10. With-profits surplus distribution II

Question 1

Two other methods of bonus distribution

Answer 1

• Revalorisation
• Contribution

Question 2

What is the revalorisation method

Answer 2

• Bonuses are expressed as a percentage (r%) of the contract’s supervisory reserve.
• The sum assured and premium are then increased by r
• For a single premium contract, the sum assured is increased by r
• Suprlus can be divided into “savings” and “insurance”
• Savings profit is what is distributed to ph

Question 3

What is “savings” profit?

Answer 3

• Profit from assets that can be distributed in whole or in part by the revalorisation method.
• i’ - i
  i’: actual interest rate
  i: expected interest rate
• Only a proportion might be distribitued (say k)
• k might have a minimum rate in policy conditions
  *

Question 4

How is the bonus calculated from the savings profit

Answer 4

1. r = i’-i’

• Only a proportion might be distribitued (say k)
• k might have a minimum rate in policy conditions
  2. r = k(i’-i) or

3. r = (ki’-i)

Question 5

What is the typical form of distributed profit under the revalorisation method

Answer 5

distributed profit = r*V(t+1)

Question 6

What is “insurance” profit?

Answer 6

• Profit arising from actual experiene being better than expected for all sources of profit other than the return on assets.
• Typically retained by company and distributed to shareholders as reward for pure insurance risks that they have borne.
• May be divided between ph and sh

Question 7

Split of savings and insurance bonus

Answer 7

• Large proportion of savings&raquo_space; ph
• Insurance:
• All may go to shareholders
• May be divided between ph and sh

Question 8

Advantages of revalorisation method

Hint: SCECA

Answer 8

• Simple to apply
• Codifies exactly how company should declare part of its profit as bonus to w/profits ph. Very little judgement is normally required, and should therefore be relatively cheap to administer.
• Exception is where ph take share of insurance profit- once profits / losses are usually spread over a period of time and judgement might be required on how to do this.
• Codification protects ph from ungenerous life insurance companies
• By taking assets at book values, including appropriately smoothed writing-up (or down) adjustments, a smooth emergence of profit is usually achieved.

Question 9

Disadvantages of revalorisation method
Hints: Discretiom,equity+deferra; mutuality and insurance profit; explanation to ph with constant P

Answer 9

• Company has no discretion in profit distribution (except to extent of spreading one-off costs, where applicable)
• Tends to discourage equity investment due to no deferral of profit distribution. All investment losses borne by the company and would lead to unacceptable insolvency risks. Also problem regarding treatment of unrealised gains which aren’t easy to distribute directly under current revalorisation systems.
• Do not share insurance profit with ph - go against principle of mutuality.
• Not easy to explain to ph with constant premium policies who see small additions to guaranteed benefits in early policy years.

Question 10

What is the principle underlying the contribution method of bonus distribution

Answer 10

Distributable surplus must be distributed among policies in the same proportion as those policies are judged to have contributed to surplue

Question 11

Contribution method definition

Answer 11

• Each policy receives share of distributable surplus in proportion to its contribution surplus.
• A dividend is calculated to determine the bonus
• Dividend is calculated for grouped homogenous groups rather than each policy
• Purpose = divide total amount of distributable profit between ph in a fair way as possible

Question 12

Give a theoretical reason for why the policies are grouped?

Answer 12

• If every policy is used to calculate the dividend, the concept of pooling risk is lost.
• For example, ph who survived the year will show a mortality profit, those who died will show a huge loss.
• So idea that actual experience is the average experience of all policies in a homogenous group is used.

Question 13

How is the dividend under the contribution method calculated?

Answer 13

dividend= (V_0+P)(i’-i) +(q-q’)(S-V_1) + [E(1+i)-E’(1+i’)]

V_0: value of contract at beginning of the year on valuation basis
V_1: value of contract at end of the year on valuation basis
P: gross premium/ actual premium paid
i’: actual rate of interest earned
i: valuation basis interest rate
q’: actual mortality rate experienced
q: valuation basis mortality rate
S: sum assured
E”: actual expenses experienced under contract
E: expenses experienced under contract in the valuation basis

Question 14

What are the 3 components of the dividend under the contribution method called?

Hint: IME

Answer 14

• Interest surplus: excess interest on the reserve plus premium
• Mortality surplus: expected death strain minus actual death strain
• Expense surplus: expense surplus accumulated to the end of the year

Question 15

How can dividends be distributed?

Answer 15

• Addition to benefits
• Cash benefit
• Reduce future premiums
• Terminal dividend may be given

Question 16

What is the terminal dividend under the contribution method?

Answer 16

The difference between the true earned asset share at maturity/claim and the sum assured.