + Tax unrealised capital gain(w/prof only)
5. Profit to shareholders (w/prof)
   
   • capital provided to support new business
   • smoothing payouts to with profit contracts
6. Cost of capital - new business strain
7. Contribution to undistributed surplus

Question 4

Explain the cost of capital element of asset share

5

Answer 4

• Capital used to cover NUB strain
• 2 Sources:
  
  • surplus from prev business undistributed
  • SH free assets
• PH and SH have ‘invested’ in new policies by funding NUB strain (loan to comp)
• So require something back for investment (loan)
• Reduce asset share with this cost

Question 5

Explain the cost of undistributed surplus in w/prof PH funds?

5

Answer 5

• Smoothing of bonuses for w/prof policies
• Protection from fluctuations in asset value
• Payout after downturn> AS
• Payout after boom < AS
• This only works if large amt of undistributed surplus to use for smoothing.

Question 6

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

Answer 6

1. Consider cashflows for large groupf of n identical lives
2. Aggregate asset share given by:
   
   • ASt+1= 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:
   
   • n*(1- q_x+t) is # polices in force.
   • AS_t+1 = [n*(AS_t + P - E_t)*(1+i_t) - S*n*q_x+t]/ n*(1- q_x+t)

Question 7

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

Answer 7

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 8

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

Answer 8

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 9

Asset share development over time?

(consider early phases, then at maturity)

3

Answer 9

• In early phases, we usually expect a negative asset share
  
  • Due to incurred expenses in excess of premiums/income (reg prem)
  • 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 - exp to + as PH ages
  * Expect growth in asset share in-force. Stepwise manner @ PA
• 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